一类带有非线性爆炸的粒子增长的数学模型

所建立的数学模型是由可数无穷多个彼此相互关联的非线性常微分方程所组成的自治系统,它刻划了在只有基本粒子和i-粒子(i≥1 ) 进行碰撞反应的系统里,粒子增长过程中密度随时间的变化规律.研究了这一自治系统解的存在性、唯一性、密度守恒以及解的渐近性质.     

一类离散的非线性爆炸方程平衡点的稳定性

本所研究的非线性爆炸方程实质上是由可数无穷多个彼此相互关联的非线性常微分方程所组成的自治系统，它刻划了在只有基本粒子与i-粒子(i≥1)进行碰撞反应的系统里，粒子增长过程中密度随时间变化规律。本证明了如果系数满足一定的假设，那么在爆炸占优的条件下，这一系列的平衡点在Lyapunov意义下是稳定的．     

一类爆炸凝结过程的数学模型

所建立的数学模型是由可数无穷多个彼此相互关联的非线性常微分方程所组成的自治系统,它刻划了在只有基本粒子与i-粒子(i≥1)进行碰撞反应的系统里,粒子增长过程中密度随时间的变化规律.本文研究了这一自治系统解的性质.     

一类Holling功能性反应模型极限环的唯一性

考虑捕食者无密度制约，食饵具有非线性密度制约的第三类Ｈｏｌｌｉｎｇ功能性反应捕食者－食饵系统．对该系统给出了完整的定性分析，证明了该系统至多有一个极限环，存在极限环的充要条件是正平衡点不稳定．     

N度对称径向扇回旋加速器的动力学稳定性及系统的相平面特征

本文导出了N度对称径向扇回旋加速器中粒子的非线性运动方程,并用数值方法分析了N=4,5,6,8,10等情况下粒子的自由振荡频率及v_x=4/3共振线前后系统的相平面特征.讨论了系统的动力学稳定性和非线性效应,并同文献[1]进行了比较,结果表明,当不考虑系统的非线性特征时,二者完全一致.     

带有弹性碰撞的离散的凝结方程

带有弹性碰撞的离散的凝结方程是反映粒子增长动力学的数学模型，它刻划了这样一种粒子反应系统；系统中任意两个粒子碰撞后一定的概率或者凝结成为更大的粒子，或者发生弹性碰撞．本文研究了这一系统发生冻肢的可能性，并给出了一个充分条件．     

一类粒子反应系统数学模型解的研究

所研究的数学模型实质上是由可数无穷多个彼此相互关联的非线性常微分方程所组成的自治系统,它刻划了在只有基本粒子与i-粒子(i≥1)进行碰撞反应的系统里,粒子增长过程中密度随时间的变化规律.本文证明了在爆炸占优的条件下,这一系统解的ω极限集只含有平衡点;在更强的条件下ω极限集只含有唯一的平衡点,并且当时间t→∞时,该系统的解强收敛于这一平衡点.     

三度对称螺旋扇回旋加速器的动力学稳定性

在三度对称螺旋扇回旋加速器中,粒子径向自由振动频率V_x总是接近于1,由于粒子在加速过程中始终处于V_x=1这条共振线附近,系统明显表现出了对磁场扰动的灵敏性,当这种扰动大于某个临界值时,系统就变得完全不稳定,因此,有必要对Vx=1共振线附近的粒子运动行为作一分析;本文试图利用非线性力学中的渐近方法(即KBM方法)对三度对称的非线性系统进行处理,并从劳斯-胡维茨判据出发来讨论系统的稳定性,导出了这种系统的临界参数,其中包括临界扰动场的一次谐波振幅和二次谐波梯度振幅。     

基于失效域重构和重要抽样法的结构动力学系统首穿失效概率

对于线性动力学系统，重构系统失效域，利用基本失效域概率构造重要抽样密度函数，提出了基于重要抽样技术的首穿失效概率估计方法；对于非线性动力学系统，构建等效线性系统，线性化原理为线性与非线性系统对安全域边界具有相同的平均上穿率.最后给出Gauss(高斯)白噪声激励的线性与非线性系统的数值算例，并与Monte-Carlo(蒙特 卡洛)方法及区域分解方法比较，结果显示该文方法是正确有效的.     

