无标度立体Koch网络上随机游走的平均吸收时间

作为一种基本的动力学过程,复杂网络上的随机游走是当前学术界研究的热点问题,其中精确计算带有陷阱的随机游走过程的平均吸收时间(mean trapping time,MTT)是该领域的一个难点.这里的MTT定义为从网络上任意一个节点出发首次到达设定陷阱的平均时间.本文研究了无标度立体Koch网络上带有一个陷阱的随机游走问题,解析计算了陷阱置于网络中度最大的节点这一情形的网络MTT指标.通过重正化群方法,利用网络递归生成的模式,给出了立体Koch网络上MTT的精确解,所得计算结果与数值解一致,并且从所得结果可以看出,立体Koch网络的MTT随着网络节点数N呈线性增长.最后,将所得结果与之前研究的完全图、规则网络、Sierpinski网络和T分形网络进行比较,结果表明Koch网络具有较高的传输效率.     

RIKEN介观器件腔中粒子输运过程的混沌性质及分形自相似结构研究

研究了粒子在RIKEN介观器件中的输运性质, RIKEN器件的理论模型是二维Sinai台球的一种, 是研究粒子逃逸曲线混沌性质和分形规律的理想模型之一. 采用逃逸曲线定性比较和分形维数定量计算两种方法, 得到了开口宽度、腔长、拐角位置、圆弧半径等器件参数对逃逸曲线混沌区域分布的影响规律. 结果发现逃逸曲线中存在分形自相似结构, 揭示了粒子在RIKEN介观器件腔中输运过程存在的混沌性质, 并首次运用"眼式结构"分析和相似比比较等方法对分形自相似结构进行了验证. 关键词： 介观器件 混沌性质 分形自相似 分形维数     

掺杂NaCl水溶液结晶形貌的分形研究

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。     

链式生物分子电磁(光)散射的T矩阵方法

具有生物蛋白酶主要功能的较小型分子集团的酶模型的人工设计,是生物有机化学家的重要研究方向。通过非接触、非破坏性的电磁散射的方法对物质结构特性进行研究是物理学的常用方法。本文模拟了具有Koch曲线形式的分形链式结构。用T矩阵的方法,研究了该分子集团的电磁散射特性。对这一不同领域的研究问题进行了有益的尝试。     

树状分形结构形成过程的实验研究

对大量金属小球在强电场作用下运动形态的演化全过程用联机摄像装置进行了实时拍摄,通过用Sandbox方法计算其稳定状态的分维数,系统地研究了分维数随电压的变化关系.结果表明：在一定电压范围内金属小球聚集体通过自组织过程形成稳定的树状分形结构,其分维数随外加电压的增加而减小.该结果对研究耗散结构的形成机理和外界动力对耗散结构的形貌影响具有参考价值. 关键词： 分形生长 自组织过程 树状结构 分维数     

分形理论在光谱识别中的应用

分形理论是研究一类不规则、混乱复杂,但其局部和整体具有相似性体系的科学。分形维数是分形理论中用于描述对象的不规则度和自相似性的基本度量。文章以符合朗伯-比尔定律的光谱信号为研究对象,在概述分形几何基本原理的基础上,提出了以分形维数作为光谱识别特征的方法,运用相空间重构得出了光谱信号的分形维数,通过对光谱信号的分形维数进行比较,达到识别不同光谱的目的,最后举例对该方法进行了说明。     

从昇华的NaCl蒸汽生长单晶体

半个世纪以来,从NaCl的蒸汽生长其单晶体的企图并没有得到正面的结果,解理面上的取向性结晶也尚未有超过数个分子层者。对于从溶液结晶出来时NaCl晶面发展的顺序,或者相对的重要性的研究已有肯定的结果。关于晶核或生长驼峰发端的位置从几率上看应在晶面何处的时尚理论未能从NaCl自溶液中结晶出来的实验加以证实或否定。为探索从蒸汽相生长NaCl单晶体的规律,本实验初步获得较大尺度的单晶体,并同时使取向性晶面上结晶达到1毫米以上的厚度。升华蒸汽来源于高纯度的从熔融体结晶出来的单晶体,并使母晶和结晶基面保持在近于NaC     

