用砖墙方法和薄层方法计算Gibbons-Maeda黑洞时空中标量场的统计力学熵

利用砖墙方法和薄层方法计算了Gibbons-Maeda黑洞背景时空中标量场的统计力学熵.用砖墙方法求得的统计力学熵有两项:其中一项与Gibbons-Maeda黑洞视界面积成正比,并且当截断因子满足一定的关系时,熵为其视界面积的四分之一;另一项是对数发散项.利用薄层方法所求得的熵只有与Gibbons-Maeda黑洞视界面积成正比的项,对数发散项被自然消去.     

厄尔尼诺/拉尼娜-南方涛动非线性扰动模型孤子的渐近解法

研究了一类厄尔尼诺/拉尼娜-南方涛动(ENSO)随机扰动模型. 首先, 利用特殊的待定系数方法得到了无扰动ENSO模型下的孤子精确解. 然后利用渐近理论和方法构造了随机扰动ENSO模型的近似解, 并举例说明得到的渐近解具有较好的精度.     

一类扰动发展方程近似解

采用了一个简单而有效的技巧, 研究了一类扰动发展方程. 首先引入求解一个相应典型方程的行波孤波解. 然后利用渐近方法得到了原扰动发展方程的近似解. 利用泛函分析的不动点定理, 指出了近似解级数的收敛性, 并讨论了近似解的精度.     

太阳电池单二极管模型中的参数提取方法

近年来,太阳电池参数提取方法获得了广泛关注.原因在于匹配的电池参数,可以有效减少内外因素对光伏阵列发电效率的影响.本文以太阳电池单二极管模型为讨论对象,对其五个参数的提取方法进行了详细介绍;对目前典型的四类太阳电池参数提取方法 (即解析提取参数方法,借助朗伯W函数函数提取参数方法,构建或利用特殊函数提取参数方法,利用智能算法提取参数方法)进行归纳与总结.阐述了这些方法的主要理论与实现途径,更重要的是对它们的优缺点进行了探讨.最后,对参数提取未来的研究动态进行了展望,以期对参数提取方法提供一些思路,为国内同行开展相关研究提供一些帮助.     

液面冲击引起液滴飞溅问题的CIP方法数值模拟

利用自主研发的CIP-ZJU（Constrained Interpolation Profile Method in Zhejiang University）高精度数学模型研究强非线性自由表面流动问题.模型在直角坐标系统下建立,采用紧致插值曲线CIP方法作为流场的基本求解器,通过多相流的方式实现固-液-气耦合同步求解,采用平衡格式的VOF（VOF/WLIC：Volume of Fluid/Weighted LineInterface Calculation）自由面捕捉方法改进了原模型,利用浸入边界方法处理运动物体.利用改进的CIP模型开展了不同类型的物体冲击液面引起的液滴飞溅现象的数值模拟,重点分析液滴飞溅过程中的自由液面变形、作用荷载和物体位置等.通过数值结果与实验结果的比较验证模型的可靠性.结果表明：平衡格式的VOF自由面捕捉方法能更精确地重构自由面,本文的数学模型可精确预测强非线性自由表面流动问题.     

随机扰动下三维流体界面不稳定性的并行计算

对三维流体界面不稳定性的数值模拟引进了新的数值计算方法,并在MPI并行计算环境下进行了数值模拟.利用LevelSet方法确定界面位置,零水平集对应界面位置.对应离散LevelSet方程和界面两侧的两套Euler方程,借助于Ghost网格方法来完成离散.对最后网格点上的两套状态量的辨认依赖于该点的LevelSet值的符号.并进行了数值计算.     

利用Ghost Fluid方法模拟激波与柱形界面相互作用

利用GhostFluid方法(后面简称Ghost方法)和γ-model方法,在同样的时空离散精度条件下,对激波与柱形界面相互作用的二维可压缩流场进行了直接模拟,并与实验结果相比较.从模拟结果看,在短时间内,Ghost方法和γ-model方法模拟的结果与实验结果基本相同,两种方法均正确地模拟出界面的位置、激波的强度和速度.但随着时间的发展,具有较大数值耗散的γ-model方法的计算结果与实验差别越来越大;而数值耗散较小的Ghost方法能较为正确地模拟界面的运动.     

光电经纬仪外场星校方法的理论与实践

研究了光电经纬仪外场星校方法.根据“X型号光电经纬仪”的探测能力建立了星库、星表.讨论了利用拍星数据解算各项误差的方法,并给出了基于视窗的可视化工程应用软件系统.     

不规则区域热传导问题无网格Petrov-Galerkin方法的数值模拟

无网格Petrov-Galerkin(MLPG)方法是一种真正的无网格方法,它利用节点计算待求量的插值函数,并利用高斯型求积公式在局部子域内进行数值积分.本文提出了一种有效的用于不规则区域的高斯型数值积分实施方法,通过数值研究表明:该方法能很好地处理不规则区域积分,其计算结果与基准解和FLUENT的计算结果吻合很好.     

界面不稳定性数值模拟中的虚拟流动方法

研究了流体界面不稳定性的一类数值模拟方法——虚拟流动方法(Ghost Fluid Method).在算法中直接针对多维问题设定虚拟区域的流动参数,在流体力学方程的计算中采用了非分裂型的高分辨SCB格式,最后利用该方法完成了R-M和R-T不稳定性问题的数值计算,得到了满意的计算结果.     

