In this paper, the lattice Boltzmann method is applied to investigate properties of magnetic fluids.
本文基于格子Boltzmann方法研究了磁流体的一些特性。
This paper reviews and summarizes the progress in this field as follows: the mathematical model and the difficulty of the analytical solutions is introduced; discusses the latest progress of the numerical solutions is discussed; the finite difference method, the Godunov method, the Boltzmann method, and the KFVS method of one-dimensional dam-break problem are introduced; the TVD method, the discontinuous finite element method, the finite volume method and characteristic method of two-dimensional dam-break problem are discussed; the applicability, the advantage and the disadvantage of each method are analyzed; and the progress in the numerical calculations of flow of fluid with free surface are presented.
回顾和总结了国内外对溃坝水流演进问题的研究进展：介绍了溃坝水流的数学模型及解析解法存在的困难，进而讨论了数值解法的最新进展；论述了求解溃坝水流一维问题的有限差分法、近似黎曼解的Godunov格式法、Boltzmann法、KFVS法和二维问题的TVD格式法、间断有限元法、有限体积法、特征线法，并分析了各种方法的适用范围和优缺点，及讨论了限制函数的使用；介绍了利用自由水面追踪方法计算溃坝水流的研究进展，并根据目前存在的不足和实际工程的需要，提出了进一步研究的方向和发展趋势。
The main research results are obtained as follows:(1) To understand the rheological properties of cohesive sediment, a linear gravity wave theory over Maxwell fluids of finite depth is presented, and a model to solve viscoelastic parameters by Genetic Algorithm and a pseudo-plastic model are developed; (2) A coupled numerical hydrodynamic model for wind waves and currents is developed, and a numerical model for multi-fraction fine sediment transport under combined action of wind, wave and current is developed; (3) Theoretical models for sediment suspension due to waves and combined waves and current are developed, and an analytical solution for sediment suspension due to waves and a semi-analytical solution for sediment suspension due to combined waves and current are obtained; (4) The Lattice Boltzmann Method is used to study the cohesive sediment transport due to combined waves and current, and simulation of wave boundary layer, combined wave and current boundary layer, and cohesive flocs settling in still and turbulent water are carried out.
其主要研究内容和取得的成果有：（1）为了了解粘性泥沙的流变规律，建立了有限深度Maxwell 粘弹性流体上线性重力波理论，并针对影响泥沙运动特性的流变特性进行研究，建立了利用遗传算法求解淤泥粘弹性参数的模式和泥床伪塑性体模型；（2）建立了近岸风浪与水流运动模拟的耦合水动力数值模型和风、浪、流共同作用下多组分细颗粒泥沙模拟的数学模型；（3）建立了波浪及波流共同作用下悬沙分布理论模型，得到了波浪作用下悬沙分布的解析解和波流共同作用下悬沙分布的半解析解；（4）将格子玻尔兹曼方法引入到波流共同作用下粘性泥沙运动的研究中，利用LBM对波浪边界层、波流边界层和粘性泥沙絮团的静水沉降和在水流中的沉降进行了模拟，为从微观角度研究波流边界层运动和粘性泥沙运动开辟了新的思路。
Using the linear Boltzmann equation and Maxwell equations, and assuming that the electron energy distribution function obeys the Boltzmann distribution, we present general expressions of the rf electric field and power absorption, discuss the influence of the discharge pressure and electron temperature on these two quantities, and find the anomalous skin depth is about 2 cm.
利用线性Boltzmann方程和Maxwell方程组，并假设电子的能量分布为麦克斯韦分布，本文推导出射频电场及功率吸收的一般表示式，并分别研究了电子温度及放电气压对射频电场和功率吸收特性的影响，发现射频电场的趋肤深度约为2cm。
Here, we point out that, within the frame of general relativity, the basic astrophysical equations are Einstein equation, Boltzmann equation of the distribution function of real matter in the presence of electromagnetical field in curved spacetime, Maxwell equation and the equation of radiative transfer of Stokes parameter of photons in curved spacetime.
这里，我们指出，在广义相对论框架下，天体物理基本方程为Einstein场方程，弯曲时空中实物质分布函数所满足的含有电磁场的Boltzmann方程，弯曲时空中Maxwell方程组和弯曲时空中光子Stokes参量所满足的辐射转移方程。
Equation Boltzmann provides entropy function with unambiguous statistic significance. It indicates that entropy in the macro state equals Constant K times the logarithm of the corresponding one in its micro state.
