Development of three dimensional constitutive theories based on lower dimensional experimental data

Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate of entropy production, etc. In this paper we show different choices for the manner in which the body stores energy and dissipates energy and satisfies the requirement of maximization of the rate of entropy production that can all describe the same experimental data. All of these three dimensional models, in one dimension, reduce to the model proposed by Burgers to describe the viscoelastic behavior of bodies.      

A thermodynamic framework for a mixture of two liquids

In this study, we extend a thermodynamic framework that has been used with some success for describing the response of a variety of single constituent continua. Using the thermodynamic framework, we obtain a model for the mixture of two compressible fluids that has a much simpler structure than the model obtained earlier within the context of mixture theory. We also investigate the response of a mixture of two fluids that is constrained to have a constant volume, using the same thermodynamic framework.     

On the Classical Necessary Second-Order Optimality Conditions

In this paper, the property of a necessary second-order optimality condition to hold with the same Lagrange multiplier for all critical vectors is investigated. It is limited to nonconvex optimization Problems in ⁿ with equality and inequality constraints; the Mangasarian-Fromovitz constraint qualification is assumed to be hold. A counterexample was given recently by Anitescu. We give some sufficient conditions and we prove that this property holds if n 2 or if the number of active inequality constraints is at most two. For three active inequality constraints and n =3, a counterexample is given.     

非线性优化修正Frisch函数方法的乘子映射

对于同时含有等式与不等式约束的非线性优化问题的修正Frisch函数方法,给出其乘子映射和解映射的导数的估计.将得到的估计用于建立修正Frisch函数方法的线性收敛速率.在线性无关的约束规范,严格互补条件和二阶充分性条件成立的前提下,证得该收敛率与1/c成正比.本文的收敛性分析依赖于矩阵的奇异值分解,其方法可以用来分析其他的修正Lagrange方法.