1.

Transscale mechanics： looking for the missing links between continuum and micro/nanoscopic reality





Y. L. Bai H. Y. Wang M. F. Xia F.J. Ke《Acta Mechanica Sinica》,2008年第24卷第2期


Problems involving coupled multiple space and time scales offer a real challenge for conventional frameworks of either particle or continuum mechanics. In this paper, four cases studies （shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics） are provided to illustrate the three levels of transscale problems （problems due to various physical mechanisms at macrolevel, problems due to microstructural evolution at macro/microlevel, problems due to the coupling of atoms/ molecules and a finite size body at micro/nanolevel） and their formulations. Accordingly, nonequilibrium statistical mechanics, coupled transscale equations and simultaneous solutions, and transscale algorithms based on atomic/molecular interaction are suggested as the three possible modes of transscale mechanics.

2.

Approximating Stationary Statistical Properties





Xiaoming WANG《数学年刊B辑(英文版)》,2009年第30卷第6期


It is wellknown that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. The main contribution of this manuscript is to provide simple and natural criterions on numerical methods （temporal and spatial discretization） that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. The result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasigeostrophic model are also discussed.

3.

The Kinetic Theory of Growth of ZrSn Diffusion Layers on Zr55Cua0Al10Ni5 Metallic Glass





柴戡 ;林铁松 ;何鹏 ;孙剑飞《中国物理快报》,2014年第11期


The growth kinetics of the intermetallic compound layer between molten pure Sn and Zr55Cu30AlloNi5 bulk metallic glass （BMG） is mainly controlled by the diffusion mechanism at stage I at which the value of the time exponent is approximately 1/2, also there is unusual or unique stage Ⅱ whose time exponent of the growth is suppressed to 1/3. It is deduced that phase transition such as nucleation, coalescence occurring in the vicinity of the interface of the diffusion layer within the BMG and the average size growing as onethird power of time, called the LifshitzSlezov law. A more elegant means of attack is based upon the FokkerPlanck approach, which permits us to calculate directly the probability of the distribution of steadystate thickness fluctuations. Physical implications of the analytical results also give the onethird power of time of distance scale. The transmission of Sn particles through a disorder system of the BMG, scattered by the local fluctuation levels, is the source of the time exponent from 1/2 to 1/3 as a macroscopic cumulative effect.

4.

THE LIOUVILLE THEOREM INVOLVING QUANTUM EFFECT





包科达 刘福绥《数学物理学报(B辑英文版)》,1986年第2期


In this article we have shown, if the wave packets are used to describe the dynamical states of particles in a manyparticle system, we can get a set of Langevintype Eq. (4.1) instead of the classical canonical eqs. of Hamilton (1.1). At the same time a diffusiontype Liouville theorem involving quantum effect (4.9) is resulted instead of the classical Liouville Eq. (1.3). it is shown that the diffusiontype Liouville eq. should cause the phase mixing in phase space and the entropy increasing in time for an isolated system.

5.

Scalar Statistics along Inertial Particle Trajectory in Isotropic Turbulence





刘亚明 柳朝晖 韩海锋 栗晶 王汉封 郑楚光《中国物理快报》,2009年第26卷第6期


The statistics of a passive scalar along inertial particle trajectory in homogeneous isotropic turbulence with a mean scalar gradient is investigated by using direct numerical simulation. We are interested in the influence of particle inertia on such statistics, which is crucial for further understanding and development of models in nonisothermal gasparticle flows. The results show that the scalar variance along particle trajectory decreases with the increasing particle inertia firstly; when the particle＇s Stokes number St is less than 1.0, it reaches the minimal value when St is around 1.0, then it increases if St increases further. However, the scalar dissipation rate along the particle trajectory shows completely contrasting behavior in comparison with the scalar variance. The mechanicaltothermal time scale ratios averaged along particle, （r）p, are approximately two times smaller than that computed in the Eulerian frame r, and stay at nearly 1.77 with a weak dependence on particle inertia. In addition, the correlations between scalar dissipation and flow structure characteristics along particle trajectories, such as strain and vorticity, are also computed, and they reach their maximum and minimum, 0.31 and 0.25, respectively, when St is around 1.0.

6.

