On the Brownian motion in a double-well potential in the overdamped limit

The Brownian motion of a particle in a double-well potential is considered and the position correlation function (excluding inertial effects) for the potential V(x)=ax²/2+bx⁴/4 is evaluated first by averaging the governing Langevin equation over its realizations. The exact solution is then obtained via matrix continued fractions by using a representation, which symmetrizes the recurrence relations for the observables generated by the averaging procedure leading to convergence of these recurrence relations unlike the previous approaches to the problem. A reliable approximate solution based on the exponential separation of the time scales of the fast intrawell and low overbarrier relaxation processes associated with the bistable potential is also given. It is shown that a knowledge of the three characteristic relaxation times (the integral, effective and the longest relaxation times) of the position correlation function allows one to accurately predict the relaxation behavior of the system in the overdamped limit for all time scales of interest.     

A stochastic particle system modeling the Carleman equation

Two species of Brownian particles on the unit circle are considered; both have diffusion coefficient >0 but different velocities (drift), 1 for one species and –1 for the other. During the evolution the particles randomly change their velocity: if two particles have the same velocity and are at distance ( being a positive parameter), they both may simultaneously flip their velocity according to a Poisson process of a given intensity. The analogue of the Boltzmann-Grad limit is studied when goes to zero and the total number of particles increases like ^–1. In such a limit propagation of chaos and convergence to a limiting kinetic equation are proven globally in time, under suitable assumptions on the initial state. If, furthermore, depends on and suitably vanishes when goes to zero, then the limiting kinetic equation (for the density of the two species of particles) is the Carleman equation.Dedicated to the memory of Paola Calderoni.     

A circle similarity algorithm for an automatic circular decomposition of blood cell images

This paper presents an iterative algorithm for circular decomposition which investigates the separation of overlapped circular particles of a binary image, in order to locate their center coordinates and to estimate their radii. Since this algorithm is based on the measure of a circle similarity of an object in an image to execute a search for concavities, object segmentation and circle recognition, its implementation is simpler than the algorithm based on polygonal approximation. In this work we compare the accuracy and robustness of the proposed circle similarity algorithm with a polygonal approximation based algorithm using synthetic images and real blood cell images. Both the algorithms are able to decompose connected blood cells. However, the input parameters of the polygonal approximation method shows high sensitivity to the shape or agglomeration of an object, while the proposed algorithm demonstrates more stable performance.     

评"相对论的质心运动定理"

在相对论情况下,质点系统的质心是一个不确定的概念,在相对论力学中,质心系（质量中心参照系）亦被有确切定义的动量中心系（系统总动量为零的参照系）所代替,本文对《相对论的质心运动定理与质量亏损》一文的论证和结果作出了评论。     

刚体绕瞬心的转动方程的计算机模拟

在《大学物理》上曾对刚体绕瞬心的转动方程进行过广泛深入的讨论，这些讨论都是建立在解析分析的基础上，本则用计算机模拟的方法研究这个方程．计算机模拟的结果不仅形象直观地表现了公式的丰富内涵，也证明计算机模拟是教学研究的一种优秀工具．     

On the non-radiating motion of a charged particle

The most general class of the electric and magnetic fields such that a charged particle moving in this field will not radiate is obtained. Apart from suitably orientated constant fields, it includes some special varying (but steady) fields.     

General form of the equation of motion of a charged particle

The most general form of the equation of motion of a charged particle is derived. The equation allows for an arbitrary self-field and is consistent with energy-momentum conservation, angular momentum conservation and the Dirac mass renormalization.     

The motion of a tagged particle and nonhomogeneous media in R1

We analyze the asymptotic behavior of a tagged particle inside an infinite system of identical elastic point masses. The main objective is to study very nonhomogeneous media—particles which are more and more dispersed far from the origin. We suggest that the limit motion of a tagged particle may serve to classify media in the nonhomogeneous case as well as in the homogeneous case.     

