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Publications of Stephanos Venakides    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds341952,
   Author = {Perez-Arancibia, C and Shipman, SP and Turc, C and Venakides,
             S},
   Title = {Domain Decomposition for Quasi-Periodic Scattering by
             Layered Media via Robust Boundary-Integral Equations at All
             Frequencies},
   Journal = {Communications in Computational Physics},
   Volume = {26},
   Number = {1},
   Pages = {265-310},
   Publisher = {Global Science Press},
   Year = {2019},
   Month = {July},
   url = {http://dx.doi.org/10.4208/cicp.OA-2018-0021},
   Doi = {10.4208/cicp.OA-2018-0021},
   Key = {fds341952}
}

@article{fds335545,
   Author = {Aristotelous, AC and Crawford, JM and Edwards, GS and Kiehart, DP and Venakides, S},
   Title = {Mathematical models of dorsal closure.},
   Journal = {Progress in Biophysics and Molecular Biology},
   Volume = {137},
   Pages = {111-131},
   Year = {2018},
   Month = {September},
   url = {http://dx.doi.org/10.1016/j.pbiomolbio.2018.05.009},
   Abstract = {Dorsal closure is a model cell sheet movement that occurs
             midway through Drosophila embryogenesis. A dorsal hole,
             filled with amnioserosa, closes through the dorsalward
             elongation of lateral epidermal cell sheets. Closure
             requires contributions from 5 distinct tissues and well over
             140 genes (see Mortensen et al., 2018, reviewed in Kiehart
             et al., 2017 and Hayes and Solon, 2017). In spite of this
             biological complexity, the movements (kinematics) of closure
             are geometrically simple at tissue, and in certain cases, at
             cellular scales. This simplicity has made closure the target
             of a number of mathematical models that seek to explain and
             quantify the processes that underlie closure's kinematics.
             The first (purely kinematic) modeling approach recapitulated
             well the time-evolving geometry of closure even though the
             underlying physical principles were not known. Almost all
             subsequent models delve into the forces of closure (i.e. the
             dynamics of closure). Models assign elastic, contractile and
             viscous forces which impact tissue and/or cell mechanics.
             They write rate equations which relate the forces to one
             another and to other variables, including those which
             represent geometric, kinematic, and or signaling
             characteristics. The time evolution of the variables is
             obtained by computing the solution of the model's system of
             equations, with optimized model parameters. The basis of the
             equations range from the phenomenological to biophysical
             first principles. We review various models and present their
             contribution to our understanding of the molecular
             mechanisms and biophysics of closure. Models of closure will
             contribute to our understanding of similar movements that
             characterize vertebrate morphogenesis.},
   Doi = {10.1016/j.pbiomolbio.2018.05.009},
   Key = {fds335545}
}

@article{fds340300,
   Author = {Venakides, S and Komineas, S and Melcher, C},
   Title = {Traveling domain walls in chiral ferromagnets},
   Journal = {Nonlinearity},
   Publisher = {London Mathematical Society},
   Year = {2018},
   Month = {June},
   Key = {fds340300}
}

@article{fds330525,
   Author = {Perez-Arancibia, C and Shipman, S and Turc, C and Venakides,
             S},
   Title = {DDM solutions of quasiperiodic transmission problems in
             layered media via robust boundary integral equations at all
             frequencies},
   Journal = {Communications in Computational Physics},
   Publisher = {Global Science Press},
   Year = {2018},
   Month = {May},
   Key = {fds330525}
}

@article{fds330399,
   Author = {Bruno, OP and Shipman, SP and Turc, C and Stephanos,
             V},
   Title = {Three-dimensional quasi-periodic shifted Green function
             throughout the spectrum, including Wood anomalies.},
   Journal = {Proceedings. Mathematical, Physical, and Engineering
             Sciences},
   Volume = {473},
   Number = {2207},
   Pages = {20170242},
   Publisher = {The Royal Society},
   Year = {2017},
   Month = {November},
   url = {http://dx.doi.org/10.1098/rspa.2017.0242},
   Abstract = {This work, part II in a series, presents an efficient method
             for evaluation of wave scattering by doubly periodic
             diffraction gratings at or near what are commonly called
             'Wood anomaly frequencies'. At these frequencies, there is a
             grazing Rayleigh wave, and the quasi-periodic Green function
             ceases to exist. We present a modification of the Green
             function by adding two types of terms to its lattice sum.
             The first type are transversely shifted Green functions with
             coefficients that annihilate the growth in the original
             lattice sum and yield algebraic convergence. The second type
             are quasi-periodic plane wave solutions of the Helmholtz
             equation which reinstate certain necessary grazing modes
             without leading to blow-up at Wood anomalies. Using the new
             quasi-periodic Green function, we establish, for the first
             time, that the Dirichlet problem of scattering by a smooth
             doubly periodic scattering surface at a Wood frequency is
             uniquely solvable. We also present an efficient high-order
             numerical method based on this new Green function for
             scattering by doubly periodic surfaces at and around Wood
             frequencies. We believe this is the first solver able to
             handle Wood frequencies for doubly periodic scattering
             problems in three dimensions. We demonstrate the method by
             applying it to acoustic scattering.},
   Doi = {10.1098/rspa.2017.0242},
   Key = {fds330399}
}

@article{fds329310,
   Author = {Kiehart, DP and Crawford, JM and Aristotelous, A and Venakides, S and Edwards, GS},
   Title = {Cell Sheet Morphogenesis: Dorsal Closure in Drosophila
             melanogaster as a Model System.},
   Journal = {Annual Review of Cell and Developmental Biology},
   Volume = {33},
   Pages = {169-202},
   Year = {2017},
   Month = {October},
   url = {http://dx.doi.org/10.1146/annurev-cellbio-111315-125357},
   Abstract = {Dorsal closure is a key process during Drosophila
             morphogenesis that models cell sheet movements in chordates,
             including neural tube closure, palate formation, and wound
             healing. Closure occurs midway through embryogenesis and
             entails circumferential elongation of lateral epidermal cell
             sheets that close a dorsal hole filled with amnioserosa
             cells. Signaling pathways regulate the function of cellular
             structures and processes, including Actomyosin and
             microtubule cytoskeletons, cell-cell/cell-matrix adhesion
             complexes, and endocytosis/vesicle trafficking. These
             orchestrate complex shape changes and movements that entail
             interactions between five distinct cell types. Genetic and
             laser perturbation studies establish that closure is robust,
             resilient, and the consequence of redundancy that
             contributes to four distinct biophysical processes:
             contraction of the amnioserosa, contraction of supracellular
             Actomyosin cables, elongation (stretching?) of the lateral
             epidermis, and zipping together of two converging cell
             sheets. What triggers closure and what the emergent
             properties are that give rise to its extraordinary
             resilience and fidelity remain key, extant
             questions.},
   Doi = {10.1146/annurev-cellbio-111315-125357},
   Key = {fds329310}
}

@article{fds320539,
   Author = {Bruno, OP and Shipman, SP and Turc, C and Venakides,
             S},
   Title = {Superalgebraically convergent smoothly windowed lattice sums
             for doubly periodic Green functions in three-dimensional
             space},
   Journal = {Proceedings. Mathematical, Physical, and Engineering
             Sciences},
   Volume = {472},
   Number = {2191},
   Pages = {20160255},
   Year = {2016},
   Month = {July},
   url = {http://dx.doi.org/10.1098/rspa.2016.0255},
   Abstract = {© 2016 The Author(s) Published by the Royal Society. This
             work, part I in a two-part series, presents: (i) a simple
             and highly efficient algorithm for evaluation of
             quasi-periodic Green functions, as well as (ii) an
             associated boundary-integral equation method for the
             numerical solution of problems of scattering of waves by
             doubly periodic arrays of scatterers in three-dimensional
             space. Except for certain 'Wood frequencies' at which the
             quasi-periodic Green function ceases to exist, the proposed
             approach, which is based on smooth windowing functions,
             gives rise to tapered lattice sums which converge
             superalgebraically fast to the Green function-that is,
             faster than any power of the number of terms used. This is
             in sharp contrast to the extremely slow convergence
             exhibited by the lattice sums in the absence of smooth
             windowing. (The Wood-frequency problem is treated in part
             II.) This paper establishes rigorously the superalgebraic
             convergence of the windowed lattice sums. A variety of
             numerical results demonstrate the practical efficiency of
             the proposed approach.},
   Doi = {10.1098/rspa.2016.0255},
   Key = {fds320539}
}

@article{fds320428,
   Author = {Komineas, S and Shipman, SP and Venakides, S},
   Title = {Lossless polariton solitons},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {316},
   Pages = {43-56},
   Publisher = {Elsevier BV},
   Year = {2016},
   Month = {February},
   url = {http://dx.doi.org/10.1016/j.physd.2015.10.018},
   Abstract = {© 2015 Elsevier B.V. All rights reserved. Photons and
             excitons in a semiconductor microcavity interact to form
             exciton-polariton condensates. These are governed by a
             nonlinear quantum-mechanical system involving exciton and
             photon wavefunctions. We calculate all non-traveling
             harmonic soliton solutions for the one-dimensional lossless
             system. There are two frequency bands of bright solitons
             when the inter-exciton interactions produce an attractive
             nonlinearity and two frequency bands of dark solitons when
             the nonlinearity is repulsive. In addition, there are two
             frequency bands for which the exciton wavefunction is
             discontinuous at its symmetry point, where it undergoes a
             phase jump of π. A band of continuous dark solitons merges
             with a band of discontinuous dark solitons, forming a larger
             band over which the soliton far-field amplitude varies from
             0 to ∞ ; the discontinuity is initiated when the operating
             frequency exceeds the free exciton frequency. The far fields
             of the solitons in the lowest and highest frequency bands
             (one discontinuous and one continuous dark) are linearly
             unstable, whereas the other four bands have linearly stable
             far fields, including the merged band of dark
             solitons.},
   Doi = {10.1016/j.physd.2015.10.018},
   Key = {fds320428}
}

@article{fds226701,
   Author = {Sergey Belov and Stephanos Venakides},
   Title = {Smooth parametric dependence of asymptotics of the
             semiclassical focusing NLS},
   Journal = {Analysis & PDE},
   Volume = {8},
   Number = {2},
   Pages = {257-288},
   Year = {2015},
   Month = {April},
   url = {http://dx.doi.org/10.2140/apde.2015.8.257},
   Abstract = {We consider the one-dimensional focusing (cubic) nonlinear
             Schrödinger equation (NLS) in the semiclassical limit with
             exponentially decaying complex-valued initial data, whose
             phase is multiplied by a real parameter. We prove smooth
             dependence of the asymptotic solution on the parameter.
             Numerical results supporting our estimates of important
             quantities are presented.},
   Doi = {10.2140/apde.2015.8.257},
   Key = {fds226701}
}

@article{fds244138,
   Author = {Komineas, S and Shipman, SP and Venakides, S},
   Title = {Continuous and discontinuous dark solitons in polariton
             condensates},
   Journal = {Physical Review B},
   Volume = {91},
   Number = {13},
   Publisher = {American Physical Society (APS)},
   Year = {2015},
   Month = {April},
   ISSN = {1098-0121},
   url = {http://dx.doi.org/10.1103/PhysRevB.91.134503},
   Abstract = {© 2015 American Physical Society. Bose-Einstein condensates
             of exciton-polaritons are described by a Schrödinger system
             of two equations. Nonlinearity due to exciton interactions
             gives rise to a frequency band of dark soliton solutions,
             which are found analytically for the lossless zero-velocity
             case. The soliton's far-field value varies from zero to
             infinity as the operating frequency varies across the band.
             For positive detuning (photon frequency higher than exciton
             frequency), the exciton wave function becomes discontinuous
             when the operating frequency exceeds the exciton frequency.
             This phenomenon lies outside the parameter regime of
             validity of the Gross-Pitaevskii (GP) model. Within its
             regime of validity, we give a derivation of a single-mode GP
             model from the initial Schrödinger system and compare the
             continuous polariton solitons and GP solitons using the
             healing length notion.},
   Doi = {10.1103/PhysRevB.91.134503},
   Key = {fds244138}
}