有限分枝分形上的自迴避迹行走

本文考虑在Sierpinski gasket及分支Koch曲线上的自迴避迹行走,运用实空间重整化群技术求出了相应的关联长度临界指数ν。结果表明,在Sierpinski gasket上,自迴避迹行走与自迴避行走属同一普适类;而在较高分枝度(R_max>3)的Koch曲线上,两者属不同普适类。 关键词：     

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。     

无格点基底表面的杂质分布对分枝状凝聚体的影响

根据含杂质熔融玻璃表面金原子凝聚的实验规律，在原子团簇具有随机的线扩散步长和刚性转动角的特征条件下，建立了含杂质无格点基底表面上改进的杂质限制团簇-团簇(IRCCA)凝聚模型.对团簇的扩散、刚性转动以及凝聚全过程进行了计算机模拟，系统地研究了杂质区域分布情况对分枝状凝聚体诸多特性的影响.结果表明规则分布的杂质对凝聚体生长的影响比随机分布的杂质大，导致杂质规则分布的基底表面上的分枝状凝聚体的数密度更大，分枝状凝聚体的回旋半径，凝聚体平均大小及分形维数更小. 关键词： 薄膜生长 Monte Carlo模拟 分形 杂质     

Strong backscattering enhancement for partially convex targets in random media

Earlier work pointed out that the radar cross section (RCS), owing to the double-passage effect on waves propagating through random media, is enhanced by a factor ranging from one up to three. However, our study has manifested numerically a strong enhancement in RCS of targets with concave-convex surfaces in continuous random media, by taking account of boundary conditions of waves on targets. We have found that when a plane wave illuminates a convex portion of the concave-convex conducting target in a random medium, the factor of enhancement oscillates about two with target size. Moreover, this enhancement becomes quite large at certain target shapes and also under a specific condition of target size and spatial coherence length of the incident H-wave. The large enhancement is considered as an anomalous feature in the behaviour of backscattered waves in random media. By analysing the scattering problem for beam-wave incidence on the same target in free space, we manifest the mechanism of such anomalous enhancement.     

Effects of interface kinetics and anisotropy on the stability of the growing crystal face and dissolution face during crystallization from solution under microgravity

The stability of the shapes of the growing crystal face and dissolution face in a two-dimensional mathematical model of crystal growth from solution under microgravity is studied. Effects of the interface kinetics and anisotropy of crystallization and dissolution on the stability are also studied. It is proved that the stable shapes of crystal growth face and dissolution face do exist, which are of suitably shaped curves with their upper parts inclined backward properly no matter whether the interface kinetics and the anisotropy are taken into account or not. The stable shapes of the growing crystal faces and dissolution faces are calculated for various cases. The interface kinetics will make the inclination degree of stable crystal growth face reduce and that of stable dissolution face reduce slightly. The anisotropy of crystallization and dissolution may make the inclination degree of stable-growing crystal face smaller or larger, and that of the stable dissolution face varies very slightly.     

Crystallization of poly(ethylene-co-octene): II Melt memory effects on first order kinetics

Dilatometric and X-ray scattering experiments of the crystallization kinetics of a sample of poly(ethylene-co-octene) show pronounced melt memory effects, i.e., the shapes of isotherms and characteristic times vary systematically with the temperature of the melt prior to cooling to the crystallization temperature. The temperature range of the effect is limited; crystallization kinetics remains constant below a melt temperature Tm l and above a melt temperature Tmh and varies only in-between. Analysis shows that the melt memory effect is caused by a variation of the characteristic time of a first order crystallization process. The process can be assigned to the in-filling of crystallites into objects of a previously generated precursor structure.     

