介绍用狄利克雷积分计算相体积的方法

在经典统计的系综理论中,与孤立系统(粒子数为N,体积为V,能量在E到E △E之间,并且△E/E<相似文献   

热力学中的特征函数

在热力学中人们引入了特征函数,即在适当选择独立变量的条件下,只用一个热力学函数就可以确定系统全部的热力学性质.这个函数叫特征函数,相应的独立交量叫特征变量. 为什么只有选则的独立变量是特征变量时,热力学函数才具有特征函数的性质呢?对这个问题我们主要以内能为例来进行分析. 不妨首先考虑最简单的情形:粒子数不变、单相、与外界只有一种功(体积膨胀功)交住. 由定义 且 只要知道U、S、T、P、V之间的关系,那么已知U为S、T、P、V任两个变量的函数.则其它函数H、F、Φ可求出. 一　选独立变量S、V. 已知:U—U(尸、叮 __.、_./ dU…     

西南师范学院1984年招收攻读硕士学位研究生理论物理专业《统计物理》试题

1.试证以下热力学函数间的关系:(20分)式中M-磁矩,H-磁场强度,T-绝对温度,CM和CB分别是定M和定H的比热. b.对于p、V、T体系恒有: c、对于p、V、T体系,当V只是的函数时,则u只是T的函数.a、b二式中, p是压强; V是体积;T是温度;u是内能。 2.按下式定义函数Y(N,v,T):(20分)式中Q(N,V,T)为正则系综的配分函数。现在如果要保证函数Y(N,V,T)能正好表示以某个热力学势为特征势的配分函数时,则　应代表什么物理量;当进一步用配分函数Y(N,v,T)决定(N,v,T)体系的体积V,熵S和吉函G. 3.请分别用分子动力论和系综理论推导理想气体绝热方程…     

高压下硝基甲烷分子温度的密度泛函计算

用密度泛函理论在B3LYP/6-311++G(2d,2P)计算水平上对硝基甲烷分子进行了结构优化、频率和热化学分析.发现:在相同温度条件下改变压强,分子熵函数产生了改变,当温度和压强条件相同时,对于不同物质熵函数的改变是相同的.以热力学理论中麦克斯韦关系为基础,通过计算等温过程中分子的熵函数对压强的变化率,用数值拟合方法得到不同压强条件下分子温度的表达式:T=T0+(1-B)[18.3858+0.5392P]V0,式中T0、V0分别表示分子系统初态的温度和体积,T、V分别表示系统在末态的温度和体积,B是体积的压缩比.在选定参数的情况下该表达式可以计算不同压强条件下CHNO含能材料的分子温度.同时,以硝基甲烷为验证,选取基本参数V0和B,计算其在C-J条件对应的爆压14GPa下,分子温度为3461K,对应爱因斯坦温度,相当于3228cm-1的能量,在实验中该能量足以激发硝基甲烷分子内振动能量重新分配过程,有可能激发C-N键的红外振动而引起单分子分解反应的发生.因此,此表达式可用于预测含能材料撞击点火过程单分子分解可能的反应通道.     

气固氢化反应热力学函数计算的近似方法

在有效原子实势近似下, 采用Gaussian 98程序及B3LYP/SDD密度泛函方法计算得到了ZrCo和ZrCoH分子的结构及能量E、熵S. 在此基础上, 近似以气态分子总能量中的振动能Ev代替该分子处于固态时的振动能量, 以电子运动和振动运动熵Sev代替分子处于固态的熵, 计算了不同温度下固态ZrCo与H2, D2, T2反应的热力学函数ΔH, ΔG, ΔS及氢化反应平衡压力, 导出了氢化反应温度与平衡压力的依赖关系. 计算得出ZrCoH, ZrCoD, ZrCoT的生成焓(398-598 K)分别为82.81 , 81.54和80.49kJ/mol, 与实验结果很好符合.     

