Velocity distributions in dissipative granular gases

Motivated by recent experiments reporting non-Gaussian velocity distributions in driven dilute granular materials, we study by numerical simulation the properties of 2D inelastic gases. We find theoretically that the form of the observed velocity distribution is governed primarily by the coefficient of restitution eta and q=N(H)/N(C), the ratio between the average number of heatings and the average number of collisions in the gas. The differences in distributions we find between uniform and boundary heating can then be understood as different limits of q, for q>1 and q less, similar 1, respectively.     

Effects of Fractal Size Distributions on Velocity Distributions and Correlations of a Polydisperse Granular Gas

By the Monte Carlo method, the effect of dispersion of disc size distribution on the velocity distributions and correlations of a polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersion can be described by a fractal dimension D, and the smooth hard discs are engaged in a two- dimensional horizontal rectangular box, colliding inelastically with each other and driven by a homogeneous heat bath. In the steady state, the tails of the velocity distribution functions rise more significantly above a Gaussian as D increases, but the non-Gaussian velocity distribution functions do not demonstrate any apparent universal form for any value of D. The spatial velocity correlations are apparently stronger with the increase of D. The perpendicular correlations are about half the parallel correlations, and the two correlations are a power-law decay function of dimensionless distance and are of a long range. Moreover, the parallel velocity correlations of postcollisional state at contact are more than twice as large as the precollisional correlations, and both of them show almost linear behaviour of the fractal dimension D.     

Convection in highly fluidized three-dimensional granular beds

Free, buoyancy-driven convection has been observed experimentally in three-dimensional highly fluidized granular flows for the first time. Positron emission particle tracking was used to determine the position of a tracer grain in a vibrofluidized bed, from which packing fraction distributions as well as the velocity fields could be determined. The convection rolls, although small compared to the magnitude of velocity fluctuations (<5%), were consistently observed for a range of grain numbers and shaker amplitudes. Density variations are a signature of free convection and, with negative temperature gradients also present, were interpreted as the mechanism by which the convection rolls were initiated.     

Symmetry properties of fluctuations in an actively driven rotor

We investigate rotational dynamics of an actively driven rotor through experiments and numerical simulations. While probability density distributions of rotor angular velocity are strongly non-Gaussian, relative probabilities of observing rotation in opposite directions are shown to be linearly related to the angular velocity magnitude. We construct a stochastic model to describe transitions between different states from rotor angular velocity data and use the stochastic model to show that symmetry properties in probability density distributions are related to the detailed fluctuation relation(FR) of entropy productions.     

Holtsmark distributions in point-vortex systems

The statistics of uncorrelated point vortices in a plane is studied analytically and numerically. Theoretical distributions are obtained with the general method developed by Holtsmark [Ann. Phys. 58, 577 (1919)] and Chandrasekhar [Rev. Mod. Phys. 15, 1 (1943)]. They are found to agree with the results of numerical tests. Randomly placed Euler vortices have nearly Gaussian velocity distributions and Lorentzian distributions of the velocity difference. Statistics of other types of point vortices is essentially non-Gaussian.     

Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.     

Evolution of a randomly modulated breather in a nonlinear medium

The evolution of a randomly modulated sine-Gordon breather in a nonlinear medium is studied theoretically. The initial wave field is affected by multiplicative noise. For breather amplitude and velocity, the probability distribution function is determined by means of the inverse scattering transform and the method of cumulants. The distributions are shown to be non-Gaussian. The mean and the most probable values of the breather amplitude and velocity are calculated.     

颗粒速度在颗粒流稀疏流-密集流转变中的作用

用实验和计算模拟的方法研究了颗粒流中的颗粒速度与颗粒流特性的关系.实验研究发现当入口流量固定时，在出口上方高速运动的颗粒会使颗粒流由稀疏流向密集流转变的临界出口尺寸变小.当颗粒流转变为密集流后，颗粒速度的作用被出口上方的颗粒堆积区所消耗，最终变得与颗粒速度无关.二维分子动力学模拟计算得到了与实验相同的结论.通过二维分子动力学模拟计算，还给出了不同颗粒速度下体系的密度和速率在空间的分布图.这些分布图显示随着颗粒到达出口上方的瞬间速度的不同，颗粒堆积区的密度和高度均会改变，并最终导致颗粒流流动状态的改变. 关键词： 颗粒流 颗粒气体 分子动力学模拟     

Turbulentlike fluctuations in quasistatic flow of granular media

We analyze particle velocity fluctuations in a simulated granular system subjected to homogeneous quasistatic shearing. We show that these fluctuations share the following scaling characteristics of fluid turbulence in spite of their different physical origins: (i) scale-dependent probability distribution with non-Gaussian broadening at small time scales; (ii) spatial power spectrum of the velocity field showing a power-law decay, reflecting long-range correlations and the self-affine nature of the fluctuations; and (iii) superdiffusion of particles with respect to the mean background flow.     

