凝聚态物理中的分形

本文回顾了近年来与凝聚态物理相关的分形研究的一些主要工作，叙述了该领域的一些新进展。着重介绍了涉及分维和分形的一些基本概念、物理思想和研究方法，较详细地讨论了分形网络上的振动和弹性性质、磁序问题、生长和熔化、多分形以及周期分形等课题。     

分形理论在物理实验教学中应用的探索

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。     

凝聚态物理中的分形

本文回顾了近年来与凝聚态物理相关的分形研究的一些主要工作,叙述了该领域的一些新进展。着重介绍了涉及分维和分形的一些基本概念、物理思想和研究方法,较详细地讨论了分形网络上的振动和弹性性质、磁序问题、生长和熔化、多分形以及周期分形等课题。     

分形研究中的复分形概念

本文介绍了分形研究领域近几年提出的复分形概念及复分形研究的新进展，对f-α谱的计算方法及物理意义也作了较详细的阐述。     

分形概念及其在材料科学中的应用

本文首先结合几个数学构造分形的例子介绍分形概念，然后对分形在材料科学中的应用作了简要介绍，主要包括：粉体生长中的分形、断裂面的分形、离子注入等非平衡方法产生的分形、表面分形、无机材料中的分形、自旋玻璃中的分形．     

关于相干长度两种表述的一致性

本文从原子能级跃迁中的不确定性关系出发，将普通物理教材中关于相干长度的两种表述统一起来。     

多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

单毛细管中赫切尔-巴尔克莱流体的分形分析

运用分形理论给出了非牛顿流体中的赫切尔-巴尔克莱流体在单毛细管中的渗流分形模型. 此模型将赫切尔-巴尔克莱流体的流量、流速、启动压力梯度和有效渗 透率与流体的流变特性、毛细管的结构参数联系起来, 并且不含经验常数, 每个参数都具有明确的物理意义, 所得分形模型更能体现出赫切尔-巴尔克莱流体流动的内在物理机理.     

关于相干长度两种表述的一致性

本文从原子能级跃迁中的不确定性关系出发，将普通物理教材中关于相干长度的两种表述统一起来．     

动力破碎分形和加载的关系

 应用由Grady和Kipp推广的Mott公式，导出了物体破碎碎块的分形公式，求出了分形维数，然后将此公式和加载及加载时间联系起来，阐明了分形维数的物理本质。     

裂缝-孔隙型双重介质油藏渗吸机理的分形分析

低渗透油藏常常伴随裂缝发育,形成裂缝-基质双重介质.自发渗吸是低渗裂缝性水驱油藏的重要采油机理,有顺向和逆向两种渗吸方式.基于基质孔隙结构的分形特征,引入分形几何对裂缝性双重介质渗吸机理的判据进行了改进,建立了渗吸机理的分形判据模型,并进一步推导了结构常数的解析表达式.结果表明,渗吸机理的判别参数是基质孔隙度、高度、孔隙分形维数、流动迂曲度、最大孔隙直径、界面张力、油水密度差以及接触角的函数.改进后的判据模型与现有结果一致.最后绘制了判别渗吸机理的图版,为利用表面活性剂提高低渗透油藏采收率提供理论依据.     

分形介质的传热与传质分析(综述)

本文论述了分形介质的分形理论和数学基础,并简要综述了用分形理论和方法研究分形介质的传热与传质特性(如多孔介质的渗透率、热导率以及池核态沸腾换热)方面目前所取得的研究进展,最后扼要展望了用分形理论和方法进一步研究分形介质的传热与传质的可能的若干课题和方向。     

Mode II brittle fracture assessment using an energy based criterion

In this paper the minimum strain energy density criterion is modified to predict the values of mode II fracture toughness reported in the literature for several brittle and quasi-brittle materials. The experimental results are all related to mode II fracture tests performed on the semicircular bend specimen. The modified mode II fracture criterion takes into account the effect of T-stress (in addition to the singular terms of stresses/strains) when calculating the strain energy density factor at a very small critical distance from the crack tip. It is shown that the proposed criterion provides significantly better predictions for mode II fracture toughness compared with the classical minimum strain energy density criterion.     

