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In the singularly perturbed limit corresponding to an asymptotically large diffusion ratio between two components, many reaction-diffusion (RD) systems will admit quasi-equilibrium spot patterns, where the concentration of one component will be localized at a discrete set of points in the domain. In this paper, we derive and study the differential algebraic… (More)

A new class of point-interaction problem characterizing the time evolution of spatially localized spots for reaction-diffusion (RD) systems on the surface of the sphere is introduced and studied. This problem consists of a differential algebraic system (DAE) of ODE's for the locations of a collection of spots on the sphere, and is derived from an asymptotic… (More)

- Philippe H. Trinh, David E. Amundsen
- J. Computational Applied Mathematics
- 2010

- S. Jonathan Chapman, Philippe H. Trinh, Thomas P. Witelski
- SIAM Journal of Applied Mathematics
- 2013

The formation of singularities in models of many physical systems can be described using self-similar solutions. One particular example is the finite-time rupture of a thin film of viscous fluid which coats a solid substrate. Previous studies have suggested the existence of a discrete, countably infinite number of distinct solutions of the nonlinear… (More)

In the singularly perturbed limit corresponding to a large diffusivity ratio between two 9 components in a reaction-diffusion (RD) system, quasi-equilibrium spot patterns are often admitted, 10 producing a solution that concentrates at a discrete set of points in the domain. In this paper, we derive 11 and study the differential algebraic equation (DAE)… (More)

- Philippe H Trinh
- Proceedings. Mathematical, physical, and…
- 2016

The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of… (More)

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