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Publications of Thomas P. Witelski    :chronological  alphabetical  combined listing:

%% Books   
@book{fds323229,
   Author = {Witelski, T and Bowen, M},
   Title = {Methods of Mathematical Modelling: Continuous Systems and
             Differential Equations},
   Pages = {1-305},
   Publisher = {Springer International Publishing},
   Year = {2015},
   Month = {September},
   ISBN = {9783319230412},
   url = {http://dx.doi.org/10.1007/978-3-319-23042-9},
   Abstract = {This book presents mathematical modelling and the integrated
             process of formulating sets of equations to describe
             real-world problems. It describes methods for obtaining
             solutions of challenging differential equations stemming
             from problems in areas such as chemical reactions,
             population dynamics, mechanical systems, and fluid
             mechanics. Chapters 1 to 4 cover essential topics in
             ordinary differential equations, transport equations and the
             calculus of variations that are important for formulating
             models. Chapters 5 to 11 then develop more advanced
             techniques including similarity solutions, matched
             asymptotic expansions, multiple scale analysis, long-wave
             models, and fast/slow dynamical systems. Methods of
             Mathematical Modelling will be useful for advanced
             undergraduate or beginning graduate students in applied
             mathematics, engineering and other applied
             sciences.},
   Doi = {10.1007/978-3-319-23042-9},
   Key = {fds323229}
}


%% Papers Published   
@article{fds376241,
   Author = {Ji, H and Witelski, TP},
   Title = {Coarsening of Thin Films with Weak Condensation},
   Journal = {SIAM Journal on Applied Mathematics},
   Volume = {84},
   Number = {2},
   Pages = {362-386},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2024},
   Month = {April},
   url = {http://dx.doi.org/10.1137/23m1559336},
   Doi = {10.1137/23m1559336},
   Key = {fds376241}
}

@article{fds371622,
   Author = {Chapman, SJ and Dallaston, MC and Kalliadasis, S and Trinh, PH and Witelski, TP},
   Title = {The role of exponential asymptotics and complex
             singularities in self-similarity, transitions, and branch
             merging of nonlinear dynamics},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {453},
   Year = {2023},
   Month = {November},
   url = {http://dx.doi.org/10.1016/j.physd.2023.133802},
   Abstract = {We study a prototypical example in nonlinear dynamics where
             transition to self-similarity in a singular limit is
             fundamentally changed as a parameter is varied. Here, we
             focus on the complicated dynamics that occur in a
             generalised unstable thin-film equation that yields
             finite-time rupture. A parameter, n, is introduced to model
             more general disjoining pressures. For the standard case of
             van der Waals intermolecular forces, n=3, it was previously
             established that a countably infinite number of self-similar
             solutions exist leading to rupture. Each solution can be
             indexed by a parameter, ϵ=ϵ1>ϵ2>⋯>0, and the prediction
             of the discrete set of solutions requires examination of
             terms beyond-all-orders in ϵ. However, recent numerical
             results have demonstrated the surprising complexity that
             exists for general values of n. In particular, the
             bifurcation structure of self-similar solutions now exhibits
             branch merging as n is varied. In this work, we shall
             present key ideas of how branch merging can be interpreted
             via exponential asymptotics.},
   Doi = {10.1016/j.physd.2023.133802},
   Key = {fds371622}
}

@article{fds370567,
   Author = {Bowen, M and King, JR and Witelski, TP},
   Title = {CAUCHY-DIRICHLET PROBLEMS FOR THE POROUS MEDIUM
             EQUATION},
   Journal = {Discrete and Continuous Dynamical Systems- Series
             A},
   Volume = {43},
   Number = {3-4},
   Pages = {1143-1174},
   Publisher = {American Institute of Mathematical Sciences
             (AIMS)},
   Year = {2023},
   Month = {March},
   url = {http://dx.doi.org/10.3934/dcds.2022182},
   Abstract = {We consider the porous medium equation subject to
             zero-Dirichlet conditions on a variety of two-dimensional
             domains, namely strips, slender domains and sectors,
             allowing us to capture a number of different classes of
             behaviours. Our focus is on intermediate-asymptotic
             descriptions, derived by formal arguments and validated
             against numerical computations. While our emphasis is on
             non-negative solutions to the slow-diffusion case, we also
             derive a number of results for sign-change solutions and for
             fast diffusion. Self-similar solutions of various kinds play
             a central role, alongside the identification of suitable
             conserved quantities. The characterisation of domains
             exhibiting infinite-time hole closure is a particular upshot
             and we highlight a number of open problems.},
   Doi = {10.3934/dcds.2022182},
   Key = {fds370567}
}

@article{fds371558,
   Author = {Sanaei, P and Breward, C and Ellis, M and Han, S and Holzer, B and Ji, H and El Kahza and H and Smith, SL and Parsa, S and Reynolds, H and Troy, J and Witelski, T and Zhang, N and Zyskin, M},
   Title = {Evaporation and deposition in porous media},
   Year = {2022},
   Month = {April},
   url = {http://dx.doi.org/10.33774/miir-2022-wq8fl},
   Abstract = {<jats:p>In this work, we consider a porous material that is
             filled with a liquid solution containing molecules from
             multiple species with known starting concentrations. As the
             solvent evaporates, molecules from these species are left
             behind and deposited on the internal pore walls within the
             porous material. We seek to (i) examine the dependence of
             the mass distribution of molecules along the pore walls and
             the drying rate/time on the pore diameter, pore length,
             fluid wetting properties, and evaporation conditions; (ii)
             develop a model a porous structure that has a distribution
             of pore sizes and in which. fluid moves due to capillary
             force; and (iii) understand how the mass distribution of
             molecules change upon cycles of wetting and
             drying.</jats:p>},
   Doi = {10.33774/miir-2022-wq8fl},
   Key = {fds371558}
}

@article{fds361219,
   Author = {Kim, R and Witelski, TP},
   Title = {Uncovering the dynamics of a circadian-dopamine model
             influenced by the light-dark cycle.},
   Journal = {Mathematical biosciences},
   Volume = {344},
   Pages = {108764},
   Publisher = {Elsevier},
   Year = {2022},
   Month = {February},
   url = {http://dx.doi.org/10.1016/j.mbs.2021.108764},
   Abstract = {The neurotransmitter dopamine (DA) is known to be influenced
             by the circadian timekeeping system in the mammalian brain.
             We have previously created a single-cell differential
             equations model to understand the mechanisms behind
             circadian rhythms of extracellular DA. In this paper, we
             investigate the dynamics in our model and study different
             behaviors such as entrainment to the 24-hour light-dark
             cycle and robust periodicity versus decoupling,
             quasiperiodicity, and chaos. Imbalances in DA are often
             accompanied by disrupted circadian rhythms, such as in
             Parkinson's disease, hyperactivity, and mood disorders. Our
             model provides new insights into the links between the
             circadian clock and DA. We show that the daily rhythmicity
             of DA can be disrupted by decoupling between interlocked
             loops of the clock circuitry or by quasiperiodic clock
             behaviors caused by misalignment with the light-dark cycle.
             The model can be used to further study how the circadian
             clock affects the dopaminergic system, and to help develop
             therapeutic strategies for disrupted DA rhythms.},
   Doi = {10.1016/j.mbs.2021.108764},
   Key = {fds361219}
}

@article{fds354949,
   Author = {Zhu, H and Zhang, P and Zhong, Z and Xia, J and Rich, J and Mai, J and Su, X and Tian, Z and Bachman, H and Rufo, J and Gu, Y and Kang, P and Chakrabarty,
             K and Witelski, TP and Huang, TJ},
   Title = {Acoustohydrodynamic tweezers via spatial arrangement of
             streaming vortices.},
   Journal = {Science advances},
   Volume = {7},
   Number = {2},
   Pages = {eabc7885},
   Year = {2021},
   Month = {January},
   url = {http://dx.doi.org/10.1126/sciadv.abc7885},
   Abstract = {Acoustics-based tweezers provide a unique toolset for
             contactless, label-free, and precise manipulation of
             bioparticles and bioanalytes. Most acoustic tweezers rely on
             acoustic radiation forces; however, the accompanying
             acoustic streaming often generates unpredictable effects due
             to its nonlinear nature and high sensitivity to the
             three-dimensional boundary conditions. Here, we demonstrate
             acoustohydrodynamic tweezers, which generate stable,
             symmetric pairs of vortices to create hydrodynamic traps for
             object manipulation. These stable vortices enable
             predictable control of a flow field, which translates into
             controlled motion of droplets or particles on the operating
             surface. We built a programmable droplet-handling platform
             to demonstrate the basic functions of planar-omnidirectional
             droplet transport, merging droplets, and in situ mixing via
             a sequential cascade of biochemical reactions. Our
             acoustohydrodynamic tweezers enables improved control of
             acoustic streaming and demonstrates a previously
             unidentified method for contact-free manipulation of
             bioanalytes and digitalized liquid handling based on a
             compact and scalable functional unit.},
   Doi = {10.1126/sciadv.abc7885},
   Key = {fds354949}
}

@article{fds355438,
   Author = {Nakad, M and Witelski, T and Domec, JC and Sevanto, S and Katul,
             G},
   Title = {Taylor dispersion in osmotically driven laminar flows in
             phloem},
   Journal = {Journal of Fluid Mechanics},
   Volume = {913},
   Publisher = {Cambridge University Press (CUP)},
   Year = {2021},
   Month = {January},
   url = {http://dx.doi.org/10.1017/jfm.2021.56},
   Abstract = {Sucrose is among the main products of photosynthesis that
             are deemed necessary for plant growth and survival. It is
             produced in the mesophyll cells of leaves and translocated
             to different parts of the plant through the phloem. Progress
             in understanding this transport process remains fraught with
             experimental difficulties, thereby prompting interest in
             theoretical approaches and laboratory studies. The Münch
             pressure and mass flow model is one of the accepted
             hypotheses describing the physics of sucrose transport in
             the phloem. It is based on osmosis creating an energy
             potential difference between the source and the sink. The
             flow responding to this energy potential is assumed laminar
             and described by the Hagen-Poiseuille equation. This study
             revisits such osmotically driven flows in tubes with
             membrane walls by including the effects of Taylor dispersion
             on mass transport. This effect has been overlooked in phloem
             flow studies. Taylor dispersion can increase the effective
             transport of solutes by increasing the apparent diffusion
             coefficient. It is shown that, in addition to the
             conventional diffusive correction derived for impermeable
             tube walls, a new adjustment to the mean advective terms
             arises because of osmotic effects. Because the molecular
             Schmidt number is very large for sucrose in water, the
             sucrose front speed and travel times have a direct
             dependence on the Péclet number for different ranges of the
             Münch number. This study establishes upper limits on
             expected Taylor dispersion enhancement of sucrose
             transport.},
   Doi = {10.1017/jfm.2021.56},
   Key = {fds355438}
}

@article{fds352385,
   Author = {Aguareles, M and Chapman, SJ and Witelski, T},
   Title = {Dynamics of spiral waves in the complex Ginzburg–Landau
             equation in bounded domains},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {414},
   Year = {2020},
   Month = {December},
   url = {http://dx.doi.org/10.1016/j.physd.2020.132699},
   Abstract = {Multiple-spiral-wave solutions of the general cubic complex
             Ginzburg–Landau equation in bounded domains are
             considered. We investigate the effect of the boundaries on
             spiral motion under homogeneous Neumann boundary conditions,
             for small values of the twist parameter q. We derive
             explicit laws of motion for rectangular domains and we show
             that the motion of spirals becomes exponentially slow when
             the twist parameter exceeds a critical value depending on
             the size of the domain. The oscillation frequency of
             multiple-spiral patterns is also analytically
             obtained.},
   Doi = {10.1016/j.physd.2020.132699},
   Key = {fds352385}
}

@article{fds353091,
   Author = {Ji, H and Witelski, T},
   Title = {Steady states and dynamics of a thin-film-type equation with
             non-conserved mass},
   Journal = {European Journal of Applied Mathematics},
   Volume = {31},
   Number = {6},
   Pages = {968-1001},
   Publisher = {Cambridge University Press (CUP)},
   Year = {2020},
   Month = {December},
   url = {http://dx.doi.org/10.1017/s0956792519000330},
   Abstract = {<jats:p>We study the steady states and dynamics of a
             thin-film-type equation with non-conserved mass in one
             dimension. The evolution equation is a non-linear
             fourth-order degenerate parabolic partial differential
             equation (PDE) motivated by a model of volatile viscous
             fluid films allowing for condensation or evaporation. We
             show that by changing the sign of the non-conserved flux and
             breaking from a gradient flow structure, the problem can
             exhibit novel behaviours including having two distinct
             classes of co-existing steady-state solutions. Detailed
             analysis of the bifurcation structure for these steady
             states and their stability reveals several possibilities for
             the dynamics. For some parameter regimes, solutions can lead
             to finite-time rupture singularities. Interestingly, we also
             show that a finite-amplitude limit cycle can occur as a
             singular perturbation in the nearly conserved
             limit.</jats:p>},
   Doi = {10.1017/s0956792519000330},
   Key = {fds353091}
}

@article{fds353254,
   Author = {Liu, W and Witelski, TP},
   Title = {Steady states of thin film droplets on chemically
             heterogeneous substrates},
   Journal = {IMA Journal of Applied Mathematics},
   Volume = {85},
   Number = {6},
   Pages = {980-1020},
   Publisher = {Oxford University Press (OUP)},
   Year = {2020},
   Month = {November},
   url = {http://dx.doi.org/10.1093/imamat/hxaa036},
   Abstract = {<jats:title>Abstract</jats:title> <jats:p>We study
             steady-state thin films on chemically heterogeneous
             substrates of finite size, subject to no-flux boundary
             conditions. Based on the structure of the bifurcation
             diagram, we classify the 1D steady-state solutions that
             exist on such substrates into six different branches and
             develop asymptotic estimates for the steady states on each
             branch. Using perturbation expansions, we show that
             leading-order solutions provide good predictions of the
             steady-state thin films on stepwise-patterned substrates. We
             show how the analysis in one dimension can be extended to
             axisymmetric solutions. We also examine the influence of the
             wettability contrast of the substrate pattern on the linear
             stability of droplets and the time evolution for dewetting
             on small domains. Results are also applied to describe 2D
             droplets on hydrophilic square patches and striped regions
             used in microfluidic applications.</jats:p>},
   Doi = {10.1093/imamat/hxaa036},
   Key = {fds353254}
}

@article{fds350458,
   Author = {Dijksman, JA and Mukhopadhyay, S and Gaebler, C and Witelski, TP and Behringer, RP},
   Title = {Erratum: Obtaining self-similar scalings in focusing flows
             [Phys. Rev. E 92, 043016 (2015)].},
   Journal = {Physical review. E},
   Volume = {101},
   Number = {5-2},
   Pages = {059902},
   Year = {2020},
   Month = {May},
   url = {http://dx.doi.org/10.1103/physreve.101.059902},
   Abstract = {This corrects the article DOI: 10.1103/PhysRevE.92.043016.},
   Doi = {10.1103/physreve.101.059902},
   Key = {fds350458}
}