@article{fds303561,
   Author = {Belov, S and Venakides, S},
   Title = {Smooth parametric dependence of asymptotics of the
             semiclassical focusing NLS},
   Journal = {Analysis & Pde},
   Volume = {8},
   Number = {2},
   Pages = {257-288},
   Publisher = {Mathematical Sciences Publishers},
   Year = {2015},
   Month = {January},
   url = {http://arxiv.org/abs/1211.7111v2},
   Abstract = {© Mathematical Sciences Publishers. We consider the
             one-dimensional focusing (cubic) nonlinear Schrödinger
             equation (NLS) in the semiclassical limit with exponentially
             decaying complex-valued initial data, whose phase is
             multiplied by a real parameter. We prove smooth dependence
             of the asymptotic solution on the parameter. Numerical
             results supporting our estimates of important quantities are
             presented.},
   Doi = {10.2140/apde.2015.8.257},
   Key = {fds303561}
}

@article{fds320540,
   Author = {Belov, S and Venakides, S},
   Title = {Long-time limit studies of an obstruction in the g-function
             mechanism for semiclassical focusing NLS},
   Year = {2015},
   Abstract = {We consider the long-time properties of the an obstruction
             in the Riemann-Hilbert approach to one dimensional focusing
             Nonlinear Schr\"odinger equation in the semiclassical limit
             for a one parameter family of initial conditions. For
             certain values of the parameter a large number of solitons
             in the system interfere with the $g$-function mechanism in
             the steepest descent to oscillatory Riemann-Hilbert
             problems. The obstruction prevents the Riemann-Hilbert
             analysis in a region in $(x,t)$ plane. We obtain the long
             time asymptotics of the boundary of the region (obstruction
             curve). As $t\to\infty$ the obstruction curve has a vertical
             asymptotes $x=\pm \ln 2$. The asymptotic analysis is
             supported with numerical results.},
   Key = {fds320540}
}

@article{fds220956,
   Author = {Oscar P. Bruno and Stephen P. Shipman and Catalin Turc and Stephanos
             Venakides},
   Title = {Efficient Evaluation of Doubly Periodic Green Functions in
             3D Scattering, Including Wood Anomaly Frequencies},
   Journal = {ArXiv>Mathematics > Analysis of PDEs},
   Year = {2013},
   Month = {July},
   url = {http://arxiv.org/abs/1307.1176},
   Abstract = {We present efficient methods for computing wave scattering
             by diffraction gratings that exhibit two-dimensional
             periodicity in three dimensional (3D) space. Applications
             include scattering in acoustics, electromagnetics and
             elasticity. Our approach uses boundary-integral equations.
             The quasi-periodic Green function is a doubly infinite sum
             of scaled 3D free-space outgoing Helmholtz Green functions.
             Their source points are located at the nodes of a
             periodicity lattice of the grating. For efficient numerical
             computation of the lattice sum, we employ a smooth
             truncation. Super-algebraic convergence to the Green
             function is achieved as the truncation radius increases,
             except at frequency-wavenumber pairs at which a Rayleigh
             wave is at exactly grazing incidence to the grating. At
             these "Wood frequencies", the term in the Fourier series
             representation of the Green function that corresponds to the
             grazing Rayleigh wave acquires an infinite coefficient and
             the lattice sum blows up. At Wood frequencies, we modify the
             Green function by adding two types of terms to it. The first
             type adds weighted spatial shifts of the Green function to
             itself with singularities below the grating; this yields
             algebraic convergence. The second-type terms are
             quasi-periodic plane wave solutions of the Helmholtz
             equation. They reinstate (with controlled coefficients) the
             grazing modes, effectively eliminated by the terms of first
             type. These modes are needed in the Green function for
             guaranteeing the well-posedness of the boundary-integral
             equation that yields the scattered field. We apply this
             approach to acoustic scattering by a doubly periodic 2D
             grating near and at Wood frequencies and scattering by a
             doubly periodic array of scatterers away from Wood
             frequencies.},
   Key = {fds220956}
}

@article{fds244139,
   Author = {Jackson, AD and Huang, D and Gauthier, DJ and Venakides,
             S},
   Title = {Destructive impact of imperfect beam collimation in
             extraordinary optical transmission.},
   Journal = {Journal of the Optical Society of America
             A},
   Volume = {30},
   Number = {6},
   Pages = {1281-1290},
   Year = {2013},
   Month = {June},
   ISSN = {1084-7529},
   url = {http://dx.doi.org/10.1364/josaa.30.001281},
   Abstract = {We investigate the difference between analytic predictions,
             numerical simulations, and experiments measuring the
             transmission of energy through subwavelength, periodically
             arranged holes in a metal film. At normal incidence, theory
             predicts a sharp transmission minimum when the wavelength is
             equal to the periodicity, and sharp transmission maxima at
             one or more nearby wavelengths. In experiments, the sharpest
             maximum from the theory is not observed, while the others
             appear less sharp. In numerical simulations using commercial
             electromagnetic field solvers, we find that the sharpest
             maximum appears and approaches our predictions as the
             computational resources are increased. To determine possible
             origins of the destruction of the sharp maximum, we
             incorporate additional features in our model. Incorporating
             imperfect conductivity and imperfect periodicity in our
             model leaves the sharp maximum intact. Imperfect
             collimation, on the other hand, incorporated into the model
             causes the destruction of the sharp maximum as happens in
             experiments. We provide analytic support through an
             asymptotic calculation for both the existence of the sharp
             maximum and the destructive impact of imperfect
             collimation.},
   Doi = {10.1364/josaa.30.001281},
   Key = {fds244139}
}

@article{fds244166,
   Author = {Shipman, SP and Venakides, S},
   Title = {An exactly solvable model for nonlinear resonant
             scattering},
   Journal = {Nonlinearity},
   Volume = {25},
   Number = {9},
   Pages = {2473-2501},
   Publisher = {IOP Publishing},
   Year = {2012},
   Month = {September},
   ISSN = {0951-7715},
   url = {http://dx.doi.org/10.1088/0951-7715/25/9/2473},
   Abstract = {This work analyses the effects of cubic nonlinearities on
             certain resonant scattering anomalies associated with the
             dissolution of an embedded eigenvalue of a linear scattering
             system. These sharp peak-dip anomalies in the frequency
             domain are often called Fano resonances. We study a simple
             model that incorporates the essential features of this kind
             of resonance. It features a linear scatterer attached to a
             transmission line with a point-mass defect and coupled to a
             nonlinear oscillator. We prove two power laws in the small
             coupling (γ→0) and small nonlinearity (μ→0) regime.
             The asymptotic relation μ→Cγ4characterizes the emergence
             of a small frequency interval of triple harmonic solutions
             near the resonant frequency of the oscillator. As the
             nonlinearity grows or the coupling diminishes, this interval
             widens and, at the relation μ→Cγ2, merges with another
             evolving frequency interval of triple harmonic solutions
             that extends to infinity. Our model allows rigorous
             computation of stability in the small μ and γ limit. The
             regime of triple harmonic solutions exhibits bistability -
             those solutions with largest and smallest response of the
             oscillator are linearly stable and the solution with
             intermediate response is unstable. © 2012 IOP Publishing
             Ltd & London Mathematical Society.},
   Doi = {10.1088/0951-7715/25/9/2473},
   Key = {fds244166}
}

@article{fds244167,
   Author = {Tovbis, A and Venakides, S},
   Title = {Semiclassical limit of the scattering transform for the
             focusing nonlinear Schrödinger equation},
   Journal = {International Mathematics Research Notices},
   Volume = {2012},
   Number = {10},
   Pages = {2212-2271},
   Publisher = {Oxford University Press (OUP)},
   Year = {2012},
   Month = {May},
   ISSN = {1073-7928},
   url = {http://dx.doi.org/10.1093/imrn/rnr092},
   Abstract = {The semiclassical limit of the focusing Nonlinear (cubic)
             Schr ̈ odinger Equation corresponds to the singularly
             perturbed Zakharov-Shabat (ZS) system that defines the
             direct and inverse scattering transforms (IST). In this
             paper, we derive explicit expressions for the leading-order
             terms of these transforms, which we call semiclassical
             limits of the direct and IST. Thus, we establish an explicit
             connection between the decaying initial data of the form
             q(x, 0) = A(x)e iS(x) and the leading order term of its
             scattering data. This connection is expressed in terms of an
             integral transform that can be viewed as a complexified
             version of the Abel transform. Our technique is not based on
             the Wentzel-Kramers-Brillouin (WKB) analysis of the ZS
             system, but on the inversion of the modulation equations
             that solve the inverse scattering problem in the leading
             order. The results are illustrated by a number of examples.
             © 2011 The Author(s).},
   Doi = {10.1093/imrn/rnr092},
   Key = {fds244167}
}

@article{fds244165,
   Author = {Tovbis, A and Venakides, S},
   Title = {Nonlinear steepest descent asymptotics for semiclassical
             limit of Integrable systems: Continuation in the parameter
             space},
   Journal = {Communications in Mathematical Physics},
   Volume = {295},
   Number = {1},
   Pages = {139-160},
   Publisher = {Springer Nature},
   Year = {2010},
   Month = {February},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/s00220-009-0984-0},
   Abstract = {The initial value problem for an integrable system, such as
             the Nonlinear Schrödinger equation, is solved by subjecting
             the linear eigenvalue problem arising from its Lax pair to
             inverse scattering, and, thus, transforming it to a matrix
             Riemann-Hilbert problem (RHP) in the spectral variable. In
             the semiclassical limit, the method of nonlinear steepest
             descent ([4,5]), supplemented by the g-function mechanism
             ([3]), is applied to this RHP to produce explicit asymptotic
             solution formulae for the integrable system. These formule
             are based on a hyperelliptic Riemann surface R = R(x, t) in
             the spectral variable, where the space-time variables (x, t)
             play the role of external parameters. The curves in the x, t
             plane, separating regions of different genuses of R(x, t),
             are called breaking curves or nonlinear caustics. The genus
             of R(x, t) is related to the number of oscillatory phases in
             the asymptotic solution of the integrable system at the
             point x, t. The evolution theorem ([10]) guarantees
             continuous evolution of the asymptotic solution in the
             space-time away from the breaking curves. In the case of the
             analytic scattering data f(z; x, t) (in the NLS case, f is a
             normalized logarithm of the reflection coefficient with time
             evolution included), the primary role in the breaking
             mechanism is played by a phase function h(z; x, t), which is
             closely related to the g function. Namely, a break can be
             caused ([10]) either through the change of topology of zero
             level curves of h(z; x, t) (regular break), or through the
             interaction of zero level curves of h(z; x, t) with
             singularities of f (singular break). Every time a breaking
             curve in the x, t plane is reached, one has to prove the
             validity of the nonlinear steepest descent asymptotics in
             the region across the curve. In this paper we prove that in
             the case of a regular break, the nonlinear steepest descent
             asymptotics can be "automatically" continued through the
             breaking curve (however, the expressions for the asymptotic
             solution will be different on the different sides of the
             curve). Our proof is based on the determinantal formula for
             h(z; x, t) and its space and time derivatives, obtained in
             [8,9]. Although the results are stated and proven for the
             focusing NLS equation, it is clear ([9]) that they can be
             reformulated for AKNS systems, as well as for the nonlinear
             steepest descend method in a more general setting. ©
             Springer-Verlag 2010.},
   Doi = {10.1007/s00220-009-0984-0},
   Key = {fds244165}
}