统计力学的系综变换

一、引言 在统计力学中一般只研究三种统计系综,他们是微正则系综(适用于孤立体系)、吉布斯正则系综(适用于与热库有热相互作用的体系)和吉布斯巨正则系综(适用于与热库有热相互作用,又与物质库有粒子数交换的体系).体系处于平衡态,三种系综的分布函数为 ρ=cδ(E-E0)(1) 　ρ=e-ψ-E/kT(2) 　ρ=e-ζ-E/kT μN/kT(3)与这三种分布相应的热力学函数分别为式中(E,V,N)是由N个粒子组成、占有空间体积V的体系具有能量E的微观状态数;S、F和O分别是嫡、自由能和热力势.(4)一(6)式与(l)一(3)式等价,他们将热力学函数与配分函数联系起来,是三…     

力与耦合系统的交互作用和随机能量共振

外界对系统作功的过程就是系统状态发生变化的过程.根据Langevin方程的随机动力学特性,采用微观动力学和宏观热力学方法,建立了基于单一随机轨线的耦合双稳系统的热力学关系.通过力与耦合系统的功交互作用定量地刻画了能量的传递和转换关系,揭示了耦合系统中存在着的随机能量共振现象.从作功与能量的关系进行分析,进一步揭示了随机共振产生的物理本质. 关键词： 耦合双稳系统 随机热力学 随机能量共振 功     

均匀物质热力学关系记忆法

均匀物质的热力学关系是研究其热力学性质的基本方程.但是这些用全微分和偏微商表示的关系形式相近,极易错乱.为了准确记忆,曾提出过不少办法[1],现经加工提炼,介绍如下. 一、热力学函数和“魔句” “Good Physicists Have Studied UnderVery Fine Teachers.”(杰出的物理学家都受到过极为优秀教师的教诲.)按照精心设计的这一句英语的词首字母,把八个热力学函数排列成G(古布斯函数),P(压强),H(焓), S(熵), U(内能), V(体积), F(自由能),T(温度),并用方框从顶角开始顺时针安置如图1.这是记忆法的基础. 二、全微分公式记忆法 图一顶角…     

新型高效热离子功率器件的性能特性研究

应用固体物理和不可逆热力学理论,研究新型高效石墨烯热离子热电功率器件的性能特性.通过数值求解器件高温和低温端的能量平衡方程,确定器件阴极板和阳极板的温度;分析输出电压和阴极板功函数对器件的伏安特性及两个极板温度的影响,确定器件在最大功率密度和最大效率时的参数特性;折衷考虑功率密度和效率,给出参数的优化取值区间;分析了高温热源温度对优化性能的影响.本文所得结果可为热离子能量转换器件的研制提供理论指导.     

聚合物介电弛豫的温度特性

运用极限的概率模型和Ngai的耦合概念,导出了聚合物介电弛豫的KohlrauschWilliamsWatts(KWW)方程(t)=exp[-(tτ)β],证明了弛豫的能量势垒为Ngai的活化能量E.由β的温度关系推出了适用于聚合物的WilliamsLandelFerry方程和过冷液体的VogelTammannFulcher方程,特别是提出了由聚合物的β(T)可导出弛豫时间的温度函数.认为KWW行为由单个衰减单元产生,幂律行为由局部区域内多个衰减单元的协同衰减造成.将活化能量E引入热刺激电流公式,得到了可通过改变升温速率测量β(T)的公式. 关键词： 介电弛豫 聚合物 极限概率模型 KWW方程     

Spin thermopower and thermoconductance in a ferromagnetic graphene nanoribbon

The spin thermoelectric properties of a zigzag edged ferromagnetic (FM) graphene nanoribbon are studied theoretically by using the non-equilibrium Green's function method combined with the Landauer-Büttiker formula. By applying a temperature gradient along the ribbon, under closed boundary conditions, there is a spin voltage ΔV(s) inside the terminal as the response to the temperature difference ΔT between two terminals. Meanwhile, the heat current ΔQ is accompanied from the 'hot' terminal to the 'cold' terminal. The spin thermopower S?=?ΔV(s)/ΔT and thermoconductance κ?=?ΔQ/ΔT are obtained. When there is no magnetic field, S versus E(R) curves show peaks and valleys as a result of band selective transmission and Klein tunneling with E(R) being the on-site energy of the right terminal. The results are in agreement with the semi-classical Mott relation. When |E(R)|??M, the quantized value of [Formula: see text] appears. In the quantum Hall regime, because Klein tunneling is suppressed, S peaks are eliminated and the quantized value of κ is much clearer. We also investigate how the thermoelectric properties are affected by temperature, FM exchange split energy and Anderson disorder. The results indicate that S and κ are sensitive to disorder. S is suppressed for even small disorder strengths. For small disorder strengths, κ is enhanced and for moderate disorder strengths, κ shows quantized values.     

