The Linear Fokker-Planck Equation for the Ornstein-Uhlenbeck Process as an (Almost) Nonlinear Kinetic Equation for an Isolated N-Particle System

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at     

环保意识调查问卷的Logistic模型

本文应用多元统计分析中的方差分析 ,logistic模型等方法对环保意识调查问卷反馈的信息进行统计分析 ,建立被调查企业对环境保护意识的logistic模型 ,进而可对企业家的环境保护意识的好坏进行判断。     

Reductions of interval nonlinear programming problem

A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed.     

Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Modified Three-Dimensional Formulations of Bending Problems of Homogeneous Plates and Beams under Complex Fixing Conditions

Modified three-dimensional formulations of bending problems of homogeneous elastic plates and beams are considered. Modification of the known three-dimensional formulations reduces to using additional constraints imposed on displacement functions. An advantage of the formulations proposed is that complex fixing conditions of plates and beams can be taken into account.     

Banach空间上有界可逆线性变换逆变换的结构

Fillmore在[1]中得到一个定理:设A,T是Banach空间X上的线性变换,A有界,若Lat(A) Lat(T)且AT=TA,则T是A的多项式.在本文里,以此作为引理,讨论了Banach空间上可逆线性变换A在什么情况下,A-1可表示为A的多项式.本文最主要的结论是定理3.4:设X是Banach空间,A是X上的有界线性变换,且可逆,则A-1是A的多项式当且仅当A-1是A的局部多项式.     

Interference of probabilities and number field structure of quantum models

We study the probabilistic consequences of the choice of the basic number field in the quantum formalism. We demonstrate that by choosing a number field for a linear space representation of quantum model it is possible to describe various interference phenomena. We analyse interference of probabilistic alternatives induced by real, complex, hyperbolic (Clifford) and p‐adic representations.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Simulation of viscous water column collapse using adapting hierarchical grids

An adaptive hierarchical grid‐based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high‐resolution interface‐capturing approach and pressure‐based coupling of the Navier–Stokes equations. The Navier–Stokes flow solution scheme is verified for simulation of flow in a lid‐driven cavity at Re=1000. Two approaches to the coupling of the Navier–Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree‐based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids. Copyright © 2005 John Wiley & Sons, Ltd.     

Energy Spectrum Width and Nonequilibrium Energy of Rayleigh Waves Scattered on a Two-Dimensional Near-Surface Electron Layer

We obtain expressions for the energy spectrum widths of Rayleigh waves corresponding to their deformational coupling to Fermi and Boltzmann electrons in a two-dimensional layer near the surface of a semibounded solid. We evaluate the nonequilibrium energy of Rayleigh waves that depends on these widths and is caused by the same coupling to the corresponding hot electrons. We show that this energy is independent of the degeneracy degree of the electrons and is given by the mean energy of free Rayleigh waves heated up to temperature of the electrons. We find conditions under which the thermodynamics is determined by this nonequilibrium energy of Rayleigh waves in films of a certain thickness with Fermi electrons near the surface and by the equilibrium energy of bulk phonons in thicker samples. All the results are obtained using the Keldysh diagram technique applied to the case of semibounded media.