@article{fds244164,
   Author = {Layton, AT and Toyama, Y and Yang, G-Q and Edwards, GS and Kiehart, DP and Venakides, S},
   Title = {Drosophila morphogenesis: tissue force laws and the modeling
             of dorsal closure.},
   Journal = {Hfsp Journal},
   Volume = {3},
   Number = {6},
   Pages = {441-460},
   Publisher = {HFSP},
   Year = {2009},
   Month = {December},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/20514134},
   Abstract = {Dorsal closure, a stage of Drosophila development, is a
             model system for cell sheet morphogenesis and wound healing.
             During closure, two flanks of epidermal tissue progressively
             advance to reduce the area of the eye-shaped opening in the
             dorsal surface, which contains amnioserosa tissue. To
             simulate the time evolution of the overall shape of the
             dorsal opening, we developed a mathematical model, in which
             contractility and elasticity are manifest in model
             force-producing elements that satisfy force-velocity
             relationships similar to muscle. The action of the elements
             is consistent with the force-producing behavior of actin and
             myosin in cells. The parameters that characterize the
             simulated embryos were optimized by reference to
             experimental observations on wild-type embryos and, to a
             lesser extent, on embryos whose amnioserosa was removed by
             laser surgery and on myospheroid mutant embryos. Simulations
             failed to reproduce the amnioserosa-removal protocol in
             either the elastic or the contractile limit, indicating that
             both elastic and contractile dynamics are essential
             components of the biological force-producing elements. We
             found it was necessary to actively upregulate forces to
             recapitulate both the double and single-canthus nick
             protocols, which did not participate in the optimization of
             parameters, suggesting the existence of additional key
             feedback mechanisms.},
   Doi = {10.2976/1.3266062},
   Key = {fds244164}
}

@article{fds244169,
   Author = {Lefew, WR and Venakides, S and Gauthier, DJ},
   Title = {Accurate description of optical precursors and their
             relation to weak-field coherent optical transients},
   Journal = {Physical Review A},
   Volume = {79},
   Number = {6},
   Pages = {063842},
   Publisher = {American Physical Society (APS)},
   Year = {2009},
   Month = {June},
   ISSN = {1050-2947},
   url = {http://dx.doi.org/10.1103/PhysRevA.79.063842},
   Abstract = {We study theoretically the propagation of a step-modulated
             optical field as it passes through a dispersive dielectric
             made up of a dilute collection of oscillators characterized
             by a single narrow-band resonance. The propagated field is
             given in terms of an integral of a Fourier type, which
             cannot be evaluated even for simple models of the dispersive
             dielectric. The fact that the oscillators have a low number
             density (dilute medium) and have a narrow-band resonance
             allows us to simplify the integrand. In this case, the
             integral can be evaluated exactly, although it is not
             possible using this method to separate out the transient
             part of the propagated field known as optical precursors. We
             also use an asymptotic method (saddle-point method) to
             evaluate the integral. The contributions to the integral
             related to the saddle points of the integrand give rise to
             the optical precursors. We obtain analytic expressions for
             the precursor fields and the domain over which the
             asymptotic method is valid. When combined to obtain the
             total transient field, we find that the agreement between
             the solutions obtained by the asymptotic and the exact
             methods is excellent. Our results demonstrate that
             precursors can persist for many nanoseconds and the chirp in
             the instantaneous frequency of the precursors can manifest
             itself in beats in the transmitted intensity. Our work
             strongly suggests that precursors have been observed in many
             previous experiments. © 2009 The American Physical
             Society.},
   Doi = {10.1103/PhysRevA.79.063842},
   Key = {fds244169}
}

@article{fds244168,
   Author = {Tovbis, A and Venakides, S},
   Title = {Determinant form of the complex phase function of the
             steepest descent analysis of Riemann-Hilbert problems and
             its application to the focusing nonlinear schrödinger
             equation},
   Journal = {International Mathematics Research Notices},
   Volume = {2009},
   Number = {11},
   Pages = {2056-2080},
   Publisher = {Oxford University Press (OUP)},
   Year = {2009},
   Month = {February},
   ISSN = {1073-7928},
   url = {http://dx.doi.org/10.1093/imrn/rnp011},
   Abstract = {We derive a determinant formula for the g-function that
             plays a key role in the steepest descent asymptotic analysis
             of the solution of 2 × 2 matrix Riemann-Hilbert problems
             (RHPs) and is closely related to a hyperelliptic Riemann
             surface. We formulate a system of transcendental equations
             in determinant form (modulation equations), that govern the
             dependence of the branchpoints αj of the Riemann surface on
             a set of external parameters. We prove that, subject to the
             modulation equations, ∂g/∂αj is identically zero for
             all the branchpoints. Modulation equations are also obtained
             in the form of ordinary differential equations with respect
             to external parameters; some applications of these equations
             to the semiclassical limit of the focusing nonlinear
             Schrödinger equation (NLS) are discussed. © The Author
             2009.},
   Doi = {10.1093/imrn/rnp011},
   Key = {fds244168}
}

@article{fds320541,
   Author = {Tovbis, A and Venakides, S},
   Title = {Determinant form of modulation equations for the
             semiclassical focusing Nonlinear Schr\" odinger
             equation},
   Year = {2009},
   Abstract = {We derive a determinant formula for the WKB exponential of
             singularly perturbed Zakharov-Shabat system that corresponds
             to the semiclassical (zero dispersion) limit of the focusing
             Nonlinear Schr\" odinger equation. The derivation is based
             on the Riemann-Hilbert Problem (RHP) representation of the
             WKB exponential. We also prove its independence of the
             branchpoints of the corresponding hyperelliptic surface
             assuming that the modulation equations are
             satisfied.},
   Key = {fds320541}
}

@article{fds341090,
   Author = {Ptitsyna, N and Shipman, SP and Venakides, S},
   Title = {Fano resonance of waves in periodic slabs},
   Journal = {Mathematical Methods in Electromagnetic Theory, Mmet,
             Conference Proceedings},
   Pages = {73-78},
   Year = {2008},
   Month = {September},
   url = {http://dx.doi.org/10.1109/MMET.2008.4580900},
   Abstract = {We investigate Fano-type anomalous transmission of energy of
             plane waves across lossless slab scatterers with periodic
             structure in the presence of non-robust guided modes. Our
             approach is based on rigorous analytic perturbation of the
             scattering problem near a guided mode and applies to very
             general structures, continuous and discrete. © 2008
             IEEE.},
   Doi = {10.1109/MMET.2008.4580900},
   Key = {fds341090}
}

@article{fds320429,
   Author = {Tovbis, A and Venakides, S and Zhou, X},
   Title = {Semiclassical Focusing Nonlinear Schrodinger equation in the
             pure radiation case: Riemann-Hilbert Problem
             approach},
   Journal = {Surveys on Discrete and Computational Geometry: Twenty Years
             Later},
   Volume = {458},
   Pages = {117-144},
   Publisher = {AMER MATHEMATICAL SOC},
   Editor = {Baik, J and Kriecherbauer, T and Li, LC and McLaughlin, KDT and Tomei,
             C},
   Year = {2008},
   ISBN = {978-0-8218-4240-9},
   Key = {fds320429}
}

@article{fds244172,
   Author = {Tovbis, A and Venakides, S and Zhou, X},
   Title = {Semiclassical focusing nonlinear schrödinger equation i:
             Inverse scattering map and its evolution for radiative
             initial data},
   Journal = {International Mathematics Research Notices},
   Volume = {2007},
   Number = {Article ID rnm094, 54 pages. doi:10.},
   Publisher = {Oxford University Press (OUP)},
   Year = {2007},
   Month = {December},
   ISSN = {1073-7928},
   url = {http://dx.doi.org/10.1093/imrn/rnm094},
   Abstract = {We consider the semiclassical limit for the focusing
             nonlinear (cubic) Schrödinger Equation (NLS) in the pure
             radiational case. We present a method of reconstructing the
             leading order terms of the solitonless initial data and of
             its evolution for a wide class of the corresponding
             reflection coefficients. © The Author 2007.},
   Doi = {10.1093/imrn/rnm094},
   Key = {fds244172}
}

@article{fds244171,
   Author = {Buckingham, R and Venakides, S},
   Title = {Long-time asymptotics of the nonlinear Schrödinger equation
             shock problem},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {60},
   Number = {9},
   Pages = {1349-1414},
   Publisher = {WILEY},
   Year = {2007},
   Month = {September},
   ISSN = {0010-3640},
   MRCLASS = {35Q55 (35B40 37K15)},
   MRNUMBER = {MR2337507},
   url = {http://dx.doi.org/10.1002/cpa.20179},
   Abstract = {The long-time asymptotics of two colliding plane waves
             governed by the focusing nonlinear Schrödinger equation are
             analyzed via the inverse scattering method. We find three
             asymptotic regions in space-time: a region with the original
             wave modified by a phase perturbation, a residual region
             with a one-phase wave, and an intermediate transition region
             with a modulated two-phase wave. The leading-order terms for
             the three regions are computed with error estimates using
             the steepest-descent method for Riemann-Hilbert problems.
             The nondecaying initial data requires a new adaptation of
             this method. A new breaking mechanism involving a complex
             conjugate pair of branch points emerging from the real axis
             is observed between the residual and transition regions.
             Also, the effect of the collision is felt in the plane-wave
             state well beyond the shock front at large times. © 2007
             Wiley Periodicals, Inc.},
   Doi = {10.1002/cpa.20179},
   Key = {fds244171}
}

@article{fds244170,
   Author = {Peralta, XG and Toyama, Y and Hutson, MS and Montague, R and Venakides,
             S and Kiehart and, DP and Edwards, GS},
   Title = {Resiliency, coordination, and synchronization of dorsal
             closure during Drosophila morphogenesis},
   Journal = {Biophysical Journal},
   Volume = {92},
   Number = {7},
   Pages = {2583-2596},
   Year = {2007},
   Month = {April},
   ISSN = {0006-3495},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17218455},
   Abstract = {Tissue dynamics during dorsal closure, a stage of Drosophila
             development, provide a model system for cell sheet
             morphogenesis and wound healing. Dorsal closure is
             characterized by complex cell sheet movements, driven by
             multiple tissue specific forces, which are coordinated in
             space, synchronized in time, and resilient to UV-laser
             perturbations. The mechanisms responsible for these
             attributes are not fully understood. We measured spatial,
             kinematic, and dynamic antero-posterior asymmetries to
             biophysically characterize both resiliency to laser
             perturbations and failure of closure in mutant embryos and
             compared them to natural asymmetries in unperturbed,
             wild-type closure. We quantified and mathematically modeled
             two processes that are upregulated to provide
             resiliency.contractility of the amnioserosa and formation of
             a seam between advancing epidermal sheets, i.e., zipping.
             Both processes are spatially removed from the laser-targeted
             site, indicating they are not a local response to
             laser-induced wounding and suggesting mechanosensitive
             and/or chemosensitive mechanisms for upregulation. In mutant
             embryos, tissue junctions initially fail at the anterior end
             indicating inhomogeneous mechanical stresses attributable to
             head involution, another developmental process that occurs
             concomitant with the end stages of closure. Asymmetries in
             these mutants are reversed compared to wild-type, and
             inhomogeneous stresses may cause asymmetries in wild-type
             closure.},
   Doi = {10.1529/biophysj.106.094110},
   Key = {fds244170}
}