QCD collisional energy loss reexamined

It is shown that at a large temperature and E --> infinity the QCD collisional energy loss reads dE/dx approximately alpha(m(D)2)T2. Compared to previous approaches, which led to dE(B)/dx approximately alpha2 T2 ln(ET/m(D)2) similar to the Bethe-Bloch formula in QED, we take into account the running of the strong coupling. As one significant consequence, due to asymptotic freedom, dE/dx becomes E independent for large parton energies. Some implications with regard to heavy ion collisions are pointed out.     

Complex methyl group and hydrogen-bonded proton motions in terms of the Arrhenius and Schrödinger equations

Equations for the temperature dependence of the spectral densities J(is)(m)(momega(I) +/-omega(T)), where m=1, 2, omega(I) and omega(T) are the resonance and tunnel splitting angular frequencies, in the presence of a complex motion, have been derived. The spin pairs of the protons or deuterons of the methyl group perform a complex motion consisting of three component motions. Two of them involve mass transportation over the barrier and through the barrier. They are characterized by k((H)) (Arrhenius) and k((T)) (Schr?dinger) rate constants, respectively. The third motion causes fluctuations of the frequencies (nomega(I)+/-omega(T)) and it is related to the lifetime of the methyl spin at the energy level influenced by the rotor-bath interactions. These interactions induce rapid transitions, changing the symmetry of the torsional sublevels either from A to E or from E(a) to E(b). The correlation function for this third motion (k((omega)) rate constant) has been proposed by Müller-Warmuth et al. The spectral densities of the methyl group hindered rotation (k((H)), k((T)) and k((omega)) rate constants) differ from the spectral densities of the proton transfer (k((H)) and k((T)) rate constants) because three compound motions contribute to the complex motion of the methyl group. The recently derived equation [Formula: see text] , where [Formula: see text] and [Formula: see text] are the fraction and energy of particles with energies from zero to E(H), is taken into account in the calculations of the spectral densities. This equation follows from Maxwell's distribution of thermal energy. The spectral densities derived are applied to analyse the experimental temperature dependencies of proton and deuteron spin-lattice relaxation rate in solids containing the methyl group. A wide range of temperatures from zero Kelvin up to the melting point is considered. It has been established that the motion characterized by k((omega)) influences the spin-lattice relaxation up to the temperature T(tun) only. This temperature is directly determined by the equation C(p)T=E(H) (thermal energy=activation energy), where C(p) is the molar heat capacity. Probably the cessation of the third motion is a result of the de Broglie wavelength related to this motion becoming too short. As shown recently, the potential barrier can be an obstacle for the de Broglie wave. The theoretical equations derived in this paper are compared to those known in the literature.     

一般完整系统Mei对称性的逆问题

动力学逆问题是星际航行学、火箭动力学、规划运动学理论的基本问题. Mei对称性是力学系统的动力学函数在群的无限小变换下仍然满足系统原来的运动微分方程的一种新的不变性. 本文研究广义坐标下一般完整系统的Mei对称性以及与Mei对称性相关的动力学逆问题. 首先, 给出系统动力学正问题的提法和解法. 引入时间和广义坐标的无限小单参数变换群, 得到无限小生成元向量及其一次扩展. 讨论由n个广义坐标确定的一般完整力学系统的运动微分方程, 将其Lagrange函数和非势广义力作无限小变换, 给出系统运动微分方程的Mei对称性定义, 在忽略无限小变换的高阶小量的情况下得到Mei对称性的确定方程, 借助规范函数满足的结构方程导出系统Mei对称性导致的Noether守恒量. 其次, 研究系统Mei对称性的逆问题. Mei对称性的逆问题的提法是: 由已知守恒量来求相应的Mei对称性. 采取的方法是将已知积分当作由Mei对称性导致的Noether守恒量, 由Noether逆定理得到无限小变换的生成元, 再由确定方程来判断所得生成元是否为Mei对称性的. 然后, 讨论生成元变化对各种对称性的影响. 结果表明, 生成元变化对Noether和Lie对称性没有影响, 对Mei 对称性有影响, 但在调整规范函数时, 若满足一定条件, 生成元变化对Mei对称性也可以没有影响. 最后, 举例说明结果的应用.     

