Thermodynamic properties of a hard-core Lennard-Jones fluid from computer simulation and the coupling parameter series expansion

ABSTRACT

The thermodynamic properties of a fluid with an interaction potential consisting in a hard-sphere core plus a Lennard-Jones tail have been obtained by Monte Carlo (MC) NVT simulation as a function of the density along several isotherms. In addition, the liquid–vapour coexistence has been determined by means of histogram-reweighting MC. These data have been used to analyse the performance of perturbation theory. To this end, the first three perturbation terms of the inverse temperature expansion of the Helmholtz free energy have been obtained by means of MC NVT simulations to test the convergence of the perturbation series and to compare with the predictions of the coupling parameter series expansion. Then, the predictions of the latter theory for the thermodynamic properties have been compared with the simulations, revealing the overall excellent performance of this perturbation theory for this model fluid, except in the vicinity of the critical point.     

Simulation from Wishart Distributions with Eigenvalue Constraints

Abstract

This article provides an efficient algorithm for generating a random matrix according to a Wishart distribution, but with eigenvalues constrained to be less than a given vector of positive values. The procedure of Odell and Feiveson provides a guide, but the modifications here ensure that the diagonal elements of a candidate matrix are less than the corresponding elements of the constraint vector, thus greatly improving the chances that the matrix will be acceptable. The Normal hierarchical model with vector outcomes and the multivariate random effects model provide motivating applications.     

Inverse acoustical characterization of natural jute sound absorbing material by the particle swarm optimization method

For modeling of jute as acoustic material, knowledge of its non-acoustical parameters like porosity, tortuosity, air flow resistivity, thermal and viscous characteristic lengths is a prime requisite. Measurement of these non-acoustical parameters is not straightforward and involves a dedicated measurement setup. So in order to overcome this issue, the inverse acoustical characterization can be used. In this paper, the particle swarm optimization method (PSO) is used as an optimization method. This method estimates the non-acoustical parameters of jute material in felt form by minimizing the error between experimental and theoretical sound absorption data. In this work, the impedance prediction models for fibrous materials like Johnson–Champoux–Allard model with rigid and limp frame and Garai–Pompoli model is used for sound absorption coefficient calculation by the transfer matrix method along with the PSO. The inverse estimated non-acoustical parameters for jute material are then compared with estimated and experimentally measured parameters for jute felts. Using these inversely predicted parameters, sound absorption of multilayer sound absorbers is also studied.     

折叠式角锥棱镜谐振腔的偏振特性理论与实验研究

建立了角锥棱镜的偏振模型,分析了角锥棱镜对入射线偏振光的偏振态的影响,分析表明角锥棱镜的单个入射区域存在特殊的偏振方向,该方向的线偏振光被角锥棱镜反射后仍然是线偏振光。利用角锥棱镜的该特性设计了腔内存在线偏振光振荡的角锥棱镜激光谐振腔,能够使用电光开关调Q,在振动环境中具有较好的抗失调稳定性。研制了激光器样机并进行了实验,在重复频率为10 Hz时,输出激光单脉冲能量大于300 mJ,光束质量因子β值在2左右,实验结果也表明角锥棱镜的棱和顶点并不影响输出激光的光束质量。     

Monte Carlo simulation of a confined hard ellipse fluid

The structural and thermodynamic properties of a confined hard ellipse fluid are studied using Monte Carlo simulation. The angular, average number densities and order parameters of hard ellipses confined between hard parallel walls are obtained for various bulk densities, aspect ratios and wall separations. The results show that the effect of the existence of the wall on the molecular fluid structure, either on their directions or their locations, with respect to the bulk, especially close to the walls, is significant. For this system the pressure is also obtained and it is shown that the average density at the wall is proportional to the pressure, βP=〈ρ_w〉. Our simulation results show that the order parameters depend on the number of the particles in the box unless it exceeds thousand.     