Brownian motion of a classical particle in quantum environment

The Klein–Kramers equation, governing the Brownian motion of a classical particle in a quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.     

原子质心运动对二能级原子发射谱的影响

研究了质心做谐振运动的二能级原子的发射谱. 当原子质心运动与光场无关联时，原子质心运动不影响原子发射谱的相位敏感性，随着原子质心运动平均能量的增加，原子发射谱峰间的相对距离变小，峰高的变化与原子质心运动和光场所处的状态有关. 当原子质心运动与光场有关联时，原子发射谱不依赖于光场与原子偶极矩的相对相位，在适当条件下原子发射谱峰的数目减少，峰高增大，峰宽变小. 关键词： 原子质心运动 二能级原子 原子发射谱 SU(2)相干态     

相对论的质心运动定理与质量亏损

在相对论情况下,为了利用质点系的静质量中心描写质点系的整体运动,需要引入一个反映质点系内部质点运动激烈程度的量纲为一的参数α．由此推导出含参数α的相对论的质心运动定理．研究表明,核反应的质量亏损是复合粒子内部能量变化的结果;核反应释放的能量来自复合粒子的内部能量,质量亏损可以用质点系参数α变化来进行解释．     

Closed-form solutions of the Schrödinger equation for a particle on the torus

Two results on the Schrödinger equation for a particle on the surface of a torus are obtained: In the first part of this note closed-form zero-energy solutions for a free particle are given. In the second part we show for which potentials depending only on the polar angle the Schrodinger equation becomes exactly solvable.     

A stochastic derivation of the Sivashinsky equation for the self-turbulent motion of a free particle

Within the framework of the Kershaw approach and of a hypothesis on spatial stochasticity, the relativistic equations of Lehr and Park, Guerra and Ruggiero, and Vigier for stochastic Nelson mechanics are obtained. In our model there is another set of equations of the hydrodynamical type for the drift velocityv _i(x _j,t) and stochastic velocityu _i(x _j,t) of a particle. Taking into account quadratic terms in l, the universal length, we obtain from these equations the Sivashinsky equations forv _i(x _j,t) in the caseu _i →0. In the limit l →0, these equations acquire the Newtonian form.     

非线性薛定谔方程的高阶分裂改进光滑粒子动力学算法

为提高传统光滑粒子动力学(SPH)方法求解高维非线性薛定谔(nonlinear Schr?dinger/Gross-Pitaevskii equation, NLS/GP)方程的数值精度和计算效率,本文首先基于高阶时间分裂思想将非线性薛定谔方程分解成线性导数项和非线性项,其次拓展一阶对称SPH方法对复数域上线性导数部分进行显式求解,最后引入MPI并行技术,结合边界施加虚粒子方法给出一种能够准确、高效地求解高维NLS/GP方程的高阶分裂修正并行SPH方法.数值模拟中,首先对带有周期性和Dirichlet边界条件的NLS方程进行求解,并与解析解做对比,准确地得到了周期边界下孤立波的奇异性,且对提出方法的数值精度、收敛速度和计算效率进行了分析;随后,运用给出的高阶分裂粒子方法对复杂二维和三维NLS/GP问题进行了数值预测,并与其他数值结果进行比较,准确地展现了非线性孤立波传播中的奇异现象和玻色-爱因斯坦凝聚态中带外旋转项的量子涡旋变化过程.     

论恒力作用下质点的相对论运动

在相对论情况下，讨论了受恒力作用的质点的运动规律。     

A simple derivation of the equation of motion for classical electrodynamics

The equation of motion recently obtained by the author is derived by an elementary method. In addition, this paper contains a careful analysis of three well-known derivations of the (incorrect) Lorentz-Dirac equation, identifying their flaws. The fundamental error in each case is a failure to appreciate that the rate of change of field momentum affects the particle differently according to whether it is an applied field or the self-field. This fundamental physical error can be understood with the aid of a simple analogy.