Application of the dissipative particle dynamics method to magnetic colloidal dispersions

The validity of the application of the dissipative particle dynamics (DPD) method to ferromagnetic colloidal dispersions has been investigated by conducting DPD simulations for a two–dimensional system. First, the interaction between dissipative and magnetic particles has been idealized as some model potentials, and DPD simulations have been carried out using such model potentials for a two magnetic particle system. In these simulations, attention has been focused on the collision time for the two particles approaching each other and touching from an initially separated position, and such collision time has been evaluated for various cases of mass and diameter of dissipative particles and model parameters, which are included in defining the equation of motion of dissipative particles. Next, a multi–particle system of magnetic particles has been treated, and particle aggregates have been evaluated, together with the pair correlation function along an applied magnetic field direction. Such characteristics of aggregate structures have been compared with the results of Monte Carlo and Brownian dynamics simulations in order to clarify the validity of the application of the DPD method to particle dispersion systems. The present simulation results have clearly shown that DPD simulations with the model interaction potential presented here give rise to physically reasonable aggregate structures under circumstances of strong magnetic particle–particle interactions as well as a strong external magnetic field, since these aggregate structures are in good agreement with those of Monte Carlo and Brownian dynamics simulations.     

Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag

We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog–Fokker–Planck equation for the one-particle velocity distribution function. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects such as Mpemba and Kovacs-like ones.     

Nonlinear Couette Flow in a Low Density Granular Gas

A model kinetic equation is solved exactly for a special stationary state describing nonlinear Couette flow in a low density system of inelastic spheres. The hydrodynamic fields, heat and momentum fluxes, and the phase space distribution function are determined explicitly. The results apply for conditions such that viscous heating dominates collisional cooling, including large gradients far from the reference homogeneous cooling state. Explicit expressions for the generalized transport coefficients (e.g., viscosity and thermal conductivity) are obtained as nonlinear functions of the coefficient of normal restitution and the shear rate. These exact results for the model kinetic equation are also shown to be good approximations to the corresponding state for the Boltzmann equation via comparison with direct Monte Carlo simulation for the latter.     

Domain Wall Migration in 3-d in the Presence of Diffusing Impurities

A new three-dimensional simulation procedure was developed for domain wall (grain boundary, APB, magnetic, etc.) migration in the presence of diffusing impurities. The simulation is based upon a kinetic Monte Carlo algorithm and an extended Ising model, incorporating both conserved and non-conserved dynamics. The simulations show a dependence of the domain wall velocity on driving force which is very similar to that seen in 2-d and in qualitative agreement with experiment. That is, the presence of a low mobility regime at small driving force and an abrupt transition to a high mobility regime at larger forces, under some conditions, and a continuous, non-linear dependence of the velocity on the force in others. The main qualitative difference between the 2-d and 3-d simulation results is in how the domain wall roughness depends on driving force. The velocity-driving force relation is not consistent with classic continuum models, but may be described, in the high velocity regime, by a theory based upon a discrete version of these models.     

热辐射输运问题的隐式蒙特卡罗方法求解

热辐射与物质相互作用及辐射光子在物质中的传输是惯性约束聚变研究中的重要课题. 介绍了基于隐式蒙特卡罗方法的辐射输运方程,在该方程的积分-微分形式基础上,推导了利于蒙特卡罗方法模拟的等价的积分输运方程;基于积分方程设计数值模拟流程,编写三维蒙特卡罗数值模拟程序;针对热辐射输运典型问题及benchmark问题开展了数值实验,计算结果验证了方法的适应性及程序的正确性. 关键词： 热辐射 惯性约束聚变 输运方程 隐式蒙特卡罗     

A hybrid method for hydrodynamic-kinetic flow Part I: A particle-grid method for reducing stochastic noise in kinetic regimes

In this work we present a hybrid particle-grid Monte Carlo method for the Boltzmann equation, which is characterized by a significant reduction of the stochastic noise in the kinetic regime.     

The Interface Kinetics of Crystal Growth Processes

A brief review of the present state of our understanding of the kinetic processes which take place on the atomic scale at the interface during crystal growth is presented in this paper. Computer simulations have played a central role in the development of this understanding. Three aspects will be discussed:(1) There are two classes of materials based on their different modes of crystallization. Molecular dynamics modeling has demonstrated that the growth rate for many simple materials is not thermally activated, but instead depends on the thermal velocity of the atoms.(2) The cooperative processes which give rise to the surface roughening transition. Kinetic Monte Carlo studies played a central role in the development of our understanding of how interface roughness dominates growth morphologies.(3) Solute trapping in alloys. Kinetic Monte Carlo simulations of alloys have led to an understanding of these kinetic effects during alloy crystallization.     

Energy diffusion controlled reaction rate in dissipative Hamiltonian systems

In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first-passage time (MFPT) of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kramers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.     

A hybrid fluid–kinetic neutral model based on a micro–macro decomposition in the SOLPS-ITER plasma edge code suite

We present a hybrid fluid–kinetic model for the hydrogenic atoms in the plasma edge that is implemented in SOLPS-ITER. A micro–macro decomposition of the kinetic equation leads to a fluid model with a continuity and parallel momentum equation (implemented in B2.5) coupled to a kinetic correction equation (implemented in EIRENE). We assess the hybrid model for a high recycling fixed background plasma. The hybrid approach leads to a reduction of the Central Processing Unit(CPU) time required to obtain the same statistical error as the full kinetic Monte Carlo (MC) simulation with approximate factors of 1.7, 4.9, and 1.9 for the particle, parallel momentum, and electron energy source, respectively. However, there is an increase in CPU time for the ion energy source. By comparing the results with our in-house plasma edge code, we conclude that the hybrid performance can be improved by adapting some default MC features in EIRENE.     