@article{fds349994,
   Author = {Witelski, TP},
   Title = {Nonlinear dynamics of dewetting thin films},
   Journal = {AIMS Mathematics},
   Volume = {5},
   Number = {5},
   Pages = {4229-4259},
   Year = {2020},
   Month = {January},
   url = {http://dx.doi.org/10.3934/math.2020270},
   Abstract = {Fluid films spreading on hydrophobic solid surfaces exhibit
             complicated dynamics that describe transitions leading the
             films to break up into droplets. For viscous fluids coating
             hydrophobic solids this process is called “dewetting”.
             These dynamics can be represented by a lubrication model
             consisting of a fourth-order nonlinear degenerate parabolic
             partial differential equation (PDE) for the evolution of the
             film height. Analysis of the PDE model and its regimes of
             dynamics have yielded rich and interesting research bringing
             together a wide array of different mathematical approaches.
             The early stages of dewetting involve stability analysis and
             pattern formation from small perturbations and self-similar
             dynamics for finite-time rupture from larger amplitude
             perturbations. The intermediate dynamics describes further
             instabilities yielding topological transitions in the
             solutions producing sets of slowly-evolving near-equilibrium
             droplets. The long-time behavior can be reduced to a
             finite-dimensional dynamical system for the evolution of the
             droplets as interacting quasi-steady localized structures.
             This system yields coarsening, the successive re-arrangement
             and merging of smaller drops into fewer larger drops. To
             describe macro-scale applications, mean-field models can be
             constructed for the evolution of the number of droplets and
             the distribution of droplet sizes. We present an overview of
             the mathematical challenges and open questions that arise
             from the stages of dewetting and how they relate to issues
             in multi-scale modeling and singularity formation that could
             be applied to other problems in PDEs and materials
             science.},
   Doi = {10.3934/math.2020270},
   Key = {fds349994}
}

@article{fds346386,
   Author = {Dijksman, JA and Mukhopadhyay, S and Behringer, RP and Witelski,
             TP},
   Title = {Thermal Marangoni-driven dynamics of spinning liquid
             films},
   Journal = {Physical Review Fluids},
   Volume = {4},
   Number = {8},
   Year = {2019},
   Month = {August},
   url = {http://dx.doi.org/10.1103/PhysRevFluids.4.084103},
   Abstract = {Thinning dynamics in spin coating of viscous films is
             influenced by many physical processes. Temperature gradients
             are known to affect thin liquid films through their
             influence on the local fluid surface tension as Marangoni
             stresses. We show here experimentally and numerically that
             adding a static temperature gradient has a significant
             effect on the equilibrium film thickness and height profile
             reached in spin coating. Most notably, we find that the
             thickness of the resulting thin film in spin coating scales
             linearly with the strength of the thermal surface tension
             gradient. Once equilibrated, the thin film height profile is
             controlled by the temperature profile. For small but
             nonnegligible Marangoni number (Ma) the surface has a
             negative curvature at the center and reaching equilibrium
             takes progressively longer with smaller Ma. In this limit,
             the steady state reached is set by competition between
             Marangoni effects and the disjoining pressure.},
   Doi = {10.1103/PhysRevFluids.4.084103},
   Key = {fds346386}
}

@article{fds340899,
   Author = {Bowen, M and Witelski, TP},
   Title = {Pressure-dipole solutions of the thin-film
             equation},
   Journal = {European Journal of Applied Mathematics},
   Volume = {30},
   Number = {2},
   Pages = {358-399},
   Year = {2019},
   Month = {April},
   url = {http://dx.doi.org/10.1017/S095679251800013X},
   Abstract = {We investigate self-similar sign-changing solutions to the
             thin-film equation, h t = -(|h| n h xxx ) x , on the
             semi-infinite domain x ≥ 0 with zero-pressure-type
             boundary conditions h = h xx = 0 imposed at the origin. In
             particular, we identify classes of first- and second-kind
             compactly supported self-similar solutions (with a
             free-boundary x = s(t) = Lt β ) and consider how these
             solutions depend on the mobility exponent n; multiple
             solutions can exist with the same number of sign changes.
             For n = 0, we also construct first-kind self-similar
             solutions on the entire half-line x ≥ 0 and show that they
             act as limiting cases for sequences of compactly supported
             solutions in the limit of infinitely many sign changes. In
             addition, at n = 1, we highlight accumulation point-like
             behaviour of sign-changes local to the moving interface x =
             s(t). We conclude with a numerical investigation of
             solutions to the full time-dependent partial differential
             equation (based on a non-local regularisation of the
             mobility coefficient) and discuss the computational results
             in relation to the self-similar solutions.},
   Doi = {10.1017/S095679251800013X},
   Key = {fds340899}
}

@article{fds338527,
   Author = {Gao, Y and Ji, H and Liu, JG and Witelski, TP},
   Title = {A vicinal surface model for epitaxial growth with
             logarithmic free energy},
   Journal = {Discrete and Continuous Dynamical Systems - Series
             B},
   Volume = {23},
   Number = {10},
   Pages = {4433-4453},
   Publisher = {American Institute of Mathematical Sciences
             (AIMS)},
   Year = {2018},
   Month = {December},
   url = {http://dx.doi.org/10.3934/dcdsb.2018170},
   Abstract = {We study a continuum model for solid films that arises from
             the modeling of one-dimensional step flows on a vicinal
             surface in the attachment-detachment-limited regime. The
             resulting nonlinear partial differential equation, ut =
             -u2(u3 + au)hhhh, gives the evolution for the surface slope
             u as a function of the local height h in a monotone step
             train. Subject to periodic boundary conditions and positive
             initial conditions, we prove the existence, uniqueness and
             positivity of global strong solutions to this PDE using two
             Lyapunov energy functions. The long time behavior of u
             converging to a constant that only depends on the initial
             data is also investigated both analytically and
             numerically.},
   Doi = {10.3934/dcdsb.2018170},
   Key = {fds338527}
}

@article{fds336414,
   Author = {Chiou, J-G and Ramirez, SA and Elston, TC and Witelski, TP and Schaeffer, DG and Lew, DJ},
   Title = {Principles that govern competition or co-existence in
             Rho-GTPase driven polarization.},
   Journal = {PLoS Comput Biol},
   Volume = {14},
   Number = {4},
   Pages = {e1006095},
   Year = {2018},
   Month = {April},
   url = {http://dx.doi.org/10.1371/journal.pcbi.1006095},
   Abstract = {Rho-GTPases are master regulators of polarity establishment
             and cell morphology. Positive feedback enables concentration
             of Rho-GTPases into clusters at the cell cortex, from where
             they regulate the cytoskeleton. Different cell types
             reproducibly generate either one (e.g. the front of a
             migrating cell) or several clusters (e.g. the multiple
             dendrites of a neuron), but the mechanistic basis for
             unipolar or multipolar outcomes is unclear. The design
             principles of Rho-GTPase circuits are captured by
             two-component reaction-diffusion models based on conserved
             aspects of Rho-GTPase biochemistry. Some such models display
             rapid winner-takes-all competition between clusters,
             yielding a unipolar outcome. Other models allow prolonged
             co-existence of clusters. We investigate the behavior of a
             simple class of models and show that while the timescale of
             competition varies enormously depending on model parameters,
             a single factor explains a large majority of this variation.
             The dominant factor concerns the degree to which the maximal
             active GTPase concentration in a cluster approaches a
             "saturation point" determined by model parameters. We
             suggest that both saturation and the effect of saturation on
             competition reflect fundamental properties of the Rho-GTPase
             polarity machinery, regardless of the specific feedback
             mechanism, which predict whether the system will generate
             unipolar or multipolar outcomes.},
   Doi = {10.1371/journal.pcbi.1006095},
   Key = {fds336414}
}

@article{fds332862,
   Author = {Ji, H and Witelski, TP},
   Title = {Instability and dynamics of volatile thin
             films},
   Journal = {Physical Review Fluids},
   Volume = {3},
   Number = {2},
   Publisher = {American Physical Society (APS)},
   Year = {2018},
   Month = {February},
   url = {http://dx.doi.org/10.1103/PhysRevFluids.3.024001},
   Abstract = {Volatile viscous fluids on partially wetting solid
             substrates can exhibit interesting interfacial instabilities
             and pattern formation. We study the dynamics of vapor
             condensation and fluid evaporation governed by a one-sided
             model in a low-Reynolds-number lubrication approximation
             incorporating surface tension, intermolecular effects, and
             evaporative fluxes. Parameter ranges for
             evaporation-dominated and condensation-dominated regimes and
             a critical case are identified. Interfacial instabilities
             driven by the competition between the disjoining pressure
             and evaporative effects are studied via linear stability
             analysis. Transient pattern formation in nearly flat
             evolving films in the critical case is investigated. In the
             weak evaporation limit unstable modes of finite-amplitude
             nonuniform steady states lead to rich droplet dynamics,
             including flattening, symmetry breaking, and droplet
             merging. Numerical simulations show that long-time behaviors
             leading to evaporation or condensation are sensitive to
             transitions between filmwise and dropwise
             dynamics.},
   Doi = {10.1103/PhysRevFluids.3.024001},
   Key = {fds332862}
}

@article{fds325294,
   Author = {Gao, Y and Ji, H and Liu, JG and Witelski, TP},
   Title = {Global existence of solutions to a tear film model with
             locally elevated evaporation rates},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {350},
   Pages = {13-25},
   Publisher = {Elsevier BV},
   Year = {2017},
   Month = {July},
   url = {http://dx.doi.org/10.1016/j.physd.2017.03.005},
   Abstract = {Motivated by a model proposed by Peng et al. (2014) for
             break-up of tear films on human eyes, we study the dynamics
             of a generalized thin film model. The governing equations
             form a fourth-order coupled system of nonlinear parabolic
             PDEs for the film thickness and salt concentration subject
             to non-conservative effects representing evaporation. We
             analytically prove the global existence of solutions to this
             model with mobility exponents in several different ranges
             and present numerical simulations that are in agreement with
             the analytic results. We also numerically capture other
             interesting dynamics of the model, including finite-time
             rupture–shock phenomenon due to the instabilities caused
             by locally elevated evaporation rates, convergence to
             equilibrium and infinite-time thinning.},
   Doi = {10.1016/j.physd.2017.03.005},
   Key = {fds325294}
}

@article{fds320453,
   Author = {Ji, H and Witelski, TP},
   Title = {Finite-time thin film rupture driven by modified evaporative
             loss},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {342},
   Pages = {1-15},
   Publisher = {Elsevier BV},
   Year = {2017},
   Month = {March},
   url = {http://dx.doi.org/10.1016/j.physd.2016.10.002},
   Abstract = {Rupture is a nonlinear instability resulting in a
             finite-time singularity as a film layer approaches zero
             thickness at a point. We study the dynamics of rupture in a
             generalized mathematical model of thin films of viscous
             fluids with modified evaporative effects. The governing
             lubrication model is a fourth-order nonlinear parabolic
             partial differential equation with a non-conservative loss
             term. Several different types of finite-time singularities
             are observed due to balances between conservative and
             non-conservative terms. Non-self-similar behavior and two
             classes of self-similar rupture solutions are analyzed and
             validated against high resolution PDE simulations.},
   Doi = {10.1016/j.physd.2016.10.002},
   Key = {fds320453}
}

@article{fds320455,
   Author = {Sanaei, P and Richardson, GW and Witelski, T and Cummings,
             LJ},
   Title = {Flow and fouling in a pleated membrane filter},
   Journal = {Journal of Fluid Mechanics},
   Volume = {795},
   Pages = {36-59},
   Publisher = {Cambridge University Press (CUP)},
   Year = {2016},
   Month = {May},
   url = {http://dx.doi.org/10.1017/jfm.2016.194},
   Abstract = {Pleated membrane filters are widely used in many
             applications, and offer significantly better surface area to
             volume ratios than equal-area unpleated membrane filters.
             However, their filtration characteristics are markedly
             inferior to those of equivalent unpleated membrane filters
             in dead-end filtration. While several hypotheses have been
             advanced for this, one possibility is that the flow field
             induced by the pleating leads to spatially non-uniform
             fouling of the filter, which in turn degrades performance.
             In this paper we investigate this hypothesis by developing a
             simplified model for the flow and fouling within a pleated
             membrane filter. Our model accounts for the pleated membrane
             geometry (which affects the flow), for porous support layers
             surrounding the membrane, and for two membrane fouling
             mechanisms: (i) adsorption of very small particles within
             membrane pores; and (ii) blocking of entire pores by large
             particles. We use asymptotic techniques based on the small
             pleat aspect ratio to solve the model, and we compare
             solutions to those for the closest-equivalent unpleated
             filter.},
   Doi = {10.1017/jfm.2016.194},
   Key = {fds320455}
}

@article{fds317250,
   Author = {Smolka, LB and McLaughlin, CK and Witelski, TP},
   Title = {Oil capture from a water surface by a falling
             sphere},
   Journal = {Colloids and Surfaces A: Physicochemical and Engineering
             Aspects},
   Volume = {497},
   Pages = {126-132},
   Publisher = {Elsevier BV},
   Year = {2016},
   Month = {May},
   ISSN = {0927-7757},
   url = {http://dx.doi.org/10.1016/j.colsurfa.2016.02.026},
   Abstract = {Motivated by contaminant remediation, we study the volume of
             oil (oleic acid) removed from a liquid lens by a falling
             particle. When a spherical particle is dropped from a fixed
             height into an oil lens that floats on top of a water
             surface, a portion of the oil adheres to the sphere. Once
             the sphere comes to rest at the subsurface, the oil forms an
             equilibrium pendant drop that remains attached to the
             sphere. We find in experiments with spheres of different
             sizes and materials, that the pendant drop volume is an
             increasing function of sphere mass for each material and a
             decreasing function of sphere density. By contrast, the
             normalized droplet volume in all of our experiments scales
             with sphere mass following Voil/Vsphere ~ M-0.544. Thus, for
             a given size, lighter spheres capture more oil relative to
             their own volume than do heavier spheres and are more
             efficient at removing oil from a water surface in our
             experiments. Estimates for the upper bound of the normalized
             droplet volume, determined from the continuous family of
             solutions of the Young-Laplace equation, show the same
             qualitative dependence on the sphere mass.},
   Doi = {10.1016/j.colsurfa.2016.02.026},
   Key = {fds317250}
}

@article{fds320454,
   Author = {George, C and Virgin, LN and Witelski, T},
   Title = {Experimental study of regular and chaotic transients in a
             non-smooth system},
   Journal = {International Journal of Non-Linear Mechanics},
   Volume = {81},
   Pages = {55-64},
   Publisher = {Elsevier BV},
   Year = {2016},
   Month = {May},
   url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2015.12.006},
   Abstract = {This paper focuses on thoroughly exploring the finite-time
             transient behaviors occurring in a periodically driven
             non-smooth dynamical system. Prior to settling down into a
             long-term behavior, such as a periodic forced oscillation,
             or a chaotic attractor, responses may exhibit a variety of
             transient behaviors involving regular dynamics, co-existing
             attractors, and super-persistent chaotic transients. A
             simple and fundamental impacting mechanical system is used
             to demonstrate generic transient behavior in an experimental
             setting for a single degree of freedom non-smooth mechanical
             oscillator. Specifically, we consider a horizontally driven
             rigid-arm pendulum system that impacts an inclined rigid
             barrier. The forcing frequency of the horizontal
             oscillations is used as a bifurcation parameter. An
             important feature of this study is the systematic generation
             of generic experimental initial conditions, allowing a more
             thorough investigation of basins of attraction when multiple
             attractors are present. This approach also yields a
             perspective on some sensitive features associated with
             grazing bifurcations. In particular, super-persistent
             chaotic transients lasting much longer than the conventional
             settling time (associated with linear viscous damping) are
             characterized and distinguished from regular dynamics for
             the first time in an experimental mechanical
             system.},
   Doi = {10.1016/j.ijnonlinmec.2015.12.006},
   Key = {fds320454}
}

