Applied Math

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Publications of Thomas P. Witelski    :recent first  alphabetical  combined  bibtex listing:

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Books

  1. T.P. Witelski and M. Bowen, Methods of Mathematical Modelling, Springer Undergraduate Mathematics Series (SUMS) (2015), ISBN 978-3-319-23041-2 [9783319230412]

Papers Published

  1. Thomas P Witelski, Merging traveling waves for the pouous-Fisher's equation, Applied Mathematics Letters, 8, 4, pp. 57-62, (1995) [gz]
  2. D. S. Cohen, Thomas P Witelski, Inaccessible states in time-dependent reaction-diffusive systems, Studies in Applied Mathematics, 97, pp. 301-319, (1996) [gz]
  3. W. L. Hogarth, J. Y. Parlange, Thomas P Witelski, The superposition principle for infiltration with power law diffusivity, Hydrology Days - Proceedings of the 17th Annual American Geophysical Union, pp. 365-374 (1997)
  4. Thomas P Witelski, Equilibrium solutions of a degenerate singular Cahn-Hilliard equation, Applied Mathematics Letters, 11, 5, pp. 127-133, (1998) [gz]
  5. F. Hendriks, Thomas P. Witelski, et al, Design of planar coils of minimum resistance for magnetic recording devices, Proceedings of the Workshop on Mathematical Problems in Industry, University of Delaware, 1999 [gz]
  6. Thomas P. Witelski, K. Ono, T. J. Kaper, On Axi-symmetric Traveling waves and Radial solutions of semi-linear elliptic equations, Natural Resource Modeling 13, 3, 2000, pp. 339-387 [ps]  [abs]
  7. Thomas P. Witelski, K. Ono, T. J. Kaper, Analysis of the critical wave speeds of scalar reaction-diffusion equations, Applied Math Letters, 14/1 (2000) pp. 65-73. [ps]  [abs]
  8. Thomas P. Witelski and A. J. Bernoff, Three-dimensional van der Waals driven thin film rupture, Physica D, 147 (1-2), pp. 155--176, (2000). [science]  [abs]
  9. Ferdinand Hendriks, Thomas P. Witelski, et al, Shape optimization of pressurized air bearings, Proceedings 2001 Workshop on Mathematical Problems in Industry, RPI  [abs]
  10. T Witelski, P Ng, J Ying, J Jundy and J Bove, An application of pattern recognition and infrared spectroscopy to water analysis, International Journal of Environmental Analytical Chemistry, vol. 44 no. 2 (1991), pp. 127-136, ISSN 0306-7319
  11. TP Witelski, An asymptotic solution for traveling waves of a nonlinear-diffusion Fisher's equation, Journal of Mathematical Biology, vol. 33 no. 1 (1994), pp. 1-16, ISSN 0303-6812 [gz], [doi]  [abs]
  12. TP Witelski, Stopping and merging problems for the porous media equation, IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), vol. 54 no. 3 (1995), pp. 227-243, ISSN 0272-4960 [gz], [doi]  [abs]
  13. DS Cohen, ABW Jr and TP Witelski, Shock formation in a multidimensional viscoelastic diffusive system, SIAM Journal on Applied Mathematics, vol. 55 no. 2 (1995), pp. 348-368 [gz]  [abs]
  14. TP Witelski, Merging traveling waves for the porous-Fisher's equation, Applied Mathematics Letters, vol. 8 no. 4 (1995), pp. 57-62, ISSN 0893-9659  [abs]
  15. TP Witelski, Shocks in nonlinear diffusion, Applied Mathematics Letters, vol. 8 no. 5 (1995), pp. 27-32, ISSN 0893-9659 [gz], [doi]  [abs]
