Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.     

Spherically symmetric static inhomogeneous cosmological models

Spherically symmetric static cosmological models filled with black-body radiation are considered. The models are isotropic about a central observer but inhomogeneous. It is suggested that the energy density of the free gravitational field, which is coupled to the isotropic radiation energy density, might play an important role in generating sufficient field (vacuum) energy (when converted into thermal energy) and initiate processes like inflation. On the central world line the energy density of the free gravitational field vanishes whereas the proper pressure and density of the isotropic black-body radiation are constants. Further, it is shown that the cosmological constant is no more arbitrary but given in terms of the central pressure and density. Also, at its maximum value the energy density of the free gravitational field is proved to be equal to one third of the combined value of radiation pressure and density.     

散斑条纹的快速高精度处理技术

本文提出一种快速高精度散斑杨氏条纹(斑纹)场处理方法——同态阀值滤波法。用它实现了散斑场条纹的快速、逐点连续高精度处理。     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Solutions of the Vlasov equation in Lagrange coordinates

We show that the method of “finite-size” particles is a discrete model of the Vlasov equation but in a different (effective) interaction potential. We calculate the effective potential explicitly in the most interesting case of the Coulomb interaction. We find the equations of motion of particles of “finite size” for the Gaussian form factor. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 138–148, April, 2007.     

<Emphasis Type="Italic">N</Emphasis>=1 supersymmetric conformal block recursion relations

We present explicit recursion relations for the four-point superconformal block functions that are essentially particular contributions of the given conformal class to the four-point correlation function. The approach is based on the analytic properties of the superconformal blocks as functions of the conformal dimensions and the central charge of the superconformal algebra. We compare the results with the explicit analytic expressions obtained for special parameter values corresponding to the truncated operator product expansion. These recursion relations are an efficient tool for numerically studying the four-point correlation function in superconformal field theory in the framework of the bootstrap approach, similar to that in the case of the purely conformal symmetry. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 476–487, September, 2007.     

有限存贮空间内可燃多孔介质流动和传热的研究

对通风条件下可燃多孔介质库房内的流动和传热特性进行了数值模拟,得到了库房有限空间内的温度场和速度场.通过比较不同的来流温度和入口流速,得到的结果表明:可燃多孔介质(弹药)内部发生化学反应并产生热量,其温度由中心向四周逐渐降低;来流流速越大,越有利于弹药的冷却;在来流速度相同的情况下,来流温度越低,越有利于散热,对于可燃多孔介质(弹药)的贮存越安全;在左侧进风口的上下两边以及可燃多孔介质(弹药)的上方,会形成漩涡.     

Smooth and Nonsmooth Lipschitz Controls for a Class of Vector Differential Equations

This paper is devoted to the study of a class of control problems associated to a nonlinear second-order vector differential equation with pointwise state constraints. The control is realized via a function of the state. We extend the results of Akkouchi, Bounabat, and Goebel to vector differential equations and furthermore consider the more general case. Under proper conditions, we prove the existence of optimal controls in the class of Lipschitz functions and obtain an optimality condition which looks somehow like the Pontryagin maximum principle for a smooth optimal control function. For a nonsmooth optimal control function, we derive a suboptimality condition by means of the Ekeland variational principle.Communicated by M. J. BalasThis work was supported by 985 Project of Jilin University. The author thanks Professor Yong Li for valuable suggestions. He also thanks Professor M. J. Balas and the anonymous referees for their comments.     

Numerical study of homogeneous dynamo based on experimental von Kármán type flows

A numerical study of the magnetic induction equation has been performed on von Kármán type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Kármán sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case.     

Detecting pipe changes via acoustic matched field processing

Detecting pipe irregularities such as intrusions can be challenging. However, subtle changes can be identified in the complex acoustic fields measured over a range of frequencies and over a time interval given an “array” of receivers. In particular, for two receivers one can coherently process the signals via matched field processing (MFP) to infer whether or not there have been changes such as new intrusions relative to undisturbed fields measured earlier. There is no acoustic modelling of the fields required, only the simple linear processor is applied, and only test data (five scenarios) are used in this demonstration. A key advantage to using MFP plus two (or more) microphones is that absolute sound levels need not be carefully measured.