@article{fds244178,
   Author = {Witelski, TP},
   Title = {Preface to the special issue on “Thin films and fluid
             interfaces”},
   Journal = {Journal of Engineering Mathematics},
   Volume = {94},
   Number = {1},
   Pages = {1-3},
   Publisher = {Springer Nature},
   Year = {2015},
   Month = {October},
   ISSN = {0022-0833},
   url = {http://dx.doi.org/10.1007/s10665-014-9760-z},
   Doi = {10.1007/s10665-014-9760-z},
   Key = {fds244178}
}

@article{fds293132,
   Author = {Dijksman, JA and Mukhopadhyay, S and Gaebler, C and Witelski, TP and Behringer, RP},
   Title = {Obtaining self-similar scalings in focusing
             flows.},
   Journal = {Physical review. E, Statistical, nonlinear, and soft matter
             physics},
   Volume = {92},
   Number = {4},
   Pages = {043016},
   Year = {2015},
   Month = {October},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/physreve.92.043016},
   Abstract = {The surface structure of converging thin fluid films
             displays self-similar behavior, as was shown in the work by
             Diez et al. [Q. Appl. Math. 210, 155 (1990)]. Extracting the
             related similarity scaling exponents from either numerical
             or experimental data is nontrivial. Here we provide two such
             methods. We apply them to experimental and numerical data on
             converging fluid films driven by both surface tension and
             gravitational forcing. In the limit of pure gravitational
             driving, we recover Diez' semianalytic result, but our
             methods also allow us to explore the entire regime of mixed
             capillary and gravitational driving, up to entirely
             surface-tension-driven flows. We find scaling forms of
             smoothly varying exponents up to surprisingly small Bond
             numbers. Our experimental results are in reasonable
             agreement with our numerical simulations, which confirm
             theoretically obtained relations between the scaling
             exponents.},
   Doi = {10.1103/physreve.92.043016},
   Key = {fds293132}
}

@article{fds244182,
   Author = {Witelski, T and Virgin, LN and George, C},
   Title = {A driven system of impacting pendulums: Experiments and
             simulations},
   Journal = {Journal of Sound and Vibration},
   Volume = {333},
   Number = {6},
   Pages = {1734-1753},
   Year = {2014},
   Month = {March},
   ISSN = {0022-460X},
   url = {http://dx.doi.org/10.1016/j.jsv.2013.11.004},
   Abstract = {This paper studies a system composed of two pendulums
             attached to a common base that is oscillated horizontally.
             The pendulums share a common pivot line, but move
             independently and are only coupled together through
             collisions. Impact dynamics for the collisions of the
             pendulums with each other and with fixed barriers yield
             complex nonlinear behaviors. Careful numerical simulation of
             the equations of motion demonstrates a close correlation
             with experimental data collected from the system. There are
             many independent parameters in this system, and one of the
             motivations for the present study is to establish the extent
             to which we can capture observed behavior with a relatively
             simple hybrid differential equation model in the face of
             several independent energy dissipation mechanisms coming
             from friction and impact. Comparison between experiments and
             simulations is based on the standard nonlinear dynamical
             system analyses of time series, phase projections, time-lag
             embedding, Poincaré sections, and frequency content.
             Grazing bifurcations and co-existence of
             impacting/non-impacting periodic/chaotic states are
             observed. © 2013 Elsevier Ltd.},
   Doi = {10.1016/j.jsv.2013.11.004},
   Key = {fds244182}
}

@article{fds244179,
   Author = {Hall Taylor and NS and Hewitt, IJ and Ockendon, JR and Witelski,
             TP},
   Title = {A new model for disturbance waves},
   Journal = {International Journal of Multiphase Flow},
   Volume = {66},
   Pages = {38-45},
   Publisher = {Elsevier BV},
   Year = {2014},
   Month = {January},
   ISSN = {0301-9322},
   url = {http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.06.004},
   Abstract = {The first part of this paper surveys the distinctive
             features of trains of disturbance waves in high-speed
             annular two-phase flow. This data is then used to construct
             a mathematical model that predicts relations between the
             speed, height, and spacing of the waves, and the net liquid
             flow rate. These relations highlight the importance of the
             vorticity in the waves, a quantity that has received little
             experimental attention. © 2014 Elsevier
             Ltd.},
   Doi = {10.1016/j.ijmultiphaseflow.2014.06.004},
   Key = {fds244179}
}

@article{fds244183,
   Author = {Smolka, LB and Witelski, TP},
   Title = {Biaxial extensional motion of an inertially driven radially
             expanding liquid sheet},
   Journal = {Physics of Fluids},
   Volume = {25},
   Number = {6},
   Pages = {062105-062105},
   Publisher = {AIP Publishing},
   Year = {2013},
   Month = {June},
   ISSN = {1070-6631},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000321272600010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {We consider the inertially driven, time-dependent biaxial
             extensional motion of inviscid and viscous thinning liquid
             sheets. We present an analytic solution describing the base
             flow and examine its linear stability to varicose
             (symmetric) perturbations within the framework of a
             long-wave model where transient growth and long-time
             asymptotic stability are considered. The stability of the
             system is characterized in terms of the perturbation
             wavenumber, Weber number, and Reynolds number. We find that
             the isotropic nature of the base flow yields stability
             results that are identical for axisymmetric and general
             two-dimensional perturbations. Transient growth of
             short-wave perturbations at early to moderate times can have
             significant and lasting influence on the long-time sheet
             thickness. For finite Reynolds numbers, a radially expanding
             sheet is weakly unstable with bounded growth of all
             perturbations, whereas in the inviscid and Stokes flow
             limits sheets are unstable to perturbations in the
             short-wave limit. © 2013 AIP Publishing
             LLC.},
   Doi = {10.1063/1.4811389},
   Key = {fds244183}
}

@article{fds244184,
   Author = {Chapman, SJ and Trinh, PH and Witelski, TP},
   Title = {Exponential Asymptotics for Thin Film Rupture.},
   Journal = {SIAM J. Appl. Math.},
   Volume = {73},
   Number = {1},
   Pages = {232-253},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2013},
   url = {http://dx.doi.org/10.1137/120872012},
   Abstract = {The formation of singularities in models of many physical
             systems can be described using self-similar solutions. One
             particular example is the finite-time rupture of a thin film
             of viscous fluid which coats a solid substrate. Previous
             studies have suggested the existence of a discrete,
             countably infinite number of distinct solutions of the
             nonlinear differential equation which describes the
             self-similar behavior. However, no analytical mechanism for
             determining these solutions was identified. In this paper,
             we use techniques in exponential asymptotics to construct
             the analytical selection condition for the infinite sequence
             of similarity solutions, confirming the conjectures of
             earlier numerical studies. © 2013 Society for Industrial
             and Applied Mathematics.},
   Doi = {10.1137/120872012},
   Key = {fds244184}
}

@article{fds244225,
   Author = {Huang, Y and Witelski, TP and Bertozzi, AL},
   Title = {Anomalous exponents of self-similar blow-up solutions to an
             aggregation equation in odd dimensions},
   Journal = {Applied Mathematics Letters},
   Volume = {25},
   Number = {12},
   Pages = {2317-2321},
   Publisher = {Elsevier BV},
   Year = {2012},
   Month = {December},
   ISSN = {0893-9659},
   url = {http://dx.doi.org/10.1016/j.aml.2012.06.023},
   Abstract = {We calculate the scaling behavior of the second-kind
             self-similar blow-up solution of an aggregation equation in
             odd dimensions. This solution describes the radially
             symmetric finite-time blowup phenomena and has been observed
             in numerical simulations of the dynamic problem. The
             nonlocal equation for the self-similar profile is
             transformed into a system of ODEs that is solved using a
             shooting method. The anomalous exponents are then retrieved
             from this transformed system. © 2012 Elsevier Ltd. All
             rights reserved.},
   Doi = {10.1016/j.aml.2012.06.023},
   Key = {fds244225}
}

@article{fds244180,
   Author = {Li, Z and Layton, AT and Bertozzi, A and Ambrose, DM and Witelski, T and Minion, ML and Butters, R},
   Title = {Preface},
   Journal = {Discrete and Continuous Dynamical Systems - Series
             B},
   Volume = {17},
   Number = {4},
   Pages = {i-ii},
   Publisher = {American Institute of Mathematical Sciences
             (AIMS)},
   Year = {2012},
   Month = {February},
   ISSN = {1531-3492},
   url = {http://dx.doi.org/10.3934/dcdsb.2012.17.4i},
   Doi = {10.3934/dcdsb.2012.17.4i},
   Key = {fds244180}
}

@article{fds244226,
   Author = {Wiebe, R and Virgin, LN and Witelski, TP},
   Title = {A parametrically forced nonlinear system with reversible
             equilibria},
   Journal = {International Journal of Bifurcation and
             Chaos},
   Volume = {22},
   Number = {6},
   Pages = {1230020-1230020},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2012},
   Month = {January},
   ISSN = {0218-1274},
   url = {http://dx.doi.org/10.1142/S0218127412300200},
   Abstract = {A nonlinear Duffing-type dynamical system, in which the
             stability of equilibria is modulated in a time-dependent
             manner, is investigated both experimentally and numerically.
             This is a low-order dynamical system with some interesting
             available choices in the coordinate system. The system is
             found to exhibit a variety of interesting nonlinear behavior
             including ultrasubharmonic resonance. Frequency content is
             used to characterize periodic and chaotic behavior and their
             relation to the parameter space. © 2012 World Scientific
             Publishing Company.},
   Doi = {10.1142/S0218127412300200},
   Key = {fds244226}
}

@article{fds244227,
   Author = {Aydemir, E and Breward, CJW and Witelski, TP},
   Title = {The effect of polar lipids on tear film dynamics.},
   Journal = {Bulletin of mathematical biology},
   Volume = {73},
   Number = {6},
   Pages = {1171-1201},
   Year = {2011},
   Month = {June},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20556530},
   Abstract = {In this paper, we present a mathematical model describing
             the effect of polar lipids, excreted by glands in the eyelid
             and present on the surface of the tear film, on the
             evolution of a pre-corneal tear film. We aim to explain the
             interesting experimentally observed phenomenon that the tear
             film continues to move upward even after the upper eyelid
             has become stationary. The polar lipid is an insoluble
             surface species that locally alters the surface tension of
             the tear film. In the lubrication limit, the model reduces
             to two coupled non-linear partial differential equations for
             the film thickness and the concentration of lipid. We solve
             the system numerically and observe that increasing the
             concentration of the lipid increases the flow of liquid up
             the eye. We further exploit the size of the parameters in
             the problem to explain the initial evolution of the
             system.},
   Doi = {10.1007/s11538-010-9555-y},
   Key = {fds244227}
}

@article{fds244229,
   Author = {Aguareles, M and Chapman, SJ and Witelski, T},
   Title = {Motion of spiral waves in the complex Ginzburg-Landau
             equation},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {239},
   Number = {7},
   Pages = {348-365},
   Publisher = {Elsevier BV},
   Year = {2010},
   Month = {April},
   ISSN = {0167-2789},
   url = {http://dx.doi.org/doi:10.1016/j.physd.2009.12.003},
   Abstract = {Solutions of the general cubic complex Ginzburg-Landau
             equation comprising multiple spiral waves are considered.
             For parameters close to the vortex limit, and for a system
             of spiral waves with well-separated centres, laws of motion
             of the centres are found which vary depending on the order
             of magnitude of the separation of the centres. In
             particular, the direction of the interaction changes from
             along the line of centres to perpendicular to the line of
             centres as the separation increases, with the strength of
             the interaction algebraic at small separations and
             exponentially small at large separations. The corresponding
             asymptotic wavenumber and frequency are determined. These
             depend on the positions of the centres of the spirals, and
             so evolve slowly as the spirals move. © 2009 Elsevier
             B.V.},
   Doi = {10.1016/j.physd.2009.12.003},
   Key = {fds244229}
}

@article{fds244230,
   Author = {Bernoff, AJ and Witelski, TP},
   Title = {Stability and dynamics of self-similarity in evolution
             equations},
   Journal = {Journal of Engineering Mathematics},
   Volume = {66},
   Number = {1},
   Pages = {11-31},
   Publisher = {Springer Nature},
   Year = {2010},
   Month = {January},
   ISSN = {0022-0833},
   url = {http://dx.doi.org/10.1007/s10665-009-9309-8},
   Abstract = {A methodology for studying the linear stability of
             self-similar solutions is discussed. These fundamental ideas
             are illustrated on three prototype problems: a simple ODE
             with finite-time blow-up, a second-order semi-linear heat
             equation with infinite-time spreading solutions, and the
             fourth-order Sivashinsky equation with finite-time
             self-similar blow-up. These examples are used to show that
             self-similar dynamics can be studied using many of the ideas
             arising in the study of dynamical systems. In particular,
             the use of dimensional analysis to derive scaling invariant
             similarity variables is discussed, as well as the role of
             symmetries in the context of stability of self-similar
             dynamics. The spectrum of the linear stability problem
             determines the rate at which the solution will approach a
             self-similar profile. For blow-up solutions it is
             demonstrated that the symmetries give rise to positive
             eigenvalues associated with the symmetries, and it is shown
             how this stability analysis can identify a unique stable
             (and observable) attracting solution from a countable
             infinity of similarity solutions. © Springer
             Science+Business Media B.V. 2009.},
   Doi = {10.1007/s10665-009-9309-8},
   Key = {fds244230}
}

@article{fds244241,
   Author = {Witelski, TP},
   Title = {The subtle art of blowing bubbles (News and Views: Fluid
             Dynamics)},
   Journal = {Nature Physics},
   Volume = {5},
   Number = {5},
   Pages = {315-316},
   Year = {2009},
   Month = {May},
   ISSN = {1745-2473},
   url = {http://links.ealert.nature.com/ctt?kn=65&m=32736150&r=MTc2NjI2MDg2NwS2&b=2&j},
   Doi = {10.1038/nphys1265},
   Key = {fds244241}
}

@article{fds244243,
   Author = {Witelski, TP and Bowen, M},
   Title = {Singular perturbation theory.},
   Journal = {Scholarpedia},
   Volume = {4},
   Number = {4},
   Pages = {3951-3951},
   Publisher = {Scholarpedia},
   Year = {2009},
   Month = {April},
   url = {http://www.scholarpedia.org/article/Singular_perturbation_theory},
   Doi = {10.4249/scholarpedia.3951},
   Key = {fds244243}
}

@article{fds244244,
   Author = {Hwang, HJ and Witelski, TP},
   Title = {Short-time pattern formation in thin film
             equations},
   Journal = {Discrete and Continuous Dynamical Systems},
   Volume = {23},
   Number = {3},
   Pages = {867-885},
   Publisher = {American Institute of Mathematical Sciences
             (AIMS)},
   Year = {2009},
   Month = {March},
   ISSN = {1078-0947},
   url = {http://aimsciences.org/journals/displayArticles.jsp?paperID=3829},
   Abstract = {We study the early stages of the nonlinear dynamics of
             pattern formation for unstable generalized thin film
             equations. For unstable constant steady states, we obtain
             rigorous estimates for the short- to intermediate-time
             nonlinear evolution which extends the mathematical
             characterization for pattern formation derived from linear
             analysis: formation of patterns can be bounded by the
             finitely many dominant growing eigenmodes from the initial
             perturbation.},
   Doi = {10.3934/dcds.2009.23.867},
   Key = {fds244244}
}

