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.     

Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles

A finite size effect in the probing of the harmonic measure in simulation of diffusion-limited aggregation (DLA) growth is investigated. We introduce a variable size of probe particles, to estimate harmonic measure and extract the fractal dimension of DLA clusters taking two limits, of vanishingly small probe particle size and of infinitely large size of a DLA cluster. We generate 1000 DLA clusters consisting of 50 million particles each, using an off-lattice killing-free algorithm developed in the early work. The introduced method leads to unprecedented accuracy in the estimation of the fractal dimension. We discuss the variation of the probability distribution function with the size of probing particles.     

局部区域粒子源与其凝聚集团关系的模拟

利用改进的DLA模型研究由局部区域粒子源释放随机运动粒子形成的凝聚集团的生长.结果显示,该凝聚集团的生长结构与粒子源的方位有关,正对着粒子源方位的生长速度相对较快,同时集团粒子在生长平面的分布与粒子源的相对距离和相对大小有关系,根据粒子源的变化呈现一定的变化规律.该结果有助于从凝聚物的生长结构特征了解粒子源的方位、并对粒子源相对距离和相对大小进行估计.     

Annealing two-dimensional diffusion-limited aggregates

We have studied the structure of annealed two-dimensional diffusion-limited aggregates (DLA). The annealing process consists of introducing internal flexibility to the original DLA rigid structure as well as excluded volume interactions between particles. From extensive Monte Carlo simulations we obtained aggregates with fractal dimension slightly higher than that obtained for two-dimensional DLA structures. This is somehow surprising since the fractal dimension of the annealed structure is determined not only by connectivity but also by the competing effects of excluded volume interactions and configurational entropy, whilst in the rigid DLA only diffusion counts for the fractal-dimension value.     

分形凝聚粒子的光散射特性研究

粒子的形状和凝聚对光散射特性有着很大的影响.基于分形生长的受限扩散(DLA)模型,模拟了凝聚粒子的三维空间分形结构,并采用回转半径法计算了凝聚粒子的分形维数.利用离散偶极子近似(DDA)方法研究了纳米石墨凝聚粒子的光散射特性,对于原始粒子数不同的凝聚粒子及分形结构不同的凝聚粒子,数值计算了散射强度和偏振度随散射角的分布...     

Fractal Aggregation Under Rotation

By means of the Monte Carlo simulation, a fractal growth model is introduced to describe diffusion-limited aggregation (DLA) under rotation. Patterns which are different from the classical DLA model are observed and the fractal dimension of such clusters is calculated. It is found that the pattern of the clusters and their fractal dimension depend strongly on the rotation velocity of the diffusing particle. Our results indicate the transition from fractal to non-fractal behavior of growing cluster with increasing rotation velocity, i.e. for small enough angular velocity ω; thefractal dimension decreases with increasing ω;, but then, with increasing rotation velocity, the fractal dimension increases and the cluster becomes compact and tends to non-fractal.     

Adsorption thermodynamics of interacting particles on diffusion-limited aggregates

Grand canonical Monte Carlo simulations have been performed in order to study adsorption thermodynamics of pairwise interacting particles on fractal surfaces. Diffusion-limited aggregates (DLA) have been used as a substrate where interacting particles are adsorbed. In order to obtain aggregates with different morphologies, DLA clusters are generated on different strongly correlated surfaces. Adsorption isotherm, adsorption energy and differential heat of adsorption were calculated for attractive and repulsive nearest-neighbor (NN) lateral interactions. For the case of repulsive couplings and low temperatures, four novel ordered phases has been found in the adsorbate, each one corresponding to the formation of a chessboard-like structure on sites with one, two, three and four NN sites, respectively. The values of coverage at which these ordered phases emerge are not symmetrical around θ=0.5. This is a consequence of the non-equivalence between vacancy and particle in the case of adsorption on fractal structures. The influence of ordered structures on thermodynamic quantities associated to the adsorbed monolayer has been analyzed and discussed in the context of the Lattice-Gas model.     

