Casimir Force of Piston Systems with Arbitrary Cross Sections under Different Boundary Conditions

We study the Casimir force between two pistons under different boundary conditions inside an infinite cylinder with arbitrary cross section. It is found that the attractive or repulsive character of the Casimir force for a scalar field is determined only by the boundary condition along the longitudinal direction and is independent of the cross section, transverse boundary conditions and the mass of the field. Under symmetric Dirichlet-Dirichlet, Neumann-Neumann and periodic longitudinal boundary conditions the Casimir force is always attractive, but is repulsive under non-symmetric Dirichlet-Neumann and anti-periodic longitudinal boundary conditions. The Casimir force of the electromagnetic field in an ideal conductive piston is also investigated. This force is always attractive regardless of the shape of the cross section and the transverse boundary conditions.     

Heat Kernel Asymptotics of Zaremba Boundary Value Problem

The Zaremba boundary-value problem is a boundary value problem for Laplace-type second-order partial differential operators acting on smooth sections of a vector bundle over a smooth compact Riemannian manifold with smooth boundary but with discontinuous boundary conditions, which include Dirichlet boundary conditions on one part of the boundary and Neumann boundary conditions on another part of the boundary. We study the heat kernel asymptotics of Zaremba boundary value problem. The construction of the asymptotic solution of the heat equation is described in detail and the heat kernel is computed explicitly in the leading approximation. Some of the first nontrivial coefficients of the heat kernel asymptotic expansion are computed explicitly. This revised version was published online in July 2006 with corrections to the Cover Date.     

Variations in the boundary conditions of coupled dynamic systems

The paper is a sequel to reference [1]. In that paper, isolation of the basic dynamic systems was achieved by imposing uncoupled boundary conditions in which the coupling impedances were removed. It is illustrated that alternate isolations, involving different boundary conditions, can be imposed. In particular, the modification introduced in the formalism when blocked boundary conditions are substituted for the uncoupled boundary conditions is discussed in some detail.     

Probability of boundary conditions in quantum cosmology

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler–DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler–DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.     

基于Rudin-Osher-Fatemi模型的图像除模糊和除噪音新模型

介绍一种依赖时间的新模型来解决图像除噪音和除模糊问题.分别使用逆反射、中值两种边界条件的数值试验比较本文新模型和Rudin-Osher-Fatemi模型.试验结果表明中值边界条件的误差比逆反射边界条件误差小.     

The geometry of open bosonic strings

The coordinate conditions usually used to describe the open string and its boundary conditions are intrinsically singular at the boundary. As a result, the boundary conditions are difficult to understand or interpret geometrically. The physical requirement that the variation of the string at the boundary yield a vanishing contribution to the variation of the action may be accomplished by the requirement that the induced metric, in non-singular coordinates, have signature (0, — 1) at the boundary and that the metric be C¹ on the boundary. These geometrically simple by analytically somewhat complicated requirements are equivalent to the usual boundary conditions. Lastly it is shown that the open string is, in a strict sense, a special case of the closed string. Some of the peculiar behavior of characteristic curves on the open string becomes clear in this context.     

Interface Shear Stress Analysis of Bond FRP Tendon Anchorage under Different Boundary Conditions

This article describes a study of an analytic interfacial stresses solution of FRP bond tendon anchorage, under different boundary conditions. The analytic solution was obtained with the cohesive zone model (CZM): the concept of the minimum relative interface displacement s _mis introduced and used as the fundamental variable to express all other parameters. The presented analytic solution agrees well with the result of experiment and that of finite element analysis (FEA). Furthermore, the interface shear stress distributions under two kinds of boundary conditions are discussed. It is indicated that the boundary conditions affected distribution of interfacial stress greatly. Under different boundary conditions, at the same load level, the peak interface shear stress corresponding to the first boundary condition is smaller than it is corresponding to the second boundary condition. The FRP tendon anchor under the first boundary condition can alleviate the peak bond stress, resulting in better uniformity in bond stress distribution.     

