| Abstract: |
| Although many mathematical models of self-propelled motion have been proposed, they are typically constructed for specific types of objects, resulting in separate formulations for different target systems. To date, no mathematical model has been established that can uniformly describe self-propelled motion across a wide range of systems, from solid objects to liquid droplets. As a first step toward a comprehensive theoretical understanding of self-propelled motion, it is therefore essential to formulate a unified set of equations capable of describing such phenomena. In this study, we propose a mathematical model that could describe self-propelled motion from liquid droplets to solid objects within a single framework. The proposed model consists of a coupled system of a phase-field equation, derived from the L2 gradient-flow structure, and a concentration-field equation. This formulation enables the description of deformable droplet motion as well as circular solid-like motion. Furthermore, by introducing a spatially inhomogeneous function into the potential term, the model can reproduce self-propelled motions with more complex shapes, such as elliptical and dumbbell-like structures. In this presentation, we investigate solid-like motions observed in the proposed model through numerical simulations and compare the results with those of previous studies and experimental observations. |
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