  16. TP Witelski and DS Cohen, Perturbed reversible systems, Physics Letters A, vol. 207 no. 1-2 (1995), pp. 83-86, ISSN 0375-9601  [abs]
  17. T WITELSKI and D COHEN, FORBIDDEN REGIONS FOR SHOCK FORMATION IN DIFFUSIVE SYSTEMS, STUDIES IN APPLIED MATHEMATICS, vol. 95 no. 3 (October, 1995), pp. 297-317, ISSN 0022-2526 [Gateway.cgi]
  18. TP Witelski, The structure of internal layers for unstable nonlinear diffusion equations, Studies in Applied Mathematics, vol. 97 no. 3 (1996), pp. 277-300 [gz]  [abs]
  19. TP Witelski, Traveling wave solutions for case II diffusion in polymers, Journal of Polymer Science, Part B: Polymer Physics, vol. 34 no. 1 (1996), pp. 141-150 [gz]  [abs]
  20. DS Cohen and TP Witelski, Inaccessible states in time-dependent reaction diffusion, Studies in Applied Mathematics, vol. 97 no. 4 (1996), pp. 301-319  [abs]
  21. TP Witelski, Segregation and mixing in degenerate diffusion in population dynamics, Journal of Mathematical Biology, vol. 35 no. 6 (1997), pp. 695-712, ISSN 0303-6812 [gz]  [abs]
  22. TP Witelski, Perturbation Analysis for Wetting Fronts in Richards' Equation, Transport in Porous Media, vol. 27 no. 2 (1997), pp. 121-134 [gz]  [abs]
  23. TP Witelski, Similarity solutions of the lubrication equation, Applied Mathematics Letters, vol. 10 no. 5 (1997), pp. 107-113 [gz]  [abs]
  24. TP Witelski and AJ Bernoff, Self-similar asymptotics for linear and nonlinear diffusion equations, Studies in Applied Mathematics, vol. 100 no. 2 (1998), pp. 153-193 [gz]  [abs]
  25. TP Witelski, Dynamics of air bearing sliders, Physics of Fluids, vol. 10 no. 3 (1998), pp. 698-708 [getabs]  [abs]
  26. TP Witelski, AY Grosberg and T Tanaka, On the properties of polymer globules in the high density limit, Journal of Chemical Physics, vol. 108 no. 21 (1998), pp. 9144-9149 [getabs]  [abs]
  27. TP Witelski, Horizontal infiltration into wet soil, Water Resources Research, vol. 34 no. 7 (1998), pp. 1859-1863 [gz]  [abs]
  28. TP Witelski, Equilibrium interface solutions of a degenerate singular Cahn-Hilliard equation, Applied Mathematics Letters, vol. 11 no. 5 (1998), pp. 127-133  [abs]
  29. AJ Bernoff, AL Bertozzi and TP Witelski, Axisymmetric surface diffusion: Dynamics and stability of self-similar pinchoff, Journal of Statistical Physics, vol. 93 no. 3-4 (1998), pp. 725-776 [gz]  [abs]
  30. MP Brenner and TP Witelski, On spherically symmetric gravitational collapse, Journal of Statistical Physics, vol. 93 no. 3-4 (1998), pp. 863-899 [gz]  [abs]
  31. TP Witelski and F Hendriks, Stability of gas bearing sliders for large bearing number: Convective instability of the tapered slider, Tribology Transactions, vol. 42 no. 1 (1999), pp. 216-222, ISSN 1040-2004 [ps]  [abs]
  32. TP Witelski, Large bearing number stability analysis for tango class gas bearing sliders©, Tribology Transactions, vol. 42 no. 3 (1999), pp. 668-674, ISSN 1040-2004 [ps]  [abs]
  33. TP Witelski and AJ Bernoff, Stability of self-similar solutions for van der Waals driven thin film rupture, PHYSICS OF FLUIDS, vol. 11 no. 9 (September, 1999), pp. 2443-2445, ISSN 1070-6631 [Gateway.cgi], [doi]  [abs]