@article{fds244188,
   Author = {Peterson, E and Shearer, M and Witelski, TP and Levy,
             R},
   Title = {Stability of traveling waves in thin liquid films driven by
             gravity and surfactant},
   Journal = {HYPERBOLIC PROBLEMS: THEORY, NUMERICS AND APPLICATIONS, PART
             2},
   Volume = {67},
   Number = {2},
   Pages = {855-+},
   Publisher = {AMER MATHEMATICAL SOC},
   Editor = {Tadmor, E and Liu, J and Tzavaras, A},
   Year = {2009},
   Month = {January},
   ISBN = {978-0-8218-4730-5},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000282769400053&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Key = {fds244188}
}

@article{fds244236,
   Author = {Gratton, MB and Witelski, TP},
   Title = {Transient and self-similar dynamics in thin film
             coarsening},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {238},
   Number = {23-24},
   Pages = {2380-2394},
   Publisher = {Elsevier BV},
   Year = {2009},
   Month = {January},
   ISSN = {0167-2789},
   url = {http://dx.doi.org/10.1016/j.physd.2009.09.015},
   Abstract = {We study coarsening in a simplified model of one-dimensional
             thin films of viscous fluids on hydrophobic substrates.
             Lubrication theory shows that such films are unstable and
             dewet to form droplets that then aggregate over long
             timescales. The masses and positions of the droplets can be
             described by a coarsening dynamical system (CDS) consisting
             of ODEs and deletion rules. We develop discrete and
             continuous mean-field models that reproduce the well-known N
             (t) = O (t- 2 / 5) long-time statistical power law for the
             number of drops. A Lifshitz-Slyozov-Wagner-type (LSW)
             continuous model predicts the self-similar distribution of
             drop masses matching with histograms produced by CDS
             simulations and the discrete mean-field model. We also
             describe the distribution of drops following homogeneous
             versus heterogeneous dewetting and use these as initial
             conditions for the CDS simulations that yield characteristic
             "staircasing" transients. Transients can also include
             recurring spike formation behavior in the mass distribution.
             For idealized initial conditions, we show that the transient
             dynamics can span the full coarsening process, bypassing the
             power law regime entirely. © 2009 Elsevier B.V. All rights
             reserved.},
   Doi = {10.1016/j.physd.2009.09.015},
   Key = {fds244236}
}

@article{fds244242,
   Author = {Smolka, LB and Witelski, TP},
   Title = {On the planar extensional motion of an inertially driven
             liquid sheet},
   Journal = {Physics of Fluids},
   Volume = {21},
   Number = {4},
   Pages = {042101-042101},
   Publisher = {AIP Publishing},
   Year = {2009},
   Month = {January},
   ISSN = {1070-6631},
   url = {http://link.aip.org/link/?PHF/21/042101},
   Abstract = {We derive a time-dependent exact solution of the free
             surface problem for the Navier-Stokes equations that
             describes the planar extensional motion of a viscous sheet
             driven by inertia. The linear stability of the exact
             solution to one- and two-dimensional symmetric perturbations
             is examined in the inviscid and viscous limits within the
             framework of the long-wave or slender body approximation.
             Both transient growth and long-time asymptotic stability are
             considered. For one-dimensional perturbations in the axial
             direction, viscous and inviscid sheets are asymptotically
             marginally stable, though depending on the Reynolds and
             Weber numbers transient growth can have an important effect.
             For one-dimensional perturbations in the transverse
             direction, inviscid sheets are asymptotically unstable to
             perturbations of all wavelengths. For two-dimensional
             perturbations, inviscid sheets are unstable to perturbations
             of all wavelengths with the transient dynamics controlled by
             axial perturbations and the long-time dynamics controlled by
             transverse perturbations. The asymptotic stability of
             viscous sheets to one-dimensional transverse perturbations
             and to two-dimensional perturbations depends on the
             capillary number (Ca); in both cases, the sheet is unstable
             to long-wave transverse perturbations for any finite Ca. ©
             2009 American Institute of Physics.},
   Doi = {10.1063/1.3094026},
   Key = {fds244242}
}

@article{fds304502,
   Author = {Witelski, TP},
   Title = {Fluid dynamics: The subtle art of blowing
             bubbles},
   Journal = {Nature Physics},
   Volume = {5},
   Number = {5},
   Pages = {315-316},
   Publisher = {Springer Nature},
   Year = {2009},
   Month = {January},
   ISSN = {1745-2473},
   url = {http://dx.doi.org/10.1038/nphys1265},
   Doi = {10.1038/nphys1265},
   Key = {fds304502}
}

@article{fds304501,
   Author = {Aguareles, M and Chapman, SJ and Witelski, T},
   Title = {Interaction of spiral waves in the complex Ginzburg-Landau
             equation.},
   Journal = {Physical review letters},
   Volume = {101},
   Number = {22},
   Pages = {224101},
   Year = {2008},
   Month = {November},
   ISSN = {0031-9007},
   url = {http://dx.doi.org/10.1103/physrevlett.101.224101},
   Abstract = {Solutions of the general cubic complex Ginzburg-Landau
             equation comprising multiple spiral waves are considered,
             and laws of motion for the centers are derived. The
             direction of the motion changes from along the line of
             centers to perpendicular to the line of centers as the
             separation increases, with the strength of the interaction
             algebraic at small separations and exponentially small at
             large separations. The corresponding asymptotic wave number
             and frequency are also determined, which evolve slowly as
             the spirals move.},
   Doi = {10.1103/physrevlett.101.224101},
   Key = {fds304501}
}

@article{fds244232,
   Author = {Santillan, ST and Plaut, RH and Witelski, TP and Virgin,
             LN},
   Title = {Large oscillations of beams and columns including
             self-weight},
   Journal = {International Journal of Non-Linear Mechanics},
   Volume = {43},
   Number = {8},
   Pages = {761-771},
   Publisher = {Elsevier BV},
   Year = {2008},
   Month = {October},
   ISSN = {0020-7462},
   url = {http://dx.doi.org/10.1016/j.ijnonlinmec.2008.04.007},
   Abstract = {Large-amplitude, in-plane beam vibration is investigated
             using numerical simulations and a perturbation analysis
             applied to the dynamic elastica model. The governing
             non-linear boundary value problem is described in terms of
             the arclength, and the beam is treated as inextensible. The
             self-weight of the beam is included in the equations. First,
             a finite difference numerical method is introduced. The
             system is discretized along the arclength, and
             second-order-accurate finite difference formulas are used to
             generate time series of large-amplitude motion of an upright
             cantilever. Secondly, a perturbation method (the method of
             multiple scales) is applied to obtain approximate solutions.
             An analytical backbone curve is generated, and the results
             are compared with those in the literature for various
             boundary conditions where the self-weight of the beam is
             neglected. The method is also used to characterize
             large-amplitude first-mode vibration of a cantilever with
             non-zero self-weight. The perturbation and finite difference
             results are compared for these cases and are seen to agree
             for a large range of vibration amplitudes. Finally,
             large-amplitude motion of a postbuckled, clamped-clamped
             beam is simulated for varying degrees of buckling and
             self-weight using the finite difference method, and backbone
             curves are obtained. © 2008 Elsevier Ltd.},
   Doi = {10.1016/j.ijnonlinmec.2008.04.007},
   Key = {fds244232}
}

@article{fds244245,
   Author = {Catllá, AJ and Schaeffer, DG and Witelski, TP and Monson, EE and Lin,
             AL},
   Title = {On spiking models for synaptic activity and impulsive
             differential equations},
   Journal = {SIAM Review},
   Volume = {50},
   Number = {3},
   Pages = {553-569},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2008},
   Month = {September},
   ISSN = {0036-1445},
   url = {http://link.aip.org/link/?SIR/50/553},
   Abstract = {We illustrate the problems that can arise in writing
             differential equations that include Dirac delta functions to
             model equations with state-dependent impulsive forcing.
             Specifically, difficulties arise in the interpretation of
             the products of distributions with discontinuous functions.
             We suggest several methods to resolve these ambiguities,
             such as using limiting sequences and asymptotic analysis,
             with applications of the results given for discrete maps.
             These suggestions are applied to a popular model describing
             synaptic connections in the brain. © 2008 Society for
             Industrial and Applied Mathematics.},
   Doi = {10.1137/060667980},
   Key = {fds244245}
}

@article{fds244234,
   Author = {DiCarlo, DA and Juanes, R and LaForce, T and Witelski,
             TP},
   Title = {Nonmonotonic traveling wave solutions of infiltration into
             porous media},
   Journal = {Water Resources Research},
   Volume = {44},
   Number = {2},
   Pages = {W02406},
   Publisher = {American Geophysical Union (AGU)},
   Year = {2008},
   Month = {February},
   ISSN = {0043-1397},
   url = {http://dx.doi.org/10.1029/2007WR005975},
   Abstract = {In uniform soils that are susceptible to unstable
             preferential flow, the water saturation may exhibit a
             nonmonotonic profile upon continuous infiltration. As this
             nonmonotonicity (also known as saturation overshoot) cannot
             be described by the conventional Richards equation, there
             have been proposed possible extensions to the unsaturated
             flow equations, including a nonmonotonic capillary
             pressure-saturation curve and a second-order hyperbolic
             term. Here, we present analytic traveling wave solutions to
             the extended Richards equation. These new solutions indeed
             display a nonmonotonic saturation profile, similar to
             previous simulation results. We show that these extensions
             need a regularization term to produce a unique solution. We
             develop complete analytic solutions using a relaxation
             regularization term, and we discuss the results in terms of
             recent measurements of saturation overshoot. Copyright 2008
             by the American Geophysical Union.},
   Doi = {10.1029/2007WR005975},
   Key = {fds244234}
}

@article{fds244222,
   Author = {Gratton, MB and Witelski, TP},
   Title = {Coarsening of unstable thin films subject to
             gravity.},
   Journal = {Physical review. E, Statistical, nonlinear, and soft matter
             physics},
   Volume = {77},
   Number = {1 Pt 2},
   Pages = {016301},
   Year = {2008},
   Month = {January},
   ISSN = {1539-3755},
   url = {http://dx.doi.org/10.1103/physreve.77.016301},
   Abstract = {Thin films of viscous fluids coating hydrophobic substrates
             are unstable to dewetting instabilities, and long-time
             evolution leads to the formation of an array of
             near-equilibrium droplets connected by ultrathin fluid
             layers. In the absence of gravity, previous use of
             lubrication theory has shown that coarsening dynamics will
             ensue-the system will evolve by successively eliminating
             small drops to yield fewer larger drops. While gravity has
             only a weak influence on the initial thin film, we show that
             it has a significant influence on the later stages of the
             coarsening dynamics, dramatically slowing the rate of
             coarsening for large drops. Small drops are relatively
             unaffected, but as coarsening progresses, these aggregate
             into larger drops whose shape and dynamics are dominated by
             gravity. The change in the mean drop shape causes a
             corresponding gradual transition from power-law coarsening
             to a logarithmic behavior.},
   Doi = {10.1103/physreve.77.016301},
   Key = {fds244222}
}

@article{fds244231,
   Author = {Aguareles, M and Chapman, SJ and Witelski, TP},
   Title = {Interaction of spiral waves in the Complex Ginzburg-Landau
             equation},
   Journal = {Physical Review Letters},
   Volume = {101},
   Number = {224101},
   Year = {2008},
   ISSN = {0031-9007},
   url = {http://link.aps.org/abstract/PRL/v101/e224101},
   Abstract = {Solutions of the general cubic complex Ginzburg-Landau
             equation comprising multiple spiral waves are considered,
             and laws of motion for the centers are derived. The
             direction of the motion changes from along the line of
             centers to perpendicular to the line of centers as the
             separation increases, with the strength of the interaction
             algebraic at small separations and exponentially small at
             large separations. The corresponding asymptotic wave number
             and frequency are also determined, which evolve slowly as
             the spirals move. © 2008 The American Physical
             Society.},
   Doi = {10.1103/PhysRevLett.101.224101},
   Key = {fds244231}
}

@article{fds244246,
   Author = {Gratton, MB and Witelski, TP},
   Title = {Coarsening of dewetting thin films subject to
             gravity},
   Journal = {Physical Review E},
   Volume = {77},
   Number = {016301},
   Pages = {1-11},
   Year = {2008},
   url = {http://link.aps.org/abstract/PRE/v77/e016301},
   Key = {fds244246}
}

@article{fds244233,
   Author = {Levy, R and Shearer, M and Witelski, TP},
   Title = {Gravity-driven thin liquid films with insoluble surfactant:
             Smooth traveling waves},
   Journal = {European Journal of Applied Mathematics},
   Volume = {18},
   Number = {6},
   Pages = {679-708},
   Publisher = {Cambridge University Press (CUP)},
   Year = {2007},
   Month = {December},
   ISSN = {0956-7925},
   url = {http://dx.doi.org/10.1017/S0956792507007218},
   Abstract = {The flow of a thin layer of fluid down an inclined plane is
             modified by the presence of insoluble surfactant. For any
             finite surfactant mass, traveling waves are constructed for
             a system of lubrication equations describing the evolution
             of the free-surface fluid height and the surfactant
             concentration. The one-parameter family of solutions is
             investigated using perturbation theory with three small
             parameters: the coefficient of surface tension, the
             surfactant diffusivity, and the coefficient of the
             gravity-driven diffusive spreading of the fluid. When all
             three parameters are zero, the nonlinear PDE system is
             hyperbolic/degenerate-parabolic, and admits traveling wave
             solutions in which the free-surface height is piecewise
             constant, and the surfactant concentration is piecewise
             linear and continuous. The jumps and corners in the
             traveling waves are regularized when the small parameters
             are nonzero; their structure is revealed through a
             combination of analysis and numerical simulation. © 2007
             Cambridge University Press.},
   Doi = {10.1017/S0956792507007218},
   Key = {fds244233}
}

@article{fds244237,
   Author = {Schaeffer, DG and Shearer, M and Witelski, TP},
   Title = {Boundary-value problems for hyperbolic equations related to
             steady granular flow},
   Journal = {Mathematics and Mechanics of Solids},
   Volume = {12},
   Number = {6},
   Pages = {665-699},
   Publisher = {SAGE Publications},
   Year = {2007},
   Month = {December},
   ISSN = {1081-2865},
   url = {http://dx.doi.org/10.1177/1081286506067325},
   Abstract = {Boundary value problems for steady-state flow in
             elastoplasticity are a topic of mathematical and physical
             interest. In particular, the underlying PDE may be
             hyperbolic, and uncertainties surround the choice of
             physically appropriate stress and velocity boundary
             conditions. The analysis and numerical simulations of this
             paper address this issue for a model problem, a system of
             equations describing antiplane shearing of an elastoplastic
             material. This system retains the relevant mathematical
             structure of elastoplastic planar flow. Even if the flow
             rule is associative, two significant phenomena appear: (i)
             For boundary conditions suggestive of granular flow in a
             hopper, in which it seems physically natural to specify the
             velocity everywhere along a portion of the boundary, no such
             solutions of the equations exist; rather, we construct a
             solution with a shear band (velocity jump) along part of the
             boundary, and an appropriate relaxed boundary condition is
             satisfied there. (ii) Rigid zones appear inside deforming
             regions of the flow, and the stress field in such a zone is
             not uniquely determined. For a nonassociative flow rule, an
             extreme form of nonuniqueness-both velocity and stress-is
             encountered. © SAGE Publications 2007.},
   Doi = {10.1177/1081286506067325},
   Key = {fds244237}
}