@article{fds304498,
   Author = {Peralta, XG and Toyama, Y and Hutson, MS and Montague, R and Venakides,
             S and Kiehart, DP and Edwards, GS},
   Title = {Upregulation of forces and morphogenic asymmetries in dorsal
             closure during Drosophila development.},
   Journal = {Biophysical Journal},
   Volume = {92},
   Number = {7},
   Pages = {2583-2596},
   Year = {2007},
   Month = {April},
   ISSN = {0006-3495},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/17218455},
   Abstract = {Tissue dynamics during dorsal closure, a stage of Drosophila
             development, provide a model system for cell sheet
             morphogenesis and wound healing. Dorsal closure is
             characterized by complex cell sheet movements, driven by
             multiple tissue specific forces, which are coordinated in
             space, synchronized in time, and resilient to UV-laser
             perturbations. The mechanisms responsible for these
             attributes are not fully understood. We measured spatial,
             kinematic, and dynamic antero-posterior asymmetries to
             biophysically characterize both resiliency to laser
             perturbations and failure of closure in mutant embryos and
             compared them to natural asymmetries in unperturbed,
             wild-type closure. We quantified and mathematically modeled
             two processes that are upregulated to provide
             resiliency--contractility of the amnioserosa and formation
             of a seam between advancing epidermal sheets, i.e., zipping.
             Both processes are spatially removed from the laser-targeted
             site, indicating they are not a local response to
             laser-induced wounding and suggesting mechanosensitive
             and/or chemosensitive mechanisms for upregulation. In mutant
             embryos, tissue junctions initially fail at the anterior end
             indicating inhomogeneous mechanical stresses attributable to
             head involution, another developmental process that occurs
             concomitant with the end stages of closure. Asymmetries in
             these mutants are reversed compared to wild-type, and
             inhomogeneous stresses may cause asymmetries in wild-type
             closure.},
   Doi = {10.1529/biophysj.106.094110},
   Key = {fds304498}
}

@article{fds320430,
   Author = {Buckingham, R and Tovbis, A and Venakides, S and Zhou,
             X},
   Title = {The semiclassical focusing nonlinear Schrodinger
             equation},
   Journal = {Recent Advances in Nonlinear Partial Differential Equations
             and Applications},
   Volume = {65},
   Series = {Proceedings of Symposia in Applied Mathematics},
   Pages = {47-80},
   Booktitle = {"Recent Advances in Nonlinear Partial Differentila Equations
             and Applications''},
   Publisher = {AMER MATHEMATICAL SOC},
   Editor = {Bonilla, LL and Carpio, A and Vega, JM and Venakides,
             S},
   Year = {2007},
   ISBN = {978-0-8218-4211-9},
   Key = {fds320430}
}

@article{fds244160,
   Author = {Tovbis, A and Venakides, S and Zhou, X},
   Title = {On the long-time limit of semiclassical (zero dispersion
             limit) solutions of the focusing nonlinear Schrödinger
             equation: Pure radiation case},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {59},
   Number = {10},
   Pages = {1379-1432},
   Publisher = {WILEY},
   Year = {2006},
   Month = {October},
   ISSN = {0010-3640},
   MRNUMBER = {MR2248894},
   url = {http://dx.doi.org/10.1002/cpa.20142},
   Abstract = {In a previous paper [13] we calculated the leading-order
             term q 0(x, t, ε) of the solution of q(x, t, ε), the
             focusing nonlinear (cubic) Schrödinger (NLS) equation in
             the semiclassical limit (ε → 0) for a certain
             one-parameter family of initial conditions. This family
             contains both solitons and pure radiation. In the pure
             radiation case, our result is valid for all times t ≥ 0.
             The aim of the present paper is to calculate the long-term
             behavior of the semiclassical solution q(x, t, ε) in the
             pure radiation case. As before, our main tool is the
             Riemann-Hilbert problem (RHP) formulation of the inverse
             scattering problem and the corresponding system of "moment
             and integral conditions," known also as a system of
             "modulation equations." © 2006 Wiley Periodicals,
             Inc.},
   Doi = {10.1002/cpa.20142},
   Key = {fds244160}
}

@article{fds244174,
   Author = {Shipman, SP and Venakides, S},
   Title = {Resonant transmission near nonrobust periodic slab
             modes.},
   Journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {71},
   Number = {2 Pt 2},
   Pages = {026611},
   Year = {2005},
   Month = {February},
   ISSN = {1539-3755},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/15783445},
   Abstract = {We present a precise theoretical explanation and prediction
             of certain resonant peaks and dips in the electromagnetic
             transmission coefficient of periodically structured slabs in
             the presence of nonrobust guided slab modes. We also derive
             the leading asymptotic behavior of the related phenomenon of
             resonant enhancement near the guided mode. The theory
             applies to structures in which losses are negligible and to
             very general geometries of the unit cell. It is based on
             boundary-integral representations of the electromagnetic
             fields. These depend on the frequency and on the Bloch wave
             vector and provide a complex-analytic connection in these
             parameters between generalized scattering states and guided
             slab modes. The perturbation of three coincident zeros-those
             of the dispersion relation for slab modes, the reflection
             constant, and the transmission constant-is central to
             calculating transmission anomalies both for lossless
             dielectric materials and for perfect metals.},
   Doi = {10.1103/physreve.71.026611},
   Key = {fds244174}
}

@article{fds320431,
   Author = {Peralta, XG and Toyama, Y and Wells, A and Tokutake, Y and Hutson, MS and Venakides, S and Kiehart, DP and Edwards, GS},
   Title = {Force regulation during dorsal closure in
             Drosophila},
   Journal = {Molecular Biology of the Cell},
   Volume = {15},
   Pages = {403A-403A},
   Publisher = {AMER SOC CELL BIOLOGY},
   Year = {2004},
   Month = {November},
   Key = {fds320431}
}

@article{fds244173,
   Author = {Tovbis, A and Venakides, S and Zhou, X},
   Title = {On semiclassical (zero dispersion limit) solutions of the
             focusing nonlinear Schrödinger equation},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {57},
   Number = {7},
   Pages = {877-985},
   Publisher = {WILEY},
   Year = {2004},
   Month = {July},
   ISSN = {0010-3640},
   MRCLASS = {35Q55 (35C20 37K15 37K40)},
   MRNUMBER = {MR2044068 (2005c:35269)},
   url = {http://dx.doi.org/10.1002/cpa.20024},
   Abstract = {We calculate the leading-order term of the solution of the
             focusing nonlinear (cubic) Schrödinger equation (NLS) in
             the semiclassical limit for a certain one-parameter family
             of initial conditions. This family contains both solitons
             and pure radiation. In the pure radiation case, our result
             is valid for all times t ≥ 0. We utilize the
             Riemann-Hilbert problem formulation of the inverse
             scattering problem to obtain the leading-order term of the
             solution. Error estimates are provided. © 2004 Wiley
             Periodicals, Inc.},
   Doi = {10.1002/cpa.20024},
   Key = {fds244173}
}

@article{fds244159,
   Author = {Lipton, RP and Shipman, SP and Venakides, S},
   Title = {Optimization of Resonances in Photonic Crystal
             Slabs},
   Journal = {Smart Structures and Materials 2005: Active Materials:
             Behavior and Mechanics},
   Volume = {5184},
   Pages = {168-177},
   Publisher = {SPIE},
   Year = {2003},
   Month = {December},
   url = {http://dx.doi.org/10.1117/12.505091},
   Abstract = {Variational methods are applied to the design of a
             two-dimensional lossless photonic crystal slab to optimize
             resonant scattering phenomena. The method is based on
             varying properties of the transmission coefficient that are
             connected to resonant behavior. Numerical studies are based
             on boundary-integral methods for crystals consisting of
             multiple scatterers. We present an example in which we
             modify a photonic crystal consisting of an array of
             dielectric rods in air so that a weak transmission anomaly
             is transformed into a sharp resonance.},
   Doi = {10.1117/12.505091},
   Key = {fds244159}
}

@article{fds244175,
   Author = {Shipman, SP and Venakides, S},
   Title = {Resonance and bound states in photonic crystal
             slabs},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {64},
   Number = {1},
   Pages = {322-342},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2003},
   Month = {October},
   ISSN = {0036-1399},
   url = {http://dx.doi.org/10.1137/S0036139902411120},
   Abstract = {Using boundary-integral projections for time-harmonic
             electromagnetic (EM) fields, and their numerical
             implementation, we analyze EM resonance in slabs of
             two-phase dielectric photonic crystal materials. We
             characterize resonant frequencies by a complex Floquet-Bloch
             dispersion relation ω = W (β) defined by the existence of
             a nontrivial nullspace of a pair of boundary-integral
             projections parameterized by the wave number β and the
             time-frequency ω. At resonant frequencies, the crystal slab
             supports a source-free EM field. We link complex resonant
             frequencies, where the imaginary part is small, to resonant
             scattering behavior of incident source fields at nearby real
             frequencies and anomalous transmission of energy through the
             slab. At a real resonant frequency, the source-free field
             supported by the slab is a bound state. We present numerical
             examples which demonstrate the effects of structural defects
             on the resonant properties of a crystal slab and surface
             waves supported by a dielectric defect.},
   Doi = {10.1137/S0036139902411120},
   Key = {fds244175}
}

@article{fds244176,
   Author = {Hutson, MS and Tokutake, Y and Chang, M-S and Bloor, JW and Venakides,
             S and Kiehart, DP and Edwards, GS},
   Title = {Forces for morphogenesis investigated with laser
             microsurgery and quantitative modeling.},
   Journal = {Science (New York, N.Y.)},
   Volume = {300},
   Number = {5616},
   Pages = {145-149},
   Year = {2003},
   Month = {April},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/12574496},
   Abstract = {We investigated the forces that connect the genetic program
             of development to morphogenesis in Drosophila. We focused on
             dorsal closure, a powerful model system for development and
             wound healing. We found that the bulk of progress toward
             closure is driven by contractility in supracellular "purse
             strings" and in the amnioserosa, whereas adhesion-mediated
             zipping coordinates the forces produced by the purse strings
             and is essential only for the end stages. We applied
             quantitative modeling to show that these forces, generated
             in distinct cells, are coordinated in space and synchronized
             in time. Modeling of wild-type and mutant phenotypes is
             predictive; although closure in myospheroid mutants
             ultimately fails when the cell sheets rip themselves apart,
             our analysis indicates that beta(PS) integrin has an
             earlier, important role in zipping.},
   Doi = {10.1126/science.1079552},
   Key = {fds244176}
}

@article{fds320432,
   Author = {Hutson, S and Tokutake, Y and Chang, M and Bloor, JW and Venakides, S and Kiehart, DP and Edwards, GS},
   Title = {Measuring the forces that drive morphogenesis:
             Laser-microsurgery and quantitative modeling applied to
             dorsal closure in Drosophila},
   Journal = {Molecular Biology of the Cell},
   Volume = {13},
   Pages = {476A-476A},
   Publisher = {American Society for Cell Biology},
   Year = {2002},
   Month = {November},
   Key = {fds320432}
}