New quantization conditions for field theory without divergence





王平《中国物理 C》,2011年第35卷第3期


Quantum field theory is a fundamental tool in particle and nuclear physics. Elemental particles are assumed to be point particles and, as a result, the loop integrals are divergent in many cases. Regularization and renormalization are introduced in order to get the physical finite results from the infinite, divergent loop integrations. We propose new quantization conditions for the fields whose base is very natural, i.e., any particle is not a point particle but a solid one with three dimensions. With this solid quantization, divergence could disappear.

7.

CoarseGrained Langevin Approximations and Spatiotemporal Acceleration for Kinetic Monte Carlo Simulations of Diffusion of Interacting Particles





Sasanka ARE Markos A. KATSOULAKIS Anders SZEPESSY《数学年刊B辑(英文版)》,2009年第30卷第6期


Kinetic Monte Carlo methods provide a powerful computational tool for the simulation of microscopic processes such as the diffusion of interacting particles on a surface, at a detailed atomistic level. However such algorithms are typically computationatly expensive and are restricted to fairly small spatiotemporal scales. One approach towards overcoming this problem was the development of coarsegrained Monte Carlo algorithms. In recent literature, these methods were shown to be capable of efficiently describing much larger length scales while still incorporating information on microscopic interactions and fluctuations. In this paper, a coarsegrained Langevin system of stochastic differential equations as approximations of diffusion of interacting particles is derived, based on these earlier coarsegrained models. The authors demonstrate the asymptotic equivalence of transient and long time behavior of the Langevin approximation and the underlying microscopic process, using asymptotics methods such as large deviations for interacting particles systems, and furthermore, present corresponding numerical simulations, comparing statistical quantities like mean paths, auto correlations and power spectra of the microscopic and the approximating Langevin processes. Finally, it is shown that the Langevin approximations presented here are much more computationally efficient than conventional Kinetic Monte Carlo methods, since in addition to the reduction in the number of spatial degrees of freedom in coarsegrained Monte Carlo methods, the Langevin system of stochastic differential equations allows for multiple particle moves in a single timestep.

8.

Traffic of indistinguishable particles in complex networks





孟庆宽 朱建阳《中国物理 B》,2009年第18卷第9期


In this paper,we apply a simple walk mechanism to the study of the traffic of many indistinguishable particlesin complex networks.The network with particles stands for a particle system,and every vertex in the network standsfor a quantum state with the corresponding energy determined by the vertex degree.Although the particles areindistinguishable,the quantum states can be distinguished.When the many indistinguishable particles walk randomlyin the system for a long enough time and the system reaches dynamic equilibrium,we find that under different restrictiveconditions the particle distributions satisfy different forms,including the BoseEinstein distribution,the FermiDiracdistribution and the nonFermi distribution(as we temporarily call it).As for the BoseEinstein distribution,we findthat only if the particle density is larger than zero,with increasing particle density,do more and more particles condensein the lowest energy level.While the particle density is very low,the particle distribution transforms from the quantumstatistical form to the classically statistical form,i.e.,transforms from the Bose distribution or the Fermi distributionto the Boltzmann distribution.The numerical results fit well with the analytical predictions.

9.

Particle behavior in homogeneous isotropic turbulence





ZhuHe ZhaohuiLiu ShengChen LeiWeng ChuguangZheng《Acta Mechanica Sinica》,2005年第21卷第2期


Direct numerical simulations were conducted to investigate the behavior of heavy particles in homogeneous isotropic turbulence. The present study focused on the effect of particle inertia and drift on the autocorrelations of the particle velocity and the fluid seen by particles and the dispersion characteristics of particles. The Lagrangian integral time scale of particles monotonically increased as the magnitude of the particle response time increased, while that of the fluid seen by particles remained relatively constant; it reached a maximum when the particle response time was close to the Kolmolgorov time scale of the flow. Particle dispersion increased as the particle inertia increased for small particles, while for larger particles, it decreased as particle inertia increased; particle eddy diffusion coefficient was maximal, and greater than that of the fluid by about 30%, at the preferential concentration. The concentration field of the particles with τp/τk≈1.0 showed that particles tend to collect in regions of low vorticity (high strain) due to preferential concentration. As the drift velocity of a particle is increased it crosses the paths of fluid elements more rapidly and will tend to lose correlation with its previous velocity faster than a fluid element will. And the correlation of particle velocities along the drift direction is more persistent than that perpendicular to the direction of drift. Simulations also showed that the continuity effect and the crossingtrajectory effect are weakened for particles with infinite inertia.