DLA模型的最可几方法研究

用最可几方法对DLA模型进行了研究，求出了DLA集团粒子的最可几分布、分维数和屏蔽指数，所得结果与计算机模拟结果相符合 关键词：     

Particle Growth in an Experimental Dusty Plasma System

The coagulation and growth process of dust particles is investigated through laboratory experiment in a plasma system. A large number of dust particles with different sizes and shapes are formed. The growth process is characterized by the scattering laser intensity and fractal dimension. The comparisons of dust particles and scattering laser intensity obtained at different rf powers are presented. The three-dimensional distribution of dust particles is also given. These results provide an experimental basis for dust growth investigation.     

Scaling in the diffusion limited aggregation model

We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/R{dep}(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/R{dep}) function on an ensemble with 1000 clusters of 5×10{7} particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10?000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.     

Effects of the screening breakdown in the diffusion-limited aggregation model

Several models based on the diffusion-limited aggregation (DLA) model were proposed and their scaling properties explored by computational and theoretical approaches. In this paper, we consider a new extension of the on-lattice DLA model in which the unitary random steps are replaced by random flights of fixed length. This procedure reduces the screening for particle penetration present in the original DLA model and, consequently, generates new pattern classes. The patterns have DLA-like scaling properties at small length of the random flights. However, as the flight size increases, the patterns are initially round and compact but become fractal for sufficiently large clusters. Their radius of gyration and number of particles at the cluster surface scale asymptotically as in the original DLA model. The transition between compact and fractal patterns is characterized by wavelength selection, and 1/k noise was observed far from the transition.Received: 2 March 2004, Published online: 14 December 2004PACS: 05.40.Fb Random walks and Levy flights - 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 05.10.Ln Monte Carlo methods     

Dipole clusters with nontrivial scale-invariant properties

In this paper the scale-invariant properties of the plane (2D) with the growth centre located on the charged particle have been considered. The dependence “number of particles with respect to radius of cluster” is presented by two power-law exponents that differs them from one power-law dependence characterizing the DLA (diffusion limited aggregation) clusters. In our case the interpretation the power-law exponents found in terms of the fractal dimension becomes unacceptable. The model considered it is supposed to be applied for consideration of similar clusters in polar liquids.     

基于超二次曲面的颗粒材料缓冲性能离散元分析

自然界或工业中普遍是由非球形颗粒组成的复杂体系,与球形颗粒相比,非球形颗粒间的高离散和咬合互锁可使冲击载荷引起的能量有效衰减实现缓冲作用.基于连续函数包络的超二次曲面单元能准确地描述非球形颗粒的几何形态,并可精确地计算单元间的接触碰撞作用.本文采用离散元方法对冲击载荷作用下非球形颗粒物质的缓冲性能进行数值分析,并与圆柱体冲击的理论结果和球体冲击的实验结果进行对比验证.在此基础之上,进一步研究了筒底作用力在不同颗粒层厚度和形状等因素影响下的变化规律.计算结果表明:不同颗粒形状都存在一个临界厚度H_c.当HH_c时,缓冲率随H的增加而增加;当HH_c时,缓冲率的变化不再显著并趋于稳定值.此外,减小颗粒表面尖锐度和增加或减小圆柱形和长方形颗粒的长宽比都会提高颗粒材料的缓冲效果.     

Inertial focusing and rotating characteristics of elliptical and rectangular particle pairs in channel flow

The lattice Boltzmann method is used to study the inertial focusing and rotating characteristics of two-dimensional elliptical particles and rectangular particles in channel flow. The results show that both elliptical particles and rectangular particles initially located on one side and two sides of channel centerline migrate first towards the equilibrium position. Then, the single-line particle train with an increasing spacing and the staggered particle train with stable spacing are formed. The axial spacing of the staggered particle pair increases with aspect ratio and Reynolds number increasing. The staggered elliptical or rectangular particle pairs form perpendicular orientation angles, which will be more obvious at larger aspect ratio and lower Reynolds number. The single-line particle trains with different shapes seldom form the perpendicular orientation angle.     

