Applied Math

Duke Applied Mathematics



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

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Books

  1. Witelski, T; Bowen, M, Methods of Mathematical Modelling: Continuous Systems and Differential Equations (September, 2015), pp. 1-305, ISBN 9783319230429 [doi]  [abs] [author's comments]

Papers Published

  1. 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)
  2. 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]
  3. 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]
  4. Ferdinand Hendriks, Thomas P. Witelski, et al, Shape optimization of pressurized air bearings, Proceedings 2001 Workshop on Mathematical Problems in Industry, RPI  [abs]
  5. Witelski, T; Ng, P; Ying, J; Jundy, J; Bove, J, An application of pattern recognition and infrared spectroscopy to water analysis, International Journal Environmental Analytical Chemistry, vol. 44 no. 2 (1991), pp. 127-136, ISSN 0306-7319
  6. Witelski, TP, 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]
  7. Witelski, TP, Stopping and merging problems for the porous media equation, IMA Journal of Applied Mathematics, vol. 54 no. 3 (1995), pp. 227-243, ISSN 0272-4960 [gz], [doi]  [abs]
  8. Cohen, DS; Jr, ABW; Witelski, TP, Shock formation in a multidimensional viscoelastic diffusive system, SIAM Journal on Applied Mathematics, vol. 55 no. 2 (1995), pp. 348-368 [gz]  [abs]
  9. Witelski, TP, Merging traveling waves for the porous-Fisher's equation, Applied Mathematics Letters, vol. 8 no. 4 (1995), pp. 57-62, ISSN 0893-9659  [abs]
  10. Witelski, TP, Shocks in nonlinear diffusion, Applied Mathematics Letters, vol. 8 no. 5 (1995), pp. 27-32, ISSN 0893-9659 [gz], [doi]  [abs]
  11. Witelski, TP; Cohen, DS, Perturbed reversible systems, Physics Letters A, vol. 207 no. 1-2 (1995), pp. 83-86, ISSN 0375-9601  [abs]
  12. WITELSKI, TP; COHEN, DS, 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]
  13. Witelski, TP, The structure of internal layers for unstable nonlinear diffusion equations, Studies in Applied Mathematics, vol. 97 no. 3 (1996), pp. 277-300 [gz]  [abs]
  14. Witelski, TP, 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]
  15. Cohen, DS; Witelski, TP, Inaccessible states in time-dependent reaction diffusion, Studies in Applied Mathematics, vol. 97 no. 4 (1996), pp. 301-319  [abs]
  16. Witelski, TP, 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]
  17. Witelski, TP, Perturbation Analysis for Wetting Fronts in Richards' Equation, Transport in Porous Media, vol. 27 no. 2 (1997), pp. 121-134 [gz]  [abs]
  18. Witelski, TP, Similarity solutions of the lubrication equation, Applied Mathematics Letters, vol. 10 no. 5 (1997), pp. 107-113 [gz]  [abs]
  19. Witelski, TP; Bernoff, AJ, Self-similar asymptotics for linear and nonlinear diffusion equations, Studies in Applied Mathematics, vol. 100 no. 2 (1998), pp. 153-193 [gz]  [abs]
  20. Witelski, TP, Dynamics of air bearing sliders, Physics of Fluids, vol. 10 no. 3 (1998), pp. 698-708 [getabs]  [abs]
  21. Witelski, TP; Grosberg, AY; Tanaka, T, 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]
  22. Witelski, TP, Horizontal infiltration into wet soil, Water Resources Research, vol. 34 no. 7 (1998), pp. 1859-1863 [gz]  [abs]
  23. Witelski, TP, Equilibrium interface solutions of a degenerate singular Cahn-Hilliard equation, Applied Mathematics Letters, vol. 11 no. 5 (1998), pp. 127-133  [abs]
  24. Bernoff, AJ; Bertozzi, AL; Witelski, TP, 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]
  25. Brenner, MP; Witelski, TP, On spherically symmetric gravitational collapse, Journal of Statistical Physics, vol. 93 no. 3-4 (1998), pp. 863-899 [gz]  [abs]
  26. Witelski, TP; Hendriks, F, 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]
  27. Witelski, TP, 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]
  28. Witelski, TP; Bernoff, AJ, 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]
  29. Witelski, TP; Bernoff, AJ, Dynamics of three-dimensional thin film rupture, Physica D: Nonlinear Phenomena, vol. 147 no. 1-2 (2000), pp. 155-176 [doi]  [abs]
  30. Witelski, TP; Ono, K; Kaper, TJ, Critical wave speeds for a family of scalar reaction-diffusion equations, Applied Mathematics Letters, vol. 14 no. 1 (2001), pp. 65-73 [doi]  [abs]
