平衡态的统计性

本文从玻尔兹曼定律出发,简单地统计出处于平衡态的气体是一最可几分布、是统计性的。     

推导正则分布和巨正则分布的最可几方法

一、引言平衡态统计物理是研究宏观系统平衡现象的理论。它的基本原理是简单的,但是它的应用却十分广泛,以致一些理论物理学家称赞它是理论物理中最完美、最精采的学科之一。然而,统计物理学这一特色,并不是为每个初学者都能体会的。例如对系综理论中具有广泛适用意义的两种平衡态统计分布——正则分布和巨正则分布的导出这一问题,按目前大多数教科书中传统方法讲述,往往使初学者感到困难较大,不易接受,甚至有人认为统计物理学是理论物理中最没有根据的一部分。为此,笔者在教学过程中作了一些探讨,感到上述误解的产生,并非统计理论本身的不正确,而常常是出于对问题的陈述不够合理,推     

多元近独立粒子系统的玻耳兹曼统计和系综统计等价性

利用平衡态统计物理的等概率原理，玻耳兹曼统计法和系综统计法，导出在平衡状态下多种近独立粒子系统的粒子数分布．结果表明．对于宏观系统而言，玻耳兹曼统计和系综统计是等价的。     

熵的两种表述的等价性

自普里戈金从玻尔兹曼方程出发证明热力学第二定律之熵增加原理,克劳修斯熵表述和玻尔兹曼熵表述在平衡态统计和非平衡态统计里都具有等价性。熵作为热力学的最基本概念被广泛应用于各个领域,比如宇宙理论、信息理论、生命科学、控制理论、概率论等。该文尝试以最简单的单原子分子理想气体系统为基础,以玻尔兹曼分布为出发点,从正反两个方向严格推证平衡态下克劳修斯熵表述与玻尔兹曼熵表述的等价性,基于此进一步说明平衡态下H函数与熵的一致性。     

系统理论的基本概念

本文介绍了系统理论的理论结构和Г－空间、系综的三种统计分布及涨落等基本概念，归纳了习题类型和解题的主要方法。     

浅论配分函数的意义和作用

统计理论是热现象微观理论的中心内容,其中由相同的近独立粒子组成的孤立系统处于平衡态时的统计分布规律——玻尔兹曼统计分布律则是统计理论中应用最广的部分,并且只要求出配分函数就能写出这个分布的表示式,进一步揭示系统的热学性质。为了讨论配分函数的意义和作用,对 N 个近独立粒子构成的理想体系,设粒子的自由     

基于MatlabGUI的麦克斯韦速率分布律的数字化教学研究

麦克斯韦速率分布律是气体分子热运动在平衡态下的统计规律。其数学表达式抽象复杂,教学中不便精确计算和绘制速率分布曲线。利用MatlabGUI可对麦克斯韦速率分布律进行数字化处理,即同一气体在不同温度下的速率分布曲线、同一温度下不同气体的速率分布曲线和三种统计速率（最概然速率、平均速率、方均根速率）的计算。该工作对麦克斯韦速率分布律的教学有较大帮助。     

麦克斯韦速率分布律的推导

用初等方法推导了麦克朗韦速率分布律,证明该分布律不仅适用于无外场的理想气体的平衡态,而且也适用于处在重力场中的理想气体以及非理想气体的平衡态。同时,对分布函数的归一化及求力学量平均值的积分限为什么能取分子速率为无限大作了解释和说明。     

系综概念的教学研究

系综概念的教学研究彭家骥在平衡态统计物理中,运用最概然分布法建立起来的玻耳兹曼统计理论、玻色统计理论和费米统计理论只适用于由近独立粒子组成的系统。然而,自然界的大多数情况却是组成系统的粒子间的相互作用不能忽略,例如,固体、液体、低温高压下的实际气体。...     

生成函数方法在N维球计算及系综理论中的应用

一、问题的提出在统计物理中,一定体积的孤立系统其能量和粒子数是固定不变的.考虑到实际系统的能量不可能严格不变,所以,对于孤立系统的能量我们理解为在E～E+△E之间,但是,△E<相似文献   

Application of two-order difference to gap statistic

Gap statistic is a well-known index of clustering validity, but its realization is difficult to be comprehended and accurately determined. A direct method is presented to improve the performance of the Gap statistic, which applies the two-order difference of within-cluster dispersion to replace the constructed null reference distribution in the Gap statistic. Hence, the realization of the Gap statistic becomes easy and is reformulated, and its uncertainty in applications is reduced. Also, the limitation of the Gap statistic is analyzed by two typical examples, that is, the Gap statistic is difficult to be applied to the dataset that contains strong-overlap or uneven-density clusters. Experiments verify the usefulness of the proposed method.     