平行吸引力场中的凝聚生长

利用DLA模型,研究平行力场对凝聚物生长的影响.结果表明:力场使凝聚物的生长失去对称性,粒子凝聚密度增加,且引力场越强,密度值越大;同时凝聚生长出现不可再生长区域,凝聚物生长迅速由生长区过渡到饱和区.     

Dissolution arrest and stability of particle-covered bubbles

Experiments show that bubbles covered with monodisperse polystyrene particles, with particle to bubble radius ratios of about 0.1, evolve to form faceted polyhedral shapes that are stable to dissolution in air-saturated water. We perform Surface Evolver simulations and find that the faceted particle-covered bubble represents a local minimum of energy. At the faceted state, the Laplace overpressure vanishes, which together with the positive slope of the bubble pressure-volume curve, ensures phase stability. The repulsive interactions between the particles cause a reduction of the curvature of the gas-liquid interface, which is the mechanism that arrests dissolution and stabilizes the bubbles.     

The Fractal Characteristic of Particles in Granular Material Flows and Its Effect on Effective Thermal Conductivity

According to the fact that many pulverized particles possess fractal characteristic, a fractal model for studying fine particles in granular material flows is first proposed. An expression of particles' fractal distribution is derived to describe the relationship between the particle fractal dimensions and particle velocity distribution function. In accordance with this model, the theoretical particle effective thermal conductivity is derived. The analytical results show that for the small Biot-Fourier number, the effective thermal conductivity increases with the square root of the granular temperature. For very large Biot-Fourier number, the effective thermal conductivity linearly increases with the granular temperature. Numerically calculated results show that the thermal conductivity increases with the particle size fractal dimensions and decreases with the particle surface fractal dimensions.     

Fractal structure of films deposited in a tokamak

The surface of amorphous films deposited in the T-10 tokamak was studied in a scanning tunnel microscope. The surface relief on a scale from 10 nm to 100 μm showed a stochastic surface topography and revealed a hierarchy of grains. The observed variety of irregular structures of the films was studied within the framework of the concept of scale invariance using the methods of fractal geometry and statistical physics. The experimental probability density distribution functions of the surface height variations are close in shape to the Cauchy distribution. The stochastic surface topography of the films is characterized by a Hurst parameter of H = 0.68–0.85, which is evidence of a nontrivial self-similarity of the film structure. The fractal character and porous structure of deposited irregular films must be considered as an important issue related to the accumulation of tritium in the ITER project. The process of film growth on the surface of tokamak components exposed to plasma has been treated within the framework of the general concept of inhomogeneous surface growth. A strong turbulence of the edge plasma in tokamaks can give rise to fluctuations in the incident flux of particles, which leads to the growth of fractal films with grain dimensions ranging from nano-to micrometer scale. The shape of the surface of some films found in the T-10 tokamak has been interpreted using a model of diffusion-limited aggregation (DLA). The growth of films according to the discrete DLA model was simulated using statistics of fluctuations observed in a turbulent edge plasma of the T-10 tokamak. The modified DLA model reproduces well the main features of the surface of some films deposited in tokamaks.     

Diffusion of oriented particles in porous media

Diffusion of particles in porous media often shows subdiffusive behavior. Here, we analyze the dynamics of particles exhibiting an orientation. The features we focus on are geometrical restrictions and the dynamical consequences of the interactions between the local surrounding structure and the particle orientation. This interaction can lead to particles getting temporarily stuck in parts of the structure. Modeling this interaction by a particular random walk dynamics on fractal structures we find that the random walk dimension is not affected while the diffusion constant shows a variety of interesting and surprising features.