@article{fds244235,
   Author = {Witelski, TP and Shearer, M and Levy, R},
   Title = {Growing surfactant waves in thin liquid films driven by
             gravity},
   Journal = {Applied Mathematics Research eXpress},
   Volume = {2006},
   Number = {15487},
   Pages = {1-21},
   Publisher = {Oxford University Press (OUP)},
   Year = {2006},
   Month = {December},
   ISSN = {1687-1200},
   url = {http://dx.doi.org/10.1155/AMRX/2006/15487},
   Abstract = {The dynamics of a gravity-driven thin film flow with
             insoluble surfactant are described in the lubrication
             approximation by a coupled system of nonlinear PDEs. When
             the total quantity of surfactant is fixed, a traveling wave
             solution exists. For the case of constantflux of surfactant
             from an upstream reservoir, global traveling waves no longer
             exist as the surfactant accumulates at the leading edge of
             the thin film profile. The dynamics can be described using
             matched asymptotic expansions for t→∞ . The solution is
             constructed from quasistatically evolving traveling waves.
             The rate of growth of the surfactant profile is shown to be
             O(√t) and is supported by numerical simulations.},
   Doi = {10.1155/AMRX/2006/15487},
   Key = {fds244235}
}

@article{fds244240,
   Author = {Bowen, M and Witelski, TP},
   Title = {The linear limit of the dipole problem for the thin film
             equation},
   Journal = {SIAM Journal on Applied Mathematics},
   Volume = {66},
   Number = {5},
   Pages = {1727-1748},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2006},
   Month = {October},
   ISSN = {0036-1399},
   url = {http://dx.doi.org/10.1137/050637832},
   Abstract = {We investigate self-similar solutions of the dipole problem
             for the one-dimensional thin film equation on the half-line
             {x ≥ 0}. We study compactly supported solutions of the
             linear moving boundary problem and show how they relate to
             solutions of the nonlinear problem. The similarity solutions
             are generally of the second kind, given by the solution of a
             nonlinear eigenvalue problem, although there are some
             notable cases where first-kind solutions also arise. We
             examine the conserved quantities connected to these
             first-kind solutions. Difficulties associated with the lack
             of a maximum principle and the non-self-adjointness of the
             fundamental linear problem are also considered. Seeking
             similarity solutions that include sign changes yields a
             surprisingly rich set of (coexisting) stable solutions for
             the intermediate asymptotics of this problem. Our results
             include analysis of limiting cases and comparisons with
             numerical computations. © 2006 Society for Industrial and
             Applied Mathematics.},
   Doi = {10.1137/050637832},
   Key = {fds244240}
}

@article{fds244247,
   Author = {Munch, A and Wagner, B and Witelski, TP},
   Title = {Lubrication models with small to large slip
             lengths},
   Journal = {Journal of Engineering Mathematics},
   Volume = {53},
   Number = {3-4},
   Pages = {259-283},
   Publisher = {Springer Nature},
   Year = {2005},
   Month = {December},
   ISSN = {0022-0833},
   url = {http://www.springerlink.com/(gpximmrigyvfihbxa2cbda45)/app/home/contribution.asp?referrer=parent&backto=issue,11,12;journal,3,197;linkingpublicationresults,1:100287,1},
   Abstract = {A set of lubrication models for the thin film flow of
             incompressible fluids on solid substrates is derived and
             studied. The models are obtained as asymptotic limits of the
             Navier-Stokes equations with the Navier-slip boundary
             condition for different orders of magnitude for the
             slip-length parameter. Specifically, the influence of slip
             on the dewetting behavior of fluids on hydrophobic
             substrates is investigated here. Matched asymptotics are
             used to describe the dynamic profiles for dewetting films
             and comparison is given with computational simulations. The
             motion of the dewetting front shows transitions from being
             nearly linear in time for no-slip to t2/3 as the slip is
             increased. For much larger slip lengths the front motion
             appears to become linear again. Correspondingly, the
             dewetting profiles undergo a transition from oscillatory to
             monotone decay into the uniform film layer for large slip.
             Increasing the slip further, to very large values, is
             associated with an increasing degree of asymmetry in the
             structure of the dewetting ridge profile. © Springer
             2005.},
   Doi = {10.1007/s10665-005-9020-3},
   Key = {fds244247}
}

@article{fds244248,
   Author = {Witelski, TP and Rienstra, SW},
   Title = {Introduction to practical asymptotics III},
   Journal = {Journal of Engineering Mathematics},
   Volume = {53},
   Number = {3-4},
   Pages = {199},
   Publisher = {Springer Nature},
   Year = {2005},
   Month = {December},
   ISSN = {0022-0833},
   url = {http://www.springerlink.com/(gpximmrigyvfihbxa2cbda45)/app/home/contribution.asp?referrer=parent&backto=issue,1,12;journal,3,197;linkingpublicationresults,1:100287,1},
   Abstract = {Introduction to special issue in the journal, TPW and SWR
             guest co-editors.},
   Doi = {10.1007/s10665-005-9027-9},
   Key = {fds244248}
}

@article{fds244249,
   Author = {Glasner, KB and Witelski, TP},
   Title = {Collision versus collapse of droplets in coarsening of
             dewetting thin films},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {209},
   Number = {1-4 SPEC. ISS.},
   Pages = {80-104},
   Publisher = {Elsevier BV},
   Year = {2005},
   Month = {September},
   url = {http://dx.doi.org/10.1016/j.physd.2005.06.010},
   Abstract = {Thin films of viscous fluids coating solid surfaces can
             become unstable due to intermolecular forces, leading to
             break-up of the film into arrays of droplets. The long-time
             dynamics of the system can be represented in terms of
             coupled equations for the masses and positions of the
             droplets. Analysis of the decrease of energy of the system
             shows that coarsening, decreasing the number of droplets
             with increasing time, is favored. Here we describe the two
             coarsening mechanisms present in dewetting films: (i) mass
             exchange leading to collapse of individual drops, and (ii)
             spatial motion leading to droplet collisions and merging
             events. Regimes where each of mechanisms are dominant are
             identified, and the statistics of the coarsening process are
             explained. © 2005 Elsevier B.V. All rights
             reserved.},
   Doi = {10.1016/j.physd.2005.06.010},
   Key = {fds244249}
}

@article{fds244250,
   Author = {Haskett, RP and Witelski, TP and Sur, J},
   Title = {Localized Marangoni forcing in driven thin
             films},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {209},
   Number = {1-4 SPEC. ISS.},
   Pages = {117-134},
   Publisher = {Elsevier BV},
   Year = {2005},
   Month = {September},
   url = {http://dx.doi.org/10.1016/j.physd.2005.06.019},
   Abstract = {We consider the use of localized Marangoni forcing to
             produce a thermocapillary "microfluidic valve" that allows
             us to control the downstream flow of a thin film of viscous
             fluid. To this end, we analyze the influence of this
             localized forcing on a flow driven by a combination of
             uniform Marangoni stresses and gravity in a one-dimensional
             model. Long-time solutions approach states that can be
             categorized in two classes, where the film thickness
             downstream of the forcing is: (I) determined by the upstream
             thickness, or (II) controlled by the forcing amplitude. The
             type II solutions are stable stationary hydraulic jumps for
             thin films. We give careful attention to the relation
             between the forcing and the downstream film flow for the
             resulting bi-stable solutions. We include a comparison of
             the one-dimensional theory with two-dimensional computations
             and experimental results. © 2005 Elsevier B.V. All rights
             reserved.},
   Doi = {10.1016/j.physd.2005.06.019},
   Key = {fds244250}
}

@article{fds244238,
   Author = {Fetzer, R and Jacobs, K and Münch, A and Wagner, B and Witelski,
             TP},
   Title = {New slip regimes and the shape of dewetting thin liquid
             films.},
   Journal = {Physical review letters},
   Volume = {95},
   Number = {12},
   Pages = {127801},
   Year = {2005},
   Month = {September},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/16197111},
   Abstract = {We compare the flow behavior of liquid polymer films on
             silicon wafers coated with either octadecyl-(OTS) or
             dodecyltrichlorosilane (DTS). Our experiments show that
             dewetting on DTS is significantly faster than on OTS. We
             argue that this is tied to the difference in the
             solid/liquid friction. As the film dewets, the profile of
             the rim advancing into the undisturbed film is monotonically
             decaying on DTS but has an oscillatory structure on OTS. For
             the first time we can describe this transition in terms of a
             lubrication model with a Navier-slip condition for the flow
             of a viscous Newtonian liquid.},
   Doi = {10.1103/physrevlett.95.127801},
   Key = {fds244238}
}

@article{fds244239,
   Author = {Witelski, TP},
   Title = {Motion of wetting fronts moving into partially pre-wet
             soil},
   Journal = {Advances in Water Resources},
   Volume = {28},
   Number = {10 SPEC. ISS.},
   Pages = {1133-1141},
   Publisher = {Elsevier BV},
   Year = {2005},
   Month = {January},
   url = {http://dx.doi.org/10.1016/j.advwatres.2004.06.006},
   Abstract = {We study the motion of wetting fronts for vertical
             infiltration problems as modeled by Richards' equation.
             Parlange and others have shown that wetting fronts in
             infiltration flows can be described by traveling wave
             solutions. If the soil layer is not initially dry, but has
             an initial distribution of water content then the motion of
             the wetting front will change due to the interaction of the
             infiltrating flow with the pre-existing soil conditions.
             Using traveling wave profiles, we construct simple
             approximate solutions of initial-boundary value problems for
             Richards' equation that accurately describe the position and
             moisture distribution of the wetting front. We show that the
             influences of surface boundary conditions and initial
             conditions produce shifts to the position of the wetting
             front. The shifts can be calculated by examining the
             cumulative infiltration, and are validated numerically for
             several problems for Richards' equation and the linear
             advection-diffusion equation. © 2005 Elsevier Ltd. All
             rights reserved.},
   Doi = {10.1016/j.advwatres.2004.06.006},
   Key = {fds244239}
}

@article{fds244251,
   Author = {Smolka, LB and Belmonte, A and Henderson, DM and Witelski,
             TP},
   Title = {Exact solution for the extensional flow of a viscoelastic
             filament},
   Journal = {European Journal of Applied Mathematics},
   Volume = {15},
   Number = {6},
   Pages = {679-712},
   Publisher = {Cambridge University Press (CUP)},
   Year = {2004},
   Month = {December},
   url = {http://dx.doi.org/10.1017/S0956792504005789},
   Abstract = {We solve the free boundary problem for the dynamics of a
             cylindrical, axisymmetric viscoelastic filament stretching
             in a gravity-driven extensional flow for the Upper Convected
             Maxwell and Oldroyd-B constitutive models. Assuming the
             axial stress in the filament has a spatial dependence
             provides the simplest coupling of viscoelastic effects to
             the motion of the filament, and yields a closed system of
             ODEs with an exact solution for the stretch rate and
             filament thickness satisfied by both constitutive models.
             This viscoelastic solution, which is a generalization of the
             exact solution for Newtonian filaments, converges to the
             Newtonian power-law scaling as t → ∞. Based on the exact
             solution, we identify two regimes of dynamical behavior
             called the weakly- and strongly-viscoelastic limits. We
             compare the viscoelastic solution to measurements of the
             thinning filament that forms behind a falling drop for
             several semi-dilute (strongly-viscoelastic) polymer
             solutions. We find the exact solution correctly predicts the
             time-dependence of the filament diameter in all of the
             experiments. As t → ∞, observations of the filament
             thickness follow the Newtonian scaling 1/√t. The
             transition from viscoelastic to Newtonian scaling in the
             filament thickness is coupled to a stretch-to-coil
             transition of the polymer molecules. © 2004 Cambridge
             University Press.},
   Doi = {10.1017/S0956792504005789},
   Key = {fds244251}
}

@article{fds244252,
   Author = {Sur, J and Witelski, TP and Behringer, RP},
   Title = {Steady-profile fingering flows in Marangoni driven thin
             films.},
   Journal = {Physical review letters},
   Volume = {93},
   Number = {24},
   Pages = {247803},
   Year = {2004},
   Month = {December},
   ISSN = {0031-9007},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15697861},
   Abstract = {We present experimental and computational results indicating
             the existence of finite-amplitude fingering solutions in a
             flow of a thin film of a viscous fluid driven by thermally
             induced Marangoni stresses. Using carefully controlled
             experiments, spatially periodic perturbations to the contact
             line of an initially uniform thin film flow are shown to
             lead to the development of steady-profile two-dimensional
             traveling wave fingers. Using an infrared laser and scanning
             mirror, we impose thermal perturbations with a known
             wavelength to an initially uniform advancing fluid front. As
             the front advances in the experiment, we observe convergence
             to fingers with the initially prescribed wavelength.
             Experiments and numerical computations show that this family
             of solutions arises from a subcritical bifurcation.},
   Doi = {10.1103/physrevlett.93.247803},
   Key = {fds244252}
}

@article{fds244253,
   Author = {Borucki, LJ and Witelski, T and Please, C and Kramer, PR and Schwendeman, D},
   Title = {A theory of pad conditioning for chemical-mechanical
             polishing},
   Journal = {Journal of Engineering Mathematics},
   Volume = {50},
   Number = {1},
   Pages = {1-24},
   Publisher = {Springer Nature},
   Year = {2004},
   Month = {December},
   url = {http://ipsapp007.kluweronline.com/ips/frames/issues.aspx?J=4678&N=JournalContents&ADS=0},
   Abstract = {Statistical models are presented to describe the evolution
             of the surface roughness of polishing pads during the
             pad-conditioning process in chemical-mechanical polishing.
             The models describe the evolution of the surface-height
             probability-density function of solid pads during fixed
             height or fixed cut-rate conditioning. An integral equation
             is derived for the effect of conditioning on a foamed pad in
             terms of a model for a solid pad. The models that combine
             wear and conditioning are then discussed for both solid and
             foamed pads. Models include the dependence of the surface
             roughness on the shape and density of the cutting tips used
             in the conditioner and on other operating parameters. Good
             agreement is found between the model, Monte Carlo
             simulations and with experimental data. © 2004 Kluwer
             Academic Publishers.},
   Doi = {10.1023/B:ENGI.0000042116.09084.00},
   Key = {fds244253}
}

@article{fds244255,
   Author = {Witelski, TP and Bernoff, AJ and Bertozzi, AL},
   Title = {Blowup and dissipation in a critical-case unstable thin film
             equation},
   Journal = {European Journal of Applied Mathematics},
   Volume = {15},
   Number = {2},
   Pages = {223-256},
   Publisher = {Cambridge University Press (CUP)},
   Year = {2004},
   Month = {April},
   url = {http://dx.doi.org/10.1017/S0956792504005418},
   Abstract = {We study the dynamics of dissipation and blow-up in a
             critical-case unstable thin film equation. The governing
             equation is a nonlinear fourth-order degenerate parabolic
             PDE derived from a generalized model for lubrication flows
             of thin viscous fluid layers on solid surfaces. There is a
             critical mass for blow-up and a rich set of dynamics
             including families of similarity solutions for finite-time
             blow-up and infinite-time spreading. The structure and
             stability of the steady-states and the compactly-supported
             similarity solutions is studied.},
   Doi = {10.1017/S0956792504005418},
   Key = {fds244255}
}

