New first- and second-order transport-diffusion dynamics with deterministic alternating shear flows converge to a given Gibbs measure at an enhanced O(ν^{1/2}) rate, faster than classical Langevin sampling at O(ν).
Mixing, Enhanced Dissipation and Phase Transition in the Kinetic Vicsek Model
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abstract
In this paper, we study the kinetic Vicsek model, which serves as a starting point for describing the polarization phenomena observed in the experiments of fibroblasts moving on liquid crystalline substrates. The long-time behavior of the kinetic equation is analyzed, revealing that, within specific parameter regimes, the mixing and enhanced dissipation phenomena stabilize the dynamics and ensure effective information communication among agents. Consequently, the solution exhibits features similar to those of a spatially-homogeneous system. As a result, we confirm the phase transition observed in the agent-based Vicsek model at the kinetic level.
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Sampling and Optimization meet Enhanced Flows
New first- and second-order transport-diffusion dynamics with deterministic alternating shear flows converge to a given Gibbs measure at an enhanced O(ν^{1/2}) rate, faster than classical Langevin sampling at O(ν).