@article{fds244158,
   Author = {Haider, MA and Shipman, SP and Venakides, S},
   Title = {Boundary-integral calculations of two-dimensional
             electromagnetic scattering in infinite photonic crystal
             slabs: Channel defects and resonances},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {62},
   Number = {6},
   Pages = {2129-2148},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2002},
   Month = {July},
   url = {http://dx.doi.org/10.1137/S003613990138531X},
   Abstract = {We compute the transmission of two-dimensional (2D)
             electromagnetic waves through a square lattice of lossless
             dielectric rods with a channel defect. The lattice is finite
             in the direction of propagation of the incident wave and
             periodic in a transverse direction. We revisit a
             boundary-integral formulation of 2D electromagnetic
             scattering [Venakides, Haider, and Papanicolaou, SIAM J.
             Appl. Math., 60 (2000), pp. 1686-1706] that is Fredholm of
             the first kind and develop a second-kind formulation. We
             refine the numerical implementation in the above paper by
             exploiting separability in the Green's function to evaluate
             the far-field influence more efficiently. The resulting cost
             savings in computing and solving the discretized linear
             system leads to an accelerated method. We use it to analyze
             E-polarized electromagnetic scattering of normally incident
             waves on a structure with a periodic channel defect. We find
             three categories of resonances: waveguide modes in the
             channel, high-amplitude fields in the crystal at frequencies
             near the edge of the frequency bandgap, and very
             high-amplitude standing fields at frequencies in a
             transmission band that are normal to the direction of the
             incident wave. These features are captured essentially
             identically with the first-kind as with the second-kind
             formulation.},
   Doi = {10.1137/S003613990138531X},
   Key = {fds244158}
}

@article{fds244155,
   Author = {El, GA and Krylov, AL and Venakides, S},
   Title = {Unified approach to KdV modulations},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {54},
   Number = {10},
   Pages = {1243-1270},
   Publisher = {WILEY},
   Year = {2001},
   Month = {October},
   url = {http://dx.doi.org/10.1002/cpa.10002},
   Abstract = {We develop a unified approach to integrating the Whitham
             modulation equations. Our approach is based on the
             formulation of the initial-value problem for the
             zero-dispersion KdV as the steepest descent for the scalar
             Riemann-Hilbert problem [6] and on the method of generating
             differentials for the KdV-Whitham hierarchy [9]. By assuming
             the hyperbolicity of the zero-dispersion limit for the KdV
             with general initial data, we bypass the inverse scattering
             transform and produce the symmetric system of algebraic
             equations describing motion of the modulation parameters
             plus the system of inequalities determining the number the
             oscillating phases at any fixed point on the (x, t)-plane.
             The resulting system effectively solves the zero-dispersion
             KdV with an arbitrary initial datum. © 2001 John Wiley &
             Sons, Inc.},
   Doi = {10.1002/cpa.10002},
   Key = {fds244155}
}

@article{fds244157,
   Author = {Deift, P and Kriecherbauer, T and McLaughlin, KR and Venakides, S and Zhou, X},
   Title = {A riemann-Hilbert approach to asymptotic questions for
             orthogonal polynomials},
   Journal = {Journal of Computational and Applied Mathematics},
   Volume = {133},
   Number = {1-2},
   Pages = {47-63},
   Publisher = {Elsevier BV},
   Year = {2001},
   Month = {August},
   ISSN = {0377-0427},
   url = {http://dx.doi.org/10.1016/S0377-0427(00)00634-8},
   Abstract = {A few years ago the authors introduced a new approach to
             study asymptotic questions for orthogonal polynomials. In
             this paper we give an overview of our method and review the
             results which have been obtained in Deift et al. (Internat.
             Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52
             (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random
             Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes,
             Vol. 3, New York University, 1999), Kriecherbauer and
             McLaughlin (Internat. Math. Res. Notices (1999) 299) and
             Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly
             consider orthogonal polynomials with respect to weights on
             the real line which are either (1) Freud-type weights dα(x)
             = e-Q(x) dx (Q polynomial or Q(x) = xβ, β>0), or (2)
             varying weights dαn(x) = e-nV(x) dx (V analytic,
             limx→∞V(x)/logx = ∞). We obtain Plancherel-Rotach-type
             asymptotics in the entire complex plane as well as
             asymptotic formulae with error estimates for the leading
             coefficients, for the recurrence coefficients, and for the
             zeros of the orthogonal polynomials. Our proof starts from
             an observation of Fokas et al. (Comm. Math. Phys. 142 (1991)
             313) that the orthogonal polynomials can be determined as
             solutions of certain matrix valued Riemann-Hilbert problems.
             We analyze the Riemann-Hilbert problems by a steepest
             descent type method introduced by Deift and Zhou (Ann. Math.
             137 (1993) 295) and further developed in Deift and Zhou
             (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al.
             (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in
             our analysis is the use of the well-known equilibrium
             measure which describes the asymptotic distribution of the
             zeros of the orthogonal polynomials. © 2001 Elsevier
             Science B.V. All rights reserved.},
   Doi = {10.1016/S0377-0427(00)00634-8},
   Key = {fds244157}
}

@article{fds244156,
   Author = {El, GA and Krylov, AL and Molchanov, SA and Venakides,
             S},
   Title = {Soliton turbulence as a thermodynamic limit of stochastic
             soliton lattices},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {152-153},
   Pages = {653-664},
   Publisher = {Elsevier BV},
   Year = {2001},
   Month = {May},
   url = {http://dx.doi.org/10.1016/S0167-2789(01)00198-1},
   Abstract = {We use the recently introduced notion of stochastic soliton
             lattice for quantitative description of soliton turbulence.
             We consider the stochastic soliton lattice on a special
             band-gap scaling of the spectral surface of genus N so that
             the integrated density of states remains finite as N → ∞
             (thermodynamic type limit). We prove existence of the
             limiting stationary ergodic process and associate it with
             the homogeneous soliton turbulence. The phase space of the
             soliton turbulence is a one-dimensional space with the
             random Poisson measure. The zero-density limit of the
             soliton turbulence coincides with the Frish-Lloyd potential
             of the quantum theory of disordered systems. © 2001
             Published by Elsevier Science B.V.},
   Doi = {10.1016/S0167-2789(01)00198-1},
   Key = {fds244156}
}

@article{fds244154,
   Author = {Georgieva, A and Kriecherbauer, T and Venakides,
             S},
   Title = {1:2 resonance mediated second harmonic generation in a 1-D
             nonlinear discrete periodic medium},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {61},
   Number = {5},
   Pages = {1802-1815},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2001},
   Month = {January},
   url = {http://dx.doi.org/10.1137/S0036139999365341},
   Abstract = {We derive traveling wave solutions in a nonlinear diatomic
             particle chain near the 1:2 resonance (κ*, ω*), where ω*
             = D(κ*), 2ω* = D(2κ*) and ω = D(κ) is the linear
             dispersion relation. To leading order, the waves have form
             ±εsin(κn - ωt) + δsin(2κn - 2ωt), where the
             near-resonant acoustic frequency ω and the amplitude ε of
             the first harmonic are given to first order in terms of the
             wavenumber difference κ - κ* and the amplitude δ of the
             second harmonic. These traveling wave solutions are unique
             within a certain set of symmetries. We find that there is a
             continuous line in parameter space that transfers energy
             from the first to the second harmonic, even in cases where
             initially almost all energy is in the first harmonic,
             connecting these waves to pure optical waves that have no
             first harmonic content.},
   Doi = {10.1137/S0036139999365341},
   Key = {fds244154}
}

@article{fds244153,
   Author = {Tovbis, A and Venakides, S},
   Title = {The eigenvalue problem for the focusing nonlinear
             Schrödinger equation: New solvable cases},
   Journal = {Physica D: Nonlinear Phenomena},
   Volume = {146},
   Number = {1-4},
   Pages = {150-164},
   Publisher = {Elsevier BV},
   Year = {2000},
   Month = {November},
   url = {http://dx.doi.org/10.1016/S0167-2789(00)00126-3},
   Abstract = {In this paper, we study the semi-classical limit of the
             Zakharov-Shabat eigenvalue problem for the focusing of NLS
             with some specific initial data. In all these cases, the
             eigenvalue problem is reduced to connection problems for the
             hypergeometric equation and for other classical equations.
             The special initial data [Suppl. Prog. Theor. Phys. 55
             (1974) 284] is contained in our family of initial data,
             parameterized by a real parameter μ, as a particular case
             μ=0. We find that beyond a certain value of the parameter
             μ, the pure-point spectrum becomes empty and all the
             scattering information is contained in the reflection
             coefficient.},
   Doi = {10.1016/S0167-2789(00)00126-3},
   Key = {fds244153}
}

@article{fds244152,
   Author = {Venakides, S and Haider, MA and Papanicolaou, V},
   Title = {Boundary integral calculations of two-dimensional
             electromagnetic scattering by photonic crystal Fabry-Perot
             structures},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {60},
   Number = {5},
   Pages = {1686-1706},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {2000},
   Month = {May},
   url = {http://dx.doi.org/10.1137/s0036139999350779},
   Abstract = {We compute the transmission properties of two-dimensional
             (2-D) electromagnetic transverse magnetic (TM) waves that
             are normally incident on a Fabry-Perot structure with
             mirrors consisting of photonic crystals. We use a boundary
             integral formulation with quadratic boundary elements and
             utilize the Ewald representation for Green's functions. We
             trace the frequencies of the Fabry-Perot cavity modes
             traversing the photonic bandgap as the cavity length
             increases and calculate corresponding Q-values.},
   Doi = {10.1137/s0036139999350779},
   Key = {fds244152}
}

@article{fds320434,
   Author = {Reed, D and Venakides, S},
   Title = {Studying the asymptotics of Selberg-type
             integrals},
   Journal = {Applied and Industrial Mathematics, Venice 2,
             1998},
   Pages = {187-198},
   Publisher = {SPRINGER},
   Editor = {Spigler, R},
   Year = {2000},
   Month = {January},
   ISBN = {0-7923-6152-0},
   Key = {fds320434}
}

@article{fds320433,
   Author = {VENAKIDES, S},
   Title = {Boundary integral calculations of two-dimensional
             electromagnetic scattering by photonic crystal Fabri-Peror
             structures},
   Journal = {Siam J. Appl. Math.},
   Volume = {60},
   Pages = {1686-1706},
   Year = {2000},
   url = {http://dx.doi.org/10.1137/S0036139999350779},
   Doi = {10.1137/S0036139999350779},
   Key = {fds320433}
}

@article{fds244145,
   Author = {Beaky, MM and Burk, JB and Everitt, HO and Haider, MA and Venakides,
             S},
   Title = {Two-dimensional photonic crystal fabry-perot resonators with
             lossy dielectrics},
   Journal = {Ieee Transactions on Microwave Theory and
             Techniques},
   Volume = {47},
   Number = {11},
   Pages = {2085-2091},
   Publisher = {Institute of Electrical and Electronics Engineers
             (IEEE)},
   Year = {1999},
   Month = {December},
   ISSN = {0018-9480},
   url = {http://dx.doi.org/10.1109/22.798003},
   Abstract = {Square and triangular lattice two-dimensional (2-D) photonic
             crystals (PC's) composed of lossy dielectric rods in air
             were constructed with a microwave bandgap between 4-8 GHz.
             Fabry-Perot resonators of varying length were constructed
             from two of these PC's of adjustable thickness and
             reflectivity. The quality factor of cavity modes supported
             in the resonators was found to increase with increasing PC
             mirror thickness, but only to a point dictated by the
             lossiness of the dielectric rods. A 2-D periodic Green's
             function simulation was found to model the data accurately
             and quickly using physical parameters obtained in separate
             measurements. Simple rules are developed for designing
             optimal resonators in the presence of dielectric loss. ©
             1999 IEEE.},
   Doi = {10.1109/22.798003},
   Key = {fds244145}
}