10.

A fluctuating latticeBoltzmann model for direct numerical simulation of particle Brownian motion





Deming Nie Jianzhong Lin《Particuology》,2009年第6期


A singlerelaxationtime fluctuating latticeBoltzmann （LB） model for direct numerical simulation （DNS） of particle Brownian motion is established by adding a fluctuating component to the latticeBoltzmann equations （LBEs）. The fluctuating term is proved to be the random stress tensor in fluctuating hydrodynamics by recovering NavierStokes equations from LBEs through a ChapmanEnskog expansion. A threedimensional implementation of the model is also presented, along with simulations of a single spherical particle and 125 spherical particles at short times. Numerical results including the meansquare displacement, velocity autocorrelation function and selfdiffusion coefficient of particles compare favorably with theoretical results and previous numerical results.

11.

Infinitely Many Signchanging Solutions for a Schrdinger Equation in R~N





洪明理 李永青《数学进展》,2006年第6期


We consider the existence of infinitely many signchanging solutions for the nonlinear timeindependent schrodinger equations of the form where Vλ(x) =λa(x) 1. This problem originates from various problems in physics and mathematical physics. In constructive field theory, (1.1) is called a nonlinear Euclidean scalar field equation. In chemical dynamics, a solution of (1.1) is a stationary state of the reaction diffusion equation

12.

粒子在拥挤环境下的亚扩散：示踪粒子与拥挤粒子的尺寸影响





马义丁 罗开富《化学物理学报》,2017年第30卷第2期


The dynamics of tracers in crowded matrix is of interest in various areas of physics, such as the diffusion of proteins in living cells. By using twodimensional (2D) Langevin dynamics simulations, we investigate the diffusive properties of a tracer of a diameter in crowded environments caused by randomly distributed crowders of a diameter. Results show that the emergence of subdiffusion of a tracer at intermediate time scales depends on the size ratio of the tracer to crowders δ. If δ falls between a lower critical size ratio and a upper one, the anomalous diffusion occurs purely due to the molecular crowding. Further analysis indicates that the physical origin of subdiffusion is the "cage effect". Moreover, the subdiffusion exponent α decreases with the increasing medium viscosity and the degree of crowding, and gets a minimum αmin=0.75 at δ=1. At long time scales, normal diffusion of a tracer is recovered. For δ≤1, the relative mobility of tracers is independent of the degree of crowding. Meanwhile, it is sensitive to the degree of crowding for δ>1. Our results are helpful in deepening the understanding of the diffusive properties of biomacromolecules that lie within crowded intracellular environments, such as proteins, DNA and ribosomes.

13.

TwoTime Diffusion Process in the Porous Medium





涂涛 郝晓杰 郭国平 郭光灿《中国物理快报》,2007年第24卷第8期


We find that there are two time scales t and ε ln t in the asymptotic behaviour of diffusion process in the porous medium, which give us a new insight to the anomalous dimension in this problem. Further we construct an iterative method to calculate the anomalous dimension and obtain an improved result.

14.

Asymptotics on Semiparametric Analysis of Multivariate Failure Time Data Under the Additive Hazards Model





HuanbinLiu LiuquanSun LixingZhu《应用数学学报(英文版)》,2005年第21卷第2期


Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time data under the additive hazards model. Simple weighted estimating functions for the regression parameters are proposed, and asymptotic distribution theory of the resulting estimators are derived. In addition, a class of generalized Wald and generalized score statistics for hypothesis testing and model selection are presented, and the asymptotic properties of these statistics are examined.

15.

Observation of intermittency in edge plasma of SUNIST tokamak





王文浩 何也熙 高喆 曾立 张国平 解丽凤 冯春华《中国物理》,2004年第13卷第12期


The temporal intermittency of the fluctuationdriven particle transport fluxes is analysed by using data obtained from Langmuir probe array in the edge of the SinoUnited Spherical Tokamak (SUNIST). The conditional statistics analysis indicates that the intermittent structures have a characteristic time width of about 30μs, which is the typical fluctuation time scaling. It is also found that the transport fluxes have a multifractal character over the fluctuation time scales, and exhibit a longtimerange correlation character with selfsimilar parameter H>0.5 in the plasma confinement time scales. Furthermore, the analyses show that the level of the intermittency and the longrange correlation of the fluxes vary with increasing plasma density. These observations are consistent with the prediction of the avalanchelike model.