Equipartition of rotational and translational energy in a dense granular gas

Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees of freedom. This equipartition persists when the particle properties, confining pressure, packing density, or spatial ordering are changed. While the translational velocity distributions are the same for both large and small particles, the angular velocity distributions scale with the particle radius. The probability distributions of all particle velocities have approximately exponential tails. Additionally, we find that the system can be described with a granular Boyle's law with a van?der?Waals-like equation of state. These results demonstrate ways in which conventional statistical mechanics can unexpectedly apply to nonequilibrium systems.     

Orientational correlation and velocity distributions in uniform shear flow of a dilute granular gas

Using particle simulations of the uniform shear flow of a rough dilute granular gas, we show that the translational and rotational velocities are strongly correlated in direction, but there is no orientational correlation-induced singularity at perfectly smooth (beta=-1) and rough (beta=1) limits for elastic collisions (e=1); both the translational and rotational velocity distribution functions remain close to a Gaussian for these two limiting cases. Away from these two limits, the orientational as well as spatial velocity correlations are responsible for the emergence of non-Gaussian high-velocity tails. The tails of both distribution functions follow stretched exponentials, with the exponents depending on normal (e) and tangential (beta) restitution coefficients.     

Statistics of particle velocities in dense granular flows

We present measurements of the particle velocity distribution in the slow flow of granular material through vertical channels. The velocities of particles adjacent to the smooth, transparent front face of the channel were determined by video imaging and particle tracking. We find that the mean velocity changes sharply in shear layers near the side walls, but remains constant in a substantial core. The velocity distribution is non-Gaussian, is anisotropic, and follows a power law at large velocities. Remarkably, the distribution is identical in the shear layer and the core. We show evidence of spatially correlated motion, and propose a mechanism for the generation of fluctuational motion in the absence of shear.     

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.     

Velocity statistics distinguish quantum turbulence from classical turbulence

By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid 4He are strongly non-Gaussian with 1/v(3) power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.     

Numerical Simulation of the Formation of Granular Shock Wave Over Cylindrical Obstacle

A two dimensional (2‐D) stream of granular flow with zero initial granular temperature passing over a cylindrical obstacle is simulated by means of both molecular dynamics (MD) simulation and finite volume method (FVM). In experiments, a bow‐shaped shock wave with higher area fraction forms in front of the obstacle that was reproduced in our simulations. Due to the different circumstances to which particles are subjected, the granular flow is divided in two zones. One is undisturbed where quantities, such as space fraction (volume fraction for 3‐D and area fraction for 2‐D geometries), velocity and granular temperature are uniformly distributed and the other is called the shock wave zone. In this region, the values of the space fraction increases and the velocity of particles changes. From the MD simulation, it is found that the area fraction of the shock wave depends on surface roughness, coefficient of restitution (COR) of particles, the obstacle diameter as well as velocity of the granular stream, and a triangular region forms with almost zero velocity, and granular temperature forms in front of the cylindrical obstacle. The bigger is the size of the obstacle, the more stable this region is. In FVM simulations solid phase velocity and area fraction distributions similar to the MD simulation results are obtained for proper parameters.     

Structure of vortices in a karman street behind a heated cylinder

The velocity and temperature fields in a wake behind a heated cylinder are investigated for Reynolds numbers in the interval 65相似文献   

Origin of non-Gaussian statistics in hydrodynamic turbulence

Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain rate with highly non-Gaussian statistics. Quantitatively, intermittency is manifested in highly elongated tails in the probability density functions of the velocity increments between pairs of points. A long-standing open issue has been to predict the origins of intermittency and non-Gaussian statistics from the Navier-Stokes equations. Here we derive, from the Navier-Stokes equations, a simple nonlinear dynamical system for the Lagrangian evolution of longitudinal and transverse velocity increments. From this system we are able to show that the ubiquitous non-Gaussian tails in turbulence have their origin in the inherent self-amplification of longitudinal velocity increments, and cross amplification of the transverse velocity increments.     

Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions

Journal of Statistical Physics - We study high-energy asymptotics of the steady velocity distributions for model kinetic equations describing various regimes in dilute granular flows. The main...     

On the velocity distributions of granular gases

We present a new approach to determine velocity distributions in granular gases to improve the Sonine polynomial expansion of the velocity distribution function, at higher inelasticities, for the homogeneous cooling regime of inelastic hard spheres. The perturbative consistency is recovered using a new set of dynamical variables based on the characteristic function and we illustrate our approach by computing the first four Sonine coefficients for moderate and high inelasticities. The analytical coefficients are compared with molecular dynamics simulations results and with a previous approach by Huthmann et al.