Supersymmetric Boundary Conditions in \mathcal{N}=4 Super Yang-Mills Theory

We study boundary conditions in ${\mathcal{N}}=4$ super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some of the scalar fields to have a “pole” at the boundary. The obvious Neumann boundary conditions can be modified by coupling to additional fields supported at the boundary. The obvious boundary conditions associated with orientifolds can also be generalized. In preparation for a separate study of how electric-magnetic duality acts on these boundary conditions, we explore moduli spaces of solutions of Nahm’s equations that appear in the presence of a boundary. Though our main interest is in boundary conditions that are Lorentz-invariant (to the extent possible in the presence of a boundary), we also explore non-Lorentz-invariant but half-BPS deformations of Neumann boundary conditions. We make preliminary comments on the action of electric-magnetic duality, deferring a more serious study to a later paper.     

探地雷达数值模拟中广义完全匹配层吸收边界条件的模拟分析

探讨探地雷达正演模拟中,应用广义完全匹配层(GPML)吸收边界条件时的模拟效果.利用时域有限差分(FDTD)法将麦克斯韦方程离散化,再采用Mur超吸收边界条件和GPML吸收边界条件吸收向外的电磁波,模拟充水岩溶的雷达图像;同时,采用GPML吸收边界条件模拟多个圆柱体异常模型和倾斜界面异常模型的探地雷达剖面图像.对模拟结果的分析可知,GPML吸收边界条件可有效地吸收向外的电磁波,其吸收效果优于Mur超吸收边界条件,在探地雷达的应用中可推广应用.     

Solvability condition in multi-scale analysis of gyroscopic continua

The solvability condition is investigated for the method of multiple scales applied to gyroscopic continua. The general framework of the multi-scale analysis is proposed for a linear gyroscopic continuous system under small nonlinear time-dependent disturbances. The solvability condition is derived from the properties of the systems. The condition holds only for appropriate boundary conditions. The appropriateness of the boundary conditions can be examined for unperturbed linear systems. An example is presented to highlight the requirements on the boundary conditions.     

Structural acoustic control of plates with variable boundary conditions: design methodology

A method for optimizing a structural acoustic control system subject to variations in plate boundary conditions is provided. The assumed modes method is used to build a plate model with varying levels of rotational boundary stiffness to simulate the dynamics of a plate with uncertain edge conditions. A transducer placement scoring process, involving Hankel singular values, is combined with a genetic optimization routine to find spatial locations robust to boundary condition variation. Predicted frequency response characteristics are examined, and theoretically optimized results are discussed in relation to the range of boundary conditions investigated. Modeled results indicate that it is possible to minimize the impact of uncertain boundary conditions in active structural acoustic control by optimizing the placement of transducers with respect to those uncertainties.     

The Independence on Boundary Conditions for the Thermodynamic Limit of Charged Systems

We study systems containing electrons and nuclei. Based on the fact that the Thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such as Neumann, periodic, or elastic boundary conditions. The result is proven for all limiting sequences of domains which are obtained by scaling a bounded open set, with smooth boundary, except for isolated edges and corners. Work partially supported by EU grant HPRN-CT-2002-00277.     

Thomas-Fermi equation with non-spherical boundary conditions

The confined atom Thomas-Fermi equation with non-spherical boundary conditions is considered. A 2-D finite element code for solving the Thomas-Fermi equation with general boundary conditions is demonstrated. Results for both Dirichlet and Neumann boundary conditions for ellipsoids of revolution are presented.     

The scattering of the field of a point source by an axisymmetric screen with a variable impedance

The method of continued boundary conditions is used to solve the acoustic diffraction problem for the case of a field generated by a point source and diffracted by an axisymmetric screen, with generalized impedance boundary conditions being satisfied at the screen surface. Two types of impedance boundary conditions are considered, which differ; at zero impedance one of them takes the form of the Dirichlet boundary condition, while the other the takes the form of the Neumann boundary condition. Both stationary and non-stationary diffraction problems are investigated. Numerical results are obtained for screens with parabolic and spherical shapes.     

