Minimizing movement scheme for intrinsic aggregation on compact Riemannian manifolds

黎曼流形上的自组织

Self-organization on Riemannian manifolds

我们考虑一个聚集模型，它包括一个积极的宏观人口密度的传输方程，其中的速度有一个非局部的功能依赖的密度，通过相互作用势建模。我们建立了一般黎曼流形上的模型，并提供了一个框架，用于构建相互作用势，导致平衡是恒定的支持。我们认为这样的潜在的两个特定的情况下（二维球和二维双曲空间）和调查分析和数值的长期行为和平衡解决方案的聚集模型在这些流形上。与其他相互作用势的数值平衡。

晶格与连续模型对聚集扩散细胞运动的分析

Lattice and Continuum Models Analysis of the Aggregation Diffusion Cell Movement

本文研究了从离散模型构建连续模型的数学过程，分析了晶格上一类强化随机游走的奇异性极限，得出了连续模型的正则性估计，并探讨了初始数据对解行为的影响。

Well-posedness and asymptotic behaviour of an aggregation model with intrinsic interactions on sphere and other manifolds

We investigate a model for collective behaviour with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle approximation. We study the long-time behaviour of solutions to the model on sphere, where the primary goal is to establish sufficient conditions for a consensus state to form asymptotically. Well-posedness of solutions and the formation of consensus are also investigated for other manifolds (e.g., a hypercylinder).

Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities

We consider a phenotype-switching chemotaxis model for aggregation, in which a chemotactic population is capable of switching back and forth between a chemotaxing state (performing chemotactic movement) and a secreting state (producing the attractant). We show that the switching rate provides a powerful mechanism for controlling the densities of spontaneously emerging aggregates. Specifically, in two- and three-dimensional settings it is shown that when both switching rates coincide and are suitably large, then the densities of both the chemotaxing and the secreting population will exceed any …

不可压缩理想流体中刚体的运动作为测地流

The movement of a solid in an incompressible perfect fluid as a geodesic flow

本文证明浸没在三维有界域不可压缩理想流体中的刚体运动经典解，是无穷维黎曼流形的测地线，即流体-刚体系统总动能时间积分作用量的临界点。

具有空间记忆的耦合非局部 PDE-ODE 系统的动力学：适定性、稳定性与分岔分析

Dynamics of a coupled nonlocal PDE-ODE system with spatial memory: well-posedness, stability, and bifurcation analysis

本文研究耦合空间记忆地图的一维非局部反应–扩散–聚集 PDE-ODE 系统，证明适定性并分析线性稳定性与稳态分岔，揭示吸引/排斥机制、多峰聚集条件及种群骤降的临界点。