@article{fds244147,
   Author = {Filip, AM and Venakides, S},
   Title = {Existence and modulation of traveling waves in particle
             chains},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {52},
   Number = {6},
   Pages = {693-735},
   Year = {1999},
   Month = {June},
   Abstract = {We consider an infinite particle chain whose dynamics are
             governed by the following system of differential equations:
             q̈n= V′ (qn-1- qn) - V′ (qn- qn+1), n = 1,2, . . . ,
             where qn(t) is the displacement of the nthparticle at time t
             along the chain axis and · denotes differentiation with
             respect to time. We assume that all particles have unit mass
             and that the interaction potential V between adjacent
             particles is a convex C∞function. For this system, we
             prove the existence of C∞, time-periodic, traveling-wave
             solutions of the form qn(t) = q(wt - kn) + βt - αn, where
             q is a periodic function q(z) = q(z + 1) (the period is
             normalized to equal 1), w and k are, respectively, the
             frequency and the wave number, α is the mean particle
             spacing, and β can be chosen to be an arbitrary parameter.
             We present two proofs, one based on a variational principle
             and the other on topological methods, in particular degree
             theory. For small-amplitude waves, based on perturbation
             techniques, we describe the form of the traveling waves, and
             we derive the weakly nonlinear dispersion relation. For the
             fully nonlinear case, when the amplitude of the waves is
             high, we use numerical methods to compute the traveling-wave
             solution and the nonlinear dispersion relation. We finally
             apply Whitham's method of averaged Lagrangian to derive the
             modulation equations for the wave parameters α, β, k, and
             w. © 1999 John Wiley & Sons, Inc.},
   Key = {fds244147}
}

@article{fds244148,
   Author = {Cheng, PJ and Venakides, S and Zhou, X},
   Title = {Long-time asymptotics for the pure radiation solution of the
             sine-Gordon equation},
   Journal = {Communications in Partial Differential Equations},
   Volume = {24},
   Number = {7-8},
   Pages = {1195-1262},
   Publisher = {Informa UK Limited},
   Year = {1999},
   Month = {January},
   url = {http://dx.doi.org/10.1080/03605309908821464},
   Doi = {10.1080/03605309908821464},
   Key = {fds244148}
}

@article{fds244149,
   Author = {Georgieva, A and Kriecherbauer, T and Venakides,
             S},
   Title = {Wave Propagation and Resonance in a One-Dimensional
             Nonlinear Discrete Periodic Medium},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {60},
   Number = {1},
   Pages = {272-294},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1999},
   Month = {January},
   url = {http://dx.doi.org/10.1137/s0036139998340315},
   Abstract = {We consider wave propagation in a nonlinear infinite
             diatomic chain of particles as a discrete model of
             propagation in a medium whose properties vary periodically
             in space. The particles have alternating masses M1 and M2
             and interact in accordance to a general nonlinear force F
             acting between the nearest neighbors. Their motion is
             described by the system of equations qqn =
             1/M1(F(yn-1-yn)-F(yn-yn+1)), qqn+1 = 1/M2(F(yn-yn+1)-F(yn+1-yn+2)),
             where {yn}n = -∞∞ is the position of the nth particle.
             Using Fourier series methods and tools from bifurcation
             theory, we show that, for nonresonant wave-numbers k, this
             system admits nontrivial small-amplitude traveling wave
             solutions g and h, depending only on the linear combination
             z = kn-ωt. We determine the nonlinear dispersion relation.
             We also show that the system sustains binary oscillations
             with arbitrarily large amplitude.},
   Doi = {10.1137/s0036139998340315},
   Key = {fds244149}
}

@article{fds244150,
   Author = {Deift, P and Kriecherbauer, T and McLaughlin, KTR and Venakides, S and Zhou, X},
   Title = {Uniform asymptotics for polynomials orthogonal with respect
             to varying exponential weights and applications to
             universality questions in random matrix theory},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {52},
   Number = {11},
   Pages = {1335-1425},
   Publisher = {WILEY},
   Year = {1999},
   Month = {January},
   url = {http://dx.doi.org/10.1002/(SICI)1097-0312(199911)52:11<1335::AID-CPA1>3.0.CO;2},
   Abstract = {We consider asymptotics for orthogonal polynomials with
             respect to varying exponential weights wn(x)dx = e-nV(x)dx
             on the line as n → ∞. The potentials V are assumed to be
             real analytic, with sufficient growth at infinity. The
             principle results concern Plancherel-Rotach-type asymptotics
             for the orthogonal polynomials down to the axis. Using these
             asymptotics, we then prove universality for a variety of
             statistical quantities arising in the theory of random
             matrix models, some of which have been considered recently
             in [31] and also in [4]. An additional application concerns
             the asymptotics of the recurrence coefficients and leading
             coefficients for the orthonormal polynomials (see also [4]).
             The orthogonal polynomial problem is formulated as a
             Riemann-Hilbert problem following [19, 20]. The
             Riemann-Hilbert problem is analyzed in turn using the
             steepest-descent method introduced in [12] and further
             developed in [11, 13]. A critical role in our method is
             played by the equilibrium measure dμv for V as analyzed in
             [8]. © 1999 John Wiley & Sons, Inc.},
   Doi = {10.1002/(SICI)1097-0312(199911)52:11<1335::AID-CPA1>3.0.CO;2},
   Key = {fds244150}
}

@article{fds244151,
   Author = {Deift, P and Kriecherbauer, T and Mclaughlin, KTR and Venakides, S and Zhou, X},
   Title = {Strong asymptotics of orthogonal polynomials with respect to
             exponential weights},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {52},
   Number = {12},
   Pages = {1491-1552},
   Year = {1999},
   Month = {January},
   url = {http://dx.doi.org/10.1002/(SICI)1097-0312(199912)52:12<1491::AID-CPA2>3.0.CO;2},
   Abstract = {We consider asymptotics of orthogonal polynomials with
             respect to weights w(x)dx = e-Q(x)dx on the real line, where
             Q(x) = Σ2mk=0qkxk, q2m > 0, denotes a polynomial of even
             order with positive leading coefficient. The orthogonal
             polynomial problem is formulated as a Riemann-Hilbert
             problem following [22, 23]. We employ the
             steepest-descent-type method introduced in [18] and further
             developed in [17, 19] in order to obtain uniform
             Plancherel-Rotach-type asymptotics in the entire complex
             plane, as well as asymptotic formulae for the zeros, the
             leading coefficients, and the recurrence coefficients of the
             orthogonal polynomials. © 1999 John Wiley & Sons,
             Inc.},
   Doi = {10.1002/(SICI)1097-0312(199912)52:12<1491::AID-CPA2>3.0.CO;2},
   Key = {fds244151}
}

@article{fds244144,
   Author = {Deift, P and Venakides, S and Zhou, X},
   Title = {An extension of the steepest descent method for
             Riemann-Hilbert problems: the small dispersion limit of the
             Korteweg-de Vries (KdV) equation.},
   Journal = {Proceedings of the National Academy of Sciences of the
             United States of America},
   Volume = {95},
   Number = {2},
   Pages = {450-454},
   Year = {1998},
   Month = {January},
   ISSN = {0027-8424},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/11038618},
   Abstract = {This paper extends the steepest descent method for
             Riemann-Hilbert problems introduced by Deift and Zhou in a
             critical new way. We present, in particular, an algorithm,
             to obtain the support of the Riemann-Hilbert problem for
             leading asymptotics. Applying this extended method to small
             dispersion KdV (Korteweg-de Vries) equation, we (i) recover
             the variational formulation of P. D. Lax and C. D. Levermore
             [(1979) Proc. Natl. Acad. Sci. USA76, 3602-3606] for the
             weak limit of the solution, (ii) derive, without using an
             ansatz, the hyperelliptic asymptotic solution of S.
             Venakides that describes the oscillations; and (iii) are now
             able to compute the phase shifts, integrating the modulation
             equations exactly. The procedure of this paper is a version
             of fully nonlinear geometrical optics for integrable
             systems. With some additional analysis the theory can
             provide rigorous error estimates between the solution and
             its computed asymptotic expression.},
   Doi = {10.1073/pnas.95.2.450},
   Key = {fds244144}
}

@article{fds244146,
   Author = {McDonald, MA and Venakides, S},
   Title = {Renormalization of the τ-functions for integrable systems:
             A model problem},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {51},
   Number = {8},
   Pages = {937-966},
   Publisher = {WILEY},
   Year = {1998},
   Month = {January},
   url = {http://dx.doi.org/10.1002/(SICI)1097-0312(199808)51:8<937::AID-CPA3>3.0.CO;2-6},
   Abstract = {We introduce a renormalization procedure for the τ-function
             of integrable systems. We illustrate the procedure using the
             supercritical Toda shock problem as a model problem. We
             start with a finite chain and take the limit of the solution
             as the number of particles N → ∞. This results in a new
             formula for the τ-function for the problem with an infinite
             chain. We apply the renormalized formula to rederive
             leading-order effects of the supercritical Toda shock
             problem. © 1998 John Wiley & Sons, Inc.},
   Doi = {10.1002/(SICI)1097-0312(199808)51:8<937::AID-CPA3>3.0.CO;2-6},
   Key = {fds244146}
}

@article{fds244141,
   Author = {Deift, P and Kriecherbauer, T and McLaughlin, KTR and Venakides, S and Zhou, X},
   Title = {Asymptotics for Polynomials Orthogonal with Respect to
             Varying Exponential Weights},
   Journal = {International Mathematics Research Notices},
   Number = {16},
   Pages = {X-782},
   Year = {1997},
   Month = {December},
   Key = {fds244141}
}

@article{fds244142,
   Author = {Deift, P and Venakides, S and Zhou, X},
   Title = {New Results in Small Dispersion KdV by an Extension of the
             Steepest Descent Method for Riemann-Hilbert
             Problems},
   Journal = {International Mathematics Research Notices},
   Number = {6},
   Pages = {284-299},
   Year = {1997},
   Month = {December},
   Key = {fds244142}
}

@article{fds244143,
   Author = {Bonilla, LL and Kindelan, M and Moscoso, M and Venakides,
             S},
   Title = {Periodic generation and propagation of traveling fronts in
             dc voltage biased semiconductor superlattices},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {57},
   Number = {6},
   Pages = {1588-1614},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1997},
   Month = {January},
   url = {http://dx.doi.org/10.1137/S0036139995288885},
   Abstract = {The continuum limit of a recently proposed model for charge
             transport in resonant-tunneling semiconductor superlattices
             (SLs) is analyzed. It is described by a nonlinear hyperbolic
             integrodifferential equation on a one-dimensional spatial
             support, supplemented by shock and entropy conditions. For
             appropriate parameter values, a time-periodic solution is
             found in numerical simulations of the model. An asymptotic
             theory shows that the time-periodic solution is due to
             recycling and motion of shock waves representing domain
             walls connecting regions of the SL where the electric field
             is almost uniform.},
   Doi = {10.1137/S0036139995288885},
   Key = {fds244143}
}

@article{fds320436,
   Author = {Deift, P and Venakides, S and Zhou, X},
   Title = {New results in small dispersion kdV by an extension of the
             steepest descent method for Riemann-Hilbert
             problems},
   Journal = {International Mathematics Research Notices},
   Number = {6},
   Pages = {285-299},
   Publisher = {DUKE UNIV PRESS},
   Year = {1997},
   Month = {January},
   Key = {fds320436}
}

@article{fds320435,
   Author = {Deift, P and Kriecherbauer, T and McLaughlin, KTR and Venakides, S and Zhou, X},
   Title = {Asymptotics for polynomials orthogonal with respect to
             varying exponential weights},
   Journal = {International Mathematics Research Notices},
   Number = {16},
   Pages = {759-782},
   Publisher = {Oxford University Press (OUP): Policy B - Oxford Open Option
             A},
   Year = {1997},
   Key = {fds320435}
}

