The Green's Function Method for Initial-Boundary Value Problem of Boltzmann Equation Boltzmann方程初边值问题的Green函数方法
The probability function is definitely a derivative of the Boltzmann probability distribution function. 函数的概率绝对是一个波尔兹曼概率分布函数的导数。
A lattice Boltzmann model for tow dimension Burgers equation is presented. The parameter in the Chapman-Enskog expansion for local equilibrium distribution function is determined by the tow dimension Burgers equation. 给出了二维Burgers方程的格子Boltzmann模型,用Burgers方程确定了平衡分布函数Chapman-Enskog展开中的待定系数。
The model Boltzmann equations, which are derived from the transformations of reduced distribution function and discrete velocity ordinate together, are solved through using an implicit flux-corrected second-order upwind TVD ( Total Variation Diminishing) scheme. 模型Boltzmann方程先后经简化分布函数和离散速度坐标变换后,采用一个隐式通量修正二阶迎风TVD格式差分求解。
In this paper it ′ s prove that the Cauchy problem for the relativistic Boltzmann equation with hard relativistic interactions has a global mild solution of the initial distribution function satisfies finite mass, energy and entropy. 本文证明了周期单元中带有某些硬相互作用的相对论Boltzmann方程初值问题在初值满足质量、能量和熵有限的条件下具有一个整体温和解。
In this paper, plasma transport equations are derived under the condition that the collision term in the equation is taken as Boltzmann form and the distribution function is approximately Maxwellian. 从等离子体动力学方程出发,采用玻尔兹曼碰撞项,在粒子分布函数偏离麦克斯韦分布甚小的情况下,作三级矩近似得到了等离子体迁移方程组。
The mathematical imitation to the adsorption isotherms of MgCl 2 · 4H 2O and MgCl 2 · 2H 2O under different temperatures indicates that Boltzmann Function is the ideal equation to describe those adsorption isotherms. 在不同温度下对MgCl2·4H2O和MgCl2·2H2O对水的吸附等温线所进行的数学模拟结果表明,Bolzmann函数是描述该等温线较为理想的方程。
The change of opacity with the basis weight fits the Boltzmann function with the relativity of 99.98%, indicating that basis weight plays a decisive role on the opacity value while the influence of scattering coefficient can be ignored. 不透明度随定量的变化采用Boltzmann函数进行非线性回归,达到99.98%的相关性,说明定量对不透明度起决定性作用而光散射系数的影响可忽略不计。
The theoretical study indicates that we are able to find a relevant Boltzmann machines whose energy function is corresponding to the LQ performance index. Boltzmann机,它的能量函数与二次型的性能指标等价。
The unified algorithm for the gas flows from rarefied transition to continuum regime can be developed by numerically solving the Boltzmann simplified velocity distribution function equation. 通过开展基于Boltzmann简化速度分布函数方程数值求解,发展起从稀薄流到连续流统一算法。
An Information Condensing Distribution and a Boltzmann Entropy Function for Continuous Maximin Problems 参变极值问题的信息凝聚分布与Boltzmann极大熵函数
After characteristic analysis of ductile-brittle transition temperature curve and comparison of several regression functions with S shape, it is found that Boltzmann function has higher correction coefficient, lower remaining errors, powerful adaptability and explicit physical meaning. 对韧脆转变温度曲线形状的分析和几种常见回归数学模型的比较发现,Boltzmann函数具有相关系数高、残差小、适应性强及参数物理意义明确的特点。
Solving the Boltzmann equation for two-component system by relaxation ap-proximation, the non-equilibrium distribution function of binary mixed gases is determined. 应用弛豫近似法求解二元系的玻耳兹曼方程,确定了二元气体的非平衡分布函数,从而导出了热扩散过程的线性唯象关系。
( Using) two distribution functions to define the vortices and stream function, we obtained two lattice Boltzmann equations to build this model. 用两个分布函数分别定义涡量和流函数,得到用两个格子Boltzmann方程建立的模型。
The Boltzmann's entropy is used to measure the spreading extent of strange attractors in this paper. The first local maximum of entropy function is suggested as a criterion for selecting delay time in reconstruction of strange attractors. 用Boltzmann统计状态熵度量怪引子的展开程度,从而提出选取延迟时间变量的第一极大熵准则。
The results show that δ_m decreases with decreasing temperature in a manner consistent with the Boltzmann function. 结果表明,总的趋势是δm随着温度的降低而下降,其规律可以比较好的用Boltzmann函数描述;
By expanding the distribution function in the lattice Boltzmann equation using Chapman-Enskog expansion and multiple-dimensioned expansion to time, series of partial differential lattice Boltzmann equation in different time scales is obtained, and thus we obtain the moments of the equilibrium distribution function. 通过对此方程中的分布函数作时间多尺度展开和Chapman-Enskog展开,可得到系列偏微分方程,从而可获得平衡态分布函数的各阶矩。
Lattice Boltzmann method describes the statistical behavior of the molecular and obtain macroscopic physical quantities by studying temporal and spatial evolution of the local particle distribution function. 通过研究局部粒子分布函数的时空演化来描述分子的统计行为和获得宏观物理量。