Hypocoercivity 和非线性产生-复合模型的反应-扩散极限

Hypocoercivity and Fast Reaction Limit for Linear Reaction Networks with Kinetic Transport

The long time behavior of a model for a first order, weakly reversible chemical reaction network is considered, where the movement of the reacting species is described by kinetic transport. The reactions are triggered by collisions with a nonmoving background with constant temperature, determining the post-reactional equilibrium velocity distributions. Species with different particle masses are considered, with a strong separation between two groups of light and heavy particles. As an approximation, the heavy species are modeled as nonmoving. Under the assumption of at least one moving species…

Hypocoercivity for a BGK model for gas mixtures

We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we can prove exponential relaxation to equilibrium with explicit rates. Our strategy is based on the entropy and spectral methods adapting Lyapunov's direct method as presented in [Achleitner-Arnold-Carlen, 2016] for the one species linearized BGK model. In comparison to the one species case, we start with two partial differential equations, one for each species…

一个动力学反应模型：衰减到平衡和宏观极限

A kinetic reaction model: decay to equilibrium and macroscopic limit

我们提出了一个动力学弛豫模型来描述两个物种的生成-复合反应。本文用两种最近的方法研究了线性化方程的衰变过程，证明了线性化方程的假充性。对于完全非线性问题，可以显示小扰动的指数衰减。宏观/快反应极限严格采用熵衰减，导致在一个非线性扩散方程的位置密度的差异。

Uniform convergence to equilibrium for a family of drift-diffusion models with trap-assisted recombination and the limiting Shockley--Read--Hall model

We consider a family of drift-diffusion-recombination systems, where the recombination of electrons and holes is facilitated by an intermediate energy-level for electrons in so-called trapped states. In particular, it has been proven in [GMS07] that the associated quasi-stationary state limit of an instantaneously fast trapped dynamics yields the famous Shockley--Read-Hall model for electron and hole recombination in semiconductor devices. The main result of this paper proves exponential convergence to equilibrium uniformly in the fast reaction limit for the drift-diffusion-recombination syste…

激子光伏双层膜的漂移-扩散-反应模型：渐近分析和二维HDG有限元格式

A Drift-Diffusion-Reaction Model for Excitonic Photovoltaic Bilayers: Asymptotic Analysis and A 2-D HDG Finite-Element Scheme

我们提出并讨论了双层有机光伏器件工作的数学模型。我们的模型耦合漂移扩散复合方程的电荷载流子（特别是，电子和空穴）与反应扩散方程的激子/极化子对和泊松方程的自洽静电势。形成双层器件的两个有机衬底的材料差（即HOMO/LUMO间隙）被包括作为功函数势。首先，我们对一维定态系统进行了渐近分析，i）重点是界面上的动力学，ii）目标是简化界面的体动力学。其次，我们提出了一个二维的混合间断有限元数值方案，这是非常适合解决i）的材料变化，ii）由此产生的强烈变化的接口和iii）必要的迎风离散的漂移-扩散方程。最后，我们比较了数值结果与近似渐近性。