玻耳兹曼方程给熵函数以明确的统计意义，它指出，某个宏观状态的熵等于玻耳兹曼常量k乘以相应微观状态数的对数。
Rubinstein. The CE method is new approach for combinatorial optimization, and has rapidly developed into a powerful and versatile technique. The basic idea behind the CE method is to transform the original optimization problem to an associated stochastic optimization problem, and then to tackle the stochastic optimization efficiently by an adaptive sampling algorithm based on Kullback-Leibler cross-entropy, importance sample and Boltzmann function.
交叉熵算法是Rubinstein发起的一种新的问题求解方法，交叉熵算法的特色是给出了用来产生好的更新学习策略的数学框架，主要思想是利用Kullback-Leibler交叉墒，重要度采样以及波尔兹曼分布，把组合优化最优解问题转化为求解辅助的简单随机优化问题。
Three dynamic behaviors are stationary asymmetric segregated state、periodic one and stationary homogeneous one. The effect of granular parameters such as mass radios of two kinds of granulars、diameter ratios、granular number、restitution coeffictients and the length of compartment on oscillation regime and clustering amplitude are investigated in detailed. The rules of dynamic characteristics of system associated with these parameters are presented. The clustering amplitude varies with the increase of applied intensity in Boltzmann function, which is found firstly.
在数值模拟方面，采用事件驱动法模拟两室、三室和四室盒装化系统中颗粒气体的演化过程，重现了颗粒混合物的三种动力学形态----非对称聚集态、振荡聚集态和对称均匀态，详细讨论了两种颗粒的质量比、直径比、颗粒个数比、恢复系数和盒子宽度等参数对振荡区间范围和聚集幅值的影响，给出了盒装化系统动力学演化特征随这些参数变化的一般规律，第一次指出系统的聚集幅值随激振强度的增加按照玻尔兹曼函数关系变化。
The avtivation time constant was measure as the monoexponential fit to the curret curve induced at＋10 mV, andτincreased from 1.04±0.17ms to 1.52±0.19ms(n=6, P＜0.05) after 0.5% drug application. The steady-state inactivation curve was fitted by a Boltzmann function.
分别用单指数和双指数方程拟合+10 mV引出电流的时间依赖性激活和失活曲线，药物浓度0.5％时，用药前后通道的激活时间常数分别为1.04±0.17ms和1.52±0.19ms(n=6，P＜0.05)，通道的快失活时间常数分别为13.00±3.72 ms和42.74±10.10ms(n=6，P＜0.05)，慢失活时间常数分别为97.75±20.79 ms和177.26±28.29ms(n=6，P＜0.05)。
This paper presents some examples to explain that adopt Boltzmann equation description the phenomena of interest will be adequate.
提出几个例子阐明采用Boltzmann方程分析来描述所关心的现象是可以胜任的。
The derivation of the Navier-Stokes equation from Lattice Boltzmann equation is given in detail in this thesis.
本文给出了从格子玻尔兹曼方程出发到Navier-Stokes 方程的详细推导。
A model equation of the Boltzmann equation for binary gas mixtures is deduced in this article.
本文提出一种二元混合气体玻耳兹曼方程式的模型方程式。
The basic Boltzmann equation in reference is improved.
改进了文献中报导的Boltzmann基本方程。
In a periodic structure, the transport property can be well described by the Boltzmann`s transport equation.
电子在周期性晶格中的传输行为，可由古典的波兹曼理论描述。
This notion was introduced by Lions and Di Perna for the study of Boltzmann equation.
重整化解的概念是Lions和Di Perna在研究Boltzmann方程中提出的，后来被应用到一类非线性抛物方程。
Some of advanced techniques exhibit many different types of spatial and temporal behavior, typically the analysis of such phenomena is based on a Boltzmann equation.
若干高新技术出现许多不同形式的空间与时间特性，这些现象的典型分析是以Boltzmann方程为基础的。
The results show that the ion excited configuration population is evidently affected by the non-Boltzmann distribution.
结果表明，它对相对激发组态密度的影响非常显著。
Furthermore, the effects of non-Boltzmann distribution on mean ion charge and ion excited configuration population are investigated.
进而研究非Boltzmann分布对平均电离度和激发组态相对密度的影响。
The model consisted of the Poisson-Boltzmann equation, the Navier-Stokes equation, and the energy equation coupled through temperature.
建立微细圆管内电渗流动的非稳态数学模型，模型通过温度将电渗流的Poisson-Boltzmann方程、动量守恒和能量守恒方程耦合起来。
In the Boltzmann statistic the quantity of fluctuations is usually negligible.
事实上，两态的能量及系统与环境在路径上的交换热均有k_BT涨落，只是在玻耳兹曼统计中，这个量级的涨落被忽略了。