  34. TP Witelski and AJ Bernoff, Dynamics of three-dimensional thin film rupture, Physica D: Nonlinear Phenomena, vol. 147 no. 1-2 (2000), pp. 155-176 [doi]  [abs]
  35. TP Witelski, K Ono and TJ Kaper, Critical wave speeds for a family of scalar reaction-diffusion equations, Applied Mathematics Letters, vol. 14 no. 1 (2001), pp. 65-73 [doi]  [abs]
  36. D Vaynblat, JR Lister and TP Witelski, Symmetry and self-similarity in rupture and pinchoff: A geometric bifurcation, European Journal of Applied Mathematics, vol. 12 no. 3 (2001), pp. 209-232 [doi]  [abs]
  37. TP Witelski, DG Schaeffer and M Shearer, A discrete model for an ill-posed nonlinear parabolic PDE, Physica D: Nonlinear Phenomena, vol. 160 no. 3-4 (2001), pp. 189-221, ISSN 0167-2789 [S0167-2789(01)00350-5], [doi]  [abs]
  38. D Vaynblat, JR Lister and TP Witelski, Rupture of thin viscous films by van der waals forces: Evolution and self-similarity, Physics of Fluids, vol. 13 no. 5 (2001), pp. 1130-1141 [GetabsServlet], [doi]  [abs]
  39. AL Bertozzi, G Grün and TP Witelski, Dewetting films: Bifurcations and concentrations, Nonlinearity, vol. 14 no. 6 (2001), pp. 1569-1592 [doi]  [abs]
  40. TP Witelski, Computing finite-time singularities in interfacial flows, MODERN METHODS IN SCIENTIFIC COMPUTING AND APPLICATIONS, vol. 75 (2002), pp. 451-487, ISSN 1568-2609, ISBN 1-4020-0782-5 [Gateway.cgi]  [abs]
  41. AJ Bernoff and TP Witelski, Linear stability of source-type similarity solutions of the thin film equation, Applied Mathematics Letters, vol. 15 no. 5 (2002), pp. 599-606, ISSN 0893-9659  [abs]
  42. TP Witelski, Nonlinear Differential Equations, Mechanics and Bifurcation, Discrete and Continuous Dynamical Systems - Series B, vol. 3 no. 4 (2003), pp. i (A special issue dedicated to David G. Schaeffer's 60th birthday.) [htm]
  43. DG Schaeffer, M Shearer and T Witelski, One-dimensional solutions of an elastoplasticity model of granular material, Math. Models and Methods in Appl. Sciences, vol. 13 no. 11 (2003), pp. 1629-1671 [html], [doi]  [abs]
  44. TP Witelski and M Bowen, ADI schemes for higher-order nonlinear diffusion equations, Applied Numerical Mathematics, vol. 45 no. 2-3 (2003), pp. 331-351 [S0168-9274(02)00194-0], [doi]  [abs]
  45. TP Witelski, Intermediate asymptotics for Richards' equation in a finite layer, Journal of Engineering Mathematics, vol. 45 no. 3-4 (2003), pp. 379-399 [A:1022609020200], [doi]  [abs]
  46. M Shearer, DG Schaeffer and TP Witelski, Stability of shear bands in an elastoplastic model for granular flow: The role of discreteness, Mathematical Models and Methods in Applied Sciences, vol. 13 no. 11 (2003), pp. 1629-1671 [doi]  [abs]
  47. KB Glasner and TP Witelski, Coarsening dynamics of dewetting films., Phys Rev E Stat Nonlin Soft Matter Phys, vol. 67 no. 1 Pt 2 (January, 2003), pp. 016302, ISSN 1539-3755 [12636597], [doi]  [abs]
  48. LB Smolka, A Belmonte, DM Henderson and TP Witelski, Exact solution for the extensional flow of a viscoelastic filament, European Journal of Applied Mathematics, vol. 15 no. 6 (2005), pp. 679-712 [doi]  [abs]