@article{fds244220,
   Author = {Witelski, TP},
   Title = {Nonlinear Differential Equations, Mechanics and
             Bifurcation},
   Journal = {Discrete and Continuous Dynamical Systems - Series
             B},
   Volume = {3},
   Number = {4},
   Pages = {i},
   Year = {2003},
   Month = {November},
   url = {http://aimsciences.org/journals/dcdsB/B3_4.htm},
   Key = {fds244220}
}

@article{fds304499,
   Author = {Shearer, M and Schaeffer, DG and Witelski, TP},
   Title = {Stability of shear bands in an elastoplastic model for
             granular flow: The role of discreteness},
   Journal = {Mathematical Models and Methods in Applied
             Sciences},
   Volume = {13},
   Number = {11},
   Pages = {1629-1671},
   Publisher = {World Scientific Pub Co Pte Lt},
   Year = {2003},
   Month = {November},
   url = {http://dx.doi.org/10.1142/S0218202503003069},
   Abstract = {Continuum models for granular flow generally give rise to
             systems of nonlinear partial differential equations that are
             linearly ill-posed. In this paper we introduce discreteness
             into an elastoplasticity model for granular flow by
             approximating spatial derivatives with finite differences.
             The resulting ordinary differential equations have bounded
             solutions for all time, a consequence of both discreteness
             and nonlinearity. We study how the large-time behavior of
             solutions in this model depends on an elastic shear modulus
             ε. For large and moderate values of ε, the model has
             stable steady-state solutions with uniform shearing except
             for one shear band; almost all solutions tend to one of
             these as t → ∞. However, when ε becomes sufficiently
             small, the single-shear-band solutions lose stability
             through a Hopf bifurcation. The value of ε at the
             bifurcation point is proportional to the ratio of the mesh
             size to the macroscopic length scale. These conclusions are
             established analytically through a careful estimation of the
             eigenvalues. In numerical simulations we find that: (i)
             after stability is lost, time-periodic solutions appear,
             containing both elastic and plastic waves, and (ii) the
             bifurcation diagram representing these solutions exhibits
             bi-stability.},
   Doi = {10.1142/S0218202503003069},
   Key = {fds304499}
}

@article{fds244256,
   Author = {Witelski, TP and Bowen, M},
   Title = {ADI schemes for higher-order nonlinear diffusion
             equations},
   Journal = {Applied Numerical Mathematics},
   Volume = {45},
   Number = {2-3},
   Pages = {331-351},
   Publisher = {Elsevier BV},
   Year = {2003},
   Month = {May},
   url = {http://dx.doi.org/10.1016/S0168-9274(02)00194-0},
   Abstract = {Alternating Direction Implicit (ADI) schemes are constructed
             for the solution of two-dimensional higher-order linear and
             nonlinear diffusion equations, particularly including the
             fourth-order thin film equation for surface tension driven
             fluid flows. First and second-order accurate schemes are
             derived via approximate factorization of the evolution
             equations. This approach is combined with iterative methods
             to solve nonlinear problems. Problems in the fluid dynamics
             of thin films are solved to demonstrate the effectiveness of
             the ADI schemes. © 2002 IMACS. Published by Elsevier
             Science B.V. All rights reserved.},
   Doi = {10.1016/S0168-9274(02)00194-0},
   Key = {fds244256}
}

@article{fds244257,
   Author = {Witelski, TP},
   Title = {Intermediate asymptotics for Richards' equation in a finite
             layer},
   Journal = {Journal of Engineering Mathematics},
   Volume = {45},
   Number = {3-4},
   Pages = {379-399},
   Year = {2003},
   Month = {April},
   url = {http://dx.doi.org/10.1023/A:1022609020200},
   Abstract = {Perturbation methods are applied to study an
             initial-boundary-value problem for Richards' equation,
             describing vertical infiltration of water into a finite
             layer of soil. This problem for the degenerate diffusion
             equation with convection and Dirichlet/Robin boundary
             conditions exhibits several different regimes of behavior.
             Boundary-layer analysis and short-time asymptotics are used
             to describe the structure of similarity solutions, traveling
             waves, and other solution states and the transitions
             connecting these different intermediate asymptotic
             regimes.},
   Doi = {10.1023/A:1022609020200},
   Key = {fds244257}
}

@article{fds244258,
   Author = {Glasner, KB and Witelski, TP},
   Title = {Coarsening dynamics of dewetting films.},
   Journal = {Physical review. E, Statistical, nonlinear, and soft matter
             physics},
   Volume = {67},
   Number = {1 Pt 2},
   Pages = {016302},
   Year = {2003},
   Month = {January},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/12636597},
   Abstract = {Lubrication theory for unstable thin liquid films on solid
             substrates is used to model the coarsening dynamics in the
             long-time behavior of dewetting films. The dominant physical
             effects that drive the fluid dynamics in dewetting films are
             surface tension and intermolecular interactions with the
             solid substrate. Instabilities in these films lead to
             rupture and other morphological changes that promote
             nonuniformity in the films. Following the initial
             instabilities, the films break up into near-equilibrium
             droplets connected by an ultrathin film. For longer times,
             the fluid will undergo a coarsening process in which
             droplets both move and exchange mass on slow time scales.
             The dynamics of this coarsening process will be obtained
             through the asymptotic reduction of the long-wave PDE
             governing the thin film to a set of ODEs for the evolution
             of the droplets. From this, a scaling law that governs the
             coarsening rate is derived.},
   Doi = {10.1103/physreve.67.016302},
   Key = {fds244258}
}

@article{fds318344,
   Author = {Glasner, KB and Witelski, TP},
   Title = {Coarsening dynamics of dewetting films},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {67},
   Number = {1 2},
   Pages = {163021-1630212},
   Year = {2003},
   Month = {January},
   Abstract = {The modelling of coarsening dynamics of dewetting films
             using lubrication theory for unstable thin liquid films on
             solid substrates was discussed. Surface tension and
             intermolecular interactions with the solid substrate were
             the dominant physical effects driving the fluid dynamics.
             The fluid underwent a coarsening process in which droplets
             moved and exchanged mass on slow time scales.},
   Key = {fds318344}
}

@article{fds325967,
   Author = {Schaeffer, DG and Shearer, M and Witelski, T},
   Title = {One-dimensional solutions of an elastoplasticity model of
             granular material},
   Journal = {Math. Models and Methods in Appl. Sciences},
   Volume = {13},
   Pages = {1629-1671},
   Year = {2003},
   Key = {fds325967}
}

@article{fds244187,
   Author = {Witelski, TP},
   Title = {Computing finite-time singularities in interfacial
             flows},
   Journal = {MODERN METHODS IN SCIENTIFIC COMPUTING AND
             APPLICATIONS},
   Volume = {75},
   Pages = {451-487},
   Publisher = {SPRINGER},
   Editor = {Bourlioux, A and Gander, MJ and Sabidussi, G},
   Year = {2002},
   Month = {January},
   ISBN = {1-4020-0782-5},
   ISSN = {1568-2609},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000180113600012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {Finite-time singularities occuring in mathematical models of
             free-surface flows indicate that important qualitative
             changes are taking place; for problems in solid and fluid
             mechanics this includes topological transitions -- blow-up,
             and pinch-off. For many problems, the dynamics leading to
             the formation of such singularities are described by
             self-similar solutions of the governing nonlinear partial
             differential equations. We present an analytical and
             numerical study of these similarity solutions and discuss
             their stability.},
   Key = {fds244187}
}

@article{fds244217,
   Author = {Bernoff, AJ and Witelski, TP},
   Title = {Linear stability of source-type similarity solutions of the
             thin film equation},
   Journal = {Applied Mathematics Letters},
   Volume = {15},
   Number = {5},
   Pages = {599-606},
   Publisher = {Elsevier BV},
   Year = {2002},
   Month = {January},
   ISSN = {0893-9659},
   url = {http://dx.doi.org/10.1016/S0893-9659(02)80012-X},
   Abstract = {We study the stability of compactly-supported source-type
             self-similar solutions of the generalized thin film equation
             ht = -(hnhxxx)x. Using linear stability analysis, applied to
             the problem in similarity variables, we show that the
             source-type solutions are stable. These results are related
             to the underlying symmetries of the PDE. For the special
             case of n = 1, analytical results are obtained for the
             spectrum, and the eigenfunctions are given in terms of
             classical orthogonal polynomials. © 2002 Elsevier Science
             Ltd. All rights reserved.},
   Doi = {10.1016/S0893-9659(02)80012-X},
   Key = {fds244217}
}

@article{fds244214,
   Author = {Witelski, TP and Schaeffer, DG and Shearer, M},
   Title = {A discrete model for an ill-posed nonlinear parabolic
             PDE},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {160},
   Number = {3-4},
   Pages = {189-221},
   Publisher = {Elsevier BV},
   Year = {2001},
   Month = {December},
   ISSN = {0167-2789},
   url = {http://dx.doi.org/10.1016/S0167-2789(01)00350-5},
   Abstract = {We study a finite-difference discretization of an ill-posed
             nonlinear parabolic partial differential equation. The PDE
             is the one-dimensional version of a simplified
             two-dimensional model for the formation of shear bands via
             anti-plane shear of a granular medium. For the discretized
             initial value problem, we derive analytically, and observed
             numerically, a two-stage evolution leading to a
             steady-state: (i) an initial growth of grid-scale
             instabilities, and (ii) coarsening dynamics. Elaborating the
             second phase, at any fixed time the solution has a piecewise
             linear profile with a finite number of shear bands. In this
             coarsening phase, one shear band after another collapses
             until a steady-state with just one jump discontinuity is
             achieved. The amplitude of this steady-state shear band is
             derived analytically, but due to the ill-posedness of the
             underlying problem, its position exhibits sensitive
             dependence. Analyzing data from the simulations, we observe
             that the number of shear bands at time t decays like t-1/3.
             From this scaling law, we show that the time-scale of the
             coarsening phase in the evolution of this model for granular
             media critically depends on the discreteness of the model.
             Our analysis also has implications to related ill-posed
             nonlinear PDEs for the one-dimensional Perona-Malik equation
             in image processing and to models for clustering
             instabilities in granular materials. © 2001 Elsevier
             Science B.V. All rights reserved.},
   Doi = {10.1016/S0167-2789(01)00350-5},
   Key = {fds244214}
}

@article{fds244213,
   Author = {Vaynblat, D and Lister, JR and Witelski, TP},
   Title = {Symmetry and self-similarity in rupture and pinchoff: A
             geometric bifurcation},
   Journal = {European Journal of Applied Mathematics},
   Volume = {12},
   Number = {3},
   Pages = {209-232},
   Publisher = {Cambridge University Press (CUP)},
   Year = {2001},
   Month = {December},
   url = {http://dx.doi.org/10.1017/S0956792501004375},
   Abstract = {Long-wavelength models for van der Waals driven rupture of a
             free thin viscous sheet and for capillary pinchoff of a
             viscous fluid thread both give rise to families of
             first-type similarity solutions. The scaling exponents in
             these solutions are independent of the dimensionality of
             problem. However, the structure of the similarity solutions
             exhibits an intriguing geometric dependence on the
             dimensionality of the system: van der Waals driven sheet
             rupture proceeds symmetrically, whereas thread rupture is
             inherently asymmetric. To study the bifurcation of rupture
             from symmetric to asymmetric forms, we generalize the
             governing equations with the dimension serving as a control
             parameter. The bifurcation is governed by leading-order
             inviscid dynamics in which viscous effects are
             asymptotically small but nevertheless provide the selection
             mechanism.},
   Doi = {10.1017/S0956792501004375},
   Key = {fds244213}
}

@article{fds244216,
   Author = {Bertozzi, AL and Grün, G and Witelski, TP},
   Title = {Dewetting films: Bifurcations and concentrations},
   Journal = {Nonlinearity},
   Volume = {14},
   Number = {6},
   Pages = {1569-1592},
   Publisher = {IOP Publishing},
   Year = {2001},
   Month = {November},
   url = {http://dx.doi.org/10.1088/0951-7715/14/6/309},
   Abstract = {Under the influence of long-range attractive and short-range
             repulsive forces, thin liquid films rupture and form complex
             dewetting patterns. This paper studies this phenomenon in
             one space dimension within the framework of fourth-order
             degenerate parabolic equations of lubrication type. We
             derive the global structure of the bifurcation diagram for
             steady-state solutions. A stability analysis of the solution
             branches and numerical simulations suggest coarsening
             occurs. Furthermore, we study the behaviour of solutions in
             the limit that short-range repulsive forces are neglected.
             Both asymptotic analysis and numerical experiments show that
             this limit can concentrate mass in δ-distributions.},
   Doi = {10.1088/0951-7715/14/6/309},
   Key = {fds244216}
}

@article{fds244212,
   Author = {Witelski, TP and Ono, K and Kaper, TJ},
   Title = {Critical wave speeds for a family of scalar
             reaction-diffusion equations},
   Journal = {Applied Mathematics Letters},
   Volume = {14},
   Number = {1},
   Pages = {65-73},
   Publisher = {Elsevier BV},
   Year = {2001},
   Month = {January},
   url = {http://dx.doi.org/10.1016/S0893-9659(00)00114-2},
   Abstract = {We study the set of traveling waves in a class of
             reaction-diffusion equations for the family of potentials
             fm(U) = 2Um(1 - U). We use perturbation methods and matched
             asymptotics to derive expansions for the critical wave speed
             that separates algebraic and exponential traveling wave
             front solutions for m → 2 and m → ∞. Also, an integral
             formulation of the problem shows that nonuniform convergence
             of the generalized equal area rule occurs at the critical
             wave speed. © 2000 Elsevier Science Ltd. All rights
             reserved.},
   Doi = {10.1016/S0893-9659(00)00114-2},
   Key = {fds244212}
}

@article{fds244215,
   Author = {Vaynblat, D and Lister, JR and Witelski, TP},
   Title = {Rupture of thin viscous films by van der waals forces:
             Evolution and self-similarity},
   Journal = {Physics of Fluids},
   Volume = {13},
   Number = {5},
   Pages = {1130-1141},
   Publisher = {AIP Publishing},
   Year = {2001},
   Month = {January},
   url = {http://ojps.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PHFLE6000013000005001130000001&idtype=cvips&gifs=Yes},
   Abstract = {The van der Waals driven rupture of a freely suspended thin
             viscous sheet is examined using a long-wavelength model.
             Dimensional analysis shows the possibility of first-type
             similarity solutions in which the dominant physical balance
             is between inertia, extensional viscous stresses and the van
             der Waals disjoining pressure, while surface tension is
             negligible. For both line rupture and point rupture the film
             thickness decreases like (t* - t)1/3 and the lateral length
             scale like (t* - t)1/2, where t* - t is the time remaining
             until rupture. In each geometry these scalings are confirmed
             by numerical simulations of the time-dependent behavior, and
             a discrete family of similarity solutions is found. The
             "lowest-order" mode in the family is the one selected by the
             time-dependent dynamics. © 2001 American Institute of
             Physics.},
   Doi = {10.1063/1.1359749},
   Key = {fds244215}
}