自由基-三重态对化学诱导动态电子极化强度的全哈密顿计算(英文)

基于考虑含E(S2Tξ-S2Tη)项的相互作用全哈密顿,利用密度矩阵运动方程,对自由基-三重态对机理的CIDEP强度进行了详细的理论计算.计算结果表明:四重态母体自由基-三重态机理(QP-RTPM)和二重态母体自由基-三重态机理(DP-RTPM)分别使稳定自由基形成发射+发射/吸收(E+E/A)和吸收+吸收/发射(A+A/E)型多重性极化,其中净E(A)极化由零场分裂相互作用产生,超精细相关E/A(A/E)极化由超精细相互作用产生.另外,零场分裂相互作用项E(S2Tξ-S2Tη),使稳定自由基的净极化减弱     

Temperature dependence of liquid volume

It is shown that the temperature dependence of the liquid volume is well described by the equation $ V = A + BT + CT^2 + V_e \exp ( - E/RT), $ V = A + BT + CT^2 + V_e \exp ( - E/RT), where A, B, C, V _e , and E are constants. This equation reflects two processes owing to which the liquid volume increases with temperature, namely, anharmonic oscillations of molecules and formation of “holes.”     

相对运动动力学系统Nielsen方程的Lie对称性与Hojman守恒量

研究相对运动动力学系统Nielsen方程的Lie对称性和Lie对称性直接导致的Hojman守恒量.在群的无限小变换下,给出相对运动动力学系统Nielsen方程Lie对称性的定义和判据;得到相对运动动力学系统Nielsen方程Lie对称性的确定方程以及Lie对称性直接导致的Hojman守恒量的表达式.举例说明结果的应用. 关键词： 相对运动动力学 Nielsen方程 Lie对称性 Hojman守恒量     

Friedmann equations and thermodynamics of apparent horizons

With the help of a masslike function which has a dimension of energy and is equal to the Misner-Sharp mass at the apparent horizon, we show that the first law of thermodynamics of the apparent horizon dE=T(A)dS(A) can be derived from the Friedmann equation in various theories of gravity, including the Einstein, Lovelock, nonlinear, and scalar-tensor theories. This result strongly suggests that the relationship between the first law of thermodynamics of the apparent horizon and the Friedmann equation is not just a simple coincidence, but rather a more profound physical connection.     

高温高密度氢（氘）的物态方程——离解效应研究

 高温高压下流体氢将发生离解化学反应，形成具有相互作用的氢分子和氢原子混合体系，此时粒子间的相互作用复杂。利用单组分流体近似的范德瓦尔斯混合模型，将混合物粒子间的相互作用等效为单组分粒子间相互作用，从而简化了对体系的统计热力学处理；并由自由能函数极小化确定化学平衡时各组分含量、体系的内能、压强。研究了温度在10 000 K以下、密度在0.6 g/cm³以下（相应摩尔体积大于3.3 cm³/mol）区间的热致离解和压致离解现象对流体氢（氘）状态方程的影响。所得结果与双组分流体变分理论计算以及第一原理的分子动力学模拟、蒙特卡罗模拟结果以及二级轻气炮实验数据进行了比较，它们之间的一致性表明：用单组分流体近似的范德瓦尔斯混合模型处理氢（氘）分子的离解区域的物态方程是成功的。     

Application of shell model in molecular dynamics simulation to MgO

The P－V－T equation of state of MgO has been simulated under high pressure and elevated temperature using the molecular dynamics (MD) method with the breathing shell model (BSM). It is found that the MD simulation with BSM is very successful in reproducing accurately the measured molar volumes of MgO over a wide range of temperature and pressure. In addition, the MD simulation reproduces accurately the measured volume compression data of MgO up to 100GPa at 300K. It is demonstrated that the MD simulated P－V－T equation of state of MgO could be applied as a useful internal pressure calibration standard at elevated temperatures and high pressures.