16.

An analysis of the chaotic motion of particles of different sizes in a gas fluidized bed





Y.Q. Feng A.B. Yu《Particuology》,2008年第6卷第6期


The dynamic behavior of individual particles during the mixing/segregation process of particle mixtures in a gas fluidized bed is analyzed. The analysis is based on the results generated from discrete particle simulation, with the focus on the trajectory of and forces acting on individual particles. Typical particles are selected representing three kinds of particle motion： a flotsam particle which is initially at the bottom part of the bed and finally fluidized at the top part of the bed; a jetsam particle which is initially at the top part of the bed and finally stays in the bottom defluidized layer of the bed; and a jetsam particle which is intermittently joining the top fluidized and bottom defluidized layers. The results show that the motion of a particle is chaotic at macroscopic or global scale, but can be well explained at a microscopic scale in terms of its interaction forces and contact conditions with other particles, particlefluid interaction force, and local flow structure. They also highlight the need for establishing a suitable method to link the information generated and modeled at different time and length scales.

17.

Environmentdependent continuous time random walk





林方 包景东《中国物理 B》,2011年第20卷第4期


A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory: the jumping distance and the waiting time,are replaced by two new ones: the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement x 2 (t) ～ t α is realized numerically and analysed theoretically,where the value of the power index α is in a region of 0 < α < 2. Particularly,the damping leads to a subdiffusion when the impact velocities are drawn from a Gaussian density function and the superdiffusive effect is related to statistical extremes,which are called rarethoughdominant events.

18.

A multifractal model for linking Lagrangian and Eulerian velocity structure functions





YuFeng Dong GuoDong Jin《Acta Mechanica Sinica》,2014年第30卷第4期


A multifractal model is developed to connect the Lagrangian multifractal dimensions with their Eulerian counterparts. We propose that the characteristic time scale of a Lagrangian quantity should be the Lagrangian time scale, and it should not be the Eulerian time scale which was widely used in previous studies on Lagrangian statistics. Using the present model, we can obtain the scaling exponents of Lagrangian velocity structure functions from the existing data or models of scaling exponents of Eulerian velocity structure functions. This model is validated by comparing its prediction with the results of experiments, direct numerical simulations, and the previous theoretical models. The comparison shows that the proposed model can better predict the scaling exponents of Lagrangian velocity structure functions, especially for orders larger than 6.

19.

Wavelet estimation of the diffusion coefficient in time dependent diffusion models





Ping CHEN~《中国科学A辑(英文版)》,2007年第50卷第11期


The estimation problem for diffusion coefficients in diffusion processes has been studied in many papers,where the diffusion coefficient function is assumed to be a 1dimensional bounded Lipschitzian function of the state or the time only.There is no previous work for the nonparametric estimation of timedependent diffusion models where the diffusion coefficient depends on both the state and the time.This paper introduces and studies a wavelet estimation of the timedependent diffusion coefficient under a more general assumption that the diffusion coefficient is a linear growth Lipschitz function.Using the properties of martingale,we translate the problems in diffusion into the nonparametric regression setting and give the L~r convergence rate.A strong consistency of the estimate is established.With this result one can estimate the timedependent diffusion coefficient using the same structure of the wavelet estimators under any equivalent probability measure.For example, in finance,the wavelet estimator is strongly consistent under the market probability measure as well as the risk neutral probability measure.

20.

Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a BrinkmanDarcy flow over a flat surface with heat generation





Faiza A.Salama《Acta Mechanica Sinica》,2011年第27卷第4期


A boundary layer analysis is presented to investigate numerically the effects of radiation,thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium.The boundary layer equations are transformed to nonlinear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order RungeKutta method with shooting technique for some values of physical parameters.Comparisons with previously published work are performed and the results are found to be in very good agreement.Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity,temperature and concentration profiles as well as the local skinfriction coefficient,wall heat transfer,particle deposition rate and wall thermophoretic deposition velocity.The results show that the magnetic field induces acceleration of the flow,rather than deceleration(as in classical magnetohydrodynamics(MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer.Also,there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter.