Approach to equilibrium for locally expanding maps in ℝ k

By using a well known technique from classical statistical mechanics of one-dimensional lattice spin systems we prove existence of an absolutely continuous invariant asymptotic measure for certain locally expanding mapsT of the unit cube in ^k . We generalize herewith in a certain sense the results of Lasota and Yorke on piecewise expanding maps of the unit interval to higher dimensions. We show a Kuzmin-type theorem for these systems from which exponential approach to equilibrium and strong mixing properties follow.Heisenberg fellow of the Deutsche Forschungsgemeinschaft     

Spectrum of coherent structures in a turbulent environment

The statistical properties of the turbulent field consisting of drift waves randomly interacting with a coherent structure are investigated. By using a nonperturbative method (analogous to the "semiclassical" approach in quantum mechanics), we calculate explicitly the generating functional of the correlations.     

Dynamical pair correlations of classical and quantum fluids perturbed with weak long-range forces

We study time dependent correlation functions of ideal classical and quantum gases using methods of equilibrium statistical mechanics. The basis for this is the path integral formalism of quantum mechanical systems. By this approach the statistical mechanics of a quantum mechanical system becomes the equivalent of a classical polymer problem in four dimensions where imaginary time is the fourth dimension. Several non-trivial results for quantum systems have been obtained earlier by this analogy. Here we will focus upon particle dynamics. First ideal gases are considered. Then interactions, that are assumed weak and of long range, are added, and methods of classical statistical mechanics are applied to obtain the leading contribution. Comparison is performed with known results of kinetic theory. These results demonstrate how methods developed for systems in thermal equilibrium also is applicable outside equilibrium. Thus, more generally, we have reason to expect that these methods will be accurate and useful for other situations of interacting many-body systems consisting of quantized particles too. To indicate so we sketch the computation of the induced Casimir force between parallel plates filled with ions for the situation where the ions are quantized, but the interaction remains electrostatic. Further in this respect we establish expressions for a leading correction to ab initio calculations for the energies of the quantized electrons of molecules. To our knowledge these two latter applications go beyond earlier results.     

Thermodynamics and statistical mechanics of dense granular media

By detailed molecular dynamics and Monte Carlo simulations of a model system we show that granular materials at rest can be described as thermodynamics systems. First, we show that granular packs can be characterized by few parameters, as much as fluids or solids. Then, in a second independent step, we demonstrate that these states can be described in terms of equilibrium distributions which coincide with the statistical mechanics of powders first proposed by Edwards. We also derive the system equation of state as a function of the "configurational temperature," its new intensive thermodynamic parameter.     

C*-algebras and Mackey's axioms

A non-commutative version of probability theory is outlined, based on the concept of a*-algebra of operators (sequentially weakly closedC*-algebra of operators). Using the theory of*-algebras, we relate theC*-algebra approach to quantum mechanics as developed byKadison with the probabilistic approach to quantum mechanics as axiomatized byMackey. The*-algebra approach to quantum mechanics includes the case of classical statistical mechanics; this important case is excluded by theW*-algebra approach. By considering the*-algebra, rather than the von Neumann algebra, generated by the givenC*-algebraA in its reduced atomic representation, we show that a difficulty encountered byGuenin concerning the domain of a state can be resolved.     

Supersymmetry and SWKB Approach to Dirac Equation with Hyperbolic Scarf Potential

By using the supersymmetric quantum mechanics and shape invariance concept, we study the Dirac equation with the hyperbolic Scarf potential and the exact energy spectrum is obtained. Also, we calculate the bound state energy eigenvalues by using the supersymmetric WKB approximation approach so that we get the same results.     

微重坏境下旋转对称贮箱内静液面方程Runge-Kutta数值解

由力学平衡方程导出了旋转对称贮箱内静液面的二阶非线性常微分方程，接着具体了球腔，旋转 椭球腔、柱面腔的边界接触角条件，最后使用Ｒｕｎｇｅ－Ｋｕｔｔａ法在计算机上得出了数值结果，绘出静液面开头曲线，分析了算法特点。     

About the non vanishing of boundary terms in correlation functions as origin of phase transitions. A microscopic proof of a Goldstone theorem in classical statistical mechanics

We give a general microscopic proof that the well known Goldstone theorem connected with spontaneous symmetry breaking in quantum statistical mechanics and quantum field theory has a counterpart in classical statistical mechanics. Our approach is mainly based on the replacement of commutators by Poisson brackets as infinitesimal generators of symmetries and on the Fourier transformed version of the so called Kubo-Martin-Schwinger property of equilibrium states. Especially we show that the phase transition is related to the non vanishing of certain boundary contributions in Poisson brackets which from the naive point of view should vanish.     

Foundations of the quantum statistics of systems in equilibrium: A measuretheoretic approach

The fundamental equations of equilibrium quantum statistical mechanics are derived in the context of a measure-theoretic approach to the quantum mechanical ergodic problem. The method employed is an extension, to quantum mechanical systems, of the techniques developed by R. M. Lewis for establishing the foundations of classical statistical mechanics. The existence of a complete set of commuting observables is assumed, but no reference is made a priori to probability or statistical ensembles. Expressions for infinite-time averages in the microcanonical, canonical, and grand canonical ensembles are developed which reduce to conventional quantum statistical mechanics for systems in equilibrium when the total energy is the only conserved quantity. No attempt is made to extend the formalism at this time to deal with the difficult problem of the approach to equilibrium.     

Statistical mechanics and the ontological interpretation

To complete our ontological interpretation of quantum theory we have to conclude a treatment of quantum statistical mechanics. The basic concepts in the ontological approach are the particle and the wave function. The density matrix cannot play a fundamental role here. Therefore quantum statistical mechanics will require a further statistical distribution over wave functions in addition to the distribution of particles that have a specified wave function. Ultimately the wave function of the universe will he required, but we show that if the universe in not in thermodynamic equilibrium then it can he treated in terms of weakly interacting large scale constituents that are very nearly independent of each other. In this way we obtain the same results as those of the usual approach within the framework of the ontological interpretation.Professor D. Bohm died on 28 October 1992, shortly after this paper was completed.