A Monte Carlo study of the coil-to-globule transition of model polymer chains near an attractive surface

When a polymer chain in solution interacts with an atomically smooth solid substrate, its conformational properties are strongly modified and deviate substantially from those of chains in bulk. In this work, the interplay of two competing transitions that affect the conformations of polymer chains near an energetically attractive surface is studied by means of Monte Carlo simulations on a cubic lattice. The transition from an extended to a compact conformation of a polymer chain near an attractive wall, as solubility deteriorates, exhibits characteristics akin to the “coil-to-globule” transition in bulk. An effective θ-temperature is determined. Its role as the transition point is confirmed in a variety of ways. The nature of the coil-to-compact transition is not qualitatively different from that in the bulk. Adsorbed polymer chains may assume “globular” or “pancake” configurations depending on the competition among adsorption strength, cohesive energy, and entropy. In a very relevant range of conditions, the dependence of the adsorbate thickness on chain-length is intermediate between that of 3-d (“semidroplets”) and 2-d (“pancake”) objects. The focus of this study is on rather long polymer chains. Several crucial features of the transitions of the adsorbed chains are N-dependent and various aspects of the adsorption and “dissolution” process are manifested clearly only at the “long chain” limit. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2462–2476, 2009     

Solving Multi-dimensional Evolution Problems with Localized Structures using Second Generation Wavelets

A dynamically adaptive numerical method for solving multi-dimensional evolution problems with localized structures is developed. The method is based on the general class of multi-dimensional second-generation wavelets and is an extension of the second-generation wavelet collocation method of Vasilyev and Bowman to two and higher dimensions and irregular sampling intervals. Wavelet decomposition is used for grid adaptation and interpolation, while O ( N ) hierarchical finite difference scheme, which takes advantage of wavelet multilevel decomposition, is used for derivative calculations. The prowess and computational efficiency of the method are demonstrated for the solution of a number of two-dimensional test problems.     

非晶态金属Al中微团簇多面体结构及其演变规律的模拟研究

对50 000个金属Al原子从液态急冷形成非晶态结构的过程进行了分子动力学模拟研究.采用原子键型和原子团簇类型指数法,发现在其微观结构的转变过程中,与不断增加的1551键型密切相关的二十面体及其缺陷结构的形成起了非常突出的作用.通过各种键型原子团簇的计算,获得团簇多面体结构的分布数据.在可视化的显示下,得到一幅十分清晰的关于团簇多面体结构的特征及其演变的图景.建立了一种简单而有效的团簇多面体结构研究方法.同时也对模拟计算结果的微观机理给出了相应的讨论,这对于深入理解非晶态结构的形成机制及其微观过程,将有重     

A comparative study of inflow conditions for two‐ and three‐dimensional spatially developing mixing layers using large eddy simulation

A series of spatially developing mixing layers are simulated using the large eddy simulation (LES) technique. A hyperbolic tangent function and data derived from boundary layer simulations are used to generate the inflow condition, and their effects on the flow are compared. The simulations are performed in both two and three dimensions. In two‐dimensional simulations, both types of inflow conditions produce a layer that grows through successive pairings of Kelvin–Helmholtz (K–H) vortices, but the composition ratio is lower for the hyperbolic tangent inflow simulations. The two‐dimensional simulations do not undergo a transition to turbulence. The three‐dimensional simulations produce a transition to turbulence, and coherent structures are found in the post‐transition region of the flow. The composition ratio of the three‐dimensional layers is reduced in comparison to the counterpart two‐dimensional runs. The mechanisms of growth are investigated in each type of simulation, and amalgamative pairing interactions are found in the pre‐transition region of the three‐dimensional simulations, and throughout the entire computational domain of those carried out in two‐dimensions. The structures beyond the post‐transition region of the three‐dimensional simulations appear to behave in a much different manner to their pre‐transition cousins, with no pairing‐type interactions observed in the turbulent flow. In order to accurately simulate spatially developing mixing layers, it is postulated that the inflow conditions must closely correspond to the conditions present in the reference experiment. Copyright © 2007 John Wiley & Sons, Ltd.     

Some continuous programming problems in numerical analysis

Many problems in the design and implementation of computational schemes may be studied using the theory and methods of mathematical programming. One seeks to minimize bounds for the errors in the calculated results obtained from a given set of input data, exploiting analytical relations. We describe optimal quadrature rules and give an application to the evaluation of the sums of power series, belonging to an important class. We present results which are based on the theory of linear and semi-infinite programming. We also study the associated complexity issues and obtain simple qualitative results for the computational work required.     

Nonlinear optimization with GAMS /LGO

The Lipschitz Global Optimizer (LGO) software integrates global and local scope search methods, to handle a very general class of nonlinear optimization models. Here we discuss the LGO implementation linked to the General Algebraic Modeling System (GAMS). First we review the key features and basic usage of the GAMS /LGO solver option, then present reproducible numerical results to illustrate its performance.     

具有谐振腔的多波切伦柯夫振荡器的粒子模拟

 设计了一种新型的多波切伦柯夫振荡器，即在第二慢波段和输出喇叭之间加一个谐振腔，并采用PIC方法模拟了器件产生微波的物理过程。结果表明这种新型器件符合普通多波切伦柯夫振荡器的基本特征，同时具有纵向尺寸短，导引磁场低，功率、效率高等优点。     

Numerical solution of the controlled Duffing oscillator by hybrid functions

A numerical method for solving the controlled Duffing oscillator is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions which consists of block-pulse functions plus Legendre polynomials are given. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of product is introduced. This matrix together with the operational matrix of integration are utilized to reduce the solution of controlled Duffing oscillator to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

On non‐Newtonian incompressible fluids with phase transitions

A modified model for a binary fluid is analysed mathematically. The governing equations of the motion consists of a Cahn–Hilliard equation coupled with a system describing a class of non‐Newtonian incompressible fluid with p‐structure. The existence of weak solutions for the evolution problems is shown for the space dimension d=2 with p? 2 and for d=3 with p? 11/5. The existence of measure‐valued solutions is obtained for d=3 in the case 2? p< 11/5. Similar existence results are obtained for the case of nondifferentiable free energy, corresponding to the density constraint |ψ| ? 1. We also give regularity and uniqueness results for the solutions and characterize stable stationary solutions. Copyright © 2006 John Wiley & Sons, Ltd.