弹性矩形板方程在非线性边界条件下整体解的存在唯一性

考虑了在非线性边界条件下的弹性矩形板方程.利用Galerkin方法,首先证明了该方程在非线性边界(a)及初值w⁰∈W,w¹∈W的条件下初边值问题存在唯一整体弱解w(t).其次证明了该方程在非线性边界(b)及初值w⁰∈W₁,w¹∈W₁的条件 关键词： 弹性矩形板方程 非线性边界条件 初边值问题 整体解     

虚阴极产生微波的一些基本特性

用Vlasov-Poisson方程对相对论电子束在单板、双板间的传播过程进行了数值模拟,给出了单板模型空间电荷积累最大的位置,不同位置上的电流J、电子数密度n、电场E的振荡频率随入射电子数密度n₀、入射速度v₀的变化关系,双板模型空间电荷积累最大的位置,J、n、E的振荡频率随入射流J₀及两板间距离的变化关系。虚阴极位置的数值结果与稳态理论给出的结果相近,它的振荡频率符合经验公式(1~√2π)ω_peb。单板时入射电子数密度按速度服从高斯分布,能散△E_n/E_n < 10%时的数值结果给出与单能情况基本相同的结论。     

MC与$lt;i$gt;M$lt;/i$gt;$lt;sub$gt;$lt;i$gt;n$lt;/i$gt;+1$lt;/sub$gt;$lt;i$gt;AC$lt;/i$gt;$lt;sub$gt;$lt;i$gt;n$lt;/i$gt;$lt;/sub$gt;稳定性与电子特征的第一性原理研究

研究MC与M_n+1AC_n(M=Sc, Ti, V, Cr, Mn; A=Al, Si, P, S; n=1, 2, 3)结构的稳定性与电子特征有利于探究三元层状结构M_n+1AC_n稳定性的内在原因和设计新型M_n+1AC_n结构. 第一性原理计算研究表明, M-3d与C-2p轨道间的电子转移对MC与M_n+1AC_n 的形成焓有较大影响. 供电子能力较强的前过渡金属可以形成稳定的MC结构. 计算结果显示, MC结构是缺电子体系, 其趋向于与具有一定供电子能力的MA结构结合形成M_n+1AC_n. 与M₂PC和M₂SC 相比, M₂AlC和M₂SiC可以更为容易地被分离成二维 M₂C结构. 关键词： MAX相结构 第一性原理 电子结构 过渡金属碳化物     

两种扩展Harper模型的波包动力学

本文通过二次矩M₂(t)和概率分布W_n(t)数值地研究了两种扩展Harper模型的波包动力学,得到了这两种模型中各个相、各条临界线以及三相点的波包扩散情况.对于第一种扩展Harper模型,发现两个金属相中波包是弹道扩散的,在绝缘体相中波包不扩散,而在三相点以及各条临界线上波包是反常扩散的.同时,发现金属相—金属相转变的临界线上的波包动力学行为与金属相—绝缘体相转变的临界线上的相同,但三相点的动力学行为与各临 关键词： 金属绝缘体转变 扩展Harper模型 波包动力学     

模糊聚类正交方法若干结果

本文提出一个新的模糊聚类方法:正交法,这种方法基于如下正交聚类原则:记截矩阵R_λ=(α₁,α₂,…,α_n),其中列向量α_j=(α_1j,α_2j,…,α_nj)^T,所谓向量α_i,α_j正交,指内积(α_i,α_j)=0。     

中子裂变链统计涨落问题的数值计算方法

研究了弱中子源驱动下,裂变系统中子裂变链统计涨落问题的数值计算方法。进行了数值计算建模、数值方法分析、数值计算检验、一类问题概率分布函数的统计涨落特征量的数值计算示范。特例数值检验表明:只要数值解方程组阶数(截断) N足够大,数值解满足归一(守恒) 律、指数增长律,并与精确解析解一致。对于非定常裂变系统中子裂变链统计涨落问题提出了一维等效模型下数值模拟的方法。     