  49. LJ Borucki, T Witelski, C Please, PR Kramer and D Schwendeman, A theory of pad conditioning for chemical-mechanical polishing, Journal of Engineering Mathematics, vol. 50 no. 1 (September, 2004), pp. 1-24 [issues.aspx], [doi]  [abs]
  50. TP Witelski, AJ Bernoff and AL Bertozzi, Blowup and dissipation in a critical-case unstable thin film equation, European Journal of Applied Mathematics, vol. 15 no. 2 (April, 2004), pp. 223-256 [doi]  [abs]
  51. J Sur, TP Witelski and RP Behringer, Steady-profile fingering flows in Marangoni driven thin films., Phys Rev Lett, vol. 93 no. 24 (December 10, 2004), pp. 247803, ISSN 0031-9007 [15697861], [doi]  [abs]
  52. TP Witelski, Motion of wetting fronts moving into partially pre-wet soil, Advances in Water Resources, vol. 28 no. 10 SPEC. ISS. (2005), pp. 1133-1141 [006], [doi]  [abs]
  53. TP Witelski and SW Rienstra, Introduction to practical asymptotics III, Journal of Engineering Mathematics, vol. 53 no. 3-4 (December, 2005), pp. 199-, ISSN 0022-0833 [contribution.asp], [doi]  [abs]
  54. KB Glasner and TP Witelski, Collision versus collapse of droplets in coarsening of dewetting thin films, Physica D: Nonlinear Phenomena, vol. 209 no. 1-4 SPEC. ISS. (September, 2005), pp. 80-104 [010], [doi]  [abs]
  55. RP Haskett, TP Witelski and J Sur, Localized Marangoni forcing in driven thin films, Physica D: Nonlinear Phenomena, vol. 209 no. 1-4 SPEC. ISS. (September, 2005), pp. 117-134 [019], [doi]  [abs]
  56. A Münch, B Wagner and TP Witelski, Lubrication models with small to large slip lengths, Journal of Engineering Mathematics, vol. 53 no. 3-4 (2005), pp. 359-383, ISSN 0022-0833 [doi]  [abs]
  57. R Fetzer, K Jacobs, A Münch, B Wagner and TP Witelski, New slip regimes and the shape of dewetting thin liquid films., Phys Rev Lett, vol. 95 no. 12 (September, 2005), pp. 127801, ISSN 0031-9007 [16197111], [doi]  [abs]
  58. A Munch, B Wagner and TP Witelski, Lubrication models with small to large slip lengths, Journal of Engineering Mathematics, vol. 53 no. 3-4 (December, 2005), pp. 259-283, ISSN 0022-0833 [contribution.asp], [doi]  [abs]
  59. TP Witelski, M Shearer and R Levy, Growing surfactant waves in thin liquid films driven by gravity, Applied Mathematics Research eXpress, vol. 2006 no. 15487 (2006), pp. 1-21, ISSN 1687-1200 [15487], [doi]  [abs]
  60. M Bowen and TP Witelski, The linear limit of the dipole problem for the thin film equation, SIAM Journal on Applied Mathematics, vol. 66 no. 5 (2006), pp. 1727-1748, ISSN 0036-1399 [050637832], [doi]  [abs]
  61. R Levy, M Shearer and TP Witelski, Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves, European Journal of Applied Mathematics, vol. 18 no. 6 (2007), pp. 679-708, ISSN 0956-7925 [S0956792507007218], [doi]  [abs]
  62. DG Schaeffer, M Shearer and TP Witelski, Boundary-value problems for hyperbolic equations related to steady granular flow, Mathematics and Mechanics of Solids, vol. 12 no. 6 (2007), pp. 665-699, ISSN 1081-2865 [1081286506067325], [doi]  [abs]
  63. MB Gratton and TP Witelski, Coarsening of unstable thin films subject to gravity, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 77 no. 1 (2008), ISSN 1539-3755 [doi]  [abs]
