Dynamically Active Compartments Coupled by a Stochastically Gated Gap Junction

We analyze a one-dimensional PDE-ODE system representing the diffusion of signaling molecules between two cells coupled by a stochastically gated gap junction. We assume that signaling molecules diffuse within the cytoplasm of each cell and then either bind to some active region of the cell’s membrane (treated as a well-mixed compartment) or pass through the gap junction to the interior of the other cell. We treat the gap junction as a randomly fluctuating gate that switches between an open and a closed state according to a two-state Markov process. This means that the resulting PDE-ODE is stochastic due to the presence of a randomly switching boundary in the interior of the domain. It is assumed that each membrane compartment acts as a conditional oscillator, that is, it sits below a supercritical Hopf bifurcation. In the ungated case (gap junction always open), the system supports diffusion-induced oscillations, in which the concentration of signaling molecules within the two compartments is either in-phase or anti-phase. The presence of a reflection symmetry (for identical cells) means that the stochastic gate only affects the existence of anti-phase oscillations. In particular, there exist parameter choices where the gated system supports oscillations, but the ungated system does not, and vice versa. The existence of oscillations is investigated by solving a spectral problem obtained by averaging over realizations of the stochastic gate.     

Asymptotic Solution of a Model Non-linear Convective Diffusion Equation

In this paper we consider the large-time solution of the equation for initial data with compact support. With m = 4 and n = 3the equation models the flow of a thin viscous sheet on an inclinedbed while for n m > 1 it has application in porous mediaflow under gravity. The equation can also be regarded as ananalogue of Burgers equation in non-linear diffusion. It isknown that two moving boundaries exist along which certain boundaryconditions are required to hold. The paper extends earlier workand determines the analytic behaviour of the moving boundariesexist along which certain boundary conditions are required tohold. The paper extends earlier work and determines the analyticbehaviour of the moving boundaries together with the structureof the solution which at large times is shown to depend cruciallyon the location in (n, m) parameter space.     

半导体中一维拟中性飘流扩散模型整体光滑解的渐近性

In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions(close to equilibrium)of the problem converge to the unique stationary solution.     

Diffusion of Dopant in Crystalline Silicon: An Asymptotic Analysis

An existing model of the diffusion of dopant in crystallinesilicon is presented. The model is used in predicting semiconductordevice properties. For small concentrations of dopant, the diffusionis linear. However, at large concentrations, enhanced diffusionoccurs. This may be modelled by a concentration-dependent diffusioncoefficient that is approximately constant at small concentrationsbut increases linearly at higher concentrations. The initialdistribution of implanted dopant is confined to a small regionof the crystal, and has a high peak concentration. This initialdistribution develops into a high-concentration region withadvancing steep fronts and decaying tail regions. In the enhancedregion, the dominant balance is given by the filtration equation,and the tail regions are dominated by quasi-steady convection—diffusion.These two regions are analysed and matched together, using singularperturbation theory.     

具扩散的生物控制模型的渐进性

讨论了具有空间扩散的生物控制系统在齐次Neumann边界条件下解的整体性态.通过线性化方法给出了局部渐近稳定条件,通过构造Lyapunov函数给出了全局稳定性的证明.     

High Concentration Arsenic Diffusion in Crystalline Silicon: An Asymptotic Analysis

For fairly high concentrations, the effective arsenic diffusioncoefficient is known to grow linearly with the concentration.In this paper, we consider the strongly enhanced diffusion ofarsenic by asymptotic methods, and extend the results of a previouspaper (King & Please, 1987) in three ways: we characterizean additional (low-concentration) region; we consider the influenceof the initial data; and we consider the case of constant surfaceconcentration.     

一个带有小参数的二维椭圆方程的渐近性分析

通过数值方法研究在边界充分(逐段)光滑区域上的带有小参数的二维椭圆方程在部分Dirichlet边界控制下的渐近性问题.对于一维的情形求解析解的结果,对高维问题提出类似的问题.但高维问题解析求解一般不可能,因此采用数值分析的方法.数值结果表明,在所选的条件下,边界值对小常数仍然不是解析的.     

