Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

The de novo design of median molecules within a property range of interest

Summary In this paper an application is presented of the median molecule workflow to the de novo design of novel molecular entities with a property profile of interest. Median molecules are structures that are optimised to be similar to a set of existing molecules of interest as an approach for lead exploration and hopping. An overview of this workflow is provided together with an example of an instance using the similarity to camphor and menthol as objectives. The methodology of the experiments is defined and the workflow is applied to designing novel molecules for two physical property datasets: mean molecular polarisability and aqueous solubility. This paper concludes with a discussion of the characteristics of this method.     

Growth, Band Structure and Optical Properties of LiSrBO3 Crystal

The bulk crystal of LiSrBO3 (8.39 g) with a size of 21mm×20mm×15mm was grown by high temperature solution growth method. The relationship between growth habit and crystal structure was discussed. The transmission spectrum shows an UV absorption edge at about 300 nm. The melting temperature of this crystal was determined to be 942 ℃ by DTA-TG measurement. The band structure of the LiSrBO3 crystal was studied by means of the first principle method. An indirect band gap was found to be about 4.0 eV,and a low dielectric constant was estimated to be about 1.9 in terms of theoretical results.     

Error in an approximate wave function and an error minimization scheme

An estimate of error in an approximate wave function for a stationary state is put forward that does not require any information about the exact state. The measure is sensitive and direct. Parameters embedded in a trial wave function can be varied to minimize this error as well, leading to a variational principle. Such a scheme works nicely for bound states and the more so for Siegert states, for which the standard energy minimization principle does not apply. Pilot calculations on the anharmonic oscillator system and the radial Stark effect in the hydrogen atom reveal the worth of the endeavor. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Fast Marching Method for Calculating Reactive Trajectories for Chemical Reactions

We present a method for computing classical Newtonian trajectories that minimize the path length or transit time from reactant to product. Our approach is based on a generalization of the fast-marching method, which allows us to construct the solution of the Hamilton-Jacobi equation for the action that optimizes the desired quantity. The resulting “reactive paths” can be interpreted as reaction coordinates but, unlike more conventional choices, they contain dynamical information about the chemical system of interest.     

基于简化的应变梯度理论下Kirchhoff板模型边值问题的提法及其应用北大核心CSCD

考虑应变梯度和速度梯度的影响,建立薄板控制微分方程及给出其边值问题的提法,修正了前人给出的薄板角点条件.采用Levy法,给出受分布力作用下简支板的挠度及自由振动频率的解析解.通过与文献中分子动力学数据对比,验证了该文模型的有效性并提出校核材料参数的一种方法.研究结果表明,增大弹性地基和应变梯度参数可以有效提高板的等效刚度,而速度梯度参数则相反.该文提出的板的边值问题为研究薄板在复杂支撑边界及外荷载等条件提供了理论依据.同时,有望为其有限元法、有限差分法和基于能量原理的Galerkin法等数值方法提供理论依据.     

Minimax principles for elliptic mixed hemivariational–variational inequalities

In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent to a mixed hemivariational–variational inequality. While the minimax principle is of independent interest, it is employed in this paper to provide an elementary proof of the solution existence of the mixed hemivariational–variational inequality. Theoretical results are illustrated in the applications of two contact problems.     

Maximum principle at infinity for complete minimal surfaces in flat 3-manifolds

The main result of this paper is the following maximum principle at infinity:Theorem.Let M ₁ and M ₂ be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M ₁,M ₂)=min(dist(M ₁,M ₂), dist(M ₂,M ₁)).In case one boundary is empty, e.g. M ₁,then dist(M ₁,M ₂)=dist(M ₂,M ₁).If both boundaries are empty, then M ₁ and M ₂ are flat.     

Large deviation analysis of the single server queue

We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.