论文标题
fokker-planck方程的粗透明，并具有排除体积效应，以保留梯度流结构
Coarse graining of a Fokker-Planck equation with excluded volume effects preserving the gradient-flow structure
论文作者
论文摘要
从微观到宏观模型的梯度流结构的传播是一个高电流兴趣的话题。在本文中，我们在模型中讨论了这种传播，以通过硬核排除或短距离排斥势相互作用的颗粒的扩散。我们将微观模型提出为瓦斯恒星度量中的高维梯度流，用于适当的自由能函数。然后，我们使用JKO方法来识别单个粒子密度在小粒子体积极限的最低级数，通过匹配的渐近扩张，超出了单个粒子密度的最低级数。虽然我们在远距离使用混乱假设的传播时，我们考虑了扩展中较小距离的相关性。通过这种方式，我们可以清楚地了解宏观梯度结构的出现，该结构因体积排除而在自由能功能中均包含校正。
The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper we discuss this propagation in a model for the diffusion of particles interacting via hard-core exclusion or short-range repulsive potentials. We formulate the microscopic model as a high-dimensional gradient flow in the Wasserstein metric for an appropriate free-energy functional. Then we use the JKO approach to identify the asymptotics of the metric and the free-energy functional beyond the lowest order for single particle densities in the limit of small particle volumes by matched asymptotic expansions. While we use a propagation of chaos assumption at far distances, we consider correlations at small distance in the expansion. In this way we obtain a clear picture of the emergence of a macroscopic gradient structure incorporating corrections in the free energy functional due to the volume exclusion.