@article{fds320437,
   Author = {Deift, P and Kriecherbauer, T and Venakides, S},
   Title = {Forced lattice vibrations: Part I},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {48},
   Number = {11},
   Pages = {1187-1249},
   Publisher = {WILEY},
   Year = {1995},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160481102},
   Abstract = {This is the First part of a two‐part series on forced
             lattice vibrations in which a semi‐infinite lattice of
             one‐dimensional particles {xn}n≧1 (Formula Presented.)
             is driven from one end by a particle x0. This particle
             undergoes a given, periodically perturbed, uniform motion,
             x0(t) = at + h(yt), where a and γ are constants and h(·)
             has period 2π. For a wide variety of restoring forces F
             (i.e., F′ > 0), numerical calculations indicate the
             existence of a sequence of thresholds γ1 = γ1(a, h, F) >
             γ2 = γ2(a,h,F) > … > γk = γk(a,h,F) > …, γk → 0,
             as k → ∞. If γk > γ > γk+1, a k‐phase wave that is
             well described by the wave form, (Formula Presented.)
             emerges and travels through the lattice. The goal of this
             series is to describe the emergence and calculate some
             properties of these wave forms. In Part I the authors first
             consider the case where F(x) = ex (i.e., Toda forces) but h
             is arbitrary, and show how to compute a basic diagnostic
             (see J(λ), formula (1.26)) for the system in terms of the
             solution of an associated scalar Riemann‐Hilbert problem,
             once a certain finite set of numbers is known. In another
             direction, the authors consider the case where F(x) is
             restoring but arbitrary, and h is small. Here the authors
             prove a general result, asserting that if there exists a
             sufficiently ample family of traveling‐wave solutions of
             the doubly infinite lattice, (Formula Presented.) then it is
             possible to construct time‐periodic k‐phase wave
             solutions with asymptotics in n of type (iii) for the driven
             system (i). In Part II, the authors prove that sufficiently
             ample families of traveling‐wave solutions of the system
             (iv) exist in the cases γ > γ1 and γ1 > γ > γ2 for
             general restoring forces F. In the case with Toda forces,
             F(x) = ex, the authors prove that sufficiently ample
             families of traveling‐wave solutions. Copyright © 1995
             Wiley Periodicals, Inc., A Wiley Company},
   Doi = {10.1002/cpa.3160481102},
   Key = {fds320437}
}

@article{fds320438,
   Author = {Deift, P and Kriecherbauer, T and Venakides, S},
   Title = {Forced lattice vibrations: Part II},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {48},
   Number = {11},
   Pages = {1251-1298},
   Publisher = {WILEY},
   Year = {1995},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160481103},
   Abstract = {This is the second part of a two‐part series on forced
             lattice vibrations in which a semi‐infinite lattice of
             one‐dimensional particles {xn}n≧1, (Formula Presented.)
             is driven from one end by a particle x0. This particle
             undergoes a given, periodically perturbed, uniform motion
             x0(t) = 2at + h(yt) where a and γ are constants and h(·)
             has period 2π. Results and notation from Part I are used
             freely and without further comment. Here the authors prove
             that sufficiently ample families of traveling‐wave
             solutions of the doubly infinite system (Formula Presented.)
             exist in the cases γ > γ1 and γ1 > γ > γ2 for general
             restoring forces F. In the case with Toda forces, F(x) = ex,
             the authors prove that sufficiently ample families of
             traveling‐wave solutions exist for all k, γk > γ >
             γk+1. By a general result proved in Part I, this implies
             that there exist time‐periodic solutions of the driven
             system (i) with k‐phase wave asymptotics in n of the type
             (Formula Presented.) with k = 0 or 1 for general F and k
             arbitrary for F(x) = ex (when k = 0, take γ0 = ∞ and X0
             ≡ 0). Copyright © 1995 Wiley Periodicals, Inc., A Wiley
             Company},
   Doi = {10.1002/cpa.3160481103},
   Key = {fds320438}
}

@article{fds244140,
   Author = {Bonilla, LL and Higuera, FJ and Venakides, S},
   Title = {The Gunn Effect: Instability of the Steady State and
             Stability of the Solitary Wave in Long Extrinsic
             Semiconductors},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {54},
   Number = {6},
   Pages = {1521-1541},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1994},
   Month = {December},
   url = {http://dx.doi.org/10.1137/s0036139992236554},
   Abstract = {A linear stability analysis of the stationary solution of a
             one-dimensional drift-diffusion model used to describe the
             Gunn effect in GaAs is performed. It is shown that for long
             semiconductor samples under dc voltage bias conditions, and
             small diffusivity, the steady state may lose stability via a
             Hopf bifurcation. In the limit of infinitely long samples,
             there is a quasicontinuum of oscillatory modes of the
             equation linearized about the steady state that a acquire
             positive real part for voltages larger than a certain
             critical value. The linear stability of the solitary wave
             characteristic of the Gunn effect is proved for an idealized
             electron velocity curve in the zero diffusion
             limit.},
   Doi = {10.1137/s0036139992236554},
   Key = {fds244140}
}

@article{fds320439,
   Author = {Deift, P and Venakides, S and Zhou, X},
   Title = {The collisionless shock region for the long‐time behavior
             of solutions of the KdV equation},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {47},
   Number = {2},
   Pages = {199-206},
   Publisher = {WILEY},
   Year = {1994},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160470204},
   Abstract = {The authors further develop the nonlinear steepest descent
             method of [5] and [6] to give a full description of the
             collisionless shock region for solutions of the KdV equation
             with decaying initial data. © 1994 John Wiley & Sons, Inc.
             Copyright © 1994 Wiley Periodicals, Inc., A Wiley
             Company},
   Doi = {10.1002/cpa.3160470204},
   Key = {fds320439}
}

@article{fds320440,
   Author = {Zhang, T and Venakides, S},
   Title = {Periodic limit of inverse scattering},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {46},
   Number = {6},
   Pages = {819-865},
   Publisher = {WILEY},
   Year = {1993},
   Month = {July},
   url = {http://dx.doi.org/10.1002/cpa.3160460603},
   Abstract = {I t is well known that a p‐periodic potential Q(x) can be
             reconstructed from spectral data of the corresponding Hill
             operator −(d 2 /dx 2 ) + Q(x) in terms of a Riemann
             θ‐function. We regard the periodic potential Q(x) as the
             pointwise limit of a scattering potential Q N , c (x)
             (defined to equal Q(x) when −Np ≦ x ≦ Np, to equal
             zero when x < Np) and to equal c 2 when x > (Np) as N →
             ∞ and c 2 → ∞. The scattering potential Q N , c (x)
             can be recovered from the scattering data of the
             corresponding Schrödinger operator in terms of a Dyson
             determinant according to a well known‐theory. We derive
             the Riemann θ‐function corresponding to the periodic
             potential Q(x) by taking the above limit of the Dyson
             determinant for the scattering potential. We first calculate
             the scattering data of the potential Q N , c (x) through
             recursive formulas in terms of the left transmission and
             reflection coefficients T and R of the potential which is
             equal to Q(x) when 0 ≦ x ≦ p and equal to zero
             otherwise. We use these data to express the Dyson
             determinant of Q N , c (x). We then expand the Dyson
             determinant into a Fredholm series and compute the main
             contributions to the expansion in the asymptotic limit N →
             ∞ and c 2 → ∞ using a method developed by Lax,
             Levermore, and Venakides in their study of the small
             dispersion limit of the initial value problem of
             Korteweg‐de Vries equation. The computation of the leading
             order contributions reduces to a quadratic functional
             maximization problem constrained by a positivity condition
             and by a mass quantization condition. The solutions to this
             maximization problem constitute the differentials on a
             Riemann surface, the main ingredients for the Riemann
             θ‐function corresponding to the periodic potential. The
             limit of the Dyson determinant for Q N , c (x) as N → ∞
             and c 2 → ∞ is shown to equal the exact Riemann
             θ‐function corresponding to the periodic potential Q(x)
             times an exponential function with exponent being a
             quadratic polynomial in x. Our calculation includes the
             correct phase shifts of the θ‐function. © 1993 John
             Wiley & Sons, Inc. Copyright © 1993 Wiley Periodicals,
             Inc., A Wiley Company},
   Doi = {10.1002/cpa.3160460603},
   Key = {fds320440}
}

@article{fds320441,
   Author = {Venakides, S and Deift, P and Oba, R},
   Title = {The toda shock problem},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {44},
   Number = {8-9},
   Pages = {1171-1242},
   Publisher = {WILEY},
   Year = {1991},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160440823},
   Doi = {10.1002/cpa.3160440823},
   Key = {fds320441}
}

@article{fds320442,
   Author = {VENAKIDES, S},
   Title = {THE KORTEWEG-DEVRIES EQUATION WITH SMALL DISPERSION -
             HIGHER-ORDER LAX LEVERMORE THEORY},
   Journal = {Applied and Industrial Mathematics},
   Volume = {56},
   Pages = {255-262},
   Publisher = {KLUWER ACADEMIC PUBL},
   Editor = {SPIGLER, R},
   Year = {1991},
   Month = {January},
   ISBN = {0-7923-0521-3},
   Key = {fds320442}
}

@article{fds244162,
   Author = {Reed, MC and Venakides, S and Blum, JJ},
   Title = {Approximate traveling waves in linear reaction-hyperbolic
             equations},
   Journal = {Siam Journal on Applied Mathematics},
   Volume = {50},
   Number = {1},
   Pages = {167-180},
   Publisher = {Society for Industrial & Applied Mathematics
             (SIAM)},
   Year = {1990},
   Month = {January},
   url = {http://dx.doi.org/10.1137/0150011},
   Abstract = {Linear reaction-hyperbolic equations of a general type
             arising in certain physiological problems do not have
             traveling wave solutions, but numerical computations have
             shown that they possess approximate traveling waves. Using
             singular perturbation theory, it is shown that as the rates
             of the chemical reactions approach ∞, solutions approach
             traveling waves. The speed of the limiting wave and the
             first term in the asymptotic expansion are computed in terms
             of the underlying chemical mechanisms.},
   Doi = {10.1137/0150011},
   Key = {fds244162}
}

@article{fds320443,
   Author = {Venakides, S},
   Title = {The korteweg‐de vries equation with small dispersion:
             Higher order lax‐levermore theory},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {43},
   Number = {3},
   Pages = {335-361},
   Publisher = {WILEY},
   Year = {1990},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160430303},
   Doi = {10.1002/cpa.3160430303},
   Key = {fds320443}
}

@article{fds320444,
   Author = {Venakides, S},
   Title = {The continuum limit of theta functions},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {42},
   Number = {6},
   Pages = {711-728},
   Publisher = {WILEY},
   Year = {1989},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160420602},
   Doi = {10.1002/cpa.3160420602},
   Key = {fds320444}
}

@article{fds320445,
   Author = {VENAKIDES, S},
   Title = {THE SMALL DISPERSION LIMIT OF THE KORTEWEG-DEVRIES
             EQUATION},
   Journal = {Differential Equations //},
   Volume = {118},
   Pages = {725-737},
   Publisher = {Marcel Dekker},
   Editor = {DAFERMOS, CM and LADAS, G and PAPANICOLAOU, G},
   Year = {1989},
   Month = {January},
   ISBN = {0-8247-8077-9},
   Key = {fds320445}
}

