Numerical simulation for the initial state of avalanche in polydisperse particle systems

Numerical simulation is employed to investigate the initial state of avalanche in polydisperse particle systems.Nucleation and propagation processes are illustrated for pentadisperse and triadisperse particle systems,respectively.In these processes,particles involved in the avalanche grow slowly in the early stage and explosively in the later stage,which is clearly different from the continuous and steady growth trend in the monodisperse system.By examining the avalanche propagation,the number growth of particles involved in the avalanche and the slope of the number growth,the initial state can be divided into three stages:T1(nucleation stage),T2(propagation stage),T3(overall avalanche stage).We focus on the characteristics of the avalanche in the T2 stage,and find that propagation distances increase almost linearly in both axial and radial directions in polydisperse systems.We also consider the distribution characteristics of the average coordination number and average velocity for the moving particles.The results support that the polydisperse particle systems are more stable in the T2 stage.

STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE SYSTEMS WITH NONCOMPACT STATE SPACE.

This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.

Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction

This paper characterizes the limits of a large system of interacting particles distributed on the real line.The interaction occurring among neighbors involves two kinds of independent actions with different rates.This system is a generalization of the voter process,of which each particle is of type A or a.Under suitable scaling,the local proportion functions of A particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wright white noise.To obtain the convergence,the tightness of these functions is derived from the moment estimate method.

Steady-State Configuration and Tension Calculations of Marine Cables Under Complex Currents via Separated Particle Swarm Optimization?

Under complex currents, the motion governing equations of marine cables are complex and nonlinear, and the calculations of cable configuration and tension become difficult compared with those under the uniform or simple currents. To obtain the numerical results, the usual Newton-Raphson iteration is often adopted, but its stability depends on the initial guessed solution to the governing equations. To improve the stability of numerical calculation, this paper proposed separated the particle swarm optimization, in which the variables are separated into several groups, and the dimension of search space is reduced to facilitate the particle swarm optimization. Via the separated particle swarm optimization, these governing nonlinear equations can be solved successfully with any initial solution, and the process of numerical calculation is very stable. For the calculations of cable configuration and tension of marine cables under complex currents, the proposed separated swarm particle optimization is more effective than the other particle swarm optimizations.

Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System

In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.The convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential,where the mollification is of algebraic scaling.The main idea of the proof is to study the time evolution of a stopped process and obtain a Gronwall type estimate by using Taylor's expansion around the limiting stochastic process.

Aircraft Observations of Liquid and Ice in Midlatitude Mixed-Phase Clouds

ABSTRACT This paper reports airborne measurements of midlatitude altostratus clouds observed over Zhengzhou, Henan Province, China on 3 March 2007. The case demonstrates mixed-phase conditions at altitudes from 3200 to 4600 m （0°C to -7.6°C）, with liquid water content ranging from 0.01 to 0.09 g m-3. In the observed mixed-phase cloud, liquid water content exhibited a bimodal distribution, whereas the maximum ice particle concentration was located in the middle part of the cloud. The liquid and ice particle data showed significant horizontal variability on the scale of a few hundred meters. The cloud droplet concentration varied greatly over the horizontal sampling area. There was an inverse relationship between the cloud droplet concentration and ice particle concentration. A gamma distribution provided the best description of the cloud droplet spectra. The liquid droplet distributions were found to increase in both size and concentration with altitude. It was inferred from the profile of the spectra parameters that the cloud droplet sizes tend to form a quasi-monodisperse distribution. Ice particle spectra in the cloud were fitted well by an exponential distribution. Finally, a remarkable power law relationship was found between the slope （λ） and intercept （No） parameters of the exponential size distribution.

A LN2-based cooling system for a next-generation liquid xenon dark matter detector

In recent years, cooling technology for liquid xenon(LXe) detectors has advanced driven by the development of dark matter(DM) detectors with target mass in the 100–1000 kg range. The next generation of DM detectors based on LXe will be in the 50,000 kg(50 t)range requiring more than 1 k W of cooling power. Most of the prior cooling methods become impractical at this level.For cooling a 50 t scale LXe detector, a method is proposed in which liquid nitrogen(LN2) in a small local reservoir cools the xenon gas via a cold finger. The cold finger incorporates a heating unit to provide temperature regulation. The proposed cooling method is simple, reliable, and suitable for the required long-term operation for a rare event search. The device can be easily integrated into present cooling systems, for example the ‘‘Cooling Bus’ ’employed for the Panda X I and II experiments. It is still possible to cool indirectly with no part of the cooling or temperature control system getting in direct contact with the clean xenon in the detector. Also, the cooling device can be mounted at a large distance, i.e., the detector is cooled remotely from a distance of 5–10 m. The method was tested in a laboratory setup at Columbia University to carry out different measurements with a small LXe detector and behaved exactly as predicted.

Some Random Batch Particle Methods for the Poisson-Nernst-Planck and Poisson-Boltzmann Equations

We consider in this paper random batch interacting particle methods forsolving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann(PB) equation as the equilibrium, in the external unbounded domain. To justify thesimulation in a truncated domain, an error estimate of the truncation is proved inthe symmetric cases for the PB equation. Then, the random batch interacting particle methods are introduced which are O(N) per time step. The particle methods cannot only be considered as a numerical method for solving the PNP and PB equations,but also can be used as a direct simulation approach for the dynamics of the chargedparticles in solution. The particle methods are preferable due to their simplicity andadaptivity to complicated geometry, and may be interesting in describing the dynamics of the physical process. Moreover, it is feasible to incorporate more physical effectsand interactions in the particle methods and to describe phenomena beyond the scopeof the mean-field equations.

Real-Time Simulation of Aeolian Sand Movement and Sand Ripple Evolution: A Method Based on the Physics of Blown Sand

Simulation and visualization of aeolian sand movement and sand ripple evolution are a challenging subject. In this paper, we propose a physically based modeling and simulating method that can be used to synthesize sandy terrain in various patterns. Our method is based on the mechanical behavior of individual sand grains, which are widely studied in the physics of blown sand. We accounted significant mechanisms of sand transportation into the sand model, such as saltation, successive saltation and collapsing, while simplified the vegetation model and wind field model to make the simulation feasible and affordable. We implemented the proposed method on the programming graphics processing unit （GPU） to get real-time simulation and rendering. Finally, we proved that our method can reflect many characteristics of sand ripple evolution through several demonstrations. We also gave several synthesized desert scenes made from the simulated height field to display its significance on application.