Traveling pulse solutions in a point mass model of diffusing particles

Elliott Ginder^1,3, Takaaki Minomo², Masaharu Nagayama^2,4, Satoshi Nakata⁵, Hiroya Yamamoto⁵

¹School of Interdisciplinary Mathematical Sciences, Meiji University, Tokyo, Japan.

²Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan.

³PRESTO, Japan Science and Technology Agency, Tokyo, Japan.

⁴CREST, Japan Science and Technology Agency, Tokyo, Japan.

⁵Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Japan.

DOI:

https://doi.org/10.7494/cmms.2017.2.0595

Abstract:

We study a partial differential equation modeling the self-motion of camphor particles atop a water surface. The model equation is presented in the form of a reaction-diffusion system where source terms are expressed by delta functions. The resulting system is a point mass model for diffusing particles, where the role of the delta functions is to express camphor source locations. In our model, point sources interact with each other and move by the gradient of the concentration field. We will discuss analytical properties of the model equation. In particular, we will study properties of traveling pulse solutions, whose existence are reduced to the solution of an ordinary differential equation, coupled with a boundary value problem. The existence and stability of solutions will be shown and we will compare our findings with those which have utilized characteristic function source terms.

Cite as:

Ginder, E., Minomo, T., Nagayama, M., Nakata, S., Yamamoto, H. (2017). Traveling pulse solutions in a point mass model of diffusing particles. Computer Methods in Materials Science, 17(2), 111 – 121. https://doi.org/10.7494/cmms.2017.2.0595

Article (PDF):

Keywords:

Camphor model, Dirac delta function, Self-motion

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