Mathematical Analysis and Numerical Simulation of a Nonlinear Thermoelastic System

Abstract

In this paper, we give a theoretical and numerical analysis of a model for small vertical vibrations of an elastic membrane coupled with a heat equation and subject to linear mixed boundary conditions. We establish the existence, uniqueness, and a uniform decay rate for global solutions to this nonlinear non-local thermoelastic coupled system with linear boundary conditions. Furthermore, we introduced a numerical method based on finite element discretization in a spatial variable and finite difference scheme in time which results in a nonlinear system to be solved by Newton’s method. Numerical experiments for one-dimensional and two-dimensional cases are presented in order to estimate the rate of convergence of the numerical solution that confirm our analysis and show the efficiency of the method.     

A note on partial differential-difference equation

In this paper, we studied a certain partial differential-difference equation which arose from crystal precipitation modeling. The uniqu existence and asymptotic behaviors of the solution were shown     

食物受限人口模型中非线性延迟微分方程数值解的振动性

本文讨论食物受限人口模型中的一个非线性延迟微分方程数值解的振动性.通过应用两种θ-方法,即线性θ-方法和单腿θ-方法,构造指数θ-方法,得到数值解振动的条件,进一步考虑非振动解的渐近行为,最后给出两个数值算例.     

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.     

CHAOS EXPANSION OF LOCAL TIME OF FRACTIONAL BROWNIAN MOTIONS

We find the chaos expansion of local time ? _T ^(H)(x,·) of fractional Brownian motion with Hurst coefficient H∈(0,1) at a point x∈R ^d . As an application we show that when H ₀ d<1 then ? _T ^(H)(x,·)∈L ²(μ). Here μ denotes the probability law of B ^(H) and H ₀=max{H ₁,…,H _d }. In particular, we show that when d=1 then ? _T ^(H)(x,·)∈L ²(μ) for all H∈(0,1).     

Stationary Solution of a Stochastic Nosocomial Epidemic Model in Hospital Intensive Care Units

In this article, the authors consider a stochastic differential equation model of an antibiotic resistant infection epidemic in a hospital intensive care unit. A set of criteria on the existence of the stationary solution and its dynamical behavior are obtained. Numerical simulations are also performed to verify the results.     

Modeling of polycrystals with gradient crystal plasticity: A comparison of strategies

This paper treats the computational modeling of size dependence in microstructure models of metals. Different gradient crystal plasticity strategies are analyzed and compared. For the numerical implementation, a dual-mixed finite element formulation which is suitable for parallelization is suggested. The paper ends with a representative numerical example for polycrystals.     

Magnetic transition and large reversible magnetocaloric effect in EuCu1.75P2 compound

The magnetocaloric effect(MCE) in EuCu1.75P2 compound is studied by the magnetization and heat capacity measurements.Magnetization and modified Arrott plots indicate that the compound undergoes a second-order phase transition at TC ～ 51 K.A large reversible MCE is observed around TC.The values of maximum magnetic entropy change(-△SxMma) reach 5.6 J·kg-1·K-1 and 13.3 J·kg-1·K-1 for the field change of 2 T and 7 T,respectively,with no obvious hysteresis loss in the vicinity of Curie temperature.The corresponding maximum adiabatic temperature changes(△Tadmax) are evaluated to be 2.1 K and 5.0 K.The magnetic transition and the origin of large MCE in EuCu1.75P2 are also discussed.     

Phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls are investigated by using a cell dynamics simulation of the time-dependent Ginzburg-Landau theory.The morphological dependence of the wall-block interaction and the distance between walls(confinement degree) has been systematically studied,and the effect of repulsive interactions between different monomers is also discussed.It is interesting that multiple novel morphological transitions are observed by changing these factors,and various multilayered sandwich structures are formed in the mixture.Furthermore,the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed.From the simulation,we find that much richer morphologies can form in a binary mixture of diblock copolymers than those in a pure diblock copolymer.Our results provide an insight into the phase behaviors under parallel wall confinement and may provide guidance for experimentalists.This model system can also give a simple way to realize orientational order transition in soft materials through confinement.