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.     

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.     

Collision Statistics of Driven Polydisperse Granular Gases

We present a dynamical model of two-dimensional polydisperse granular gases with fractal size distribution, in which the disks are subject to inelastic mutual collisions and driven by standard white noise. The inhomogeneity of the disk size distribution can be measured by a fractal dimension df. By Monte Carlo simulations, we have mainly investigated the effect of the inhomogeneity on the statistical properties of the system in the same inelasticity case. Some novel results are found that the average energy of the system decays exponentially with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state after a long evolution time. Furthermore, the inhomogeneity has great influence on the steady-state statistical properties. With the increase of the fractal dimension df, the distributions of path lengths and free times between collisions deviate more obviously from expected theoretical forms for elastic spheres and have an overpopulation of short distances and time bins. The collision rate increases with df, but it is independent of time. Meanwhile, the velocity distribution deviates more strongly from the Gaussian one, but does not demonstrate any apparent universal behavior.     

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.     

Dynamic Properties of Two-Dimensional Polydisperse Granular Gases

We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results： a single granular temperature does not characterize a multi-component mixture and each species attains its own ＂granular temperature＂; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value olD augments.     

Dynamic Properties of Two-Dimensional Polydisperse Granular Gases

We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results: a single granular temperature does not characterize a multi-component mixture and each species attains its own "granular temperature"; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value of D augments.     

Steady-State Properties of Driven Polydisperse Granular Mixtures

We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions, driven by a homogeneous heat bath at zero gravity. The width of particle size distribution is characterized by the only
parameter, namely, the fractal dimension D. The energy dissipation of the mixture is increased as D increases or as e decreases. Furthermore, it is found that the steady-state properties of the mixture such as the collision rate, granular temperature, kinetic pressure and velocity distribution depend sensitively on size distribution parameter D.     

Investigation of Dynamic Behavior in 1D Non-uniform Granular System

We present a non-uniform granular system in one-dimensional case, whose granularity distribution has the fractal characteristic. The particles are subject to inelastic mutual collisions and obey Langevin equation between collisions. By Monte Carlo simulation we study the dynamic actions of the system. Far from the equilibrium, i.e., τ 〉〉 τe, the results of simulation indicate that the inhomogeneity of the system and the inelasticity of the particles have great influences on the dynamic properties of the system, and correspondingly the influence of the inhomogeneity is more significant.     

高斯白噪声相位调制的激光光谱展宽

激光器是现代光学中一种常用的光源,分析其谱宽特性对于激光的研究具有重要意义.由于高性能窄线宽激光的半高全宽通常在几十M Hz以内,难以直接满足宽光谱领域的应用需求,因而无法发挥其在成本和性能方面的优势,这在一定程度上限制了激光的发展.如果在激光内部直接进行调制实现线宽展宽,又会导致频率的严重漂移,破坏稳频特性.为了在激...     

Blind Additive Gaussian White Noise Level Estimation from a Single Image by Employing Chi-Square Distribution

The additive Gaussian white noise (AGWN) level in real-life images is usually unknown, for which the empirical setting will make the denoising methods over-smooth fine structures or remove noise incompletely. The previous noise level estimation methods are easily lost in accurately estimating them from images with complicated structures. To cope with this issue, we propose a novel noise level estimation scheme based on Chi-square distribution, including the following key points: First, a degraded image is divided into many image patches through a sliding window. Then, flat patches are selected by using a patch selection strategy on the gradient maps of those image patches. Next, the initial noise level is calculated by employing Chi-square distribution on the selected flat patches. Finally, the stable noise level is optimized by an iterative strategy. Quantitative, with association, to qualitative results of experiments on synthetic real-life images validate that the proposed noise level estimation method is effective and even superior to the state-of-the-art methods. Extensive experiments on noise removal using BM3D further illustrate that the proposed noise level estimation method is more beneficial for achieving favorable denoising performance with detail preservation.     

Global Analysis of Response in the Piezomagnetoelastic Energy Harvester System under Harmonic and Poisson White Noise Excitations

The piezomagnetoelastic energy harvester system subjected to harmonic and Poisson white noise excitations is studied by using the generalized cell mapping method. The transient and stationary probability density functions (PDFs) of response based on the global viewpoint are obtained by the matrix analysis method. Monte Carlo simulation results verify the accuracy of this method. It can be observed that evolutionary direction of transient and stationary PDFs is in accordance with the unstable manifold for this system, and a stochastic P-bifurcation occurs as the intensity of Poisson white noise increases. This study presents an efficient numerical tool to solve the stochastic response of a three-dimensional dynamical system and provides a new idea to analyze the energy harvester system.     

Stochastic Analysis of Predator–Prey Models under Combined Gaussian and Poisson White Noise via Stochastic Averaging Method

In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministic models for the two cases where preys are abundant and the predator population is large, respectively. Then, under some natural assumptions of small perturbations and system parameters, the stochastic models are introduced. The stochastic averaging method is generalized to compute the statistical responses described by stationary probability density functions (PDFs) and moments for population densities in the ecosystems using a perturbation technique. Based on these statistical responses, the effects of ecosystem parameters and the noise parameters on the stationary PDFs and moments are discussed. Additionally, we also calculate the Gaussian approximate solution to illustrate the effectiveness of the perturbation results. The results show that the larger the mean arrival rate, the smaller the difference between the perturbation solution and Gaussian approximation solution. In addition, direct Monte Carlo simulation is performed to validate the above results.