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101.
Optical solitary waves that propagate in a Kerr medium exhibiting a power-law nonlocal response are studied analytically. The first-principles stability analysis based on quantum field theory shows that within the whole range of the exponent (the fractal dimension) the solitary wave can be stabilized. 相似文献
102.
Differential equations and maps are the most frequently studied examples of dynamical systems and may be considered as continuous
and discrete time-evolution processes respectively. The processes in which time evolution takes place on Cantor-like fractal
subsets of the real line may be termed as fractal-time dynamical systems. Formulation of these systems requires an appropriate
framework. A new calculus calledF
α-calculus, is a natural calculus on subsetsF⊂ R of dimension α,0 < α ≤ 1. It involves integral and derivative of order α, calledF
α-integral andF
α-derivative respectively. TheF
α-integral is suitable for integrating functions with fractal support of dimension α, while theF
α-derivative enables us to differentiate functions like the Cantor staircase. The functions like the Cantor staircase function
occur naturally as solutions ofF
α-differential equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems.
We discuss construction and solutions of some fractal differential equations of the form
whereh is a vector field andD
F,t
α
is a fractal differential operator of order α in timet. We also consider some equations of the form
whereL is an ordinary differential operator in the real variablex, and(t,x) ∈F × Rn whereF is a Cantor-like set of dimension α.
Further, we discuss a method of finding solutions toF
α-differential equations: They can be mapped to ordinary differential equations, and the solutions of the latter can be transformed
back to get those of the former. This is illustrated with a couple of examples. 相似文献
103.
In the present paper we give an overview of topological properties of self-affine tiles. After reviewing some basic results on self-affine tiles and their boundary we give criteria for their local connectivity and connectivity. Furthermore, we study the connectivity of the interior of a family of tiles associated to quadratic number systems and give results on their fundamental group. If a self-affine tile tessellates the space the structure of the set of its ‘neighbors’ is discussed. 相似文献
104.
K.?L.?YaoEmail author Q.?M.?Liu Z.?L.?Liu X.?W.?Liu G.?Y.?Sun 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,35(3):365-370
We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation
of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase.
The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays
the same type of critical behavior as the pair contact process with diffusion 2A↦3A, 2A↦.
Received 14 October 2002 Published online 14 February 2003
RID="a"
ID="a"e-mail: Haye.Hinrichsen@physik.uni-wuppertal.de 相似文献
105.
We construct two examples of spaces homeomorphic to R
n
(n3) each of which has a closed geodesic and admits no isoperimetric inequality. The first is a complete polyhedral metric space of nonpositive curvature, and the second is an incomplete Riemannian space with nonpositive sectional curvatures. 相似文献
106.
从极优基未必能迅达最优基:兼与文献[1]作者商榷 总被引:2,自引:2,他引:0
本对献[1]提出的“求解线性规划的快速换基迭代法”从多阶段决策的观点阐述并举证了从极优基未必能快速到达最优基的论断。旨在说明用此方法求解一般线性规划问题时不一定能实现快速换基迭代的概念。 相似文献
107.
108.
The paper addresses a class of boundary value problems in some self-similar ramified domains, with the Laplace or Helmholtz equations. Much stress is placed on transparent boundary conditions which allow the solutions to be computed in subdomains. A self similar finite element method is proposed and tested. It can be used for numerically computing the spectrum of the Laplace operator with Neumann boundary conditions, as well as the eigenmodes. The eigenmodes are normalized by means of a perturbation method and the spectral decomposition of a compactly supported function is carried out. Finally, a numerical method for the wave equation is addressed. 相似文献
109.
针对火灾烟颗粒的形状特点,提出并建立火灾烟颗粒分形结构凝团的形状模型,并对烟颗粒扫描电镜(SEM)图像进行分析,获取分形结构模型中的单个凝团中基本颗粒个数、凝团分形维数、基本颗粒半径等参数.利用该模型对火灾烟颗粒的形状进行模拟的结果表明,该模型能够较好反映出烟颗粒的形貌特征.利用形状模型对火灾烟颗粒散射进行初步计算表明,在其他参数相同的情况下,相对于同体积的球形颗粒,分形凝团具有前向散射较弱,后向散射较强的特征. 相似文献
110.
随着信息产业国际化趋势的发展,广域网理论的研究显得越来越重要,中提出了网络的分形生长结构模型和生长方法,从全新的角度讨论广域网的生长、发展的过程。该结构模型将是描述互连广域的重要工具。 相似文献