The Thermal Conductivity Theory of Non-uniform Granular Flow and the Mechanism Analysis

According to the fractal characteristics appearing in non-uniform granular system, we found the fractalmodel to study the effective thermal conductivity in the mixed system. Considering the quasi-equilibrium, we bringforward the fractal velocity probability distribution function. The equipartition of energy is employed to the non-uniform granular system, and the granular temperature is derived. We investigate the thermal conductivity in granularflow due to the movement of the particles, namely the heat transfer induced by the streaming mode only. The thermalconductivity in the mixed system changes with the fractal parameters such as the solid fraction v, structural characterparameter η, and fractal dimension D of size distribution. These parameters depict the characteristics of the thermalconductivity in the actual complex granular system. Comparing our conclusion with the correlative experimental dataand the theoretical conclusion of binary mixture of granular materials, the results can qualitatively confirm the generalityof our prediction on the granular system.     

A Fractal Model for the Effective Thermal Conductivity of Granular Flow with Non—uniform Particles

The equipartition of energy applied in binary mixture of granular flow is extended to granular flow with non-uniform particles.Based on the fractal characteristic of granular flow with non-uniform particles as well as energy equipartition,a fractal velocity distribution function and a fractal model of effective thermal conductivity are derived.Thermal conduction resulted from motions of particles in the granular flow,as well as the effect of fractal dimension on effective thermal conductivity,is discussed.     

The Fractal Characteristic of Particles in Granular Material Flows and Its Effect on Effective Thermal Conductivity

According to the fact that many pulverized particles possess fractal characteristic, a fractal model for studying fine particles in granular material flows is first proposed. An expression of particles' fractal distribution is derived to describe the relationship between the particle fractal dimensions and particle velocity distribution function. In accordance with this model, the theoretical particle effective thermal conductivity is derived. The analytical results show that for the small Biot-Fourier number, the effective thermal conductivity increases with the square root of the granular temperature. For very large Biot-Fourier number, the effective thermal conductivity linearly increases with the granular temperature. Numerically calculated results show that the thermal conductivity increases with the particle size fractal dimensions and decreases with the particle surface fractal dimensions.     

Steady State Properties of One-Dimensional Non-uniform Granular Gases Subjected to Gaussian White Noise Driving

We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time T of the Brownian process is greater than the mean collision time To, the energy evolution of the system exponentially decays, with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state in which the velocity distribution strongly deviates from the Gaussian one. Three other aspects have also been studied for the steady state： the visualized change of the particle density, the entropy of the system and the correlations in the velocity of particles. And the results of simulations indicate that the system has strong spatial clustering; Furthermore, the influence of the inelasticity and inhomogeneity on dynamic behaviors have also been extensively investigated, especially the dependence of the entropy and the correlations in the velocity of particles on the restitute coefficient e and the fractal dimension D.     

Temperature Properties in Polydisperse Granular Mixtures

Numerical simulations are employed to consider the problem of determining the granular temperatures of the species of a homogeneous heated granular mixture with a power-law size distribution. The partial granular temperature ratios are studied as functions of the fractal dimension D, the restitution coefficient e, the rescaled viscosity time, the average occupied area fraction φ, the total particle number N and the number fraction. Different species of particles in a power-law system typically do not have the same mean kinetic energy, namely the granular temperature. It is found that the extent of nonequipartition of kinetic energy is determined by the fractal dimension D, the restitution coefficient e and the rescaled viscosity time, while is insensitive to the total particle number N , the area fraction φ and the number fraction.     

Dynamic behavior of non-uniform granular gases system with the fractal characteristic in one dimension

A one-dimensional dynamic model of polydisperse granular mixture with a power-law size distribution is presented, in which the particles are subject to inelastic mutual collisions and driven by Gaussian white noise. The particle size distribution of the mixture has the fractal characteristic, and a fractal dimension D as a measurement of the inhomogeneity of the particle size distribution is introduced. We define the global granular temperature and the kinetic pressure of the mixture, and obtain their expressions. By molecular dynamics simulations, we have mainly investigated how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the steady-state dynamic properties of the system, focusing on the global granular temperature, kinetic pressure, velocity distribution and distribution of interparticle spacing. Some novel results are found that, with the increase of the fractal dimension D, the global granular temperature and the kinetic pressure decrease, the velocity distribution deviates more obviously from the Gaussian one and the particles cluster more pronouncedly at the same value of the restitution coefficient e (0<e<1). On the other hand, as the restitution coefficient e decreases, the dynamic behavior has the similar evolution as above at the fixed fractal dimension D. The dynamic behavior changing with e and D is, respectively, presented.     

