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．     

分形多孔介质中的热传导

本文将多孔介质视为由骨架和空隙组成的二元混合介质,研究了多孔介质中的热传导过程,发现分形结构中的导热规律与孔隙的分布有关,存在着与实体导热完全不同的特征。计算表明,分形介质中的导热过程除了与基质(骨架)的分形维数有关外,还与基质率以及反映介质中热量传递动态过程有关。     

分形理论及其在聚集生长研究中的应用

分形理论是现代非线性科学的一个重要分支,近年来发展越来越快,应用研究也越来越广泛。本文简要介绍了分形的基本理论及其在聚集生长研究中的应用,最后展望了分形理论的应用前景及其发展前景。     

多重分形谱及其在材料研究中的应用

详细讨论了多重分形谱中各参量的物理意义,拽出随机多重分形谱中出现异常区的原因。提出了一种舒去少量异常小的分布概率的方法,局部消除了异常区,最后介绍了一些多重分形谱在材料研究中的应用。     

纹理高阶分形特征在海面舰船目标检测中的应用

针对复杂海面环境下的舰船目标检测，分析了高阶分形特征缝隙在纹理分类中的应用，提出了一种基于分形维与缝隙的目标检测新方法，并利用该方法对海面舰船目标进行了检测。实验结果表明利用纹理分形维与缝隙特征进行海面舰船目标检测，可以取得较单一分形维检测更高的准确率。     

分形在物理学中的应用

 一、分形理论的基本内容分形是对没有特征长度但有某种意义下的自相似性的形体和结构的总称。分形体系是具有无标度性的自相似结构。自相似结构可用分形维数来表示,这个维数可以是分数,或是一个连续变化的数。分形维数是描述分形的重要参数,有多种定义和计算方法。一般地,如把一个Ｄ维几何物体的尺寸放大Ｌ倍,就得到ＬＤ个原来的几何图像。令ＬＤ=Ｋ,则有Ｄ=ｌｎＫｌｎＬ上式可作为豪斯道夫维数的定义,并且能毫无困难地推广到非整数的范围。分形几何中的主要角色是由传统数学中的“病态”结构所扮演的,如科契曲线、谢尔品斯基海绵等,它们都具有严格的自相似结构,属于有规分形。     

反常输运现象中的分数阶扩散方程

 根据连续性方程,可以得到分形上的标准扩散方程。然而这个标准扩散方程并不能真正描述分形介质中的反常扩散,其根源在于分形介质中的扩散具有记忆效应,为了得到更普遍的扩散方程,通过讨论早期提出的扩散方程的缺陷,可以得到分数阶扩散方程,并且更具有普遍性。     

多重分形在掌纹识别中的研究

通过对掌纹的概率密度分布和配分函数的分析，得到掌纹分布具有一定的多重分形性.进一步求取掌纹多重分形谱的宽度、极大值以及谱曲线的不对称程度，并提出以这些参数作为掌纹识别的特征量.这可能为多重分形理论在生物特征识别领域中的应用带来新的思路与方法. 关键词： 分形 模式识别     

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。     

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。     

Patterns and Symmetries in the Visual Cortex and in Natural Images

As borders between different entities, lines are an important element of natural images. Indeed, the neurons of the mammalian visual cortex are tuned to respond best to lines of a given orientation. This preferred orientation varies continuously across most of the cortex, but also has vortex-like singularities known as pinwheels. In attempting to describe such patterns of orientation preference, we are led to consider underlying rotation symmetries: Oriented segments in natural images tend to be collinear; neurons are more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underlying topography. This is verified by direct statistical tests in both natural images and in cortical maps. Using the statistics of natural scenes we construct filters that are best suited to extracting information from such images, and find qualitative similarities to mammalian vision. PACS84.35+i 89.70.+c 87.57.Nk     

Solitons and Vortices in Plasmas

The various types of nonlinear wave solutions in plasmas are reviewed. First, the generation, pro- pagation, and stability of solitary waves are demonstrated for some simple examples. Then, relevant two-and three-dimensional models for Langniuir solitons are proposed and investigated. The collapse as an effective dissipation mechanism in plasmas is discussed in detail. Finally, simple models of two-dimensional vortex motion and their consequences are considered.     

Twin walls in anorthoclase are enriched in alkali and depleted in Ca and Al

Abstract

Composition profiles have been measured in transformation twin walls of the albite type in anorthoclase. Regions close to the walls between two twin domains are enriched in K and Na and depleted in Ca and Al. Microanalysis experiments show high mobility of alkali cations close to twin boundaries. Twin walls are generated via the displacive phase transition C2/m?C[lbar] in Al, Si disordered feldspar, and the chemical heterogeneity is a fingerprint for the subsequent diffusion of alkali and earth alkali ions during the cooling history of the sample.     

