Simple computation of reaction–diffusion processes on point clouds
Online Publication Date2013-05-20
Print Publication Date2013-06-04
Permanent link to this recordhttp://hdl.handle.net/10754/599619
MetadataShow full item record
AbstractThe study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.
CitationMacdonald CB, Merriman B, Ruuth SJ (2013) Simple computation of reaction–diffusion processes on point clouds. Proc Natl Acad Sci USA 110: 9209–9214. Available: http://dx.doi.org/10.1073/pnas.1221408110.
SponsorsC.B.M. thanks Dr. Chandrasekhar Venkataraman (University of Sussex) for useful discussions on bulk-coupled reaction-diffusion models. The work of C. B. M. was supported by Award KUK-C1-013-04 from King Abdullah University of Science and Technology (KAUST). The work of S.J.R. was partially supported by a Natural Sciences and Engineering Research Council of Canada Discovery Grant and by Award KUK-C1-013-04 from KAUST.
PubMed Central IDPMC3677480
CollectionsPublications Acknowledging KAUST Support
- Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces.
- Authors: Dhillon DS, Milinkovitch MC, Zwicker M
- Issue date: 2017 Apr
- The surface finite element method for pattern formation on evolving biological surfaces.
- Authors: Barreira R, Elliott CM, Madzvamuse A
- Issue date: 2011 Dec
- A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction-Diffusion Equations on Surfaces.
- Authors: Shankar V, Wright GB, Kirby RM, Fogelson AL
- Issue date: 2016 Jun 1
- The geometry and motion of reaction-diffusion waves on closed two-dimensional manifolds.
- Authors: Grindrod P, Gomatam J
- Issue date: 1987
- Sparse dynamics for partial differential equations.
- Authors: Schaeffer H, Caflisch R, Hauck CD, Osher S
- Issue date: 2013 Apr 23