通道宽度对二维粗糙边界斜面颗粒流的影响

在此之前已经报道了二维斜面颗粒流在通道中的分布规律以及二维斜面粗糙边界附近的颗粒 流量密度（ξ=ρ·ν）分布.本文则主要研究通道宽度W对边界附近颗粒流量密度(ξ=ρ· ν)分布的影响.结果表明，颗粒流量密度随通道宽度的变化（ξ W）存在一临界通道宽度W c.在本实验条件下临界通道宽度Wc=70d.当通道宽度小于临界宽度Wc时 ，通道中距边界20d—30d区间内的相对颗粒流量密度随斜面倾斜角的变化可描述为ξ∝( sinθ)α，α是与通道宽度W有关的参数，其数值在032至085之间. 关键词： 二维颗粒流 颗粒物质 颗粒流量密度     

粒径均匀散体导热系数的分形描述

本文以分形理论为工具,采用填充率、散体颗粒直径等宏观易等测参数较准确地描述了颗粒散体的几何结构;运用导热与逾渗的类比,建立了均匀散体导热系数的逾渗模型,模型的预测值与实验测量结果基本一致。     

Non-Gaussian and Clustering Behavior in One-Dimensional Polydisperse Granular Gas System

We present a one-dimensional dynamic model of polydisperse granular mixture with the fractal characteristic of the particle size distribution, in which the particles are subject to inelastic mutual collisions and are driven by Gaussian white noise. The inhomogeneity of the particle size distribution is described by a fractal dimension D. The stationary state that the mixture reaches is the result of the balance between energy dissipation and energy injection. By molecular dynamics simulations, we have mainly studied how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the velocity distribution and distribution of interparticle spacing in the steady-state.The simulation results indicate that, in the inelasticity case, the velocity distribution strongly deviates from the Gaussian one and the system has a strong spatial clustering. Thus the inhomogeneity and the inelasticity have great effects on the velocity distribution and distribution of interparticle spacing. The quantitative information of the non-Gaussian velocity distribution and that of clustering are respectively represented.     

Density Waves in One-Dimensional Granular Flows Driven by Non-Uniform Force Field

We introduce a non-uniform gravity-like force field to control the granular flow state in a quasi-onedimensional system, and study the system by the molecular dynamics simulation. We find that the granular flow under non-uniform force field can be well described by a density wave with fixed time period if a fixed particle number condition is used. The base frequency of the density wave does not depend on the position of the flow, while both the average density and oscillation amplitude of the flow vary continuously with the position. The formation of the density wave results from the aggregation of the granules in the decelerated region and the feed-back mechanism in the fixed particle number condition.     

Validation of the Wiedemann–Franz law in a granular s-wave superconductor in the nanometer scale

The present study tries to evaluate the validity of the Wiedemann–Franz law in a granular s-wave superconductor in the presence of concentrated impurities. By using Green's function method and the Kubo formula technique, three distinct contributions of the Aslamazov–Larkin, the Maki–Thompson and, the density of states are calculated for both the electrical conductivity and the thermal conductivity in a granular s-wave superconductor. It is demonstrated that these different contributions to the fluctuation conductivity depend differently on the tunneling because of their different natures. This study examines the transport in a granular superconductor system in three dimensions in the limit of large tunneling conductance,which makes it possible to ignore all localization effects and the Coulomb interaction. We find that the tunneling is efficient near the critical temperature and that there is a crossover to the characteristic behavior of a homogeneous system.When it is far from the critical temperature, the tunneling is not effective and the system behaves as an ensemble of real zero-dimensional grains. The results show that the Wiedemann–Franz law is violated in both temperature regions.     

Global Pressure of One-Dimensional Polydisperse Granular Gases Driven by Gaussian White Noise

We study the global pressure of a one-dimensional polydisperse granular gases system for the first time,in which the size distribution of particles has the fractal characteristic and the inhomogeneity is described by a fractal dimension D. The particles are driven by Gaussian white noise and subject to inelastic mutual collisions. We define the global pressure P of the system as the impulse transferred across a surface in a unit of time, which has two contributions,one from the translational motion of particles and the other from the collisions. Explicit expression for the global pressure in the steady state is derived. By molecular dynamics simulations, we investigate how the inelasticity of collisions and the inhomogeneity of the particles influence the global pressure. The simulation results indicate that the restitution coefficient e and the fractal dimension D have significant effect on the pressure.     

Density Waves in One-Dimensional Granular Flows Driven by Non-Uniform Force Field

We introduce a non-uniform gravity-like force field to control the granular flow state in a quasi-one-dimensional system, and study the system by the molecular dynamics simulation. We find that the granular flow under non-uniform force field can be well described by a density wave with fixed time period if a fixed particle number condition is used. The base frequency of the density wave does not depend on the position of the flow, while both the average density and oscillation amplitude of the flow vary continuously with the position. The formation of the density wave results from the aggregation of the granules in the decelerated region and the feed-back mechanism in the fixed particle number condition.     