@article{fds320446,
   Author = {Venakides, S},
   Title = {The infinite period limit of the inverse formalism for
             periodic potentials},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {41},
   Number = {1},
   Pages = {3-17},
   Publisher = {WILEY},
   Year = {1988},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160410103},
   Doi = {10.1002/cpa.3160410103},
   Key = {fds320446}
}

@article{fds320447,
   Author = {Venakides, S},
   Title = {The Zero Dispersion Limit of the Korteweg-Devries Equation
             with Periodic Initial Data},
   Journal = {Transactions of the American Mathematical
             Society},
   Volume = {301},
   Number = {1},
   Pages = {189-226},
   Publisher = {American Mathematical Society},
   Year = {1987},
   Month = {May},
   url = {http://dx.doi.org/10.2307/2000334},
   Doi = {10.2307/2000334},
   Key = {fds320447}
}

@article{fds320448,
   Author = {Venakides, S},
   Title = {The zero dispersion limit of the korteweg-de vries equation
             with periodic initial data},
   Journal = {Transactions of the American Mathematical
             Society},
   Volume = {301},
   Number = {1},
   Pages = {189-226},
   Publisher = {American Mathematical Society (AMS)},
   Year = {1987},
   Month = {January},
   url = {http://dx.doi.org/10.1090/S0002-9947-1987-0879569-7},
   Abstract = {We study the initial value problem for the Korteweg-de Vries
             equation (FORMULA PRESENTED) in the limit of small
             dispersion, i.e., 0. When the unperturbed equation (FORMULA
             PRESENTED) develops a shock, rapid oscillations arise in the
             solution of the perturbed equation (i) In our study: a. We
             compute the weak limit of the solution of (i) for periodic
             initial data as 0. b. We show that in the neighborhood of a
             point (x, t) the solution u(x, t,) can be approximated
             either by a constant or by a periodic or by a quasiperiodic
             solution of equation (i). In the latter case the associated
             wavenumbers and frequencies are of order O(1/). c. We
             compute the number of phases and the wave parameters
             associated with each phase of the approximating solution as
             functions of x and t. d. We explain the mechanism of the
             generation of oscillatory phases. Our computations in a and
             c are subject to the solution of the Lax-Levermore evolution
             equations (7.7). Our results in b-d rest on a plausible
             averaging assumption. © 1987 American Mathematical
             Society.},
   Doi = {10.1090/S0002-9947-1987-0879569-7},
   Key = {fds320448}
}

@article{fds320449,
   Author = {Venakides, S},
   Title = {Long time asymptotics of the korteweg-de vries
             equation},
   Journal = {Transactions of the American Mathematical
             Society},
   Volume = {293},
   Number = {1},
   Pages = {411-419},
   Publisher = {American Mathematical Society (AMS)},
   Year = {1986},
   Month = {January},
   url = {http://dx.doi.org/10.1090/S0002-9947-1986-0814929-0},
   Abstract = {We study the long time evolution of the solution to the
             Korteweg- de Vries equation with initial data u(x) which
             satisfy lim y(.x) = -1, lim U(x) = 0. (Formula presented) We
             show that as t →∞the step emits a wavetrain of solitons
             which asymptotically have twice the amplitude of the initial
             step. We derive a lower bound of the number of solitons
             separated at time t for t large. © 1986 American
             Mathematical Society.},
   Doi = {10.1090/S0002-9947-1986-0814929-0},
   Key = {fds320449}
}

@article{fds320450,
   Author = {Venakides, S},
   Title = {Long Time Asymptotics of the Korteweg-de Vries
             Equation},
   Journal = {Transactions of the American Mathematical
             Society},
   Volume = {293},
   Number = {1},
   Pages = {411-411},
   Publisher = {JSTOR},
   Year = {1986},
   Month = {January},
   url = {http://dx.doi.org/10.2307/2000288},
   Doi = {10.2307/2000288},
   Key = {fds320450}
}

@article{fds320451,
   Author = {Venakides, S},
   Title = {The generation of modulated wavetrains in the solution of
             the Korteweg—de vries equation},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {38},
   Number = {6},
   Pages = {883-909},
   Publisher = {WILEY},
   Year = {1985},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160380616},
   Doi = {10.1002/cpa.3160380616},
   Key = {fds320451}
}

@article{fds320452,
   Author = {Venakides, S},
   Title = {The zero dispersion limit of the korteweg‐de vries
             equation for initial potentials with non‐trivial
             reflection coefficient},
   Journal = {Communications on Pure and Applied Mathematics},
   Volume = {38},
   Number = {2},
   Pages = {125-155},
   Publisher = {WILEY},
   Year = {1985},
   Month = {January},
   url = {http://dx.doi.org/10.1002/cpa.3160380202},
   Abstract = {The inverse scattering method is used to determine the
             distribution limit as ϵ → 0 of the solution u(x, t, ϵ)
             of the initial value problem. Ut − 6uux + ϵ2uxxx = 0,
             u(x, 0) = v(x), where v(x) is a positive bump which decays
             sufficiently fast as x x→±α. The case v(x) ≪ 0 has
             been solved by Peter D. Lax and C. David Levermore [8], [9],
             [10]. The computation of the distribution limit of u(x, t,
             ϵ) as ϵ → 0 is reduced to a quadratic maximization
             problem, which is then solved. Copyright © 1985 Wiley
             Periodicals, Inc., A Wiley Company},
   Doi = {10.1002/cpa.3160380202},
   Key = {fds320452}
}

@article{fds10163,
   Author = {El, G.A. and Krylov, A.L. and Molchanov, S.A. and Venakides,
             S.},
   Title = {Soliton turbulence as a thermodynamic limit of stochastic
             soliton lattices. In Advances in nonlinear mathematics and
             science.},
   Journal = {Physica D 152/153 (2001), 653--664},
   Key = {fds10163}
}

@article{fds9749,
   Author = {S. Venakides and M. Haider and V. Papanicolaou},
   Title = {Boundary Integral Calculations of 2-d Electromagnetic
             Scattering by Photonic Crystal Fabry-Perot
             Structures},
   Journal = {SIAM J. Appl. Math. vol. 60/5, (2000), pp.
             1636-1706},
   Key = {fds9749}
}

@article{fds9752,
   Author = {A. Georgieva and T. Kriecherbauer and Stephanos
             Venakides},
   Title = {Wave Propagation and Resonance in a 1-d Nonlinear Discrete
             Periodic Medium},
   Journal = {SIAM J. Appl. Math., vol. 60/1, (1999), pp.
             272-294},
   Key = {fds9752}
}

@article{fds9506,
   Author = {P. Deift and T. Kriecherbauer and K. T-R McLaughlin and S. Venakides and X. Zhou},
   Title = {Strong Asymptotics of Orhtogonal Polynomials with Respect to
             Exponential Weights},
   Journal = {CPAM, vol.52 (1999) 1491-1552.},
   Key = {fds9506}
}

@article{fds8925,
   Author = {M. McDonald and S. Venakides},
   Title = {Renormalization of the Tau Function for Integrable Systems:
             A Model Problem},
   Journal = {CPAM, Vol 51, 1998, 937-966.},
   Key = {fds8925}
}

@article{fds8924,
   Author = {P. Deift and S. Venakides and X. Zhou},
   Title = {An Extension of the Method of Steepest Descent for
             Riemann-Hilbert Problems: The Small Dispersion Limit of the
             Korteweg-de Vries (KdV) Equation},
   Journal = {Proc. Ntl. Acad. Sc. USA, vol. 95, Jan 1998,
             450-454.},
   Key = {fds8924}
}

@article{fds9390,
   Author = {P. Deift and S. Venakides and X. Zhou},
   Title = {New Results in the Small-Dispersion KdV by an Extension of
             the Method of Steepest Descent for Riemann-Hilbert
             Problems},
   Journal = {IMRN, 1997, N0. 6, 285-299.},
   Key = {fds9390}
}

@article{fds9389,
   Author = {P. Deift and T. Kriecherbauer and K. T-R McLaughlin and S. Venakides and X. Zhou},
   Title = {Asymptotics of Polynomials Orthogonal with Respect to
             Varying Exponential Weights},
   Journal = {IMRN, 1997 No 16, pp. 759-782},
   Key = {fds9389}
}

@article{fds9395,
   Author = {P. Deift and T. Kriecherbauer and S. Venakides},
   Title = {Forced Lattice Vibrations Part II},
   Journal = {Comm. Pure Appl. Math. 48, 1995, 1251-1298.},
   Key = {fds9395}
}

@article{fds9394,
   Author = {P. Deift and T. Kriecherbauer and S. Venakides},
   Title = {Forced Lattice Vibrations Part I},
   Journal = {Comm. Pure Appl. Math. 48,1995, 1187-1250.},
   Key = {fds9394}
}

@article{fds9410,
   Author = {L. L. Bonilla and F. Higuera and S. Venakides},
   Title = {The Stability of the Steady State of the Gunn
             Oscillator},
   Journal = {SIAM J. Appl. Math. vol. 54, No 6, (1994), pp.
             1521-1541.},
   Key = {fds9410}
}

@article{fds9409,
   Author = {P. Deift and S. Venakides and X. Zhou},
   Title = {The Collisionless Shock Region for the Long Time Behavior of
             the Solutions of the KdV Equation},
   Journal = {CPAM. vol. 47, (1994), pp. 199-206.},
   Key = {fds9409}
}

@article{fds9408,
   Author = {P. D. Lax and C. D. Levermore and S. Venakides},
   Title = {The Generation and Propagation of Oscillations in Dispersive
             IVP's and their Limiting Behavior},
   Journal = {Important Developments in Soliton Theory 1980--1990}, T.
             Fokas and V.E. Zakharov eds., Springer-Verlag, Berlin
             (1992).},
   Key = {fds9408}
}

@article{fds9399,
   Author = {S. Venakides},
   Title = {The solution of completely integrable systems in the
             continuum limit of the spectral data},
   Journal = {IMA Proceedings, vol. 2, (1986) pp. 337-356..},
   Key = {fds9399}
}

@article{fds9396,
   Author = {S. Venakides},
   Title = {The zero-dispersion limit of the Korteweg-de Vries equation
             with non-trivial reflection coefficient},
   Journal = {Comm. Pure and Appl. Math. 38, pp. 125-155,
             1985.},
   Key = {fds9396}
}


%% Preprints   
@article{fds226041,
   Author = {Stavros Komineas and Stephen P. Shipman and Stephanos
             Venakides},
   Title = {Lossless Polariton Solitons},
   Journal = {arXiv},
   Year = {2014},
   url = {http://arxiv.org/abs/1409.4067},
   Abstract = {Photons and excitons in a semiconductor microcavity interact
             to form exciton-polariton condensates. These are governed by
             a nonlinear quantum-mechanical system involving exciton and
             photon wavefunctions. We calculate all non-traveling
             harmonic soliton solutions for the one-dimensional lossless
             system. There are two frequency bands of bright solitons
             when the inter-exciton interactions produce a repulsive
             nonlinearity and two frequency bands of dark solitons when
             the nonlinearity is attractive. In addition, there are two
             frequency bands for which the exciton wavefunction is
             discontinuous at its symmetry point, where it undergoes a
             phase jump of π. A band of continuous dark solitons merges
             with a band of discontinuous dark solitons, forming a larger
             band over which the soliton far-field amplitude varies from
             0 to ∞; the discontinuity is initiated when the operating
             frequency exceeds the free exciton frequency. The far fields
             of the solitons in the lowest and highest frequency bands
             (one discontinuous and one continuous dark) are linearly
             unstable, whereas the other four bands have linearly stable
             far fields, including the merged band of dark
             solitons.},
   Key = {fds226041}
}

 

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

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