A new type of periodie boundary condition useful for high-temperature atomistic simulations of grain boundaries: Applications in semiconductors

A new type of boundary condition, named Möbius or antiperiodic boundary conditions, is proposed and tested, both analytically and within the context of numerical simulations. It is shown that these boundary conditions are very useful for twist grain boundary atomistic simulations. By contrast to the use of the ordinary Born von Kármán periodic boundary conditions, they allow only one grain boundary per box instead of two. The risk of migration and overinteraction of two grain boundaries at high temperature is thus avoided while more complex grain boundaries can also be tackled at the same computer price. Such examples are presented and discussed.     

Attractive and repulsive Casimir vacuum energy with general boundary conditions

The infrared behaviour of quantum field theories confined in bounded domains is strongly dependent on the shape and structure of space boundaries. The most significant physical effect arises in the behaviour of the vacuum energy. The Casimir energy can be attractive or repulsive depending on the nature of the boundary. We calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most general type of boundary conditions depending on four parameters. The analysis provides a powerful method to identify which boundary conditions generate attractive or repulsive Casimir forces between the plates. In the interface between both regimes we find a very interesting family of boundary conditions which do not induce any type of Casimir force. We also show that the attractive regime holds far beyond identical boundary conditions for the two plates required by the Kenneth–Klich theorem and that the strongest attractive Casimir force appears for periodic boundary conditions whereas the strongest repulsive Casimir force corresponds to anti-periodic boundary conditions. Most of the analysed boundary conditions are new and some of them can be physically implemented with metamaterials.     

On the role of the boundary conditions in the Ginzburg-Landau theory

The effect of the boundary conditions for solutions on the Ginzburg-Landau (GL) equations for superconducting plates in the vortex-free limit is studied by numerical methods. Based on the self-consistent solution of the system of GL equations, the dependence of the critical current I _c on the external magnetic field and the distribution of the order parameter over the plate thickness are determined. When solving the equations with general boundary conditions, it was found that the critical temperature and critical current density decreased in comparison with those obtained by solving equations with ordinary boundary conditions. According to the results of this study, the use of general boundary conditions leads to a number of interesting results which were not observed when using ordinary boundary conditions. The range of the applicability of the vortex-free limit for the films of thickness of the order of the coherence length ξ are discussed. The effect of boundary conditions on the applicability of this limit is analyzed.     

Non-periodic boundary conditions for molecular simulations of condensed matter

A formally exact effective boundary potential is defined that can be combined with hard-wall boundary conditions to allow computer simulations to be performed that mimic an infinite system. The effective potential accounts for the interactions that would be present across the boundary if the system were truly infinite. The exact many-body potential is approximated by one- and two-body potentials. The algorithm is implemented and tested for a Lennard–Jones fluid. The advantages of the present formulation over the widely used periodic boundary conditions are discussed.     

Effect of boundary conditions on quantum-anti-dots in the presence of a magnetic field

Many people have studied the conductance properties through an array of anti-dots, especially since the observation of Weiss oscillations. In most cases, however, in which the recursive Greenźs functions are used on a spatial lattice, periodic boundary conditions are employed. In this paper, we analyse the effects of boundary conditions and magnetic field on the conductance behavior in a number of anti-dot-shaped, GaAs/AlGaAs 2DEG quantum systems. The effect of periodic boundary conditions causes a reduction in the overall conductance. The effect of changing the boundary conditions is more profound for lower numbers of anti-dots.     

Vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment

The free vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment is carried out by the 3D elasticity theory and the Chebyshev–Ritz method. The material properties are assumed to be temperature dependent and graded in the thickness direction. The mixed boundary conditions which include upper and lower surfaces partially fixed, inner side partially fixed and outer side partially fixed are considered, respectively. The accuracy of the present approach for solving the free vibration of the plates with different boundary conditions is validated by comparing the present numerical results with the results available. The effects of the different mixed boundary conditions, the temperature rise, the material graded index and the geometrical parameters on the eigen-frequencies are studied.