Global Pressure of One-Dimensional Polydisperse Granular Gases Driven by Gaussian White Noise

We study the global pressure of a one-dimensional polydisperse granular gases system for the first time, in which the size distribution of particles has the fractal characteristic and the inhomogeneity is described by a fractal dimension D. The particles are driven by Gaussian white noise and subject to inelastic mutual collisions. We define the global pressure P of the system as the impulse transferred across a surface in a unit of time, which has two contributions, one from the translational motion of particles and the other from the collisions. Explicit expression for the global pressure in the steady state is derived. By molecular dynamics simulations, we investigate how the inelasticity of collisions and the inhomogeneity of the particles influence the global pressure. The simulation results indicate that the restitution coefficient e and the fractal dimension D have significant effect on the pressure.     

静态堆积颗粒中的力链分布

颗粒物质是由众多离散颗粒组成的软凝聚态物质,涉及多个物理层次结构和机制,是多尺度问题. 首先阐述了颗粒物质多尺度力学的研究框架,指出颗粒间接触力链构成的细观尺度是核心,颗粒物质显示出的独特静态堆积特性和动态流变特性都与细观尺度力链的复杂演变规律直接相关. 围绕着定量描述力链特征这一目标,采用严格的球形颗粒Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论,对重力作用下12000个球心共面的二维等径颗粒静态堆积进行了离散动力学模拟,对力链分布特征、接触力规律等做了量化分析,考察了颗粒 关键词： 颗粒物质 力链 离散模型 多尺度力学     

Directed segregation in compartmentalized bi-disperse granular gas

A bi-disperse granular gas in an asymmetrical two-compartment system is studied experimentally. The presence of asymmetry within the range of our experimental parameters results in a directed segregated state and a directed clustering state. This deterministic system does not depend on the initial conditions. A modified flux model based on Lohse's flux model for bi-disperse granular gases is derived. The modified flux model explains qualitatively the experimental results.     

A Fractal Model for Effective Thermal Conductivity of Isotropic Porous Silica Low-k Materials

We establish a new model based on fractal theory and cubic spline interpolation to study the effective thermal conductivity of isotropic porous silica low-k materials. A 3D fractal model is introduced to describe the structure of the silica xerogel and silica hybrid materials （such as methylsilsesquioxane, MSQ）. Combined with fractal structure, a more suitable medium approximation is developed to study the isotropic porous silica xerogel and MSQ materials. Cubic spline interpolation for fitting discrete predictions from the fractal model is used to obtain the continuous function of the effective thermal conductivity versus porosity. Compared with other common models, the effective thermal conductivity predicted by our model presents better agreement with the experimental data for all porosity. These results indicate that the proposed model is valid.     

分形结构纳米复合材料热导率的分子动力学模拟研究

提出了一基于Sierpinski分形结构的Si/Ge纳米复合材料结构,以调控纳米复合材料的热导率.采用非平衡分子动力学方法模拟研究了分形结构Si/Ge纳米复合材料的导热性能,给出了硅原子百分比、轴向长度以及截面尺寸对分形结构纳米复合材料热导率的影响规律,并与传统矩形结构进行了对比.研究结果表明,分形结构纳米复合材料增强了Si/Ge界面散射作用,使得热导率低于传统矩形结构,这为提高材料的热电效率提供了有效途径.Si原子百分比、截面尺寸、轴向长度皆对分形结构纳米复合材料热导率存在着重要影响.纳米复合材料热导率随着Si原子百分比的增加呈先减小后增加的趋势,随轴向长度的增加则呈单调增大趋势.     

带有点缺陷的二维颗粒系统离散元模拟

首先用离散元方法研究了颗粒系统在各向同性挤压和纯剪切状态下粒子间力的分布情况,并与相同条件下的实验结果进行对比. 然后模拟了带有不同数目点缺陷的二维颗粒系统在各向同性挤压和纯剪切时粒子间力的分布情况,并与无缺陷的情况做了比较,发现了点缺陷对颗粒系统的影响规律. 关键词： 颗粒系统 离散元 点缺陷 力概率分布     

The anisotropy of free path in a vibro-fluidized granular gas

The free path of a vibro-fluidized two-dimensional(2D) inelastic granular gas confined in a rectangular box is investigated by 2D event-driven molecular simulation. By tracking particles in the simulation, we analyze the local free path.The probability distribution of the free path shows a high tail deviating from the exponential prediction. The anisotropy of the free path is found when we separate the free path to x and y components. The probability distribution of y component is exponential, while x component has a high tail. The probability distribution of angle between the relative velocity and the unit vector joined two particle centers deviates from the distribution of two random vectors, indicating the existence of the dynamic heterogeneities in our system. We explain these results by resorting to the kinetic theory with two-peak velocity distribution. The kinetic theory agrees well with the simulation result.