Surface modification of bismuth and tin under the action of a powerful ion beam of nanosecond duration

Features of bismuth and tin sample morphology during irradiation by a powerful ion beam of nanosecond duration have been studied. It has been established that particles of various shapes are formed on the metal surface due to an increase in the bismuth melt volume during crystallization.     

Polycrystalline silicon thin films prepared by Ni silicide induced crystallization and the dopant effects on the crystallization

Intrinsic and doped polycrystalline silicon thin films were grown by the Ni silicide seeds induced crystallization. The Ni first reacted to Si forming a silicide seeds, then these seeds act as nuclei, from which the grains start to grow laterally. Compared with traditional Ni induced lateral crystallization, polycrystalline silicon thin film was grown by Ni silicide induced crystallization with low Ni contamination and large grain sizes. It can be found that the Ni silicide induced crystallization rate is accelerated by p-type doping and is decelerated by n-type doping. And the slightly and strongly phosphorous-doped polycrystalline silicon can be obtained with different grain shapes. Also, the sheet resistance of doped polycrystalline silicon decreases with the increasing of the doping atoms. A reasonable explanation is presented for the dopant effects on the growth rate, microstructure and electronic properties of the samples.     

Computer simulations of the condensation of nanoparticles from the gas phase

The crystallization of Ni nanoclusters from the gas phase is investigated with the help of molecular dynamics simulations using empirical tight-binding potentials. In these simulations, the condensation of hot liquid droplets from the gas phase is observed which later crystallize and agglomerate. It is shown that agglomeration of crystallized particles is the dominating growth mode and that the shapes of the final particles are similar to the shapes of experimentally grown Ni nanoparticles. In the second part, the evolution of the structure and the morphology of an agglomerated particle during sintering at 600 and 900K is studied. While in both cases the original disordered interface between the agglomerated particles vanishes, the shapes of the resulting particles differ considerably due to the different surface diffusion rates.     

Local Fractal Connections to Characterize the Spatial Processes of Deforestation in the Ecuadorian Amazon

Deforestation by human activities is a common issue in Amazonian countries. This occurs at different spatial and temporal scales causing primary forest loss and land fragmentation issues. During the deforestation process as the forest loses connectivity, the deforested patches create new intricate connections, which in turn create complex networks. In this study, we analyzed the local connected fractal dimension (LCFD) of the deforestation process in the Sumaco Biosphere Reserve (SBR) with two segmentation methods, —CA-wavelet and K-means—to categorize the complexity of deforested patches’ connections and then relate these with the spatial processes. The results showed an agreement with both methods, in which LCFD values below 1 corresponded to isolated patches with simple shapes and those above 1 signified more complex and connected patches. From CA-wavelet a threshold of 1.57 was detected allowing us to identify and discern low and high land transformation, while the threshold for K-means was 1.61. Both values represent the region from which deforestation performs local aggressive expansion networks. The thresholds were used to map the LCFD in which all spatial processes were visually detected. However, the threshold of 1.6 ± 0.03 was more effective in discerning high land transformation. such as shrinkage and attrition, in the deforestation process in the SBR.     

周长-面积关系及分形维数的计算机模拟

 本文利用分形理论中周长-面积关系的基本概念，对初始形状为三角形的不同大小的Koch曲线围成的岛，模拟了不同条件下，测量D值的变化规律，并进一步指出应用这一关系所应满足的条件及实际测量中有限层次的影响，探讨了所需条件在实际应用中的物理意义。     

Diffusion-Limited Aggregation with Polygon Particles

Diffusion-limited aggregation (DLA) assumes that particles perform pure random walk at a finite temperature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a ramified fractal structure, how the particle shape influences the formed morphology is still unclear. In this work, we perform the off-lattice two-dimensional DLA simulations with different particle shapes of triangle, quadrangle, pentagon, hexagon, and octagon, respectively, and compare with the results for circular particles. Our results indicate that different particle shapes only change the local structure, but have no effects on the global structure of the formed fractal cluster. The local compactness decreases as the number of polygon edges increases.