Existence of a Weak Solution for the Phase Change Problem with Joule's Heating

A phase change problem with Joule's heat ing describes tbe processes of electric heating in a conducting material. It is modeled as a coupled system of nonlinear partial differential equations with quadratic growth in the gradient. We establish the existence of a weak solution for the problem in two dimensions.     

基于VOF方法的带相变的自由界面的计算

对于气液自由界面上存在相变(蒸发、沸腾或凝结)的情况,由于此时不仅物性分布是不连续的,速度场也发生了不连续,这无论对于捕捉或追踪自由界面的算法本身还是流场的求解都带来了一定的困难.本文提出一种基于VOF方法的计算带相变的自由界面的算法,对这种情况下的关键问题一速度场的不连续性给出了解决方法.并用编制的二维程序计算了水平壁面上的膜态沸腾,并将计算结果与理论公式进行了比较.     

Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system

We consider a model for the flow of a mixture of two viscous and incompressible fluids in a two or three dimensional channel-like domain. The model consists of the Navier-Stokes equations governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids. We prove the instability of certain stationary solutions for such a system endowed with periodic boundary conditions on elongated domains (0,2π/α₀)×(0,2π) or (0,2π/α₀)×(0,2π)×(0,2π/β₀) for a special class of periodic body forces, provided that α₀ and β₀ are small enough. As a consequence, we deduce a lower bound for the Hausdorff dimension of the global attractor.     

Adaptive extremal optimization by detrended fluctuation analysis

Global optimization is one of the key challenges in computational physics as several problems, e.g. protein structure prediction, the low-energy landscape of atomic clusters, detection of community structures in networks, or model-parameter fitting can be formulated as global optimization problems. Extremal optimization (EO) has become in recent years one particular, successful approach to the global optimization problem. As with almost all other global optimization approaches, EO is driven by an internal dynamics that depends crucially on one or more parameters. Recently, the existence of an optimal scheme for this internal parameter of EO was proven, so as to maximize the performance of the algorithm. However, this proof was not constructive, that is, one cannot use it to deduce the optimal parameter itself a priori. In this study we analyze the dynamics of EO for a test problem (spin glasses). Based on the results we propose an online measure of the performance of EO and a way to use this insight to reformulate the EO algorithm in order to construct optimal values of the internal parameter online without any input by the user. This approach will ultimately allow us to make EO parameter free and thus its application in general global optimization problems much more efficient.     

The convergence of conjugate gradient method with nonmonotone line search

The conjugate gradient method is a useful and powerful approach for solving large-scale minimization problems. Liu and Storey developed a conjugate gradient method, which has good numerical performance but no global convergence under traditional line searches such as Armijo line search, Wolfe line search, and Goldstein line search. In this paper we propose a new nonmonotone line search for Liu-Storey conjugate gradient method (LS in short). The new nonmonotone line search can guarantee the global convergence of LS method and has a good numerical performance. By estimating the Lipschitz constant of the derivative of objective functions in the new nonmonotone line search, we can find an adequate step size and substantially decrease the number of functional evaluations at each iteration. Numerical results show that the new approach is effective in practical computation.     

Gauge invariance,charge conservation,and variational principles

We present new results on the correspondence between symmetries, conservation laws and variational principles for field equations in general non-abelian gauge theories. Our main result states that second order field equations possessing translational and gauge symmetries and the corresponding conservation laws are always derivable from a variational principle. We also show by the way of examples that the above result fails in general for third order field equations.     

Laser-effected darkening in TPEs with TiO2 additives

Investigations were carried out for laser-effected darkening and damage-free laser marking on thermoplastic elastomers (TPEs). Titanium dioxide (TiO₂) was studied as the laser-sensitive additive to the TPEs for its role in enhancing laser marking contrast and its effect on the TPE properties. Laser beam characteristics, processing variables and percentage loading of TiO₂ in the TPEs were found to have significant effect on the marking contrast. Surface damage-free and high contrast marking have been achieved with short pulse UV lasers. The laser-effected darkening was found to penetrate into the material in the order of a few tens of microns. XPS analysis was carried out to understand the laser-effected darkening mechanism. Potential applications of the technique are highlighted.     

The eigenvalue complementarity problem

In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming Problem with Complementarity Constraints and a Global Optimization Problem. A finite Reformulation–Linearization Technique (Rlt)-based tree search algorithm is introduced for processing the EiCP via the lattermost of these formulations. Computational experience is included to highlight the efficacy of the above formulations and corresponding techniques for the solution of the EiCP.     

Integro-differential equations of hyperbolic type with positive definite kernels

The main purpose of this work is to study the damping effect of memory terms associated with singular convolution kernels on the asymptotic behavior of the solutions of second order evolution equations in Hilbert spaces. For kernels that decay exponentially at infinity and possess strongly positive definite primitives, the exponential stability of weak solutions is obtained in the energy norm. It is also shown that this theory applies to several examples of kernels with possibly variable sign, and to a problem in nonlinear viscoelasticity.