Philippe H. Trinh

Research

My research interests include:

  • Classical hydrodynamics: free-surface flows; gravity-capillary waves; wave-structure interactions; ship hydrodynamics; Korteweg-de Vries-type equations and nonlinear waves
  • Low Reynolds number flows: theory and modeling of viscosity and surface-tension dominated flows, including thin film or Hele-Shaw-type problems; the study of fluid instabilities (e.g. gravity-driven dripping of thin films)
  • Elasticity and solid mechanics: coupling fluid mechanics with solid mechanics; understanding fluid-structure interactions between free-surfaces and elastic membranes (e.g. contact lenses), theory and modeling of tissue and tumour growth.
  • Formation and dynamics of biological patterns: studying the dynamics of patterns in reaction-diffusion problems
  • Singular perturbation theory: exponential asymptotics and asymptotics beyond-all-orders; singularity formation in fluid and solid phenomena (e.g. rupturing of thin films and solids, moving contact line problems, etc.)
  • Numerical methods: notably boundary integral methods for free-surface flows

I love that I'm able to work and learn from some of the best mathematicians and physicists in their fields, and you can see some of them here.

Journal and Book Publications

Submitted or pre-print publications

Trinh, P. H. 2016 A nonlinear reduction for gravity waves generated by moving bodies. (Pre-Print.)

Trinh, P. H., Wilson, S. K. & Stone, H. A. 2016 An elastic plate on a thin viscous film. (Pre-Print)

Hammoud, N., Trinh, P. H., Howell, P. D. & Stone, H. A. 2016 The influence of van der Waals interactions on a bubble moving in a tube. (Pre-Print)

2016 publications

Trinh, P. H. 2016 A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents. Proc. Roy. Soc. A. 472, 20150833.PDF

Crew, S.C. & Trinh, P. H. 2016 New singularities for Stokes waves. J. Fluid Mech. 798, 256-283.PDF

Trinh, P. H. & Ward, M. J. 2016 The dynamics of localized spot patterns for reaction-diffusion systems on the sphere. Nonlinearity. 299, 766 PDF

2015 publications

Ren, W., Trinh, P. H., & E, W. 2015 On the distinguished limits of the Navier slip model of the moving contact line problem. J. Fluid Mech. 772, 107-126. PDF

Trinh, P. H. & Chapman, S.J. 2015 Exponential asymptotics and problems with coalescing singularities. Nonlinearity. 28, 1229. PDF

2014 publications

Trinh, P. H., Wilson, S. K. & Stone, H. A. 2014 A pinned or free-floating rigid plate on a thin viscous film. J. Fluid Mech. 760, 407- 430. PDF

Trinh, P. H., Kim, H., Hammoud, N., Howell, P.D., Chapman, S.J. & Stone, H.A. 2014 Curvature suppresses the Rayleigh-Taylor instability. Phys. Fluids. 26, 051704. PDF

Trinh, P. H. & Chapman, S. J. 2014 The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls. J. Fluid Mech. 741, 492-513. PDF

2013 publications

Trinh, P. H. & Chapman, S. J. 2013 New gravity-capillary waves at low speeds. Part 1: Linear theory. J. Fluid Mech. 724, 367–391. PDF

Trinh, P. H. & Chapman, S. J. 2013 New gravity-capillary waves at low speeds. Part 2: Nonlinear theory. J. Fluid Mech. 724, 392–424. PDF

Chapman, S. Jonathan, Trinh, Philippe H. & Witelski, Thomas P. 2013 Exponential asymptotics for thin film rupture. SIAM Journal on Applied Mathematics 73 (1), 232–253. PDF

Wexler, J. S., Trinh, P. H., Berthet, H., Quennouz, N., du Roure, Olivia, Huppert, H. E., Linder, A. & Stone, H. A. 2013 Bending of elastic fibres in viscous flows: the influence of confinement. J. Fluid Mech. 720, 517–544. PDF

Pre-2013 publications

Trinh, P. H., Chapman, S. J. & Vanden-Broeck, J.-M. 2011 Do waveless ships exist? Results for single-cornered hulls. J. Fluid Mech. 685, 413–439. PDF

Trinh, P. H. 2010 Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances, chap. Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves, pp. 121–126. SpringerWienNewYork. PDF

Trinh, P. & Amundsen, D. 2010 Unifying steady-state resonant solutions of a broad class of KdV-type equations. J. Comp. App. Math. 234 (6), 1788–1795. PDF

Conference proceedings and reports

Jamieson-Lane, A., Trinh, P. H. & Ward, M. J. 2015 Localized spot patterns on the sphere for reaction-diffusion systems: theory and open problems. In Proceedings for CAIMS 2015. Waterloo, Canada. PDF

Trinh, P. H. 2010 Exponential asymptotics and free-surface flows. PhD thesis, University of Oxford.

Trinh, P. H., Chapman, S. J. & Vanden-Broeck, J.-M. 2010 The existence and non-existence of waveless ships. In Proceedings 25th International Workshop on Water Waves and Floating Bodies. Harbin, China: Harbin Engineering University.

Trinh, P. H. 2007 Unifying resonant solutions of the KdV, modified KdV, and extended KdV equations. Master’s thesis, School of Mathematics and Statistics, Carleton University, Canada.