传输-凝聚-成核模型的稳态

Boundary value for a nonlinear transport equation emerging from a stochastic coagulation-fragmentation type model

We investigate the connection between two classical models of phase transition phenomena, the (discrete size) stochastic Becker-Döring, a continous time Markov chain model, and the (continuous size) deterministic Lifshitz-Slyozov model, a nonlinear transport partial differential equation. For general coefficients and initial data, we introduce a scaling parameter and prove that the empirical measure associated to the stochastic Becker-Döring system converges in law to the weak solution of the Lifshitz-Slyozov equation when the parameter goes to 0. Contrary to previous studies, we use a weak to…

Long-time asymptotics for polymerization models

This study is devoted to the long-term behavior of nucleation, growth and fragmentation equations, modeling the spontaneous formation and kinetics of large polymers in a spatially homogeneous and closed environment. Such models are, for instance, commonly used in the biophysical community in order to model in vitro experiments of fibrillation. We investigate the interplay between four processes: nucleation, polymeriza-tion, depolymerization and fragmentation. We first revisit the well-known Lifshitz-Slyozov model, which takes into account only polymerization and depolymerization, and we show t…

微管形成反应对流扩散方程稳态的存在性与稳定性

Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation

本文推广了微管动力学的Dogterom-Leibler模型，考虑GTP-微管蛋白浓度对伸长速率及伸长/缩短相寿命的影响，并引入阻尼项形式的成核速率，研究边界条件下稳态的存在性与稳定性，首次将Evans函数数值与解析计算作为微管动力学研究的新数学工具。

计算大小结构化种群模型稳态及其稳定性的数值框架

A numerical framework for computing steady states of size-structured population models and their stability

本文提出一种计算一般演化方程稳态近似解的数值框架，用于研究稳态的存在性和稳定性，并通过线性Sinko-Streifer模型和非线性种群平衡方程验证其有效性。

Superfluids Passing an Obstacle and Vortex Nucleation

We consider a superfluid described by the Gross-Pitaevskii equation passing an obstacle \[ε^2 Δu+ u(1-|u|^2)=0 \ \mbox{in} \ {\mathbb R}^d \backslash Ω, \ \ \frac{\partial u}{\partial ν}=0 \ \mbox{on}\ \partial Ω\] where $ Ω$ is a smooth bounded domain in $ {\mathbb R}^d$ ($d\geq 2$), which is referred as the obstacle and $ ε>0$ is sufficiently small. We first construct a vortex free solution of the form $ u= ρ_ε(x) e^{i \frac{Φ_ε}ε}$ with $ ρ_ε(x) \to 1-|\nabla Φ^δ(x)|^2, Φ_ε(x) \to Φ^δ(x) $ where $Φ^δ(x)$ is the unique solution for the subsonic irrotational flow equation \[ \nabla ( (1-|\nab…