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    Simple computation of reaction–diffusion processes on point clouds

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    Type
    Article
    Authors
    Macdonald, Colin B.
    Merriman, Barry
    Ruuth, Steven J.
    KAUST Grant Number
    KUK-C1-013-04
    KUK-C1-013-04
    Date
    2013-05-20
    Online Publication Date
    2013-05-20
    Print Publication Date
    2013-06-04
    Permanent link to this record
    http://hdl.handle.net/10754/599619
    
    Metadata
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    Abstract
    The 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.
    Citation
    Macdonald 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.
    Sponsors
    C.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.
    Publisher
    Proceedings of the National Academy of Sciences
    Journal
    Proceedings of the National Academy of Sciences
    DOI
    10.1073/pnas.1221408110
    PubMed ID
    23690616
    PubMed Central ID
    PMC3677480
    ae974a485f413a2113503eed53cd6c53
    10.1073/pnas.1221408110
    Scopus Count
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