Fractal patterns of fluid domains for displacement processes in porous media

Percolation invasion displacement of a compressible defender is examined for two cases: when only the smallest accessible site is entered at each step and when all accessible sites less than the size given by a reducing back pressure are entered at each time step. Although the fractions of invading fluid are different, their scaling properties are equivalent. The effect of limited control of a back pressure in a real displacement and the effect of viscosity in a real time displacement are examined. In these cases the scaling properties of a percolation process at breakthrough are removed. As a result, one should expect that realistic displacement models will not have the singular properties usually attributed to percolation processes.     

A necessary and sufficient condition for the existence of an exponential attractor

We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.     

Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension

Recurrent bivariate fractal interpolation surfaces (RBFISs) generalise the notion of affine fractal interpolation surfaces (FISs) in that the iterated system of transformations used to construct such a surface is non-affine. The resulting limit surface is therefore no longer self-affine nor self-similar. Exact values for the box-counting dimension of the RBFISs are obtained. Finally, a methodology to approximate any natural surface using RBFISs is outlined.     

基于相空间、熵和复杂度变化的表面肌电信号分析

采集20名男性实验对象在静态背伸疲劳负荷试验和动态等长负荷试验中的表面肌电信号,用混沌、分形理论的方法处理肌电信号、周期信号、随机信号,研究它们的延迟时间、重构相空间、熵值和复杂度等非线性指标的变化规律和特点.结果发现,表面肌电信号的延迟时间、重构相空间、熵值和复杂度等各种非线性特性均介于周期信号和随机信号之间,表现出混沌信号的特征.     

Localized Coherent Structures with Chaotic and Fractal Behaviors in a(2+1)-Dimensional Modified Dispersive Water-Wave System

In this work, we reveal a novel phenomenon that the localized coherent structures of some (2 1 )-dimensionalphysical models possess chaotic and fractal behaviors. To clarify these interesting phenomena, we take the (2 1)-dimensional modified dispersive water-wave system as a concrete example. Starting from a variable separation approach,a general variable separation solution of this system is derived. Besides the stable localized coherent soliton excitationslike dromions, lumps, rings, peakons, and oscillating soliton excitations, some new excitations with chaotic and fractalbehaviors are derived by introducing some types of lower dimensional chaotic and fractal patterns.     

Explicit finite-difference procedures for elastodynamic analysis of layered media

Summary Explicit finite-difference procedures are proposed to simulate the elastodynamic response of layered media. To avoid large numerical dispersion and dissipation, different grid sizes are used for different material layers so that the CFL number in each layer can be set to one in the limit. The master-slave technique is applied to deal with the mismatch of grids along the material interface. The interface can be either bonded or unbonded. The dynamic contact between two layers along an unbonded interface is also considered. Numerical examples are presented. Received 4 August 1997; accepted for publication 24 April 1998     

The Dirichlet,Neumann and Mixed Boundary Value Problems of the Theory of Elasticity in n-Dimensional Domains with Boundaries Containing Closed Cuspidal Edges

The Dirichlet, Neumann and mixed problems of statics of the theory of elasticity for anisotropic homogeneous media are studied in n-dimensional (n ≧ 2) domains with boundaries containing closed cuspidal edges. Theorems of the existence and uniqueness of solutions of these problems in the Besov and Bessel potential spaces are obtained. Smoothness of solutions in a closed domain occupied by elastic medium is investigated.     

一类Moran测度的Lq-谱

此文考虑了一类Moran分形，在其生成过程中每一阶的压缩比及压缩比的个数可以是不相同的，证明了支撑在此类Moran分形上的Moran测度的L^q-谱的存在性．     

Fractal characteristics of critical and localized states in incommensurate quantum systems

Incommensurate quantum systems with two competing periodicities exhibit metallic (with Bloch-type extended wave functions), insulating (with exponentially localized wave functions) as well ascritical (with fractal wave functions) phases. An exact renormalization method, which takes into account the inherent incommensurability, is used to obtain the phase diagram of various quantum models for the two-dimensional electron gas and for quantum spin chains in a magnetic field. In this approach, the scaling properties of the fractal eigenstates are characterized by a fixed point or a strange invariant set of the renormalization flow. One of our novel results is the existence of self-similar fluctuations in the localized states once the exponentially decaying envelope is factorized out. In almost all cases under investigation here, the universality classes can be broadly classified as those of the nearest-neighbor square or triangular lattices.