我国卫生资源配置公平性现状分析

卫生资源的公平配置是我国建设和谐社会的重要内容之一.研究根据历年的统计数据,采用国内外公平性研究的统计分析方法,对我国主要卫生资源在各省市自治区配置的公平性进行了分析.分析结果表明:本世纪来,我国三项主要卫生资源指标(医疗机构床位、执业(助理)医师、注册护士)在各省市自治区配置是基本公平的,并且公平性在逐年提高.     

扁球面网壳在动静荷载作用下的非线性稳定性

根据薄壳非线性动力学理论和拟壳法的思想,给出了扁球面网壳在动、静荷载协同作用下的非线性动力学控制方程.然后利用扁球面网壳的非线性动力学变分方程和协调方程,在夹紧固定的边界条件下,通过Galerkin作用得到一个含二次和三次的非线性动力学微分方程.用Floquet指数方法研究了系统的分岔问题,讨论了平衡点（奇点）邻域的稳定性问题.指出了系统在纯动态作用和在动静荷载协同作用下其平衡位置的变化情况.     

均匀分布中次序统计量的性质

本文研究了服从Beta分布的均匀分布中次序统计量的若干性质。     

若干有偏估计的后验Fisher信息比和后验似然距离统计量(英文)

本文通过后验对数似然函数,提出了若干有偏估计的后验Fisher信息比和后验似然距离统计量。这些统计量解决了模型扰动对有偏估计的影响度量问题。     

Testing Colour Proportions of M&Ms

We test the claimed colour proportions of plain M&M's candies using Pearson's x² statistic. The null distribution of this statistic is examined through a Minitab simulation.     

Monte Carlo Based Null Distribution for an Alternative Goodness-of-Fit Test Statistic in IRT Models

Assessing the correspondence between model predictions and observed data is a recommended procedure for justifying the application of an IRT model. However, with shorter tests, current goodness-of-fit procedures that assume precise point estimates of ability, are inappropriate. The present paper describes a goodness-of-fit statistic that considers the imprecision with which ability is estimated and involves constructing item fit tables based on each examinee's posterior distribution of ability, given the likelihood of their response pattern and an assumed marginal ability distribution. However, the posterior expectations that are computed are dependent and the distribution of the goodness-of-fit statistic is unknown. The present paper also describes a Monte Carlo resampling procedure that can be used to assess the significance of the fit statistic and compares this method with a previously used method. The results indicate that the method described herein is an effective and reasonably simple procedure for assessing the validity of applying IRT models when ability estimates are imprecise.     

Evaluation of a New Mean Scaled and Moment Adjusted Test Statistic for SEM

Recently a new mean scaled and skewness adjusted test statistic was developed for evaluating structural equation models in small samples and with potentially nonnormal data, but this statistic has received only limited evaluation. The performance of this statistic is compared to normal theory maximum likelihood and 2 well-known robust test statistics. A modification to the Satorra–Bentler scaled statistic is developed for the condition that sample size is smaller than degrees of freedom. The behavior of the 4 test statistics is evaluated with a Monte Carlo confirmatory factor analysis study that varies 7 sample sizes and 3 distributional conditions obtained using Headrick's fifth-order transformation to nonnormality. The new statistic performs badly in most conditions except under the normal distribution. The goodness-of-fit χ² test based on maximum-likelihood estimation performed well under normal distributions as well as under a condition of asymptotic robustness. The Satorra–Bentler scaled test statistic performed best overall, whereas the mean scaled and variance adjusted test statistic outperformed the others at small and moderate sample sizes under certain distributional conditions.     

A New Statistic for Detection of Aberrant Answer Changes

As noted by Fremer and Olson, analysis of answer changes is often used to investigate testing irregularities because the analysis is readily performed and has proven its value in practice. Researchers such as Belov, Sinharay and Johnson, van der Linden and Jeon, van der Linden and Lewis, and Wollack, Cohen, and Eckerly have suggested several statistics for detection of aberrant answer changes. This article suggests a new statistic that is based on the likelihood ratio test. An advantage of the new statistic is that it follows the standard normal distribution under the null hypothesis of no aberrant answer changes. It is demonstrated in a detailed simulation study that the Type I error rate of the new statistic is very close to the nominal level and the power of the new statistic is satisfactory in comparison to those of several existing statistics for detecting aberrant answer changes. The new statistic and several existing statistics were shown to provide useful information for a real data set. Given the increasing interest in analysis of answer changes, the new statistic promises to be useful to measurement practitioners.     

玻色、费米粒子统计方法的研究

采用计算最可几值的方法,研究了多元玻色子(boson)、费米子(fermion)系统粒子的统计分布规律,揭示了单元粒子系统与多元粒子系统统计分布的一致性.