Generating orthogonal matrix polynomials satisfying second order differential equations from a trio of triangular matrices

The method developed in [A.J. Durán, F.A. Grünbaum, Orthogonal matrix polynomials satisfying second order differential equations, Int. Math. Res. Not. 10 (2004) 461–484] led us to consider matrix polynomials that are orthogonal with respect to weight matrices W(t) of the form , , and (1−t)^α(1+t)^βT(t)T^*(t), with T satisfying T^′=(2Bt+A)T, T(0)=I, T^′=(A+B/t)T, T(1)=I, and T^′(t)=(−A/(1−t)+B/(1+t))T, T(0)=I, respectively. Here A and B are in general two non-commuting matrices. We are interested in sequences of orthogonal polynomials (P_n)_n which also satisfy a second order differential equation with differential coefficients that are matrix polynomials F₂, F₁ and F₀ (independent of n) of degrees not bigger than 2, 1 and 0 respectively. To proceed further and find situations where these second order differential equations hold, we only dealt with the case when one of the matrices A or B vanishes.The purpose of this paper is to show a method which allows us to deal with the case when A, B and F₀ are simultaneously triangularizable (but without making any commutativity assumption).     

Cayley digraphs with normal adjacency matrices

In this paper we give a criterion for the adjacency matrix of a Cayley digraph to be normal in terms of the Cayley subset S. It is shown with the use of this result that the adjacency matrix of every Cayley digraph on a finite group G is normal iff G is either abelian or has the form for some non-negative integer n, where Q₈ is the quaternion group and is the abelian group of order 2ⁿ and exponent 2.     

矩阵方程AX=B的双反对称最佳逼近解

本文主要讨论下而两个问题并得到相关结果:问题Ⅰ:给定A ∈ R~(k×n),B ∈ R~(k×n),求X ∈ BASR~(n×n),使得AX=B.问题Ⅱ:给定X* ∈R~(n×n),求X使得‖X-X~*‖=minX∈S_E‖X-X~*‖,其中S_E是问题Ⅰ的解集合,‖·‖是Frobenius范数.通过对上述问题的讨论给出了问题Ⅰ解存在的充分必要条件和其解的一般表达式同时给出了问题Ⅱ的解,算法,和数值例子.     

Divisibility properties of power LCM matrices by power GCD matrices on gcd-closed sets

Let e and n be positive integers and S={x₁,…,x_n} a set of n distinct positive integers. For x∈S, define . The n×n matrix whose (i,j)-entry is the eth power (x_i,x_j)^e of the greatest common divisor of x_i and x_j is called the eth power GCD matrix on S, denoted by (S^e). Similarly we can define the eth power LCM matrix [S^e]. Bourque and Ligh showed that (S)∣[S] holds in the ring of n×n matrices over the integers if S is factor closed. Hong showed that for any gcd-closed set S with |S|≤3, (S)∣[S]. Meanwhile Hong proved that there is a gcd-closed set S with max_x∈S{|G_S(x)|}=2 such that (S)?[S]. In this paper, we introduce a new method to study systematically the divisibility for the case max_x∈S{|G_S(x)|}≤2. We give a new proof of Hong’s conjecture and obtain necessary and sufficient conditions on the gcd-closed set S with max_x∈S{|G_S(x)|}=2 such that (S^e)|[S^e]. This partially solves an open question raised by Hong. Furthermore, we show that such factorization holds if S is a gcd-closed set such that each element is a prime power or the product of two distinct primes, and in particular if S is a gcd-closed set with every element less than 12.     

Non-existence of a massive scalar field for the Marder universe in Lyra and Riemannian geometries

In this paper, we have studied a massive scalar field for a Marder type universe in the context of Lyra and Riemannian geometries. From the exact solutions obtained we show that the massive scalar field does not survive in Lyra and Riemannian geometries for an anisotropic Marder type universe. Therefore we have solved the massless scalar field problem in Lyra and Riemann geometries for two cases. Also we have obtained vacuum solutions for homogeneous and anisotropic Marder space-time in Lyra geometry and the solutions obtained are compared by considering Lyra and Riemann geometries. Finally, some physical and kinematical properties are discussed by using graphics.