  64. M Aguareles, SJ Chapman and TP Witelski, Interaction of spiral waves in the Complex Ginzburg-Landau equation, Physical Review Letters, vol. 101 no. 224101 (2008), ISSN 0031-9007 (doi:10.1103/PhysRevLett.101.224101.) [e224101], [doi]  [abs]
  65. ST Santillan, RH Plaut, TP Witelski and LN Virgin, Large oscillations of beams and columns including self-weight, International Journal of Non-Linear Mechanics, vol. 43 no. 8 (2008), pp. 761-771, ISSN 0020-7462 [007], [doi]  [abs]
  66. DA DiCarlo, R Juanes, T LaForce and TP Witelski, Nonmonotonic traveling wave solutions of infiltration into porous media, Water Resources Research, vol. 44 no. 2 (February, 2008), pp. W02406, ISSN 0043-1397 [2007WR005975], [doi]  [abs]
  67. AJ Catllá, DG Schaeffer, TP Witelski, EE Monson and AL Lin, On spiking models for synaptic activity and impulsive differential equations, SIAM Review, vol. 50 no. 3 (2008), pp. 553-569, ISSN 0036-1445 [553], [doi]  [abs]
  68. MB Gratton and TP Witelski, Coarsening of dewetting thin films subject to gravity, Physical Review E, vol. 77 no. 016301 (2008), pp. 1-11 [e016301]
  69. M Aguareles, SJ Chapman and T Witelski, Interaction of spiral waves in the complex Ginzburg-Landau equation, Physical Review Letters, vol. 101 no. 22 (2008), ISSN 0031-9007 [doi]  [abs]
  70. MB Gratton and TP Witelski, Coarsening of unstable thin films subject to gravity., Phys Rev E Stat Nonlin Soft Matter Phys, vol. 77 no. 1 Pt 2 (January, 2008), pp. 016301, ISSN 1539-3755 [18351928], [doi]  [abs]
  71. E Peterson, M Shearer, TP Witelski and R Levy, Stability of traveling waves in thin liquid films driven by gravity and surfactant, HYPERBOLIC PROBLEMS: THEORY, NUMERICS AND APPLICATIONS, PART 2, vol. 67 no. 2 (2009), pp. 855-868, ISBN 978-0-8218-4730-5 [Gateway.cgi]
  72. MB Gratton and TP Witelski, Transient and self-similar dynamics in thin film coarsening, Physica D: Nonlinear Phenomena, vol. 238 no. 23-24 (2009), pp. 2380-2394, ISSN 0167-2789 [015], [doi]  [abs]
  73. LB Smolka and TP Witelski, On the planar extensional motion of an inertially driven liquid sheet, Physics of Fluids, vol. 21 no. 4 (2009), pp. 042101, ISSN 1070-6631 [042101], [doi]  [abs]
  74. TP Witelski and M Bowen, Singular perturbation theory., Scholarpedia, vol. 4 no. 4 (2009), pp. 3951-3951 [Singular_perturbation_theory], [doi]
  75. HJ Hwang and TP Witelski, Short-time pattern formation in thin film equations, Discrete and Continuous Dynamical Systems, vol. 23 no. 3 (March, 2009), pp. 867-885, ISSN 1078-0947 (doi: 10.3934/dcds.2009.23.867.) [displayArticles.jsp], [doi]  [abs]
  76. TP Witelski, Fluid dynamics: The subtle art of blowing bubbles, Nature Physics, vol. 5 no. 5 (2009), pp. 315-316, ISSN 1745-2473 [doi]
  77. TP Witelski, The subtle art of blowing bubbles (News and Views: Fluid Dynamics), Nature Physics, vol. 5 no. 5 (May, 2009), pp. 315-316, ISSN 1745-2473 (doi:10.1038/nphys1265.) [=NDgyMTgzMzQS1&mt=1&rt=0], [doi]
