A new model for self-organized dynamics and its flocking behavior

具有全对全交互核的欧拉型自组织系统弱解的无条件群集行为

Unconditional flocking for weak solutions to self-organized systems of Euler-type with all-to-all interaction kernel

本文证明一维全对全交互核欧拉型自组织系统，对任意BV初值，其全局熵弱解无需额外假设即无条件指数收敛到群集轮廓。

从 Cucker-Smale 型动力学集群模型到自组织流体动力学模型

From Kinetic Flocking Model of Cucker-Smale Type to Self-Organized Hydrodynamic model

本文针对带约束势的动力学 Cucker-Smale 模型，提出基于广义碰撞不变量（GCI）的 Hilbert 展开方法，严格建立其到自组织流体动力学模型的流体动力学极限，克服了线性化算子非对称和方向向量归一化非线性带来的困难。

Critical thresholds in flocking hydrodynamics\\with nonlocal alignment

We study the large-time behavior of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dynamics, e.g., Cucker-Smale and Motsch-Tadmor models \cite{CS,MT}. We prove that in analogy with the agent-based models, the presence of non-local alignment enforces \emph{strong} solutions to self-organize into a macroscopic flock. This then raises the question of existence of such strong solutions. We address this question in one- and two-dimensional setups, proving global regularity for \emph{sub-critical} initial …

Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights

We derive a sufficient condition for asymptotic flocking in the Cucker-Smale model with self-delay (also called reaction delay) and with non-symmetric interaction weights. The condition prescribes smallness of the delay length relative to the decay rate of the inter-agent communication weight. The proof is carried out by a bootstrapping argument combining a decay estimate for the group velocity diameter with a variant of the Gronwall-Halanay inequality.

Hydrodynamic limits for kinetic flocking models of Cucker-Smale type

We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The self-propelling and friction forces together with the alignment and the noise are interpreted as a collision/interaction mechanism acting with equal strength. We show that the set of generalized collision invariants, introduced in \cite{DM08}, is equivalent in our setting to the more classical notion of collision invariants, i.e., the kernel of a suitably linear…

Toner-Tu 模型的全局存在性与渐近稳定性

Global existence and asymptotic stability for the Toner-Tu model of flocking

本文解析研究了 Toner-Tu 流体动力学模型在有序相稳态解附近的全局适定性，证明解在 Sobolev 空间中多项式稳定，并探讨了肌动蛋白丝动力学变体。