Dynamic models of pest propagation and pest control

This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel I(k)=Ik and a fragmentation rate kernel L(i,j)=L, we find that the total number M₀^A(t) and the total mass of the pest aggregates M₁^A(t) both increase exponentially with time if L ≠ 0. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel J₁(k)=J₁k, it is found that only when I<J₁B₀ (B₀ is the concentration of catalyst aggregates) can the pests be killed off. Otherwise, the pest aggregates can survive. In the model of pest control with a natural enemy, a pest aggregate loses one of its individuals and the number of natural enemies increases by one. For this system, we find that no matter how many natural enemies there are at the beginning, pests will be eliminated by them eventually.     

一维长程关联无序系统的局域性

研究了在紧束缚近似下,由de Moura和Lyra提出的一维长程关联无序模型的局域性. 分布在［-W/2,W/2］区间的格点位能,其关联函数〈ε_iεj〉的傅里叶变换满足S(k)∝k^-α,其中关联强度α>0. 利用participation ratio不仅证实了在α>2和W<4 关键词： 安德森局域化 长程关联 扩展态     

一类广义强阻尼Sine-Gordon方程的整体解

同时考虑黏性效应及外阻尼作用研究了一类广义强阻尼Sine-Gordon方程-利用Galerkin方法,首先证明了该方程在初值u(x,0)∈H¹₀(Ω),u_t(x,0)∈L²(Ω)的条件下初边值问题存在整体弱解u(x,t),并证明了整体弱解关于初始条件具有 关键词： Sine-Gordon型方程 强阻尼 Galerkin方法 整体解     

排列形状及阵列数目对纳米导线阵列场发射性能的影响

为了进一步研究纳米导线阵列的排列形状以及阵列数目对其场发射行为的影响，利用镜像悬浮球模型对正方形以及六边形排列的纳米导线阵列的场发射行为进行计算与模拟，近似的得到纳米导线阵列的场发射增强因子满足如下的变化趋势：β=h/ρ(1/1+W)+1/2(1/1+W)²+3,其中h为纳米导线的高度，ρ为纳米导线的半径，W是以R为自变量的函数，R为纳米导线阵列的间距.结果显示纳米导线阵列的排列形状对其场发射性能的影响较小，而阵列间距则是影响场发射性能的关键因素：当R<R₀时，场发射增强因子随着阵列间距的减小而急剧减小；当R>R₀时，场发射增强因子基本不变，其中R₀为导线阵列场发射的最佳间距.进一步研究表明改变纳米导线阵列的数目基本不会改变阵列的场发射性能随间距的变化趋势，但是随着阵列数目的增加，R₀会有一定程度的减小，场发射增强因子也会降低. 关键词： 纳米导线 场发射 增强因子 阵列数目     

A Note on Exact Solutions to Linear Differential Equations by the Matrix Exponential

It is known that the solution to a Cauchy problem of linear differential equations: $$x'(t)=A(t)x(t), \quad {with}\quad x(t_0)=x_0,$$ can be presented by the matrix exponential as $\exp({\int_{t_0}^tA(s)\,ds})x_0,$ if the commutativity condition for the coefficient matrix $A(t)$ holds: $$\Big[\int_{t_0}^tA(s)\,ds,A(t)\Big]=0.$$ A natural question is whether this is true without the commutativity condition. To give a definite answer to this question, we present two classes of illustrative examples of coefficient matrices, which satisfy the chain rule $$ \frac d {dt}\, \exp({\int_{t_0}^t A(s)\, ds})=A(t)\,\exp({\int_{t_0}^t A(s)\, ds}),$$ but do not possess the commutativity condition. The presented matrices consist of finite-times continuously differentiable entries or smooth entries.     

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation.     