Compressive Brittle Fracture Prediction in Blunt V-Notched PMMA Specimens by Means of the Strain Energy Density Approach

The paper aims to examine the suitability of the strain energy density criterion in predicting the fracture behavior of blunt V-notched specimens under compression load. Recent studies on local stress fields have shown that the strain energy density, averaged over a specific control volume which embraces the notch round border, could be a robust parameter in the brittle fracture assessment of several materials. A set of experimental results recently published in the literature on compressive brittle fracture of V-notched specimens made out of polymethyl methacrylate has here been considered. Finite element analyses have been performed on plane strain condition and experimental data have been summarized by means of the SED criterion. It has been shown that the proposed criterion permits a satisfactory evaluation of the fracture load of polymethyl methacrylate specimens weakened by notches having different opening angles and radii.     

Current challenges for statistical physics in fracture and plasticity

Statistical physics has been applied in the last decades to several problems in mechanics, including fracture and plasticity. Concept drawn from percolation, fractal geometry, phase-transitions, and interface depinning have been used with varying degrees of success to understand these problems. In this colloquium, I describe recent successes and current challenging problems for statistical physics in fracture and plasticity, focusing on the roughness of cracks, fracture size effects and micron-scale plasticity.     

Formation of different surface reliefs of metallic glasses under mechanical stress

The micro- and nanoreliefs of loaded lateral surfaces and fracture surfaces of foils of the Fe₇₇Ni₁Si₉B₁₃, Fe₅₈Ni₂₀Si₉B₁₃, and Fe₇₀Cr₁₅B₁₅ amorphous alloys have been investigated using scanning tunneling and atomic force microscopy. The isotropic and anisotropic surface reliefs have been examined. The fractal dimensions of the surfaces of loaded specimens and the fracture surfaces along and across the direction of crack propagation have been estimated using the box counting method. Fractal characteristics of the surfaces, such as the Hölder exponent and the half-width of the singularity spectrum, have been calculated using the wavelet transform method. It has been found that, on the topographies with a clearly pronounced anisotropy of the relief, the surface is fractal in only one direction, and the surface is fractal in two directions on the topographies with a less pronounced anisotropy of the relief. The fractal characteristics of the lateral surfaces and the fracture surfaces with allowance made for their anisotropy have close values. It has been shown that the formation of two types of fracture surfaces is adequately described in terms of the model of a cellular automaton.     

Proteins: coexistence of stability and flexibility

We introduce an equation for protein native topology based on recent analysis of data from the Protein Data Bank and on a generalization of the Landau-Peierls instability criterion for fractals. The equation relates the protein fractal dimension df, the spectral dimension ds, and the number of amino acids N. Deviations from the equation may render a protein unfolded. The fractal nature of proteins is shown to bridge their seemingly conflicting properties of stability and flexibility. Over 500 proteins have been analyzed (df, ds, and N) and found to obey this equation of state.     

Numerical simulation of deformation and fracture of a material with a polysilazane-based coating

The paper studies the localization of plastic deformation and fracture in a material with a porous coating. A dynamic boundary value problem in the plane strain formulation is solved. The numerical simulation is performed by the finite difference method. The composite structure corresponds to the experimentally observed one and is specified explicitly in the calculation. A generation procedure of the initial finite-difference grid is developed to describe the coating structure with adjustable porosity and geometry of the substrate-coating interface. Constitutive equations for the steel substrate include an elastic-plastic model of an isotropically hardening material. The ceramic coating is described by a brittle fracture model on the basis of the Huber criterion which accounts for crack nucleation in triaxial tension zones. It is shown that the specific character of deformation and fracture of the studied composite results from the presence of local tensile regions in the vicinity of pores and along the coating-substrate interface, in both tension and compression of the coated material. The interrelation between inhomogeneous plastic flow in the steel substrate and crack propagation in the coating is studied.     

K1c与DF关系的几点注记

 本文根据裂端塑性区的不同结构和不同的断裂机制，从理论上讨论了断裂韧性K_1c与断口分形维数D_F间的定量关系。从而，指出了分形用于耗散系统研究时，耗散能的分析与计算将起着重要的作用。     

Clustering in determinate and stochastic fields

Computer models of gradient-controlled growth are studied. Algorithms used in this class of models allow for the formation of a variety of clusters that have different, including fractal, structures. The problem of formation of nonbranching isolated vertical clusters is solved by using an algorithm that corresponds to a high-gradient long-range potential concentrated in a narrow interval.