The changes in free energies and entropies from analytical radial distribution functions

The changes in Helmholtz free energies and entropies in dense fluids have been evaluated using three known analytical expressions for radial distribution functions (RDFs) of Lennard–Jones (L-J) fluid. This method provides a simpler and a more expeditious way for the calculation of free energy and entropy in L-J dense fluids through statistical mechanics. Previously, integral equations or perturbation theories were used for this purpose. Such approach not only tests the power of analytical distribution functions in predicting the changes in Helmholtz free energies and entropies, but also specifies better expressions in determining these properties. The results are compared with experimental data and an accurate analytic equation of state for the L-J fluid. It is shown if an expression properly presents RDFs as a function of interparticle distance, density and temperature, it is possible to calculate the changes in Helmholtz free energies and entropies from analytical distribution functions.     

态射的广义Moore—Penrose逆

本文定义了态射的广义Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆，给出了它存在的一些充要条件，确定了它的一些表达式，推广了关于态射的Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆的相应结果。     

One-dimensional photonic crystal design

In this article we present a method to determine the band spectrum, band gaps, and discrete energy levels, of a one-dimensional photonic crystal with localized impurities. For one-dimensional crystals with piecewise constant refractive indices we develop an algorithm to recover the refractive index distribution from the period map. Finally, we derive the relationship between the period map and the scattering matrix containing the information on the localized modes.     

A Fast, Direct Algorithm for the Lippmann–Schwinger Integral Equation in Two Dimensions

The state-of-the-art, large-scale numerical simulations of the scattering problem for the Helmholtz equation in two dimensions rely on iterative solvers for the Lippmann–Schwinger integral equation, with an optimal CPU time O(m ³ log(m)) for an m-by-m wavelength problem. We present a method to solve the same problem directly, as opposed to iteratively, with the obvious advantage in efficiency for multiple right-hand sides corresponding to distinct incident waves. Analytically, this direct method is a hierarchical, recursive scheme consisting of the so-called splitting and merging processes. Algebraically, it amounts to a recursive matrix decomposition, for a cost of O(m ³), of the discretized Lippmann–Schwinger operator. With this matrix decomposition, each back substitution requires only O(m ² log(m)); therefore, a scattering problem with m incident waves can be solved, altogether, in O(m ³ log(m)) flops.     

Classification of extremal contractions from smooth fourfolds of -type

We investigate divisorial contractions of extremal rays from
smooth fourfolds. When the exceptional divisor is contracted to a curve, we prove that the divisor is a -bundle or quadric bundle over a smooth curve and the contraction is the blowing up along the curve. Furthermore we determine the local analytic structure of the contraction.

     

Fundamental frequency of a doubly connected membrane: a modified perturbation method

The fundamental frequency of a membrane is the square root ofthe lowest eigenvalue of the negative Laplace operator withDirichlet boundary conditions. A doubly connected membrane withthe inner region of vanishing maximal dimension 2c is consideredin this paper. A modified perturbation method is developed toprovide an asymptotic expansion (c 0) for the fundamental frequencyof the membrane. The first three order terms of the asymptoticexpansion for the fundamental frequency of a doubly connectedmembrane with the circular inner region are derived explicitly.The results are compared with the exact solutions and the approximationsdetermined by other investigators. The error of the perturbationcalculations compared with the exact values is less than 1%as c is less than or equal to 0·25 and is less than 4%as c is less than or equal to 0·35.     

On Connectedness via Closure Operators

This paper describes a convenient modification of the approach presented in the paper Closure operators and connectedness by G. Castellini and D. Hajek, which is shown to give a suitable generalization of left- and right-constant subcategories, both at the object and the morphism levels. We show in particular that the framework we introduce here allows the simultaneous study of the classes of connected topological spaces, of concordant continuous maps and of monotone continuous maps.     

On classification of polarized varieties with non-integral nef values

Let be an -dimensional normal projective variety with only Gorenstein, terminal, -factorial singularities. Let be an ample line bundle on . Let denote the nef value of . The classification of via the nef value morphism is given for the situations when satisfies or .

     

电子成像均匀约束磁场的产生及测试分析

为增加离子与原子碰撞成像系统中探测电子的立体角，设计了一约束电子的复合型亥姆霍兹线圈装置.对复合型亥姆霍兹线圈的磁场分布进行了理论计算和分析，并对制作的复合型亥姆赫兹线圈产生的磁场进行了实验测量，得出磁场的均匀性好于±0.6%. 关键词： 亥姆霍兹线圈 磁场分布 磁场均匀性     

First-principles molecular dynamics simulation of biased electrode/solution interface

First-principles molecular dynamics simulations have been carried out for water in contact with Pt(1 1 1) surface. To apply negative bias potential to the water/Pt interface, excess electrons were added to our slab model using the recently developed computational scheme called “effective screening medium (ESM)”. Water molecules located away from the surface reoriented themselves to screen the electric field, but they responded differently near the surface. Water molecules nearest to the surface, forming a distinct layered structure with the hydrogen atom directed to the surface, increased the density with increasing field. On these bases, we discuss microscopic aspects of the electric double layer.