Cluster Formation in Diffusive Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914121540173824 |
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| author | Leimkuhler, Benedict Lohmann, René Pavliotis, Grigorios A. Whalley, Peter A. |
| author_facet | Leimkuhler, Benedict Lohmann, René Pavliotis, Grigorios A. Whalley, Peter A. |
| contents | In this paper, we study the formation of clusters for stochastic interacting particle systems (SIPS) that interact through short-range attractive potentials in a periodic domain. We consider kinetic (underdamped) Langevin dynamics and focus on the low-friction regime. Employing a linear stability analysis for the kinetic McKean-Vlasov equation, we show that, at sufficiently low temperatures, and for sufficiently short-ranged interactions, the particles form clusters that correspond to metastable states of the mean-field dynamics. We derive the friction and particle-count dependent cluster-formation time and numerically measure the friction-dependent times to reach a stationary state (given by a state in which all particles are bound in a single cluster). By providing both theory and numerical methods in the inertial stochastic setting, this work acts as a bridge between cluster formation studies in overdamped Langevin dynamics and the Hamiltonian (microcanonical) limit. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_25034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cluster Formation in Diffusive Systems Leimkuhler, Benedict Lohmann, René Pavliotis, Grigorios A. Whalley, Peter A. Numerical Analysis Mathematical Physics Analysis of PDEs Probability In this paper, we study the formation of clusters for stochastic interacting particle systems (SIPS) that interact through short-range attractive potentials in a periodic domain. We consider kinetic (underdamped) Langevin dynamics and focus on the low-friction regime. Employing a linear stability analysis for the kinetic McKean-Vlasov equation, we show that, at sufficiently low temperatures, and for sufficiently short-ranged interactions, the particles form clusters that correspond to metastable states of the mean-field dynamics. We derive the friction and particle-count dependent cluster-formation time and numerically measure the friction-dependent times to reach a stationary state (given by a state in which all particles are bound in a single cluster). By providing both theory and numerical methods in the inertial stochastic setting, this work acts as a bridge between cluster formation studies in overdamped Langevin dynamics and the Hamiltonian (microcanonical) limit. |
| title | Cluster Formation in Diffusive Systems |
| topic | Numerical Analysis Mathematical Physics Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2510.25034 |