Growth of clusters in a first-order phase transition

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59T _c, whereT _c is the critical temperature, and the concentration of minority atoms was=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc ₁(1-)³ w(t),c ₁ (1–)⁴ Q _l w(t)^l(2l10); wherec _l is the concentration of clusters of sizel;Q ₂,...,Q ₁₀ are known constants, the cluster partition functions;t is the time; andw(t)=0.015(1+7.17t ^–1/3). The distribution of large clusters (l20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c _l ,(t)=–(d/dl) [lnt+p (l/t)], where is a function given by those authors and is defined by(x)=C _o e–x-C ₁ e ^–4x/3-C ₂ e ^–5x/3;C ₀,C ₁,C ₂ are constants determined by considering how the total number of particles in large clusters changes with time.Supported by the U.S. Air Force Office of Scientific Research under Grant No. 78-3522 and by the U.S. Department of Energy under Contract No. EY-76-C-02-3077*000.     

Inverse optimization for linearly constrained convex separable programming problems

In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem, and when the answer is positive, find the parameter values that have the smallest adjustments. A sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values. Inverse optimization formulations are presented with ℓ₁ and ℓ₂ norms. These inverse optimization problems are either linear programming when ℓ₁ norm is used in the formulation, or convex quadratic separable programming when ℓ₂ norm is used.     

A Ferroelectric Frequency-Doubling Material-Potassium Lithium Niobate

The potassium lithium niobate crystals have been grown up. The shapes of solid-melt interfaces which maintaining the steady growth of the potassium lithium niobate crystals have been described. The optical transmission spectrum of the crystal has been surveyed. The perfected crystals showed good Second Harmonic Generation properties.     

The complementary unboundedness of dual feasible solution sets in convex programming

F.E. Clark has shown that if at least one of the feasible solution sets for a pair of dual linear programming problems is nonempty then at least one of them is both nonempty and unbounded. Subsequently, M. Avriel and A.C. Williams have obtained the same result in the more general context of (prototype posynomial) geometric programming. In this paper we show that the same result is actually false in the even more general context of convex programming — unless a certain regularity condition is satisfied.We also show that the regularity condition is so weak that it is automatically satisfied in linear programming (prototype posynomial) geometric programming, quadratic programming (with either linear or quadratic constraints),l _p -regression analysis, optimal location, roadway network analysis, and chemical equilibrium analysis. Moreover, we develop an equivalent regularity condition for each of the usual formulations of duality.Research sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR-73-2516.     

Proof of gridlock in a polymer model

It has been suggested that some lattice models of polymers, especially ones that incorporate more realistic excluded volume interactions extending to further neighbors, may be subject to gridlock. A model is defined to have the property of gridlock if it cannot melt at any temperature unless a density decrease is allowed. Classical theories of polymer melting are incompatible with the property of gridlock. This paper proves rigorously that a two-dimensional square-lattice model of polymer chains that have nearest-neighbor excluded volume interactions (called the X1S model) has the gridlock property. The proof uses elementary concepts from graph theory. Also, different interpretations of the X1S model are given in terms of real polymers. This leads to a discussion of a number of different classes of melting depending upon whether the intramolecular rotameric energies and the attractive intermolecular energies are antagonistic to or supportive of the melting transition.     

摄动有限体积法重构近似高精度的意义

研讨有限体积(FV)方法重构近似高精度的作用问题.FV方法中积分近似采用中点规则为二阶精度时,重构近似高精度(精度高于二阶)的意义和作用是一个有争议的问题.利用数值摄动技术[1,2]构造了标量输运方程的积分近似为二阶精度、重构近似为任意阶精度的迎风型和中心型摄动有限体积(PFV)格式.迎风PFV格式无条件满足对流有界准则(CBC),中心型PFV格式为正型格式,两者均不会产生数值振荡解.利用PFV格式求解模型方程的数值结果表明:与一阶迎风和二阶中心格式相比,PFV格式精度高、对解的间断分辨率高、稳定性好、雷诺数的适用范围大,数值地"证实"重构近似高精度和PFV格式的实际意义和好处.     

表面人工低维结构的功能设计与构造

可控地构造具有一定功能的表面人工低维结构,并且总结、理解体系微观结构对其宏观性质影响的一般规律,不仅对探索低维基本物理以及其中的新奇量子现象至关重要,更是微电子工业保持持续发展的关键前提.这方面的研究包括发展新的生长技术实现对体系形成过程的精确控制,对获得的材料做高分辨率的表征;从理论上则要理解体系的生长过程,阐明热力学、动力学的作用机理,从而指导制备技术的发展.深入研究表面人工低维结构的性质更可能导致新物理现象与原理的发现,产生全新的器件概念,进一步反馈给体系功能的设计,推动基础研究与应用探索的发展.文章简要介绍了表面物理国家重点实验室近年来在表面人工低维结构的功能设计与构造方面的研究成果     

Strategies to cure numerical shock instability in the HLLEM Riemann solver

The HLLEM scheme is a popular contact and shear preserving approximate Riemann solver that is known to be plagued by various forms of numerical shock instability. In this paper, we clarify that the shock instability exhibited by this scheme is primarily triggered by the spurious activation of the antidiffusive terms present in the first and third Riemann flux components on the transverse interfaces adjoining the shock front due to numerical perturbations. These erroneously activated terms are shown to counteract the favorable damping mechanism provided by its inherent HLL-type diffusive terms, causing an unphysical variation of the conserved quantity ρu both along and across the numerical shock. To prevent this, two distinct strategies are proposed termed as S elective W ave M odification and A nti D iffusion C ontrol. The former focuses on enhancing the quantity of the favorable HLL-type dissipation available on these critical flux components by carefully increasing the magnitudes of certain nonlinear wave speed estimates, while the latter focuses on directly controlling the magnitude of these critical antidiffusive terms. A linear perturbation analysis is performed to gauge the effectiveness of these cures and to estimate a von Neumann–type stability bounds on the CFL number associated with their use. Results from a variety of classic shock instability test cases show that the proposed strategies are able to provide excellent shock stable solutions even on grids that are highly elongated across the shock front without compromising the accuracy on inviscid contact or shear dominated viscous flows.     

Nonlinear corrector for Reynolds-averaged Navier-Stokes equations

The scope of this paper is to present a nonlinear error estimation and correction for Navier-Stokes and Reynolds-averaged Navier-Stokes equations. This nonlinear corrector enables better solution or functional output predictions at fixed mesh complexity and can be considered in a mesh adaptation process. After solving the problem at hand, a corrected solution is obtained by solving again the problem with an added source term. This source term is deduced from the evaluation of the residual of the numerical solution interpolated on the h/2 mesh. To avoid the generation of the h/2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. One of the main feature of this approach is that it automatically takes into account all the properties of the considered numerical method. The numerical examples point out that it successfully improves solution predictions and yields a sharp estimate of the numerical error. Moreover, we demonstrate the superiority of the nonlinear corrector with respect to linear corrector that can be found in the literature.     

Compressibility of random walker trajectories on growing networks

We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability distribution is bounded as the network size tends to infinity. This means that the growth of a space coupled to a random walker situated in it constrains its dynamics to a set of typical random walker trajectories, and walker trajectories inside the growing space are compressible.