@article{fds244211,
   Author = {Witelski, TP and Bernoff, AJ},
   Title = {Dynamics of three-dimensional thin film rupture},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {147},
   Number = {1-2},
   Pages = {155-176},
   Publisher = {Elsevier BV},
   Year = {2000},
   Month = {December},
   url = {http://dx.doi.org/10.1016/S0167-2789(00)00165-2},
   Abstract = {We consider the problem of thin film rupture driven by van
             der Waals forces. A fourth-order nonlinear PDE governs the
             low Reynolds number lubrication model for a viscous liquid
             on a solid substrate. Finite-time singularities in this
             equation model rupture leading to formation of dry spots in
             the film. Our study addresses the problem of rupture in the
             full three-dimensional geometry. We focus on stability and
             selection of the dynamics determined by the initial
             conditions on small finite domains with planar and
             axisymmetric geometries. We also address the final stages of
             the dynamics - self-similar dynamics for point, line, and
             ring rupture. We will demonstrate that line and ring rupture
             are unstable and will generically destabilize to produce
             axisymmetric rupture at isolated points.},
   Doi = {10.1016/S0167-2789(00)00165-2},
   Key = {fds244211}
}

@article{fds342143,
   Author = {Witelski, TP and Ono, K and Kaper, TJ},
   Title = {On axisymmetric traveling waves and radial solutions of
             semi-linear elliptic equations},
   Journal = {Natural Resource Modeling},
   Volume = {13},
   Number = {3},
   Pages = {339-388},
   Year = {2000},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/local/radial.ps},
   Abstract = {Combining analytical techniques from perturbation methods
             and dynamical systems theory, we present an
             elementaryapproach to the detailed construction of
             axisymmetric diffusive interfaces in semi-linear elliptic
             equations. Solutions of the resulting non-autonomous radial
             differential equations can be expressed in terms of a
             slowlyvarying phase plane system. Special analytical results
             for the phase plane system are used to produce closed-form
             solutions for the asymptotic forms of the curved front
             solutions. These axisym-metric solutions are fundamental
             examples of more general curved fronts that arise in a wide
             variety of scientific fields, and we extensivelydiscuss a
             number of them, with a particular emphasis on connections to
             geometric models for the motion of interfaces. Related
             classical results for traveling waves in one-dimensional
             problems are also reviewed briefly. Manyof the results
             contained in this article are known, and in presenting known
             results, it is intended that this article be expositoryin
             nature, providing elementarydemonstrations of some of the
             central dynamical phenomena and mathematical techniques. It
             is hoped that the article serves as one possible avenue of
             entree to the literature on radiallysymmetric solutions of
             semilinear elliptic problems, especiallyto those articles in
             which more advanced mathematical theoryis developed. © 2000
             Rocky Mountain Mathematics Consortium.},
   Doi = {10.1111/j.1939-7445.2000.tb00039.x},
   Key = {fds342143}
}

@article{fds244186,
   Author = {Witelski, TP and Bernoff, AJ},
   Title = {Stability of self-similar solutions for van der Waals driven
             thin film rupture},
   Journal = {Physics of Fluids},
   Volume = {11},
   Number = {9},
   Pages = {2443-2445},
   Publisher = {AIP Publishing},
   Year = {1999},
   Month = {January},
   ISSN = {1070-6631},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000081906000002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {Recent studies of pinch-off of filaments and rupture in thin
             films have found infinite sets of first-type similarity
             solutions. Of these, the dynamically stable similarity
             solutions produce observable rupture behavior as localized,
             finite-time singularities in the models of the flow. In this
             letter we describe a systematic technique for calculating
             such solutions and determining their linear stability. For
             the problem of axisymmetric van der Waals driven rupture
             (recently studied by Zhang and Lister), we identify the
             unique stable similarity solution for point rupture of a
             thin film and an alternative mode of singularity formation
             corresponding to annular “ring rupture.”. © 1999,
             American Institute of Physics. All rights
             reserved.},
   Doi = {10.1063/1.870138},
   Key = {fds244186}
}

@article{fds244209,
   Author = {Witelski, TP and Hendriks, F},
   Title = {Stability of gas bearing sliders for large bearing number:
             Convective instability of the tapered slider©},
   Journal = {Tribology Transactions},
   Volume = {42},
   Number = {1},
   Pages = {216-222},
   Publisher = {Informa UK Limited},
   Year = {1999},
   Month = {January},
   ISSN = {1040-2004},
   url = {http://www.math.duke.edu/~witelski/local/stle97.ps},
   Abstract = {The dynamics and stability of tapered air bearing sliders
             used for computer hard disk drive magnetic recording heads
             is examined using analytical methods. Lubrication theory is
             applied to determine the lift on the slider from the
             Reynolds equation in the limit of large bearing number. The
             dynamics of the slider are given by a nonlinear
             integro-differential equation. Linear stability analysis of
             this model yields valuable insight into the behavior of the
             slider. Most significantly, it is found that convective
             effects can not be neglected and yield either damping or
             instability depending on the slider configuration. This
             analysis is also applied to determine the response of the
             slider motion due to deviations in the disk surface. © 1999
             Taylor & Francis Group, LLC.},
   Doi = {10.1080/10402009908982211},
   Key = {fds244209}
}

@article{fds244210,
   Author = {Witelski, TP and Hendriks, F},
   Title = {Large bearing number stability analysis for tango class gas
             bearing sliders},
   Journal = {Tribology Transactions},
   Volume = {42},
   Number = {3},
   Pages = {668-674},
   Publisher = {Informa UK Limited},
   Year = {1999},
   Month = {January},
   ISSN = {1040-2004},
   url = {http://www.math.duke.edu/~witelski/local/gas2.ps},
   Abstract = {Air bearing sliders in the Tango class use load bearing pads
             with inlet-throttled leading edges to control the mass flux
             and lift. The influence of leakage or diffusion effects is
             always present in real sliders. In some designs such as
             railed taper flat designs leakage is dominant. The behavior
             of such sliders must be determined with numerical methods
             that obscure deeper understanding. Many aspects of the
             behavior of Tango class sliders can be understood with the
             vast simplification allowed by inlet throttling. In this
             paper such a simplified analysis is applied to describe a
             complete air bearing slider composed of two pads. The
             conditions for static level flight are determined, as well
             as the linear stability of heaving and pitching
             oscillations. Both stable and unstable modes are identified.
             Either damping or amplification can result from convective
             effects in the absence of mechanical damping. In real
             implementations of Tango class sliders instability has not
             been observed thanks to diffusion. The present analysis can
             serve as a guide to select initial choices for the operating
             parameters that correspond to maximum convective damping. ©
             1999 Taylor and Francis Group, LLC.},
   Doi = {10.1080/10402009908982268},
   Key = {fds244210}
}

@article{fds244204,
   Author = {Witelski, TP and Grosberg, AY and Tanaka, T},
   Title = {On the properties of polymer globules in the high density
             limit},
   Journal = {Journal of Chemical Physics},
   Volume = {108},
   Number = {21},
   Pages = {9144-9149},
   Publisher = {AIP Publishing},
   Year = {1998},
   Month = {June},
   url = {http://ojps.aip.org/journal_cgi/getabs?KEY=JCPSA6&cvips=JCPSA6000108000021009144000001&gifs=Yes},
   Abstract = {We re-examine quantitative mean-field theory for the
             collapsed globule phase of a polymer chain taking full
             account of its finite compressibility. The mathematical
             properties of the nonlinear mean-field equations describing
             the structure of the globule are formulated. Our results
             explain findings and observations of the recent computer
             simulation and experimental studies. While the effects are
             due to the restricted compressibility, they are seen well
             before the globule reaches its dry maximal density. © 1998
             American Institute of Physics.},
   Doi = {10.1063/1.476361},
   Key = {fds244204}
}

@article{fds244202,
   Author = {Witelski, TP and Bernoff, AJ},
   Title = {Self-similar asymptotics for linear and nonlinear diffusion
             equations},
   Journal = {Studies in Applied Mathematics},
   Volume = {100},
   Number = {2},
   Pages = {153-193},
   Publisher = {WILEY},
   Year = {1998},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/articles/selfsim.ps.gz},
   Abstract = {The long-time asymptotic solutions of initial value problems
             for the heat equation and the nonlinear porous medium
             equation are self-similar spreading solutions. The
             symmetries of the governing equations yield three-parameter
             families of these solutions given in terms of their mass,
             center of mass, and variance. Unlike the mass and center of
             mass, the variance, or "time-shift," of a solution is not a
             conserved quantity for the nonlinear problem. We derive an
             optimal linear estimate of the long-time variance. Newman's
             Lyapunov functional is used to produce a maximum entropy
             time-shift estimate. Results are applied to nonlinear
             merging and time-dependent, inhomogeneously forced diffusion
             problems.},
   Doi = {10.1111/1467-9590.00074},
   Key = {fds244202}
}

@article{fds244203,
   Author = {Witelski, TP},
   Title = {Dynamics of air bearing sliders},
   Journal = {Physics of Fluids},
   Volume = {10},
   Number = {3},
   Pages = {698-708},
   Publisher = {AIP Publishing},
   Year = {1998},
   Month = {January},
   url = {http://ojps.aip.org/journal_cgi/getabs?KEY=PHFLE6&cvips=PHFLE6000010000003000698000001&gifs=Yes},
   Abstract = {In this paper we present new results for the dynamics of a
             problem tor the interaction of a compressible gas flow with
             a movable rigid surface. Compressible lubrication theory is
             applied to describe the dynamics of the vertical motion of
             air bearing sliders used in computer hard disk drives. In
             the limit of large bearing number we show this problem can
             be reduced to a nonlinear integrodifferential equation.
             Linear stability analysis and perturbation methods show that
             over the range of possible slider positions there is an
             infinite sequence of Hopf bifurcations yielding stable large
             amplitude periodic orbits. The dynamics of near-crash
             behavior and interaction with a moving disk surface are also
             addressed. © 1998 American Institute of
             Physics.},
   Doi = {10.1063/1.869595},
   Key = {fds244203}
}

@article{fds244205,
   Author = {Witelski, TP},
   Title = {Horizontal infiltration into wet soil},
   Journal = {Water Resources Research},
   Volume = {34},
   Number = {7},
   Pages = {1859-1863},
   Publisher = {American Geophysical Union (AGU)},
   Year = {1998},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/articles/wetsoil.ps.gz},
   Abstract = {We obtain the long-time asymptotic similarity solution for
             the wetting front for water absorption from a constant
             source into a homogenous layer of soil with a preexisting
             moisture distribution. The presence of the initial water
             distribution in the soil introduces a time shift that
             advances the position of the wetting front. The time shift
             be explicitly calculated for any form of diffusivity. A
             dynamic time shift is derived to yield a very efficient
             means for estimating the water content distribution and
             front position for all times in Brooks-Corey-type soil
             models.},
   Doi = {10.1029/98WR00775},
   Key = {fds244205}
}

@article{fds244206,
   Author = {Witelski, TP},
   Title = {Equilibrium interface solutions of a degenerate singular
             Cahn-Hilliard equation},
   Journal = {Applied Mathematics Letters},
   Volume = {11},
   Number = {5},
   Pages = {127-133},
   Publisher = {Elsevier BV},
   Year = {1998},
   Month = {January},
   url = {http://dx.doi.org/10.1016/S0893-9659(98)00092-5},
   Abstract = {We present an analysis of the equilibrium diffusive
             interfaces in a model for the interaction of layers of pure
             polymers. The discussion focuses on the important
             qualitative features of the solutions of the nonlinear
             singular Cahn-Hilliard equation with degenerate mobility for
             the Flory-Huggins-deGennes free energy model. The spatial
             structure of possible equilibrium phase separated solutions
             are found. Using phase plane analysis, we obtain
             heteroclinic and homoclinic degenerate weak compact-support
             solutions that are relevant to finite domain boundary value
             problems and localized impurities in infinite layers. ©
             1998 Elsevier Science Ltd. AU rights reserved.},
   Doi = {10.1016/S0893-9659(98)00092-5},
   Key = {fds244206}
}

@article{fds244207,
   Author = {Bernoff, AJ and Bertozzi, AL and Witelski, TP},
   Title = {Axisymmetric surface diffusion: Dynamics and stability of
             self-similar pinchoff},
   Journal = {Journal of Statistical Physics},
   Volume = {93},
   Number = {3-4},
   Pages = {725-776},
   Publisher = {Springer Nature},
   Year = {1998},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/articles/surfdiff.ps.gz},
   Abstract = {The dynamics of surface diffusion describes the motion of a
             surface with its normal velocity given by the surface
             Laplacian of its mean curvature. This flow conserves the
             volume enclosed inside the surface while minimizing its
             surface area. We review the axisymmetric equilibria: the
             cylinder, sphere, and the Delaunay unduloid. The sphere is
             stable, while the cylinder is long-wave unstable. A
             subcritical bifurcation from the cylinder produces a
             continuous family of unduloid solutions. We present
             computations that suggest that the stable manifold of the
             unduloid forms a separatrix between states that relax to the
             cylinder in infinite time and those that tend toward
             finite-time pinchoff. We examine the structure of the
             pinchoff, showing it has self-similar structure, using
             asymptotic, numerical, and analytical methods. In addition
             to a previously known similarity solution, we find a
             countable set of similarity solutions, each with a different
             asymptotic cone angle. We develop a stability theory in
             similarity variables that selects the original similarity
             solution as the only linearly stable one and consequently
             the only observable solution. We also consider similarity
             solutions describing the dynamics after the topological
             transition.},
   Doi = {10.1023/b:joss.0000033251.81126.af},
   Key = {fds244207}
}

@article{fds244208,
   Author = {Brenner, MP and Witelski, TP},
   Title = {On spherically symmetric gravitational collapse},
   Journal = {Journal of Statistical Physics},
   Volume = {93},
   Number = {3-4},
   Pages = {863-899},
   Publisher = {Springer Nature},
   Year = {1998},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/articles/grav.ps.gz},
   Abstract = {This paper considers the dynamics of a classical problem in
             astrophysics, the behavior of spherically symmetric
             gravitational collapse starting from a uniform, density
             cloud of interstellar gas. Previous work on this problem
             proposed a universal self-similar solution for the collapse
             yielding a collapsed mass much smaller than the mass
             contained in the initial cloud. This paper demonstrates the
             existence of a second threshold not far above the marginal
             collapse threshold - above which the asymptotic collapse is
             not universal. In this regime, small changes in the initial
             data or weak stochastic forcing leads to qualitatively
             different collapse dynamics. In the absence of
             instabilities, a progressing wave solution yields a
             collapsed uniform core with infinite density. Under some
             conditions the instabilities ultimately lead to the
             well-known self-similar dynamics. However, other
             instabilities can cause the density profile to become
             non-monotone and produce a shock in the velocity. In
             presenting these results, we outline pitfalls of numerical
             schemes that can arise when computing collapse.},
   Doi = {10.1023/b:joss.0000033167.19114.b8},
   Key = {fds244208}
}

@article{fds244201,
   Author = {Witelski, TP},
   Title = {Similarity solutions of the lubrication equation},
   Journal = {Applied Mathematics Letters},
   Volume = {10},
   Number = {5},
   Pages = {107-113},
   Publisher = {Elsevier BV},
   Year = {1997},
   Month = {September},
   url = {http://www.math.duke.edu/~witelski/articles/amslube.ps.gz},
   Abstract = {We present a method for constructing closed-form similarity
             solutions of the fourth-order nonlinear lubrication
             equation. By extending a technique used to study
             second-order degenerate diffusion problems, corresponding
             interface profiles and diffusion coefficient functions can
             be derived in exact form. Different classes of spreading and
             shrinking solutions are obtained using this
             approach.},
   Doi = {10.1016/S0893-9659(97)00092-X},
   Key = {fds244201}
}

