~~NOTOC~~ ====== Research ====== I am often too busy to keep this page updated. Rather than have a long list of outdated updates, it suffices to say that there is a lot of interesting research I do, and you can drop by the department to see it! You are better off looking at my [[https://scholar.google.co.uk/citations?user=y7K3OG4AAAAJ&hl=en|Google Scholar]] for papers. A good way to learn about what I do is to examine my PhD student talks! Here are a few that have been recorded over the last little while. * [[https://youtu.be/qRt9Cr4A_eM|Piotr Morawiecki gives a talk on mathematical models of flooding]] * [[https://youtu.be/J0Ujpkkr6oc|Josh Shelton gives a talk on parasitic gravity-capillary waves]] * [[https://youtu.be/iJzRnyDH7zs|Yyanis Johnson-Llambias gives a talk on water waves due to flows past smoothed bodies]] For researchers who are interested in my work on better understanding differences in flood estimation models, see a dedicated section: [[research_flooding|Asymptotics for intermodel comparisons of flood-estimation models]]. ===== Research interests ===== 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 /* ===== Journal and Book Publications ===== ==== Submitted or pre-print publications ==== **Trinh, P. H.**, Wilson, S. K. & Stone, H. A. 2016 [[http://arxiv.org/abs/1410.8558|An elastic plate on a thin viscous film]]. (Pre-Print) ==== 2018 publications ==== Chandler, T. G. J. & **Trinh, P. H.** 2018 [[https://doi.org/10.1017/jfm.2018.708|Complex singularities near the intersection of a free surface and wall.]] Part 1. Vertical jets and rising bubbles. J. Fluid Mech. 856, 323–350. ==== 2017 publications ==== **Trinh, P. H.** 2017 [[https://doi.org/10.1017/jfm.2016.818|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 [[https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.2.063601|The influence of van der Waals interactions on a bubble moving in a tube]]. Phys. Rev. Fluids 2, 063601. ==== 2016 publications ==== **Trinh, P. H.** 2016 [[http://rspa.royalsocietypublishing.org/content/472/2191/20150833.abstract| A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents]]. Proc. Roy. Soc. A. 472, 20150833.{{papers:2016-trinh-topological.pdf|PDF}} Crew, S.C. & **Trinh, P. H.** 2016 [[http://dx.doi.org/10.1017/jfm.2016.309|New singularities for Stokes waves]]. J. Fluid Mech. 798, 256-283.{{:papers:2016-crew-trinh-stokeswave.pdf|PDF}} **Trinh, P. H.** & Ward, M. J. 2016 [[http://iopscience.iop.org/article/10.1088/0951-7715/29/3/766/meta|The dynamics of localized spot patterns for reaction-diffusion systems on the sphere]]. Nonlinearity. 299, 766 {{:papers:2016-trinh-ward-spotpatterns.pdf|PDF}} ==== 2015 publications ==== Ren, W., **Trinh, P. H.**, & E, W. 2015 [[http://dx.doi.org/10.1017/jfm.2015.173|On the distinguished limits of the Navier slip model of the moving contact line problem]]. J. Fluid Mech. 772, 107-126. {{:papers:2015-ren-trinh-E-mcl.pdf|PDF}} **Trinh, P. H.** & Chapman, S.J. 2015 [[http://dx.doi.org/10.1088/0951-7715/28/5/1229|Exponential asymptotics and problems with coalescing singularities]]. Nonlinearity. 28, 1229. {{:papers:2015-trinh-chapman-coalescing.pdf|PDF}} ==== 2014 publications ==== **Trinh, P. H.**, Wilson, S. K. & Stone, H. A. 2014 [[http://dx.doi.org/10.1017/jfm.2014.526|A pinned or free-floating rigid plate on a thin viscous film]]. J. Fluid Mech. 760, 407- 430. {{:papers:2014-trinh-wilson-stone-rigidplate.pdf|PDF}} **Trinh, P. H.**, Kim, H., Hammoud, N., Howell, P.D., Chapman, S.J. & Stone, H.A. 2014 [[http://dx.doi.org/10.1063/1.4876476|Curvature suppresses the Rayleigh-Taylor instability.]] Phys. Fluids. 26, 051704. {{:papers:2014-trinh-etal-cylinder.pdf|PDF}} **Trinh, P. H.** & Chapman, S. J. 2014 [[http://dx.doi.org/10.1017/jfm.2013.589|The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls.]] J. Fluid Mech. 741, 492-513. {{:papers:2014-trinh-chapman-nhull.pdf|PDF}} ==== 2013 publications ==== **Trinh, P. H.** & Chapman, S. J. 2013 [[http://dx.doi.org/10.1017/jfm.2013.110|New gravity-capillary waves at low speeds. Part 1: Linear theory.]] J. Fluid Mech. 724, 367–391. {{:papers:2013-trinh-chapman-gravlinear.pdf|PDF}} **Trinh, P. H.** & Chapman, S. J. 2013 [[http://dx.doi.org/10.1017/jfm.2013.129|New gravity-capillary waves at low speeds. Part 2: Nonlinear theory.]] J. Fluid Mech. 724, 392–424. {{:papers:2013-trinh-chapman-gravnonlinear.pdf|PDF}} Chapman, S. Jonathan, **Trinh, Philippe H.** & Witelski, Thomas P. 2013 [[http://dx.doi.org/10.1137/120872012|Exponential asymptotics for thin film rupture]]. SIAM Journal on Applied Mathematics 73 (1), 232–253. {{:papers:2013-chapman-trinh-witelski-rupture.pdf|PDF}} Wexler, J. S., **Trinh, P. H.**, Berthet, H., Quennouz, N., du Roure, Olivia, Huppert, H. E., Linder, A. & Stone, H. A. 2013 [[http://dx.doi.org/10.1017/jfm.2013.49|Bending of elastic fibres in viscous flows: the influence of confinement.]] J. Fluid Mech. 720, 517–544. {{:papers:2013-wexler-etal-fibre.pdf|PDF}} ==== Pre-2013 publications ==== **Trinh, P. H.**, Chapman, S. J. & Vanden-Broeck, J.-M. 2011 [[http://dx.doi.org/10.1017/jfm.2011.325|Do waveless ships exist? Results for single-cornered hulls]]. J. Fluid Mech. 685, 413–439. {{:papers:2011-trinh-chapman-vandenbroeck-1hull.pdf|PDF}} **Trinh, P. H.** 2010 [[https://www.springer.com/materials/mechanics/book/978-3-7091-0407-1|Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances]], chap. //Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves//, pp. 121–126. SpringerWienNewYork. {{:papers:2010-trinh-exponential.pdf|PDF}} **Trinh, P.** & Amundsen, D. 2010 [[http://dx.doi.org/10.1016/j.cam.2009.08.029|Unifying steady-state resonant solutions of a broad class of KdV-type equations]]. J. Comp. App. Math. 234 (6), 1788–1795. {{:papers:2010-trinh-amundsen-kdv.pdf|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. {{:papers:trinh_spotshort.pdf|PDF}} **Trinh, P. H.** 2010 [[http://ora.ox.ac.uk/objects/uuid%3Ae87b1f22-2569-4c0f-86a2-5bde76f34953|Exponential asymptotics and free-surface flows]]. PhD thesis, University of Oxford. **Trinh, P. H.**, Chapman, S. J. & Vanden-Broeck, J.-M. 2010 [[http://www.iwwwfb.org/Abstracts/iwwwfb25/iwwwfb25_45.pdf|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. */