洛仑兹破缺标量场的霍金隧穿辐射

把洛仑兹破缺的标量场方程推广到弯曲时空中,并通过Aether-like项对标量场方程进行修正,该项所产生的效应也会影响到黑洞时空视界附近处的物理效应.接着,进一步在半经典近似下得到了修正的Hamilton-Jacobi方程,然后用这一修正的Hamilton-Jacobi方程研究了史瓦西黑洞的隧穿辐射特征,并讨论了洛仑兹破缺对黑洞霍金辐射和黑洞熵的影响.结果表明,u~α=δ_t~αu~t,δ_r~αu~r形式的Aether-like项的效应可能使黑洞温度增加,而黑洞熵降低.该工作可以帮助我们更深刻地理解弯曲时空中的洛仑兹破缺效应的物理性质.     

长水波近似方程的多孤子解

利用直接而简单的齐次平衡方法，给出了长水波近似方程的多孤子解.本方法可进一步推广研究一大类非线性波动方程. 关键词：     

凸形晶粒的各向异性三维von Neumann方程研究

三维晶粒长大规律是材料科学研究的核心问题之一, 本文通过考虑实际多晶组织中晶界能和晶界迁移率的不均匀性和各向异性因素对晶粒三晶棱处两面角大小的影响, 借助经典体视学中晶粒界面积分平均曲率与平均切直径的关系, 经推导得到了适合于凸形晶粒的一般性三维von Neumann方程, 结果表明实际凸形晶粒的准确长大速率可以表示为晶粒的平均切直径、三晶棱总长度和三晶棱处两面角的函数. 所得方程经过了Kelvin十四面体和5种规则多面体验证, 对于三维von Neumann方程(Nature, 2007, 446:1053)进一步推广并应用于实际金属和陶瓷材料具有重要的意义.     

推广的B-BBM方程和B-BBM方程的显式精确解

研究了BBM方程和推广的B-BBM方程解之间的形变理论,通过给出的一类新的形变关系可从BBM方程的已知解形变出推广的B-BBM方程的显式精确解,并附有这种方法的应用举例.还对B-BBM方程运用齐次平衡法获得其解的显式表示 关键词： 形变理论 齐次平衡法 显式精确解 推广的B-BBM方程 B-BBM方程     

一类广义Boussinesq方程和Boussinesq-Burgers方程新的显式精确解

利用一种推广的代数方法，求解了一类广义Boussinesq方程(B(m，n)方程)和Boussinesq-Burgers方程(B-B方程).获得了其多种形式的显式精确解，包括孤波解、三角函数解、有理函数解、Jacobi椭圆函数周期解和Weierstrass椭圆函数周期解，进一步丰富了这两类方程的解. 关键词： Boussinesq方程 Boussinesq-Burgers方程 推广的代数方法 显式精确解     

广义Birkhoff系统的一类积分

将Birkhoff方程添加一附加项成为广义Birkhoff方程.将Birkhoff方程的一类积分推广并应用于广义Birkhoff方程.举例说明结果的应用. 关键词： Birkhoff方程 广义Birkhoff方程 积分     

Berthelot流体的热力学性质和参数解

研究了Berthelot流体的热力学性质.导出了单原子Berthelot流体Helmholtz自由能、熵、吉布斯函数、内能和焓;求得了Berthelot流体两相共存的的参数解,并用参数解讨论了Berthelot流体的相图和热力学量在临界点的行为及其相关性质.本文的研究为符合Berthelot流体的物质提供了热力学及其相变的解析理论.     

推广的投影Riccati方程法及其应用

将求非线性发展方程精确解的投影Riccati方程法给以推广,并借助符号计算软件Maple求出了Whitham-Broer-Kaup方程的新的精确解. 关键词： 投影Riccati方程法 Whitham-Broer-Kaup方程 孤波解     

KdV-Burgers方程的孤波解

对双曲函数法进行了深入探讨,推广了该方法的某些使用条件,借助计算机代数系统Mathe matica,进一步获得了KdV-Burgers方程的两组扭状孤波解. 关键词： 双曲函数法 KdV-Burgers方程 行波解 计算机代数系统Mathe matica     

变系数广义Gardner方程的微分不变量及群分类

应用李无穷小不变规则,得到了变系数广义Gardner方程的连续等价变换.从等价代数开始,构造了一阶微分不变量并依据微分不变量对方程作了群分类.最后,通过等价变换将变系数Gardner 方程映射为常系数mKdV方程、KdV-mKdV方程.同时,也得到了变系数广义Gardner方程的一些精确解. 关键词： 李无穷小不变规则 微分不变量 群分类 变系数广义 Gardner方程     

Fokker-Planck equation with fractional coordinate derivatives

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations, with averaging with respect to a fast variable, is used. The main assumption is that the correlation function of probability densities of particles to make a step has a power-law dependence. As a result, we obtain a Fokker-Planck equation with fractional coordinate derivative of order 1<α<2.     