@article{fds244199,
   Author = {Witelski, TP},
   Title = {Segregation and mixing in degenerate diffusion in population
             dynamics},
   Journal = {Journal of Mathematical Biology},
   Volume = {35},
   Number = {6},
   Pages = {695-712},
   Publisher = {Springer Nature},
   Year = {1997},
   Month = {January},
   ISSN = {0303-6812},
   url = {http://www.math.duke.edu/~witelski/articles/jmbseg.ps.gz},
   Abstract = {We study the qualitative properties of degenerate diffusion
             equations used to describe dispersal processes in population
             dynamics. For systems of interacting populations, the forms
             of the diffusion models used determine if the population
             will intermix or remain disjoint (segregated). The dynamics
             and stability of segregation boundaries between competing
             populations is analyzed. General population models with
             segregation and mixing interactions are derived and
             connections to behavior in fluid mechanical systems are
             addressed. © Springer-Verlag 1997.},
   Doi = {10.1007/s002850050072},
   Key = {fds244199}
}

@article{fds244200,
   Author = {Witelski, TP},
   Title = {Perturbation Analysis for Wetting Fronts in Richards'
             Equation},
   Journal = {Transport in Porous Media},
   Volume = {27},
   Number = {2},
   Pages = {121-134},
   Year = {1997},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/articles/richards.ps.gz},
   Abstract = {Perturbation methods are used to study the interaction of
             wetting fronts with impervious boundaries in layered soils.
             Solutions of Richards' equation for horizontal and vertical
             infiltration problems are considered. Asymptotically
             accurate solutions are constructed from outer solutions and
             boundary-layer corrections. Results are compared with
             numerical simulations to demonstrate a high level of
             accuracy.},
   Doi = {10.1023/A:1006513009125},
   Key = {fds244200}
}

@article{fds244197,
   Author = {Witelski, TP},
   Title = {Traveling wave solutions for case II diffusion in
             polymers},
   Journal = {Journal of Polymer Science, Part B: Polymer
             Physics},
   Volume = {34},
   Number = {1},
   Pages = {141-150},
   Publisher = {WILEY},
   Year = {1996},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/articles/case2.ps.gz},
   Abstract = {Case II diffusion of penetrant liquids in polymer films is
             characterized by constant-velocity propagation of a phase
             interface. We review the development of viscoelastic models
             describing case II diffusion and then present a phase plane
             analysis for traveling wave solutions. For simplified,
             piecewise-constant coefficient models we give closed-form
             analytic solutions showing the dependence on various
             physical parameters in both viscous and viscoelastic
             diffusive systems. We will also compare the results of our
             analysis with results from numerical simulations of more
             general models. © 1996 John Wiley & Sons,
             Inc.},
   Doi = {10.1002/(SICI)1099-0488(19960115)34:1<141::AID-POLB12>3.0.CO},
   Key = {fds244197}
}

@article{fds244196,
   Author = {Witelski, TP},
   Title = {The structure of internal layers for unstable nonlinear
             diffusion equations},
   Journal = {Studies in Applied Mathematics},
   Volume = {97},
   Number = {3},
   Pages = {277-300},
   Publisher = {WILEY},
   Year = {1996},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/articles/vch.ps.gz},
   Abstract = {We study the structure of diffusive layers in solutions of
             unstable nonlinear diffusion equations. These equations are
             regularizations of the forward-backward heat equation and
             have diffusion coefficients that become negative. Such
             models include the Cahn-Hilliard equation and the
             pseudoparabolic viscous diffusion equation. Using singular
             perturbation methods we show that the balance between
             diffusion and higher-order regularization terms uniquely
             determines the interface structure in these equations. It is
             shown that the well-known "equal area" rule for the
             Cahn-Hilliard equation is a special case of a more general
             rule for shock construction in the viscous Cahn-Hilliard
             equation.},
   Doi = {10.1002/sapm1996973277},
   Key = {fds244196}
}

@article{fds244198,
   Author = {Cohen, DS and Witelski, TP},
   Title = {Inaccessible states in time-dependent reaction
             diffusion},
   Journal = {Studies in Applied Mathematics},
   Volume = {97},
   Number = {4},
   Pages = {301-319},
   Publisher = {WILEY},
   Year = {1996},
   Month = {January},
   url = {http://dx.doi.org/10.1002/sapm1996974301},
   Abstract = {Using asymptotic methods we show that the long-time dynamic
             behavior in certain systems of nonlinear parabolic
             differential equations is described by a time-dependent,
             spatially inhomogeneous nonlinear evolution equation. For
             problems with multiple stable states, the solution develops
             sharp fronts separating slowly varying regions. By studying
             the basins of attraction of Abel's nonlinear differential
             equation, we demonstrate that the presence of explicit time
             dependence in the asymptotic evolution equation creates
             "forbidden regions" where the existence of interfaces is
             excluded. Consequently, certain configurations of stable
             states in the nonlinear system become inaccessible and
             cannot be achieved from any set of real initial
             conditions.},
   Doi = {10.1002/sapm1996974301},
   Key = {fds244198}
}

@article{fds244191,
   Author = {Witelski, TP},
   Title = {Stopping and merging problems for the porous media
             equation},
   Journal = {IMA Journal of Applied Mathematics (Institute of Mathematics
             and Its Applications)},
   Volume = {54},
   Number = {3},
   Pages = {227-243},
   Publisher = {Oxford University Press (OUP)},
   Year = {1995},
   Month = {December},
   ISSN = {0272-4960},
   url = {http://www.math.duke.edu/~witelski/articles/porous.ps.gz},
   Abstract = {A class of boundary value problems for nonlinear diffusion
             equations is studied. Using singular perturbation theory and
             matched asymptotic expansions, the author analyses the
             interactions of compact-support solutions of the porous
             media equation with fixed boundaries and with other
             solutions. The boundary layer analysis yields results on how
             'stopping' and 'merging' disturbances at the interface
             propagate back into the solution. Analysis is also extended
             to cover merging problems for the fourth-order lubrication
             equation. © 1995 Oxford University Press.},
   Doi = {10.1093/imamat/54.3.227},
   Key = {fds244191}
}

@article{fds244195,
   Author = {Witelski, TP and Cohen, DS},
   Title = {Perturbed reversible systems},
   Journal = {Physics Letters A},
   Volume = {207},
   Number = {1-2},
   Pages = {83-86},
   Publisher = {Elsevier BV},
   Year = {1995},
   Month = {October},
   ISSN = {0375-9601},
   url = {http://dx.doi.org/10.1016/0375-9601(95)00662-M},
   Abstract = {For a class of nonlinear evolution equations describing
             reversible processes with several equilibrium solutions, we
             will demonstrate that the addition of time-dependent
             disturbances can significantly change the stability
             properties of the model. In particular, we will show that
             the introduction of bounded time-dependent forcing can cause
             singular changes in the basins of attraction for Abel's
             nonlinear ordinary differential equation. ©
             1995.},
   Doi = {10.1016/0375-9601(95)00662-M},
   Key = {fds244195}
}

@article{fds244185,
   Author = {Witelski, TP and Cohen, DS},
   Title = {Forbidden Regions for Shock Formation in Diffusive
             Systems},
   Journal = {Studies in Applied Mathematics},
   Volume = {95},
   Number = {3},
   Pages = {297-317},
   Publisher = {WILEY},
   Year = {1995},
   Month = {October},
   ISSN = {0022-2526},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1995RY07600004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Abstract = {We consider an initial-boundary value problem for a
             nonlinear parabolic system. Using perturbation methods, this
             problem is reduced to one of considering an evolution
             equation for the long-time asymptotics of the system. This
             model can be related to the leading order approximation for
             a spatially inhomogeneous reaction-diffusion system with
             time-dependent forcing. The evolution equation yields
             solutions with steady state shocks. We study some of the
             subtle effects introduced by time-dependent forcing. Most
             significant among these effects is the creation of
             "forbidden regions" where stationary shocks cannot form.
             Results are presented for bi- and tri-stable one-dimensional
             models as well as multidimensional systems.},
   Doi = {10.1002/sapm1995953297},
   Key = {fds244185}
}

@article{fds244192,
   Author = {Cohen, DS and White, AB and Witelski, TP},
   Title = {Shock formation in a multidimensional viscoelastic diffusive
             system},
   Journal = {SIAM Journal on Applied Mathematics},
   Volume = {55},
   Number = {2},
   Pages = {348-368},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1995},
   Month = {January},
   url = {http://www.math.duke.edu/~witelski/articles/vemshock.ps.gz},
   Abstract = {We examine a model for non-Fickian 'sorption overshoot'
             behavior in diffusive polymer-penetrant systems. The
             equations of motion proposed by Cohen and White [SIAM J.
             Appl. Math., 51 (1991), pp. 472-483] are solved for
             two-dimensional problems using matched asymptotic
             expansions. The phenomenon of shock formation predicted by
             the model is examined and contrasted with similar behavior
             in classical reaction-diffusion systems. Mass uptake curves
             produced by the model are examined and shown to compare
             favorably with experimental observations.},
   Doi = {10.1137/S0036139993269333},
   Key = {fds244192}
}

@article{fds244193,
   Author = {Witelski, TP},
   Title = {Merging traveling waves for the porous-Fisher's
             equation},
   Journal = {Applied Mathematics Letters},
   Volume = {8},
   Number = {4},
   Pages = {57-62},
   Publisher = {Elsevier BV},
   Year = {1995},
   Month = {January},
   ISSN = {0893-9659},
   url = {http://dx.doi.org/10.1016/0893-9659(95)00047-T},
   Abstract = {We study a reaction-diffusion equation model for population
             dynamics. By focusing on the diffusive behavior expected in
             a population that seeks to avoid over-crowding, we derive a
             nonlinear-diffusion porous-Fisher's equation. Using explicit
             traveling wave solutions, initially-separated, expanding
             populations are studied as they first coalesce. The
             nonlinear interactions of the merging populations are
             examined using perturbation theory and the method of matched
             asymptotic expansions. Results are also extended to the
             axisymmetric case. © 1995.},
   Doi = {10.1016/0893-9659(95)00047-T},
   Key = {fds244193}
}

@article{fds244194,
   Author = {Witelski, TP},
   Title = {Shocks in nonlinear diffusion},
   Journal = {Applied Mathematics Letters},
   Volume = {8},
   Number = {5},
   Pages = {27-32},
   Publisher = {Elsevier BV},
   Year = {1995},
   Month = {January},
   ISSN = {0893-9659},
   url = {http://www.math.duke.edu/~witelski/articles/shock.ps.gz},
   Abstract = {Using two models that incorporate a nonlinear
             forward-backward heat equation, we demonstrate the existence
             of well-defined weak solutions containing shocks for
             diffusive problems. Occurrence of shocks is connected to
             multivalued inverse solutions and nonmonotone potential
             functions. Unique viscous solutions are determined from
             perturbation theory by matching to a shock layer condition.
             Results of direct numerical simulations are also discussed.
             © 1995.},
   Doi = {10.1016/0893-9659(95)00062-U},
   Key = {fds244194}
}

@article{fds244190,
   Author = {Witelski, TP},
   Title = {An asymptotic solution for traveling waves of a
             nonlinear-diffusion Fisher's equation},
   Journal = {Journal of Mathematical Biology},
   Volume = {33},
   Number = {1},
   Pages = {1-16},
   Publisher = {Springer Nature},
   Year = {1994},
   Month = {November},
   ISSN = {0303-6812},
   url = {http://www.math.duke.edu/~witelski/articles/jmbfish.ps.gz},
   Abstract = {We examine traveling-wave solutions for a generalized
             nonlinear-diffusion Fisher equation studied by Hayes [J.
             Math. Biol. 29, 531-537 (1991)]. The density-dependent
             diffusion coefficient used is motivated by certain polymer
             diffusion and population dispersal problems. Approximate
             solutions are constructed using asymptotic expansions. We
             find that the solution will have a corner layer (a shock in
             the derivative) as the diffusion coefficient approaches a
             step function. The corner layer at z = 0 is matched to an
             outer solution for z < 0 and a boundary layer for z > 0 to
             produce a complete solution. We show that this model also
             admits a new class of nonphysical solutions and obtain
             conditions that restrict the set of valid traveling-wave
             solutions. © 1994 Springer-Verlag.},
   Doi = {10.1007/BF00160171},
   Key = {fds244190}
}

@article{fds244228,
   Author = {Witelski, T and Ng, P and Ying, J and Jundy, J and Bove,
             J},
   Title = {An application of pattern recognition and infrared
             spectroscopy to water analysis},
   Journal = {International Journal of Environmental Analytical
             Chemistry},
   Volume = {44},
   Number = {2},
   Pages = {127-136},
   Publisher = {Informa UK Limited},
   Year = {1991},
   ISSN = {0306-7319},
   url = {http://dx.doi.org/10.1080/03067319108027542},
   Abstract = {A mathematical methodology is presented that shows potential
             for the interpretation of infrared spectra through a
             technique of pattern recognition. A number of water samples
             and simple alkanes were studied to examine the sensitivity
             and discriminating qualities of the methodology. With 2500
             comparisons each of tap water versus tap water or distilled
             water versus tap water, the technique performed well in
             selecting the targeted reagent. The same is true for the
             comparisons of n-pentane, as the window compound, versus
             n-heptane, n-octane, n-nonane and n-decane. Comparisons of
             these n-alkanes to n-pentane gave fitting tolerances of
             15.3, 21.2, 20.9 and 24.7%, respectively. When n-pentane was
             compared to itself, the tolerance fit was 2.7 %, showing the
             ease of discrimination. These results suggest that this
             computer-aided phase space transformation method is
             sensitive, offers good analytical precision, and is capable
             of detecting small differences in the infrared spectra of
             compounds and mixture studied. Preliminary data also suggest
             that the method has potential for monitoring the quality of
             water. © 1991, Taylor & Francis Group, LLC. All rights
             reserved.},
   Doi = {10.1080/03067319108027542},
   Key = {fds244228}
}

@article{fds10239,
   Author = {Ferdinand Hendriks and Thomas P. Witelski and et
             al},
   Title = {Shape optimization of pressurized air bearings},
   Journal = {Proceedings 2001 Workshop on Mathematical Problems in
             Industry, RPI},
   Abstract = {Group project report edited and compiled by
             TPW.},
   Key = {fds10239}
}

@article{fds9561,
   Author = {F. Hendriks and Thomas P. Witelski and et al},
   Title = {Design of planar coils of minimum resistance for magnetic
             recording devices},
   Journal = {Proceedings of the Workshop on Mathematical Problems in
             Industry, University of Delaware, 1999},
   url = {http://www.math.duke.edu/~witelski/local/spiral.ps.gz},
   Key = {fds9561}
}

@article{fds8730,
   Author = {W. L. Hogarth and J. Y. Parlange and Thomas P Witelski},
   Title = {The superposition principle for infiltration with power law
             diffusivity},
   Journal = {Hydrology Days - Proceedings of the 17th Annual American
             Geophysical Union, pp. 365-374 (1997)},
   Key = {fds8730}
}

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320