广义Eady模型的非线性稳定性

对于广义Eady模型，分别讨论了密度函数是常数函数与指数函数两种情形，利用变分原理，考虑到动量守恒的约束条件，得到了优化的Poincare不等式，从而得到了新的非线性稳定性定理，并且得到了在径向长度分别不大于纬向长度的0．84402倍及0．86068倍时（这对于地球的实际情况是成立的），非线性稳定性判据与线性稳定性判据是一致的．     

Instantaneous gelation in coagulation dynamics

The coagulation equations are a model for the dynamics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters. For a certain class of rate coefficients we prove that the density is not conserved on any time interval.Dedicated to Klaus Kirchgässner on the occasion of his sixtieth birthday     

On an exact solution of master equations for the model of reversible growth

The set of master equations for the monomer quasi-chemical reversible-growth model in a heterogeneous open medium material is studied. The exact solution to the master equations is obtained for the case where the velocity constants for the growth and decay reactions are linear in the particle number. It is shown that the model under consideration is canonically invariant w.r.t. the Polya distribution with a time-dependent mean size of the clusters.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 108, No. 2, pp. 327–336, August, 1996.     

On the Evolution of Large Clusters in the Becker-D?ring Model

Summary. We consider the Becker-D?ring equations for large times. It is well-known [2] that if the total density of monomers exceeds a critical value, the excess density is contained in larger and larger clusters as time proceeds. We rigorously derive for general coefficients that the evolution of these large clusters is described by a nonlocal transport equation, which is for specific coefficients the classical coarsening model by Lifshitz, Slyozov, and Wagner (LSW). Our proof exploits the estimate of the energy and the energy dissipation rate given by the Lyapunov functional for the Becker-D?ring equations. We also provide a detailed asymptotic expansion of the higher-order dynamics.     

Homogenisation for the Stokes equations in randomly perforated domains under almost minimal assumptions on the size of the holes

We prove the homogenisation to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical holes. The fluid satisfies a no-slip boundary condition at the holes. The balls generating the holes have centres distributed according to a Poisson point process and i.i.d. unbounded radii satisfying a suitable moment condition. We stress that our assumption on the distribution of the radii does not exclude that, with overwhelming probability, the holes contain clusters made by many overlapping balls. We show that the formation of these clusters has no effect on the limit Brinkman equations. Due to the incompressibility condition and the lack of a maximum principle for the Stokes equations, our proof requires a very careful study of the geometry of the random holes generated by the class of probability measures considered.     

A Scaling Limit of the Becker-Döring Equations in the Regime of Small Excess Density

The Becker-Doring equations serve as a model for the nucleation of a new thermodynamic phase in a first-order phase transformation. This corresponds to the case when the total density of monomers exceeds a critical value and the excess density is contained in larger and larger clusters as time proceeds. It has been derived in Penrose [J. Stat. Phys. 89:1/2 (1997), 305-320] and Niethammer [J. Nonlin. Sci. 13:1 (2003), 115-155] that the evolution of these large clusters can on a certain large time scale be described by a nonlocal transport equation coupled with the constraint that the total volume of new phase is conserved. For specific coefficients this equation is well known as a classical mean-field model for coarsening. In the present paper we consider the regime of small excess density on a large time scale, but not as large as in Penrose (1997) or Niethammer (2003). We show rigorously that the leading order dynamics are governed by another variant of the classical mean-field model in which total mass is preserved.     

Unique solvability of the periodic Cauchy problem for wave-hierarchy problems with dissipation

Wave-hierarchy problems appear in a variety of applications such as traffic flows, roll waves down an open inclined channel and multiphase flows. Usually, these are described by the compressible Navier-Stokes equations with specific non-linearities; in a fluidized bed model they contain an additional pressure gradient term and are supplemented by an elliptic equation for this unknown pressure. These equations admit solutions periodic in space as well as in time, i.e. periodic travelling waves. Therefore, the corresponding initial value problem with periodic boundary conditions is solved locally in time in appropriate Sobolev spaces. Some remarks are made concerning global solutions, the occurrence of clusters or voids and the bifurcation of time periodic solutions, respectively.     

Weak solutions to the Cauchy problem for the diffusive discrete coagulation-fragmentation system

The initial value problem for the discrete coagulation-fragmentation system with diffusion is studied. This is an infinite countable system of reaction-diffusion equations describing coagulation and fragmentation of discrete clusters moving by spatial diffusion in all space . The model considered in this work is a generalization of Smoluchowski's discrete coagulation equations. Existence of global-in-time weak solutions to the Cauchy problem is proved under natural assumptions on initial data for unbounded coagulation and fragmentation coefficients. This work extends existence theory for this system from the case of clusters distribution on bounded domain subject to no-flux boundary condition to the case of all