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.     

Description of the pressure and temperature dependences of permittivity of nonpolar gases by the generalized Van der Waals−Berthelot equation

The equation of state of model gases is considered for describing the experimental pressure dependence of the permittivity of argon. It is shown that the generalized Van der Waals?Berthelot equation describes the pressure dependence of permittivity of argon with a good accuracy.     

变系数广义KdV方程新的类孤波解和精确解

用普通KdV方程作变换，构造变系数广义KdV方程的解，获得了变系数广义KdV方程新的Jacobi椭圆函数精确解、类孤波解、三角函数解和Weierstrass椭圆函数解. 关键词： KdV方程 变系数广义KdV方程 类孤波解 精确解     

The effects of deviations from Lorentz–Berthelot rules on the properties of a simple mixture

Generally, the parameters in the interaction potential between like molecules in a mixture can be determined in a relatively straightforward manner from the properties of the pure components. However, the determination of the parameters in the interaction potential between the unlike pairs in the mixtures is more difficult. As a result, these parameters are usually estimated from averages of the like parameters. The most common recipes are the Lorentz–Berthelot mixing rules, where the energy and molecular size parameters are presumed to be geometric and arithmetic averages, respectively. There have been some studies of the consequences of deviations from the energy rule but almost no studies of the consequences of deviations from the size rule. Here, we study the effects of deviations from both rules on the radial distribution functions of a simple mixture. We find from simulations that, for this mixture, the effect of deviations from the energy rule on the radial distribution function are rather small but that the effect of deviations from the size rule can be significant and are interesting.     

Nonlinear Self-Adjointness and Conservation Laws for the Hyperbolic Geometric Flow Equation

We study the nonlinear self-adjointness of a class of quasilinear 2D second order evolution equations by applying the method of Ibragimov. Which enables one to establish the conservation laws for any differential equation. We first obtain conditions determining the self-adjointness for a sub-class in the general case. Then, we establish the conservation laws for hyperbolic geometric flow equation on Riemman surfaces.     

Graphene under perpendicular incidence of electromagnetic waves: Gaps and band structure

We study the energy spectrum for the problem of graphene's carriers under perpendicular incidence of electromagnetic waves. To obtain the spectrum, we solve the Dirac equation under such a field. Then a generalized Mathieu equation is obtained. The limiting cases of strong and weak fields, as well as long and short wavelengths, are analyzed. The energy spectrum is obtained numerically by using the Whittaker method, and a perturbation method is used to obtain the analytical separatrix curve between allowed and forbidden states. The energy spectrum presents bands, and a gap at the Fermi energy. The gap is linear on the electromagnetic wave intensity.     

A new application of Riccati equation to some nonlinear evolution equations

By means of symbolic computation, a new application of Riccati equation is presented to obtain novel exact solutions of some nonlinear evolution equations, such as nonlinear Klein-Gordon equation, generalized Pochhammer-Chree equation and nonlinear Schrödinger equation. Comparing with the existing tanh methods and the proposed modifications, we obtain the exact solutions in the form as a non-integer power polynomial of tanh (or tan) functions by using this method, and the availability of symbolic computation is demonstrated.     

Generalized moment expansion for nonadiabatic transition reaction

We discuss the generalized moments of the nonadiabatic transition reaction by using the stochastic Liouville equation for the study of outer-sphere electron transfer in polar solvents characterized by Debye dielectric relaxation. We obtain an approximate expression for the generalized moments which incorporates the width of the transition with arbitrary initial condition far from equilibrium. For low barriers, we derive an analytical expression for the rate corresponding to harmonic potential surfaces in the overdamped regime. For Fokker-Planck operators of Smoluchowski type, we introduce a new method to solve all of the generalized moments by using the eigenfunction expansion method.     

一维元胞自动机随机交通流模型的宏观方程分析

在一维局部作用元胞自动机交通流模型中引入刹车噪声与产生、消失概率,得到一完全随机的元胞自动机交通流模型.利用玻耳兹曼近似,建立了该模型的宏观动力学方程,并对宏观方程在特殊条件下的解进行了理论分析和计算机模拟. 关键词： 元胞自动机 交通流 Burgers方程 激波