  78. M Aguareles, SJ Chapman and T Witelski, Motion of spiral waves in the complex Ginzburg-Landau equation, Physica D: Nonlinear Phenomena, vol. 239 no. 7 (April, 2010), pp. 348-365, ISSN 0167-2789 [003], [doi]  [abs]
  79. AJ Bernoff and TP Witelski, Stability and dynamics of self-similarity in evolution equations, Journal of Engineering Mathematics, vol. 66 no. 1 (March, 2010), pp. 11-31, ISSN 0022-0833 [s10665-009-9309-8], [doi]  [abs]
  80. E Aydemir, CJ Breward and TP Witelski, The effect of polar lipids on tear film dynamics., Bull Math Biol, vol. 73 no. 6 (2011), pp. 1171-1201 [20556530], [doi]  [abs]
  81. T Witelski, D Ambrose, A Bertozzi, A Layton, Z Li and M Minion, Preface: Special issue on fluid dynamics, analysis and numerics, Discrete and Continuous Dynamical Systems - Series B, vol. 17 no. 4 (June, 2012), pp. i-ii, ISSN 1531-3492 [doi]
  82. Y Huang, TP Witelski and AL Bertozzi, Anomalous exponents of self-similar blow-up solutions to an aggregation equation in odd dimensions, Applied Mathematics Letters, vol. 25 no. 12 (2012), pp. 2317-2321, ISSN 0893-9659 [doi]  [abs]
  83. R Wiebe, LN Virgin and TP Witelski, A parametrically forced nonlinear system with reversible equilibria, International Journal of Bifurcation and Chaos, vol. 22 no. 6 (2012), pp. 1230020, ISSN 0218-1274 [doi]  [abs]
  84. T Witelski, LN Virgin and C George, A driven system of impacting pendulums: Experiments and simulations, Journal of Sound and Vibration, vol. 333 no. 6 (March, 2014), pp. 1734-1753, ISSN 0022-460X [doi]  [abs]
  85. SJ Chapman, PH Trinh and TP Witelski, Exponential Asymptotics for Thin Film Rupture., SIAM Journal of Applied Mathematics, vol. 73 no. 1 (2013), pp. 232-253 [120872012], [doi]
  86. LB Smolka and TP Witelski, Biaxial extensional motion of an inertially driven radially expanding liquid sheet, PHYSICS OF FLUIDS, vol. 25 no. 6 (2013), ISSN 1070-6631 [Gateway.cgi], [doi]
  87. NS Hall Taylor, IJ Hewitt, JR Ockendon and TP Witelski, A new model for disturbance waves, International Journal of Multiphase Flow, vol. 66 (November, 2014), pp. 38-45, ISSN 0301-9322 [doi]
  88. TP Witelski, Preface to the special issue on “Thin films and fluid interfaces”, Journal of Engineering Mathematics, vol. 94 no. 1 (October, 2015), pp. 1-3, ISSN 0022-0833 [doi]
  89. JA Dijksman, S Mukhopadhyay, C Gaebler, TP Witelski and RP Behringer, Obtaining self-similar scalings in focusing flows., Physical review. E, Statistical, nonlinear, and soft matter physics, vol. 92 no. 4 (2015), pp. 043016, ISSN 1539-3755 [doi]  [abs]
  90. P. Sanaei, G.W. Richardson, T. Witelski, L.J. Cummings, Flow and fouling in a pleated membrane filter, Journal of Fluid Mechanics, vol. 795 (2016), pp. 36-59
  91. C. George, L. N. Virgin, T.P. Witelski, Experimental study of regular and chaotic transients in a nonsmooth system, International Journal of Nonlinear Mechanics, vol. 81 (2016), pp. 55-64 [doi]
  92. LB Smolka, CK McLaughlin and TP Witelski, Oil capture from a water surface by a falling sphere, Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 497 (2016), pp. 126-132, ISSN 0927-7757 [doi]

Duke University * Arts & Sciences * Mathematics * August 30, 2016

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