  31. Vaynblat, D; Lister, JR; Witelski, TP, 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]
  32. Witelski, TP; Schaeffer, DG; Shearer, M, 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]
  33. Vaynblat, D; Lister, JR; Witelski, TP, 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]
  34. Bertozzi, AL; Grün, G; Witelski, TP, Dewetting films: Bifurcations and concentrations, Nonlinearity, vol. 14 no. 6 (2001), pp. 1569-1592 [doi]  [abs]
  35. Witelski, TP, Computing finite-time singularities in interfacial flows, vol. 75 (2002), pp. 451-487, ISSN 1568-2609, ISBN 1-4020-0782-5 [Gateway.cgi]  [abs]
  36. Bernoff, AJ; Witelski, TP, 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]
  37. Witelski, TP, 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]
  38. Witelski, TP; Bowen, M, 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]
  39. Witelski, TP, 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]
  40. Shearer, M; Schaeffer, DG; Witelski, TP, 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]
  41. Glasner, KB; Witelski, TP, Coarsening dynamics of dewetting films, Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 67 no. 1 2 (2003), pp. 163021-1630212  [abs]
  42. Schaeffer, DG; Shearer, M; Witelski, T, One-dimensional solutions of an elastoplasticity model of granular material, Math. Models and Methods in Appl. Sciences, vol. 13 (2003), pp. 1629-1671
  43. Glasner, KB; Witelski, TP, Coarsening dynamics of dewetting films., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 67 no. 1 Pt 2 (January, 2003), pp. 016302, ISSN 1539-3755 [12636597], [doi]  [abs]
  44. Merdan, H; Caginalp, G, Decay of solutions to nonlinear parabolic equations: renormalization and rigorous results, Discrete and Continuous Dynamical Systems - Series B, vol. 3 no. 4 (August, 2003), pp. 565-588 [doi]
  45. Smolka, LB; Belmonte, A; Henderson, DM; Witelski, TP, 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]
  46. Borucki, LJ; Witelski, T; Please, C; Kramer, PR; Schwendeman, D, 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]
  47. Witelski, TP; Bernoff, AJ; Bertozzi, AL, 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]
  48. Sur, J; Witelski, TP; Behringer, RP, Steady-profile fingering flows in Marangoni driven thin films., Physical Review Letters, vol. 93 no. 24 (December 10, 2004), pp. 247803, ISSN 0031-9007 [15697861], [doi]  [abs]
  49. Witelski, TP, 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]
  50. Münch, A; Wagner, B; Witelski, TP, Lubrication models with small to large slip lengths, Journal of Engineering Mathematics, vol. 53 no. 3-4 (December, 2005), pp. 359-383, ISSN 0022-0833 [contribution.asp], [doi]  [abs]
  51. Witelski, TP; Rienstra, SW, 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]
  52. Glasner, KB; Witelski, TP, 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]
  53. Haskett, RP; Witelski, TP; Sur, J, 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]
  54. Fetzer, R; Jacobs, K; Münch, A; Wagner, B; Witelski, TP, New slip regimes and the shape of dewetting thin liquid films., Physical Review Letters, vol. 95 no. 12 (September, 2005), pp. 127801, ISSN 0031-9007 [16197111], [doi]  [abs]
  55. Witelski, TP; Shearer, M; Levy, R, 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]
  56. Bowen, M; Witelski, TP, 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]
  57. Levy, R; Shearer, M; Witelski, TP, 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]
  58. Schaeffer, DG; Shearer, M; Witelski, TP, Boundary-value problems for hyperbolic equations related to steady granular flow, Mathematics & Mechanics of Solids, vol. 12 no. 6 (2007), pp. 665-699, ISSN 1081-2865 [1081286506067325], [doi]  [abs]
  59. Gratton, MB; Witelski, TP, 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]
  60. Aguareles, M; Chapman, SJ; Witelski, TP, 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]
  61. Santillan, ST; Plaut, RH; Witelski, TP; Virgin, LN, 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]
  62. DiCarlo, DA; Juanes, R; LaForce, T; Witelski, TP, 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]
