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.

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

Chandler, T. G. J. & **Trinh, P. H.** 2018 Complex singularities near the intersection of a free surface and wall. Part 1. Vertical jets and rising bubbles. J. Fluid Mech. 856, 323–350.

**Trinh, P. H.** 2017 On reduced models for gravity waves generated by moving bodies. J. Fluid Mech. 813, 824-859.

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. Phys. Rev. Fluids 2, 063601.

**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

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

**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

**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

**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

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.

Last modified: 2019/03/25 00:09