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1.
We study the structure of space-filling bearings (SFB) and Apollonian packings (AP) by determining the scaling behavior of the density distribution of points where the circles touch each other. Application of the sand box method to the average of theqth power of the number of touching points reveals the multifractal aspects of the structure of SFB and AP. 相似文献
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This paper presents a novel and data-independent method to construct a type of partially connected feedforward neural network (FNN). The proposed networks, called Apollonian network-based partially connected FNNs (APFNNs), are constructed in terms of the structures of two-dimensional deterministic Apollonian networks. The APFNNs are then applied in various experiments to solve function approximation, forecasting and classification problems. Their results are compared with those generated by partially connected FNNs with random connectivity (RPFNNs), different learning algorithm-based traditional FNNs and other benchmark methods. The results demonstrate that the proposed APFNNs have a good capacity to fit complicated input and output relations, and provide better generalization performance than traditional FNNs and RPFNNs. The APFNNs also demonstrate faster training speed in each epoch than traditional FNNs. 相似文献
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We introduce the Mellin transform of the balanced invariant measure associated to the Julia set generated by a rational transformation. We show that its analytic continuation is a meromorphic function, the poles of which are on a semi-infinite periodic lattice. This allows one to have an understanding of the behavior of the measure near a repulsive fixed point. Trace identities corresponding to the fact that the analytically continued Mellin transform vanishes at negative integers are derived for the polynomial case. The quadratic map is first analyzed in detail, and the analytic properties of the inverse of the Green's function are exhibited. Of interest is the appearance of a dense set of spikes at dyadic points when the Julia set is disconnected. These results are used to study the residues of the Mellin transform. A certain number of physically interesting consequences are derived for the spectral dimensionality of quantum mechanical systems, the excitation spectrum of which displays unusual oscillations. The appearance of complex critical indices for thermodynamical systems is also discussed in the conclusion.Supported in part by a N.A.T.O. Postdoctoral fellowship. 相似文献
5.
Amnon Aharony 《Journal of statistical physics》1984,34(5-6):931-939
Both the infinite cluster and its backbone are self-similar at the percolation threshold,p
c
. This self-similarity also holds at concentrationsp nearp
c
, for length scalesL which are smaller than the percolation connectedness length,. ForL<, the number of bonds on the infinite cluster scales asL
D
, where the fractal dimensionalityD is equal to(d-/v). Geometrical fractal models, which imitate the backbone and on which physical models are exactly solvable, are presented. Above six dimensions, one has D=4 and an additional scaling length must be included. The effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed. 相似文献
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Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization. 相似文献
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水溶液结晶是研究分形形貌的重要实验之一。本文通过改变溶液浓度,溶质组分和结晶温度等宏观实验参数,用分形维数的方法研究了这些参数对结晶形貌的影响。指出在低浓度下的非平衡态中溶液结晶形貌具有分形结构;不同晶体的生长作用力相互竞争,混乱度最大的情况下形成的分形结构最凸出,生长作用力是影响晶体形貌的主要因素;同时,分子热运动也是影响结晶形貌的因素之一。 相似文献
10.
利用太赫兹时域光谱(terahertz time domain spectroscopy,简称THz-TDS),研究了亚波长金属分形结构在THz波段的透射增强特性.分别从实验和理论两个方面,研究了铜箔上各级分形结构THz透射增强现象的产生机理.结果表明,在低频区的透射增强主要是由低级分形线中电子运动的共振引起的,而高频区的透射增强则主要由高级分形线中电子运动的共振引起的.从而将这种透射增强效应归结为分形结构中电子的共振辐射,即分形结构的局域共振效应.
关键词:
分形
太赫兹
透射
共振峰 相似文献
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LI Rui ZHANG Duan-Ming HUANG Ming-Tao SU Xiang-Ying CHEN Zhi-Yuan ZHU Hong-Ying ZHANG Lin 《理论物理通讯》2007,48(2):343-347
We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results: a single granular temperature does not characterize a multi-component mixture and each species attains its own "granular temperature"; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value olD augments. 相似文献
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LI Rui ZHANG Duan-Ming HUANG Ming-Tao SU Xiang-Ying CHEN Zhi-Yuan ZHU Hong-Ying ZHANG Lin 《理论物理通讯》2007,48(8):343-347
We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results: a single granular temperature does not characterize a multi-component mixture and each species attains its own "granular temperature"; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value of D augments. 相似文献
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Some results on the behavior and estimation of the fractal dimensions of distributions on attractors
C. D. Cutler 《Journal of statistical physics》1991,62(3-4):651-708
The strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation. In this paper we first provide a rigorous mathematical framework for the study of dimension, focusing on pointwise dimension(x) and the generalized Renyi dimensionsD(q), and give a rigorous proof of inequalities first derived by Grassberger and Procaccia and Hentschel and Procaccia. We then specialize to the problem of statistical estimation of the correlation dimension and information dimension. It has been recognized for some time that the error estimates accompanying the usual procedures (which generally involve least squares methods and nearest neighbor calculations) grossly underestimate the true statistical error involved. In least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates. We then develop an estimation procedure for which corrects for an important bias term (the local measure density) and provides confidence intervals for. The general applicability of this method is illustrated with various numerical examples. 相似文献
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M.A. Jafarizadeh 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,4(1):103-112
Using the symmetry of (
d
+1)-simplex fractals with decimation number b
=2, the current distribution has been determined. Then using the renormalization group technique, based on the independent Schur's
invariant polynomials of current distributions, the multifractal spectrum of even moments of current distributions has been
evaluated analytically up to order six for an arbitrary value of d. Also the scaling exponents of order 8 and order 10 have been calculated numerically up to d
=30.
Received: 19 November 1997 / Revised: 21 January 1998 / Accepted: 9 February 1998 相似文献
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将分形面积度量和分形拟合误差相结合,提出一种复杂背景下扩展目标检测方法。运用分形面积度量进行目标和背景的边缘检测,并结合扩展目标特性确定目标所在区域范围,实现初检。计算原始图像各像素分形拟合误差特征,并运用概率松弛迭代法进行分形特征增强,利用增强特征进一步抑制初检结果中的自然背景。最后运用数学形态学操作剔除背景粘连,实现扩展目标精确检测。实验结果表明:该方法能够有效、可靠地检测复杂背景下的扩展目标,并能较好保持目标的外形轮廓。 相似文献
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This paper gives an overview of the utilization of fractals in physical optics, especially of Koch fractals and their diffractals. The term fractal itself is defined and some basic characteristics of fractals are mentioned. Constructions of the most typical Koch curves are also depicted. Laser diffraction experiments using regular, random and modified Koch curves are described and the corresponding diffraction patterns (intensity distributions of diffractals) are shown. Some interesting properties of these diffraction patterns are discussed. 相似文献
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分形理论在物理实验教学中应用的探索 总被引:1,自引:2,他引:1
综述了作者近年来将分形理论引入基础物理实验教学中的尝试与实践,介绍了分形维数的测定方法及其应用,阐述了教师参与适量的科学研究是实现基础物理实验教学现代化的重要保证。 相似文献
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The problem of long-range bond percolation (LRBP) is studied both with scaling arguments and simulation methods. New scaling relations are proposed for the mean-field region and the fractal properties of the LRBP clusters are also investigated. 相似文献