  63. Catllá, AJ; Schaeffer, DG; Witelski, TP; Monson, EE; Lin, AL, 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]
  64. Gratton, MB; Witelski, TP, Coarsening of dewetting thin films subject to gravity, Physical Review E, vol. 77 no. 016301 (2008), pp. 1-11 [e016301]
  65. Aguareles, M; Chapman, SJ; Witelski, T, Interaction of spiral waves in the complex Ginzburg-Landau equation, Physical Review Letters, vol. 101 no. 22 (2008), ISSN 0031-9007 [doi]  [abs]
  66. Gratton, MB; Witelski, TP, Coarsening of unstable thin films subject to gravity., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 77 no. 1 Pt 2 (January, 2008), pp. 016301, ISSN 1539-3755 [18351928], [doi]  [abs]
  67. Peterson, E; Shearer, M; Witelski, TP; Levy, R, 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]
  68. Gratton, MB; Witelski, TP, 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]
  69. Smolka, LB; Witelski, TP, 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]
  70. Witelski, TP; Bowen, M, Singular perturbation theory., Scholarpedia, vol. 4 no. 4 (2009), pp. 3951-3951 [Singular_perturbation_theory], [doi]
  71. Hwang, HJ; Witelski, TP, 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]
  72. Witelski, TP, Fluid dynamics: The subtle art of blowing bubbles, Nature Physics, vol. 5 no. 5 (2009), pp. 315-316, ISSN 1745-2473 [doi]
  73. Witelski, TP, 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]
  74. Aguareles, M; Chapman, SJ; Witelski, T, 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]
  75. Bernoff, AJ; Witelski, TP, 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]
  76. Aydemir, E; Breward, CJW; Witelski, TP, The effect of polar lipids on tear film dynamics., Bulletin of Mathematical Biology, vol. 73 no. 6 (2011), pp. 1171-1201 [20556530], [doi]  [abs]
  77. Witelski, T; Ambrose, D; Bertozzi, A; Layton, A; Li, Z; Minion, M, 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]
  78. Huang, Y; Witelski, TP; Bertozzi, AL, 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]
  79. Wiebe, R; Virgin, LN; Witelski, TP, A parametrically forced nonlinear system with reversible equilibria, International Journal of Bifurcation & Chaos, vol. 22 no. 6 (2012), pp. 1230020, ISSN 0218-1274 [doi]  [abs]
  80. Witelski, T; Virgin, LN; George, C, 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]
  81. Chapman, SJ; Trinh, PH; Witelski, TP, Exponential Asymptotics for Thin Film Rupture., SIAM Journal of Applied Mathematics, vol. 73 no. 1 (2013), pp. 232-253 [120872012], [doi]
  82. Smolka, LB; Witelski, TP, 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]
  83. Hall Taylor, NS; Hewitt, IJ; Ockendon, JR; Witelski, TP, A new model for disturbance waves, International Journal of Multiphase Flow, vol. 66 (November, 2014), pp. 38-45, ISSN 0301-9322 [doi]
  84. Witelski, TP, 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]
  85. Dijksman, JA; Mukhopadhyay, S; Gaebler, C; Witelski, TP; Behringer, RP, 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]
  86. George, C; Virgin, LN; Witelski, T, Experimental study of regular and chaotic transients in a non-smooth system, International Journal of Non-Linear Mechanics, vol. 81 (2016), pp. 55-64 [doi]
  87. Sanaei, P; Richardson, GW; Witelski, T; Cummings, LJ, Flow and fouling in a pleated membrane filter, Journal of Fluid Mechanics, vol. 795 (2016), pp. 36-59 [doi]
  88. Smolka, LB; McLaughlin, CK; Witelski, TP, 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]
  89. Ji, H; Witelski, TP, Finite-time thin film rupture driven by modified evaporative loss, Physica D: Nonlinear Phenomena, vol. 342 (March, 2017), pp. 1-15 [doi]
  90. Gao, Y; Ji, H; Liu, J-G; Witelski, TP, Global existence of solutions to a tear film model with locally elevated evaporation rates, Physica D: Nonlinear Phenomena, vol. 350 (July, 2017), pp. 13-25 [doi]

Papers Accepted

  1. Thomas P. Witelski, K. Ono, T. J. Kaper, Analysis of the critical wave speeds of scalar reaction-diffusion equations, Applied Math Letters, [Boston University Center for BioDynamics Technical Report No. 5, (1998)] , accepted 2000 [ps]  [abs]

Duke University * Arts & Sciences * Mathematics * August 22, 2017

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