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171.
M. B. Hastings 《Journal of statistical physics》2002,107(5-6):1031-1042
We consider a general model of branch competition that automatically leads to a critical branching configuration. This model is inspired by the 4– expansion of the dielectric breakdown model, but the mechanism of arriving at the critical point may be of relevance to other branching systems as well, such as fractures. The exact solution of this model clarifies the direct renormalization procedure used for the dielectric breakdown model, and demonstrates nonperturbatively the existence of additional irrelevant operators with complex scaling dimensions leading to discrete scale invariance. The anomalous exponents are shown to depend upon the details of branch interaction; we contrast with the branched growth model in which these exponents are universal to lowest order in 1–, and show that the branched growth model includes an inherent branch interaction different from that found in the dielectric breakdown model. We consider stationary and non-stationary regimes, corresponding to different growth geometries in the dielectric-breakdown model. 相似文献
172.
Multi-Fractal Formalism for Quasi-Self-Similar Functions 总被引:1,自引:0,他引:1
The study of multi-fractal functions has proved important in several domains of physics. Some physical phenomena such as fully developed turbulence or diffusion limited aggregates seem to exhibit some sort of self-similarity. The validity of the multi-fractal formalism has been proved to be valid for self-similar functions. But, multi-fractals encountered in physics or image processing are not exactly self-similar. For this reason, we extend the validity of the multi-fractal formalism for a class of some non-self-similar functions. Our functions are written as the superposition of similar structures at different scales, reminiscent of some possible modelization of turbulence or cascade models. Their expressions look also like wavelet decompositions. For the computation of their spectrum of singularities, it is unknown how to construct Gibbs measures. However, it suffices to use measures constructed according the Frostman's method. Besides, we compute the box dimension of the graphs. 相似文献
173.
For a translation invariant Gibbs measure on the configuration space X of a lattice finite spin system, we consider the set X
of generic points. Using a Breiman type convergence theorem on the set X
of generic points of an arbitrary translation invariant probability measure on X, we evaluate the Hausdorff dimension of the set X
with respect to any metric out of a wide class of scale metrics on X (including Billingsley metrics generated by Gibbs measures). 相似文献
174.
We investigate finite lattice approximations to the Wilson renormalization group in models of unconstrained spins. We discuss first the properties of the renormalization group transformation (RGT) that control the accuracy of this type of approximation and explain different methods and techniques to practically identify them. We also discuss how to determine the anomalous dimension of the field. We apply our considerations to a linear sigma model in two dimensions in the domain of attraction of the Ising fixed point using a Bell–Wilson RGT. We are able to identify optimal RGTs which allow accurate computations of quantities such as critical exponents, fixed-point couplings and eigenvectors with modest statistics. We finally discuss the advantages and limitations of this type of approach. 相似文献
175.
Huonan Lin 《中国科学A辑(英文版)》1999,42(9):932-944
The problem of uniform dimensions for multi-parameter processes, which may not possess the uniform stochastic Hölder condition, is investigated. The problem of uniform dimension for multi-parameter stable processes is solved. That is, ifZ is a stable (N,d, α)-process and αN ?d, then $\forall E \subseteq \mathbb{R}_ + ^N , \dim Z\left( E \right) = \alpha \cdot \dim E$ holds with probability 1, whereZ(E) = {x : ?t ∈E,Z t =x} is the image set ofZ onE. The uniform upper bounds for multi-parameter processes with independent increments under general conditions are also given. Most conclusions about uniform dimension can be considered as special cases of our results. 相似文献
176.
用电沉积方法得到了不同浓度硫酸锌电解液的分形凝聚图像;进行图像处理,得到了其分形维数与浓度的关系曲线;用粒子扩散限制凝聚模型解释了此关系 相似文献
177.
178.
Li Huishi 《数学年刊B辑(英文版)》1994,15(4):463-468
It is proved that for a left Noetherian z-graded ring A,if every finitely generated graded A-module has finite projective dimension(i.e-,A is gr-regular)then every finitely generated A-module has finite projective dimension(i.e.,A is regular).Some applications of this result to filtered rings and some classical cases are also given. 相似文献
179.
有阻尼Sine-Gordon方程的全局吸引子的维数 总被引:4,自引:0,他引:4
本文通过引入新范数,得到有阻尼Sine-Gordon方程的Dirichlet问题的全局吸引子的维数的一个估计.结果表明:当“阻尼”与“扩散”同时增大或正弦项系数减小时,吸引子的维数减小.特别地,得到了零维吸引子存在的参数条件. 相似文献
180.
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