Dislocation Transport in Single Crystals and Dislocation-based Micromechanical Hardening

The higher-dimensional kinematical dislocation continuum theory of Hochrainer (2006) and a homogenized version thereof by Hochrainer, Zaiser and Gumbsch (2010) are reviewed. A three-dimensional Finite Element solution of the homogenized theory is presented, interpreted physically and compared to the results of the Geometrically Necessary Dislocations theory. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational Evolution of Dislocations in Single Crystals

Journal of Nonlinear Science - In this paper, we provide an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal. The variational problem...     

A Continuum Theory of Dislocations for Single Crystals

The kinematics of oriented media is discussed with referenceto continuous distributions of dislocations. Certain constitutiveassumptions are made which are appropriate to a dynamical theoryof plasticity for single crystals. The theory is illustratedby a simple example in which the deformation is infinitesimal.     

From Dislocation Motion to an Additive Velocity Gradient Decomposition, and Some Simple Models of Dislocation Dynamics

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a ``small deformation" setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived. In the finite deformation setting, it is shown that an additive decomposition of the total velocity gradient into elastic and plastic parts emerges naturally from a micromechanical starting point that involves no notion of plastic deformation but only the elastic distortion, material velocity, dislocation density and the dislocation velocity. Moreover, a plastic spin tensor emerges naturally as well.     

Exact Simple Waves on Shear Flows in a Compressible Barotropic Medium

Self-similar solutions describing simple waves on shear flows in a finite compressible barotropic atmosphere are found. These include the simple waves on shear flows in water as a special case. By making use of a number of transformations it becomes possible to write these solutions in an exact form. This form, though not explicit, is similar to the incomplete Beta function which seems to characterize this class of nonlinear physical problems.     

简单剪切有限塑性内时理论分析

在有限塑性内时理论中引入Jaumann率、广义Jaumann率、扶率及Wu率,并以此分析了简单剪切大变形问题．结果验证了简单剪切变形中,采用次弹性或内时刚塑性材料的Jaumann率客观模型,随单调递增的剪切变形剪切应力和法向应力都会出现振荡现象．这说明振荡现象的出现不取决于弹塑性模型,而与选取不同的客观率有很大的关系．同时指出在简单剪切大变形时,法向应力并不为零．     

Domain Structure of Bulk Ferromagnetic Crystals in Applied Fields Near Saturation

We investigate the ground state of a uniaxial ferromagnetic plate with perpendicular easy axis and subject to an applied magnetic field normal to the plate. Our interest is in the asymptotic behavior of the energy in macroscopically large samples near the saturation field. We establish the scaling of the critical value of the applied field strength below saturation at which the ground state changes from the uniform to a multidomain magnetization pattern and the leading order scaling behavior of the minimal energy. Furthermore, we derive a reduced sharp interface energy, giving the precise asymptotic behavior of the minimal energy in macroscopically large plates under a physically reasonable assumption of small deviations of the magnetization from the easy axis away from domain walls. On the basis of the reduced energy and by a formal asymptotic analysis near the transition, we derive the precise asymptotic values of the critical field strength at which non-trivial minimizers (either local or global) emerge. The non-trivial minimal energy scaling is achieved by magnetization patterns consisting of long slender needle-like domains of magnetization opposing the applied field.     

Mathematical Modeling of Czochralski Type Growth Processes for Semiconductor Bulk Single Crystals

This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e. g., silicon (Si) or gallium arsenide (GaAs) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations. In this paper, we describe a mathematical model that is under use for the simulation of real-life growth scenarios, and we give an overview of mathematical results and numerical simulations that have been obtained for it in recent years.     

The Endomorphism Structure of Simple Faithful S-acts

   Communicated by     

Structure of Nonunital Purely Infinite Simple Rings

In this note, we study the notion of purely infinite simple ring in the case of nonunital rings, and we obtain an analog to Zhang's Dichotomy for σ-unital purely infinite simple C*-algebras in the purely algebraic context.     

自由剪切流大尺度结构的二次稳定性*

本文用二次稳定性理论研究自由剪切湍流中周期性基本流空间增长扰动的稳定性。数值结果表明三维亚谐扰动对横向波数有很强的选择性,二维亚谐波的空间增长率最大。与之相反,基本模式的三维扰动在很大的波数范围内存在不稳定性,证明β=0时存在“转移”不稳定性;当KH波的幅值A≥0.06时出现分叉现象。     

Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations

Galerkin (spectral) methods are explored for the numerical simulation of incompressible flows within simple boundaries. A major part of the paper is devoted to the development of transform methods for efficient simulation of flows in box geometries with periodic and free-slip boundary conditions. Techniques for incorporating known symmetries and invariances into transform methods are illustrated for the Taylor-Green vortex. Galerkin methods for accurate and efficient representation of rigid no-slip boundary conditions are also explained. A class of pseudospectral approximations is introduced in order to handle more complicated dynamical interactions in more complicated geometries. Later papers in this series will demonstrate the important advantages of spectral methods over finite-difference methods for simulation of many of the flows of current interest and will present specific numerical results for various transition and turbulent flows.     

一种简单神经Mealy机的构造

构造一种新型神经Mealy机,神经Mealy机具有一定的学习能力,它主要通过学习来获得(von Newman)计算机结构,可以较好地避免普通计算机那样损毁一条电路就带来灾难性后果的情况.其本质是将递归神经网络通过BP优化算法,对Mealy机进行模拟得到,并通过实验对该网络的学习性能进行研究分析.基于形式文法和自动机的等价性,用神经网络来实现文法推导.先采用神经网络对样本集进行学习,这些样本可由一个经典Mealy机生成,然后从训练完的神经网络提取出自动机.     

DNA序列中的结构与简化模型

本文简述 2 0 0 0年全国大学生数学建模竞赛 A题的科学研究背景 ,以及题目的立意和设计 .进而对解答 A题的大学生们的出色方法进行介绍与评述     

On Boundary-Value Problems for the Laplacian in Bounded Domains with Micro Inhomogeneous Structure of the Boundaries

We consider boundary-value problems with rapidly alternating types of boundary conditions. We present the classification of homogenized （limit） problems depending on the ratio of small parameters, which characterize the diameter of parts of the boundary with different types of boundary conditions. Also we study the respective spectral problem of this type.     

关于内7-闭单群的结构

研究内ｐ－闭群的结构是一个很活跃的课题．对于ｐ＝２，３，５的内ｐ－闭群的结构已经被确定（见［１，２，３］）．本文确定内７－闭单群的结构     

横观各向同性电磁弹性介质中裂纹对SH波的散射

研究横观各向同性电磁弹性介质中裂纹和反平面剪切波之间的相互作用．根据电磁弹性介质的平衡运动微分方程、电位移和磁感应强度微分方程,得到SH波传播的控制场方程．引入线性变换,将控制场方程简化为Helmholtz方程和两个Laplace方程A·D2通过Fourier变换,并采用非电磁渗透型裂面边界条件,得到了柯西奇异积分方程组．利用Chebyshev多项式求解积分方程,得到应力场、电场和磁场以及动应力强度因子的表达,并给出了数值算例．     

Boundaries of varieties in projective manifolds

We give a characterization of the boundaries of holomorphic chains in complex projective space. This extends previous work of the authors and complements results of Dolbeault and Henkin.     

The S-Matrix and Acoustic Signal Structure in Simple and Compounds Waveguides

AMS(MOS) 35P25 Secondary: 76Q05