Stochastic Asymptotic Stability of Nowak-May Model with Variable Diffusion Rates

We consider a stochastically perturbed Nowak-May model of virus dynamics within a host. We prove the global existence of unique strong solution. Using the Lyapunov method, we found sufficient conditions for the stochastic asymptotic stability of equilibrium solutions of this model.     

Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors

The well-posedness of smooth solution to a 3-Dsimplified Energy-Transport model is discussed in this paper. We prove the local existence, uniqueness, and asymptotic behavior of solution to the equations with hybrid cross-diffusion. The smooth solution convergences to a stationary solution with an exponential rate as time tends to infinity when the initial date is a small perturbation of the stationary solution.     

Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model

Methodology and Computing in Applied Probability - In this paper, we consider a convoluted smoothed nonparametric approach for the unknown coefficients of diffusion model based on high frequency...     

带利息力和干扰的批量索赔一般到达风险模型

本文在经典风险模型的基础上,将索赔到达过程推广为更新过程,索赔可以批量到达,且带有常数利息力和Brown运动干扰项,得到一个新的风险模型,运用Markov骨架过程的方法,得出盈余过程的瞬时分布和生存概率.     

Stability and Asymptotic Analysis of a Fluid-Particle Interaction Model

We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov–Fokker–Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.     

Modelling of Surfactant Concentration in a Coupled Bulk Surface Problem

Surface active agents (surfactants) are on high interest for physical and chemical industries. Their presence lowers the surface tension of fluids. This is used to achieve special flow properties. These mechanisms are not only influenced by the overall amount of surfactant. They highly depend on the local surfactant distribution. The surfactant concentration is modeled by two convection diffusion equations, one in the bulk and the other on its surface. Adsorption- and desorption processes are included and lead to a (non linear) coupling of both equations. We present a numerical scheme for solving the coupled problem. Additionally, first analytical results will be given. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation

The authors consider a free interface problem which stems from a gas-solid model in combustion with pattern formation. A third-order, fully nonlinear, self-consistent equation for the flame front is derived. Asymptotic methods reveal that the interface approaches a solution to the Kuramoto-Sivashinsky equation. Numerical results which illustrate the dynamics are presented.     

带干扰风险的破产模型的研究

本文对古典风险模型中保险公司按单位时间常数率收到保险费的假设做了改进,将每次收到的保险费的次数看作是复合泊松过程,将每次收到的保费和每次的理陪额均看作是服从指数分布的随机变量,并引入带干扰风险的扰动项,从而对古典风险模型进行推广,且给出了相应的破产概率上界,分析了破产概率的上界与准备金,索赔额,净保费和扰动方差之间的关系.     

一类带扩散的聚合物模型的定性分析

本文研究一类带扩散的聚合物模型,并在参数γ＞0和γ＜0两种不同情形给出定性分析.主要运用抛物型方程比较原理和相应常微分方程的结论得到反应扩散方程的先验估计和渐近性分析.     

A Stochastic Model for Transport of Particulate Matter in Air: An Asymptotic Analysis

A branching particle system with changes of size is considered as a model for transport of particulate matter in air. This type of model is motivated by problems arising in the context of air pollution. High-density fluctuation limits for the process recording the positions and sizes of the particles through time are presented. These results allow to compute approximate probabilities for the temporal and spatial concentrations of particles of given sizes (in particular the small-sized pollutant particles which pose a health hazard).     

重尾索赔下带干扰风险模型破产概率的局部解

著名的Embrechts-Goldie-Veraverbeke公式给出了在重尾索赔下Gramér-Lundberg风险模型关于破产概率的等价式,唐启鹤又给出了一个局部化的结果,本文将上述风险模型推广到带干扰的Gramér- Lundberg风险模型,得到了索赔分布F∈S~*时破产概率局部解的等价式．虽然[9]也得到了同样的结果,但是[9]中犯了概念性的错误,本文指出了该错误,然后给予了严格的证明．     

Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size

This Note presents the derivation of the 2nd-order asymptotic expansion of the eigenvalues and the eigenfunctions of the operator associated to an interior elliptic equation supplemented by a Dirichlet boundary condition on a domain consisting of two cavities linked by a hole of small size. The asymptotic expansion is carried out with respect to the size of the hole. The main feature of the method is to yield a robust numerical procedure making it possible to compute the eigenvalues without resorting to a refined mesh around the hole. To cite this article: A. Bendali et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).