A nonlinear oblique derivative boundary value problem for the heat equation Part 2: Singular self-similar solutions

This paper continues the study started in [12]. In the upper half-plane, consider the elliptic equation

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, submitted to the nonlinear oblique derivative boundary condition U_x = UU_z on the axis x = 0. The solution of this problem appears to be the self-similar solution of the heat equation with the same boundary condition. As goes to 0, the function U converges to the non trivial solution U of the corresponding degenerate problem. Moreover there exists z₀ > 0 such that U vanishes for z ≥ z₀, is C^∞ on ]0, z₀[× ₊, is continuous on the boundary x = 0 and is discontinuous on the half-axis {z = 0, x> 0}.     

基于分形漏桶整形器的通用处理器共享系统性能分析

为了分析自相似业务流对通用处理器共享（GPS）系统性能的影响,研究了GPS系统性能与业务流自相似参数等因素之间的关系.通过使用分形漏桶的包络曲线对进入GPS系统的自相似业务流进行整形,推导了利用自相似业务流作为输入的GPS系统的队列长度和时延统计上界.数值结果与分析显示,基于分形漏桶的GPS系统性能模型对自相似业务流具有较好的性能.     

Limit Theorems for Multiplicative Processes

Let W be a non-negative random variable with EW=1, and let {W _i } be a family of independent copies of W, indexed by all the finite sequences i=i ₁i _n of positive integers. For fixed r and n the random multiplicative measure ⁿ _r has, on each r-adic interval at nth level, the density with respect to the Lebesgue measure on [0,1]. If EW log Wr, the sequence { ⁿ _r } _n converges a.s. weakly to the Mandelbrot measure _r . For each fixed 1n, we study asymptotic properties for the sequence of random measures { ⁿ _r } _r as r. We prove uniform laws of large numbers, functional central limit theorems, a functional law of iterated logarithm, and large deviation principles. The function-indexed processes is a natural extension to a tree-indexed process at nth level of the usual smoothed partial-sum process corresponding to n=1. The results extend the classical ones for { ¹ _r } _r , and the recent ones for the masses of { _r } _r established in Ref. 23.     

Self-similar solutions to the generalized deterministic KPZ equation

Geometric properties of shape functions of self-similar solution to the equation are studied, and q are positive numbers. These shapes-the solutions of the corresponding nonlinear ODE-are of very different nature. The properties usually depend on three critical values of q (1, 3/2 and 2). For the range 1<q<2 the dependence of is more remarkable, for example there is no global existence in general.     

The asymptotic behavior of fragmentation processes

The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the evolution of a mass that falls apart randomly as time passes. We investigate their pathwise asymptotic behavior as t. In the so-called homogeneous case, we first point at a law of large numbers and a central limit theorem for (a modified version of) the empirical distribution of the fragments at time t. These results are reminiscent of those of Asmussen and Kaplan [3] and Biggins [12] for branching random walks. Next, in the same vein as Biggins [10], we also investigate some natural martingales, which open the way to an almost sure large deviation principle by an application of the Gärtner-Ellis theorem. Finally, some asymptotic results in the general self-similar case are derived by time-change from the previous ones. Properties of size-biased picked fragments provide key tools for the study. Mathematics Subject Classification (2000) 60J25, 60G09     

Tangent Fields and the Local Structure of Random Fields

A tangent field of a random field X on ^N at a point z is defined to be the limit of a sequence of scaled enlargements of X about z. This paper develops general properties of tangent fields, emphasising their rich structure and strong invariance properties which place considerable constraints on their form. The theory is illustrated by a variety of examples, both of a smooth and fractal nature.     

正常色散光纤放大器中超短脉冲的自相似演化条件

在正常色散条件下,超短光脉冲在光纤放大器中可以演化成具有线性啁啾的自相似抛物脉冲,其演化结果可影响脉冲的压缩质量.采用分步傅里叶方法数值研究了正常色散光纤放大器中,初始输入脉冲宽度、能量、光纤增益和色散系数对超短脉冲自相似演化结果的影响.发现色散长度是脉冲能否实现自相似演化的关键因素.当色散长度与光纤长度相近(几倍)时,脉冲可以实现自相似演化;两者相差越大,脉冲的自相似演化程度越差.增加初始脉冲能量可以加速脉冲的自相似演化,缩短自相似演化的距离.放大器总增益一定时,增益系数越大,脉冲受非线性扭曲的影响越大,使脉冲的自相似演化结果越差;增益系数为0.95 m-1时放大器可获得的总增益比3.8 m-1时大3.3 dB.     

THE INVERSION OF CIRCULANT MATRIX

The method of inverting the circulant matrix and the expression of inversion of the circulant matrix are obtained in this paper.     

稀甲烷/氢气预混湍流传播火焰实验研究

本文采用定容湍流燃烧弹获取了稀甲烷/氢气/空气在强湍流条件下的火焰发展历程,研究了湍流火焰在负马克斯坦数条件下的传播特性.结果表明,湍流火焰呈现自相似传播特性,即使在强湍流条件下,湍流传播火焰仍然会受到不稳定性的影响.并且随着马克斯坦数的减小,不稳定性对湍流传播火焰的影响增强。同时,本文获得一种新的湍流燃烧速度拟合公式,包含了负马克斯坦数条件下不稳定性对湍流燃烧速度的影响。     

Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity

We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in Rn, n=2,3, namely the MHD with positive viscosity and zero resistivity. In the special case of zero magnetic field the system reduces to the Navier-Stokes equations in Rn. In this paper we exclude the scenario of finite time singularity in the form of self-similarity, under suitable integrability conditions on the velocity and the magnetic field. We also prove the nonexistence of asymptotically self-similar singularity. This provides us information on the behavior of solutions near possible singularity of general type as described in Corollary 1.1.