An application of cell theory to molecular models of n-alkane solids

Solid phase properties for hard sphere chain molecular models of n-alkanes are calculated using the cell theory, and a numerical method for implementation of cell theory for chain molecules is described. Good agreement with Monte Carlo simulations for solid phase properties is obtained from the theory. By using cell theory for the solid phase and an equation of state for the fluid phase, solid-phase equilibrium can be calculated. The predictions are in quite good agreement with Monte Carlo simulation results. Cell theory is used to assess the impact of an approximate treatment used in earlier work for the effect of the temperature dependence of the molecular flexibility upon the solid phase properties of a hard chain model with a realistic torsional potential.     

Dissipative Time Dependent Density Functional Theory

The simplest density functional theory due to Thomas, Fermi, Dirac and Weizsäcker is employed to describe the non-equilibrium thermodynamic evolution of an electron gas. The temperature effect is introduced via the Fermi-Dirac entropy, while the irreversible dynamics is described by a non-linear diffusion equation. A dissipative Kohn-Sham equation is also proposed, which improves the Thomas-Fermi-Weizsäcker kinetic functional.     

Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study

In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.     

Dynamic properties of the Monte Carlo method in statistical mechanics

By means of the Monte Carlo sampling technique the equilibrium thermodynamics of fluids and magnets can be calculated numerically. We show that the questions of convergence and accuracy of this method can be understood in terms of the dynamics of the appropriate stochastic model. Also, we discuss to what extent various choices of transition probabilities lead to different dynamic properties of the system. As examples of applications, we consider Ising and Heisenberg spin systems. The numerical results about the dynamic correlation functions are compared to simple approximations taken from the theory of the kinetic Ising model.     

Chemical potential,Helmholtz free energy and entropy of argon with kinetic Monte Carlo simulation

We present a method based on kinetic Monte Carlo (kMC) to determine the chemical potential, Helmholtz free energy and entropy of a fluid within the course of a simulation. The procedure requires no recourse to auxiliary methods to determine the chemical potential, such as the implementation of a Widom scheme in Metropolis Monte Carlo simulations, as it is determined within the course of the simulation. The equation for chemical potential is proved, for the first time in the literature, to have a direct connection with inverse Widom potential theory in using real molecules rather than ghost molecules. We illustrate this new procedure by several examples, including fluid argon and adsorption of argon as a non-uniform fluid on a graphite surface and in slit pores.     

Equation of Motion in Hybrid Monte Carlo

The equation of motion and molecular dynamics for simulating lattice field theory using the Hybrid Monte Carlo (HMC) algorithm are described. Some techniques for improving the HMC efficiency are discussed.     

Two-scale modeling of adsorption processes at structured surfaces

We present an algorithm for the simulation of vicinal surface growth. It combines a lattice gas anisotropic Ising model with a phase-field model. The molecular behavior of individual adatoms is described by the lattice gas model. The microstructure dynamics on the vicinal surface are calculated using the phase-field method. In this way, adsorption processes on two different length scales can be described: nucleation processes on the terraces (lattice gas model) and step-flow growth (phase field model). The hybrid algorithm that is proposed here, is therefore able to describe an epitaxial layer-by-layer growth controlled by temperature and by deposition rate. This method is faster than kinetic Monte Carlo simulations and can take into account the stochastic processes in a comparable way.     

Van hove self-correlation function of a hard-disk fluid: Enskog theory and computer simulation

The van Hove self-correlation function in a hard-disk fluid is analyzed using the Lorentz-Enskog kinetic equation and the kinetic model method of solution. Numerical convergence of the model solutions is demonstrated and accurate model results are used to interpret molecular dynamics simulation data at finite wave numbers. It is found that at about 60% of freezing density the error in the Enskog theory can be mainly attributed to an underestimate of the effective self-diffusion coefficient, but at 90% freezing density a theory which treats correlated collisions is needed to describe the width behavior of the singleparticle density fluctuation spectrum.     

Electron boltzmann kinetic equation averaged over fast electron bouncing and pitch-angle scattering for fast modeling of electron cyclotron resonance discharge

The electron distribution function (EDF) in an electron cyclotron resonance (ECR) discharge is far from Maxwellian. The self-consistent simulation of ECR discharges requires a calculation of the EDF on every magnetic line for various ion density profiles. The straightforward self-consistent simulation of ECR discharges using the Monte Carlo technique for the EDF calculation is very computer time expensive, since the electron and ion time scales are very different. An electron Boltzmann kinetic equation averaged over the fast electron bouncing and pitch-angle scattering was derived in order to develop an effective and operative tool for the fast modeling (FM) of low-pressure ECR discharges. An analytical solution for the EDF in a loss cone was derived. To check the validity of the FM, one-dimensional (in coordinate) and two-dimensional (in velocity) Monte Carlo simulation codes were developed. The validity of the fast modeling method is proved by comparison with the Monte Carlo simulations. The complete system of equations for FM is presented and ready for use in a comprehensive study of ECR discharges. The variations of plasma density and of wall and sheath potentials are analyzed by solving a self-consistent set of equations for the EDF.     

The Limiting Kinetic Equation of the Consistent Boltzmann Algorithm for Dense Gases

This paper establishes a theoretical foundation for the Consistent Boltzmann Algorithm (CBA) by deriving the limiting kinetic equation. The formulation is similar to the proof by one of the authors that the Boltzmann equation is the limiting kinetic equation for Direct Simulation Monte Carlo [W. Wagner, J. Statist. Phys. 66:1011 (1992)]. For a simplified model distilled from CBA, the limiting equation is solved numerically, and very good agreement with the predictions of the theory is found.