The fate of Li and Be in stars and in the laboratory

We connect the observed under-abundances of Li and Be in dwarfs, with recent results on nuclear cross sections at low energies: for collisions of protons with atomic or molecular targets, the measured cross sections seem too high with respect to extrapolations for bare nuclei. Phenomenologically, these anomalous nuclear interactions can be described in terms of an effective screening potentialU _lab in the range of few hundred eV: in the presence of the electron cloud, nuclei become more transparent to each other as if the effective collision energy is aumented byU _lab. This implies that fusion cross sections are enlarged and at the same time elastic cross sections are lowered. If something similar occurs in stellar plasma, the nuclear burning temperatures are lowered, whereas diffusion processes are enhanced. We find that the observed Li and Be abundances in the Hyades and in the Sun can be reproduced for effective screening potentials of the plasma in the range of 600–700 eV, close to that found by experiments in the laboratory.     

Laser nanofabrication in photoresists and azopolymers

Recent progress in the field of single‐ and two‐photon nanofabrication, both 2‐ and 3‐dimensional, in photopolymerizable resins and in films of photoisomerizable azopolymers are reviewed. The basic processes as well as technological advances and applications of nanofabrication by light are discussed. Recent advances and achievements in polymer photomechanics and light‐activated molecular movement in azopolymers are also reviewed.     

Fluid spheres and R- and T-regions in general relativity

R- and T-regions of spacetime are first defined in a particular coordinate system and then with the aid of the Schwarzschild vacuum solution are shown to represent the outside and inside of a black hole respectively. A certain class of interior solutions, relating to a perfect fluid, are also considered and it is found that these R- and T-solutions have distinct physical properties. The R-solutions are static, spherically symmetric, permanent, and have a classical analogue, while the corresponding T-solutions, which are wholly time dependent, are cylindrical, temporary, and do not have a classical analogue. It is shown that these T-solutions cannot be generated from their R-region counterparts. Particular T-solutions are also presented in which the corresponding fluid occupies the whole of a T-region. The fluid would under certain circumstances be black body radiation while for other cases the internal pressure is always greater than the density.     

Excitonic and electronic states in ellipsoidal and semiellipsoidal quantum dots

A simple model is assumed to obtain analytical solutions of the Schrödinger equation in prolate spheroidal coordinates for the electron–hole pair confined to an ellipsoidal quantum dot (EQD) or to a semiellipsoidal quantum dot (SEQD). Numerical calculations are carried out to find the excitonic states as well as the electronic states decoupled from holes in such geometries. Their dependence on the inverse of the eccentricity of the ellipsoidal surfaces for different interfocal distances is investigated. The binding energy and the recombination radiation energy are calculated for GaAs and InAs QDs; the same dependences are also investigated. Comparison with previous calculations and experiments shows a good order-of-magnitude agreement. It is demonstrated that some of the available states in an EQD are forbidden in the SEQD and, consequently, some of the photoluminescence lines observed in the former case are suppressed in the latter geometry.     

Normal spectral emissivity of platinum in the red and in the green in vacuum and helium

The spectral emissivity of platinum for λ=0.645 μm and λ=0.546 μm has been measured by using a De Vos blackbody in ultrahigh vacuum and in helium. Changes in enissivity brought about by heat treatment and changing ambiences, are illustrated and discussed and the results are compared with previously published data. The emissivities determined turned out to be appreciably lower than the measurements of previous investigators. The determined values for 1100<T(K)<1800 are for 0.645 μ between 0.237 and 0.249 in vacuum, and between 0.185 and 0.290 in helium; and for 0.546 μm between 0.250 and 0.312 for vacuum and between 0.219 and 0.321 in helium.     

Stripes and superconductivity in cuprates

Holes doped into the CuO₂ planes of cuprate parent compounds frustrate the antiferromagnetic order. The development of spin and charge stripes provides a compromise between the competing magnetic and kinetic energies. Static stripe order has been observed only in certain particular compounds, but there are signatures which suggest that dynamic stripe correlations are common in the cuprates. Though stripe order is bad for superconducting phase coherence, stripes are compatible with strong pairing. Ironically, magnetic-field-induced stripe order appears to enhance the stability of superconducting order within the planes.     

Phonons and librons in solid hydrogen and deuterium

The coupled system of phonons and librons is treated in the Random Phase Approximation. The short range correlations are taken into account by an effective Hamiltonian. Dispersion curves and spectra are calculated for both the fcc and hcp phases. All calculations are performed a) with quadrupole-quadrupole forces only b) including the other anisotropic forces.