MULTI-SCALE NUMERICAL MODEL FOR SIMULATING CONCRETE MATERIAL BASED ON FRACTAL THEORY

A new multi-scale numerical model is presented using the fractal theory and adopting FEM to simulate the failure of concrete.The relation between the fractal box dimension in large scale and the damage to concrete in small scale is deduced.And the evolutionary process of elastic modulus and strength in small scale is given.Consequently,the multi-scale numerical model is proposed to describe the constitutive relation of concrete between small scale and large scale.A two-dimensional static analysis of a concrete block is performed by using this model and the calculation result is discussed.The propagation of cracks of the concrete block is also studied.     

Optimal quantization for dyadic homogeneous Cantor distributions

For a large class of dyadic homogeneous Cantor distributions in ?, which are not necessarily self‐similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non‐existence of the quantization coefficient. The class contains all self‐similar dyadic Cantor distributions, with contraction factor less than or equal to 1/3. For these distributions we calculate the quantization errors explicitly. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

拟矩形剖分上的样条空间的维数

矩形剖分~(记为$\Delta_{QR}$)~是指在矩形剖分~(记为$\Delta_{R}$)的基础上进行局部修改后得到的剖分,通常包括T-剖分~(记为$\Delta_{T}$)~和L-剖分~(记为$\Delta_{L}$).本文利用光滑余因子协调方法讨论了该剖分上的二元样条空间$S^\mu_k(\Delta_{QR})$的维数.在满足一定约束条件下, 得到了仅依赖于样条空间的次数,光滑度和剖分拓扑结构的显式维数公式.     

Solvable infinite-dimensional linear groups with restrictions on the nonabelian subgroups of infinite rank

Under study are the solvable nonabelian linear groups of infinite central dimension and sectional p-rank, p ≥ 0, in which all proper nonabelian subgroups of infinite sectional p-rank have finite central dimension. We describe the structure of the groups of this class.     

Intersections and polar functions of fractional brownian sheets

Let B^H={B^H（t）,t∈R^N＋}be a real-valued（N,d）fractional Brownian sheet with Hurst index H=（H1,…,HN）.The characteristics of the polar functions for B^H are discussed.The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of B^H is obtained.The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for B^H are presented.Furthermore,it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions.A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Holder condition is also solved.     

Critical Slowing Down in One-Dimensional Maps and Beyond

This is a brief review on critical slowing down near the Feigenbaum period-doubling bifurcation points and its consequences. The slowing down of numerical convergence leads to an “operational” fractal dimension D=2/3 at a finite order bifurcation point. There is a cross-over to D ₀=0.538... when the order goes to infinity, i.e., to the Feigenbaum accumulation point. The problem of whether there exists a “super-scaling” for the dimension spectrum D _q ^W that does not depend on the primitive word W underlying the period-n-tupling sequence seems to remain open     

Consistency conditions on the least squares estimator in single common factor analysis model

Summary This paper is concerned with the consistency of estimators in a single common factor analysis model when the dimension of the observed vector is not fixed. In the model several conditions on the sample sizen and the dimensionp are established for the least squares estimator (L.S.E.) to be consistent. Under some assumptions,p/n→0 is a necessary and sufficient condition that the L.S.E. converges in probability to the true value. A sufficient condition for almost sure convergence is also given.     

On the Hausdorff Dimension of Regular Points of Inviscid Burgers Equation with Stable Initial Data

Consider an inviscid Burgers equation whose initial data is a Lévy α-stable process Z with α>1. We show that when Z has positive jumps, the Hausdorff dimension of the set of Lagrangian regular points associated with the equation is strictly smaller than 1/α, as soon as α is close to 1. This gives a partially negative answer to a Conjecture of Janicki and Woyczynski (J. Stat. Phys. 86(1–2):277–299, 1997). Along the way, we contradict a recent Conjecture of Z. Shi () about the lower tails of integrated stable processes.     

Distributional Dimension of Fraetal Sets in Local Fields

The distributional dimension of fractal sets in R^n has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dimD in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions. Keywords local field, B-type space, F-type space, distributional dimension, Hausdorff dimension Fourier dimension     

Flow dimension and capacity for structuring urban street networks

This paper aims to measure the efficiency of urban street networks (a kind of complex networks) from the perspective of the multidimensional chain of connectivity (or flow). More specifically, we define two quantities: flow dimension and flow capacity, to characterize structures of urban street networks. To our surprise, for the topologies of urban street networks, previously confirmed as a form of small world and scale-free networks, we find that (1) the range of their flow dimensions is rather wider than their random and regular counterparts, (2) their flow dimension shows a power-law distribution, and (3) they have a higher flow capacity than their random and regular counterparts. The findings confirm that (1) both the wider range of flow dimensions and the higher flow capacity can be a signature of small world networks, and (2) the flow capacity can be an alternative quantity for measuring the efficiency of networks or that of the individual nodes. The findings are illustrated using three urban street networks (two in Europe and one in the USA).