Anomalous transport in fluid fleld with random waiting time depending on the preceding jump length

Anomalous(or non-Fickian) transport behaviors of particles have been widely observed in complex porous media.To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields,in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced,and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived.As examples,two generalized advection-dispersion equations for Gaussian distribution and levy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation.     

Decoherence for a two-qubit system in a spin-chain environment

The quantum coherence and correlation dynamics for a two-qubit system in the Ising spin-chain environment are studied. A sudden change of coherence is found near the critical point, which provides us with an effective way to detect the quantum phase transition. By studying the relationship between quantum discord and coherence, we find that coherence displays the behavior of classical correlation for t t_0, and of quantum discord for t t_0, where t_0 is the time-point of a sudden transition between classical and quantum decoherence.     

A statistical analysis of the kinetics of chain-branching chemical reactions with quadratic chain termination

Analytical and numerical simulations of stochastic phenomena in the kinetics of chain-branching reactions with linear and quadratic chain termination during fast changes in external conditions that cause sharp transitions of the governing parameter through the critical point were studied. A statistical analysis was performed based on nonlinear stochastic differential equations of Langevin type for the concentration of active species and on the corresponding Fokker-Planck equations for the probability distribution function of the concentration of these species. An expression for the statistical distribution of the induction period of the reaction and its mean and variance were calculated from an approximate analytical solution. The time evolution of the probability density function of the concentration of active species was presented graphically.     

Randomly flashing diffusion: Asymptotic properties

The theory of abstract Markov operators and semigroups is applied for studying asymptotics of a randomly flashing diffusion process. The probability distribution of the process is determined by a set of two partial differential equations and sufficient conditions for the existence of a stationary solution of the equations are formulated, and convergence of solutions to the stationary solution is proved.     

Boundary Conditions for the Dynamical Equations of Quantum Mechanics

We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over???∞?<?t?<?+∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t ₀: t ₀?≤?t?<?+∞, for which the mathematicians would choose t ₀?=?0,¹ but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time $ t_0^{(i) } $ for an ensemble of individual quanta.     

Probability Distribution Function of Passive Scalars in Shell Models

A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 (1988) 983; K. Ohkitani and M. Yakhot, Prog. Theor. Phys. 81 (1988) 329]. As in the original problem, the prescribed random velocity field is Gaussian and δ correlated in time. Deterministic differential equations are regarded as nonlinear Langevin equation. Then, the Fokker-Planck equations of PDF for passive scalars are obtained and solved numerically. In energy input range (n<5, n is the shell number.), the probability distribution function (PDF) of passive scalars is near the Gaussian distribution. In inertial range (5≤n≤16) and dissipation range (n≥17), the probability distribution function (PDF) of passive scalars has obvious intermittence. And the scaling power of passive scalar is anomalous. The results of numerical simulations are compared with experimental measurements.     

强激光场中一维原子的渐近边界条件

用Fourier变换推导了强激光场中一维原子模型的渐近边界条件,分析了三类渐近边界条件的误差,用第一类渐近边界条件和非齐线性正则方程的辛算法计算了强激光场中一维氢原子的几率分布和平均能量,并将结果与理论分析进行了比较.     

Absence of classical lumps

Solutions of the equations of classical Yang-Mills theory in four dimensional Minkowski space are studied. It is proved (Theorem 1) that there is no finite energy (nonsingular) solution of the Yang-Mills equations having the property that there exists ?,R,t ₀>0 such that $$E_R (t) = \int\limits_{|\bar x| \leqq R} {\theta _{00} (t,\bar x)d^3 \bar x \geqq \varepsilon foreveryt > t_0 ,} $$ \(\theta _{00} (\bar x,t)\) being the energy density. Previously known theorems on the absence of finite energy nonsingular solutions that radiate no energy out to spatial infinity are particular cases of Theorem 1. The result stated in Theorem 1 is not restricted to the Yang-Mills equations. In fact, it extends to a large class of relativistic equations (Theorem 2).