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The dynamics of weakly interacting fronts in an adsorbate-induced phase transition model

Shin-Ichiro Ei;  Tohru Tsujikawa — 2009

Kybernetika

Hildebrand et al. (1999) proposed an adsorbate-induced phase transition model. For this model, Takei et al. (2005) found several stationary and evolutionary patterns by numerical simulations. Due to bistability of the system, there appears a phase separation phenomenon and an interface separating these phases. In this paper, we introduce the equation describing the motion of two interfaces in ℝ 2 and discuss an application. Moreover, we prove the existence of the traveling front solution which approximates...

Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats

Shin-Ichiro Ei;  Kota Ikeda;  Masaharu Nagayama;  Akiyasu Tomoeda — 2014

Mathematica Bohemica

Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices to investigate a linearized...

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