Research on Mathematical Problems in the dynamics of thin films of viscous liquids and the evolution of fluid interfaces

Research publications

Jie Zhang, Robert P. Behringer, Alexander Oron, Marangoni Convection in Binary Mixtures arXiv physics/0612002
Ryan P. Haskett, Shomeek Mukhopadhyay, Dynamics of Perfectly Wetting Drops under Gravity arXiv cond-mat/0612266
Karen E. Daniels, Shomeek Mukhopadhyay, Robert P. Behringer Instabilities in droplets spreading on gels arXiv cond-mat/0606296
M. Bowen and T. P. 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.
A. Munch and B. Wagner and T.P. Witelski, Lubrication models with small to large slip lengths, Journal of Engineering Mathematics, vol. 53 no. 3-4 (December, 2005), pp. 259-383
R. Fetzer, K. Jacobs, A. Munch, B. Wagner, T.P. Witelski, New slip regimes and the shape of dewetting thin liquid films, Physical Review Letters, vol. 95 no. 12 (September, 2005), pp. 127801
R. Levy and M. Shearer, The Motion of a Thin Film Driven by Surfactant and Gravity, SIAM Journal of Applied Mathematics, vol. 66 no. 5 (2006), pp. 1588-1609, DOI
T. Witelski, M. Shearer and R. Levy, Growing Surfactant Waves in Thin Liquid Films Driven by Gravity, AMRX, 2006.
R. Levy with I. Ipsen, D. Finkel, C. Kuster, M. Lasater, and J. Reese, Communicating Applied Mathematics: Four Examples, SIAM Review, vol. 48 no. 2 (2006), pp. 359-389.
R. P. Behringer and M. Shearer, Preface: Nonlinear dynamics of thin films and fluid interfaces, special issue, Physica D, 209, 1-4 (2005), p. vii--viii.
- Articles by Ben Amar+Bonn, Bertsch+Giacomelli+Karali, Betelu+Fontelos, Bowen+Sur+Bertozzi+Behringer, Diez+Gomba+Gratton+Kondic, Edmonstone+Matar+Craster, Glasner+Witelski, Grigoriev, Haskett+Witelski+Sur, Kondic+Diez, Levy+Shearer, Munch+Evans, Munch+Wagner, Norman+Miksis, Novick-Cohen+Hari, Schwartz+Roux+Cooper-White, Segin+Tilley+Kondic.
H.-W. Lu, K. Glasner, A. L. Bertozzi, and C.-J. Kim, A Diffuse Interface Model for Electrowetting Droplets in a Hele-Shaw Cell submitted to J. Fluid Mech., 2005.
Edward Welsh, Bjorn Birnir, and Andrea L. Bertozzi, Shocks in the Evolution of an Eroding Channel, submitted to Computers and Geosciences, 2005.
Junjie Zhou, B. Dupuy, A. L. Bertozzi, and A. E. Hosoi, Theory for Shock Dynamics in Particle-Laden Thin Films, Physical Review Letters, 94, 117803 (2005), PRL
Mark Bowen, Jeanman Sur, Andrea L. Bertozzi and Robert P. Behringer, Nonlinear dynamics of two-dimensional undercompressive shocks, Physica D, 209, 1-4, 2005, pp. 36--48. DOI
R. Levy and M. Shearer, Kinetics and nucleation for driven thin film flow, Physica D, 209, 1-4, 2005, pp. 145--163. DOI
K. B. Glasner and T. P. Witelski, Collision versus collapse of droplets in coarsening of dewetting thin films, Physica D, 2005, 209, 1-4 pp. 80-104. DOI
R. P. Haskett, T. P. Witelski, J. Sur, Localized Marangoni forcing in driven thin films, Physica D, 2005, 209, 1-4 pp. 117-134. DOI
J. Sur, T. P. Witelski, and R. P. Behringer, Steady-Profile Fingering Flows in Marangoni Driven Thin Films, Physical Review Letters, 93, 247803, (2004), PRL
M. Shearer and P.G. LeFloch, Nonclassical Riemann solvers with nucleation, Isaac Newton Institute for Math. Sciences preprint, Proceedings A, Royal Soc. Edinburgh, 134A (2004), 961-984. PDF
M. Shearer and R. Levy, Comparison of Dynamic Contact Line Models for Driven Thin Liquid Films, Euro. J. Applied Math., 2004, 15, 6, pp 625--642. DOI
L. B. Smolka, A. Belmonte, Andrew, D. M. Henderson, T. P. Witelski, Exact solution for the extensional flow of a viscoelastic filament, European J. Appl. Math. 15 (2004), no. 6, 679--712.
T. P. Witelski, A. J. Bernoff, A. L. Bertozzi, Blowup and dissipation in a critical-case unstable thin film equation, European J. Appl. Math. 15 (2004), no. 2, 223--256.
J. Sur, A. L. Bertozzi, and R. P. Behringer, Reverse Undercompressive Shock Structures in Driven Thin Film Flow, Physical Review Letters, 90, 126105,1-4, March 28, 2003, PRL
T. P. Witelski and M. Bowen, ADI schemes for higher-order nonlinear diffusion equations, Applied Numerical Mathematics, 45, 2-3, May 2003, 331-351, DOI
R. Buckingham, M. Shearer, and A. L. Bertozzi, Thin film traveling waves and the Navier slip condition, SIAM J. Appl. Math., vol 63 (2), 2003, pp. 722-744 SIAM link
K. B. Glasner and T. P. Witelski, Coarsening dynamics of dewetting thin films, Physical Review E, 67, 016302, 1-12, 2003, PRE
Andrea L. Bertozzi and Mark Bowen, Thin films and moving contact lines, Proceedings of the NATO Adv. Study Institute, Montreal Canada, pp. 31-79., 2002
Thomas P. Witelski, Computing finite-time singularities in interfacial flows, Proceedings of the NATO Adv. Study Institute, Montreal Canada, pp. 451-487, 2002
A. J. Bernoff and Thomas P. Witelski, Linear stability of source-type similarity solutions of the thin film equation, Applied Mathematics Letters 15 (2002), pp. 599-606, DOI
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)., DOI
Andrea Bertozzi, Andreas Munch, Michael Shearer, and Kevin Zumbrun, Stability of compressive and undercompressive thin film travelling waves, European J. of Appl. Math. (12) 3, pp.253-291, 2001, DOI
Javier Diez, Lou Kondic, and Andrea Bertozzi, Global models for moving contact lines, Phys. Rev. E. 63, 011208 (January 2001), PRE
Andrea L. Bertozzi, Guenther Gruen, and Thomas P. Witelski, Dewetting films: bifurcations and concentrations, Nonlinearity, 14,6 (2001) pp 1569--1592, IOP

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