Measurement of Aggregate Fractal Dimensions Using Static Light Scattering

Aggregates formed from colloidal particles will vary in shape according to the aggregation regime prevalent. Compact structures are formed when the aggregation is slow, whilst loose tenuous structures are formed when rapid (or diffusion limited) aggregation prevails. These structures can be fractal in nature, that is, there is a relationship between porosity and the number of primary particles making up the aggregate, and is described by the fractal dimension, d_F. Fractal dimensions of hematite aggregates have been measured experimentally using the static light scattering technique. Fractal dimensions varied with aggregation regimes; for the rapid aggregation regime, d_F was found to be 2.8, whilst for conditions in which aggregation was slow (retardation forces prevail), d_F's of 2.3 were measured. For conditions which lead to aggregation in which both diffusion and retardation forces play a part, structures with fractal dimensions such that 2.3 < d_F < 2.8 were found. The effects of adsorbed fulvic acid, a naturally occuring organic acid, on the kinetics of hematite aggregation and on the resulting structure of hematite aggregates were also investigated. The study of aggregate structure shows that the fractal dimensions of hematite aggregates which are partially coated with fulvic acid molecules are higher than those obtained with no adsorbed fulvic acid. The scattering exponents obtained from static light scattering experiments of these aggregates range from 2.83 ± 0.08 to 3.42 ± 0.1. The scattering exponents of greater than 3 indicate that the scattering is the result of objects that contains pores which are bounded by surfaces with a fractal structure, and can be related only to surface fractal dimension. The high fractal dimensions are due to restructuring within the aggregates, which only occured at low coverage by the organic acid.     

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.     

Cluster-cluster aggregation in binary mixtures

The structure and aggregation kinetics of three-dimensional clusters composed of two different monomeric species at three concentrations are thoroughly investigated by means of extensive, large-scale computer simulations. The aggregating monomers have all the same size and occupy the cells of a cubic lattice. Two bonding schemes are considered: (a) the binary diffusion-limited cluster-cluster aggregation (BDLCA) in which only the monomers of different species stick together, and (b) the invading binary diffusion-limited cluster-cluster aggregation (IBDLCA) in which additionally monomers of one of the two species are allowed to bond. In the two schemes, the mixed aggregates display self-similarity with a fractal dimension d(f) that depends on the relative molar fraction of the two species and on concentration. At a given concentration, when this molar fraction is small, d(f) approaches a value close to the reaction-limited cluster-cluster aggregation of one-component systems, and when the molar fraction is 0.5, d(f) becomes close to the value of the diffusion-limited cluster-cluster aggregation model. The crossover between these two regimes is due to a time-decreasing reaction probability between colliding particles, particularly at small molar fractions. Several dynamical quantities are studied as a function of time. The number of clusters and the weight-average cluster size display a power-law behavior only at small concentrations. The dynamical exponents are obtained for molar fractions above 0.3 but not at or below 0.2, indicating the presence of a critical transition between a gelling to a nongelling system. The cluster-size distribution function presents scaling for molar fractions larger than 0.2.     

Colored diffusion-limited aggregation for urban migration

In this paper we study the growth probability and cluster morphologies which emerge in an off-lattice, two-dimensional, colored diffusion-limited aggregation model for urban dynamics, particularly migration. To reach this goal, three immobile interacting clusters that include the geographical concept of gravity are studied by exact enumeration. In our simulations we find a strong correlation between the seed’s distance, migration rules and number of aggregated particles. The growth probability of a certain angular subset and its rate and route of convergence to a Normal distribution when migration cost is acting are also shown. We search how all the factors mentioned above determine the cluster morphologies.     

Levels of complexity in turbulent time series for weakly and high Reynolds number

We use the detrended fluctuation analysis (DFA), the detrended cross correlation analysis (DCCA) and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long-term nonlinear levels of complexity in weakly and high turbulent flow. The DFA analysis indicate that there is a time scaling region in the fluctuation function, segregating regimes with different scaling exponents. We discuss that this time scaling region is related to inertial range in turbulent flows. The DCCA exponent implies the presence of power-law cross correlations. In addition, we conclude its multifractality for high Reynold’s number in inertial range. Further, we find that turbulent time series exhibit complex features by magnitude and sign scaling exponents.     

Kinetics of an n-Species Aggregation Chain Model with Complete Annihilation

The kinetic behavior of an n-species (n ≥ 3) aggregation-annihilation chain reaction model is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible complete annihilation reaction occurs only between two species with adjacent number. Based on the rnean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions of the clustermass distributions for the system. The results show that the kinetic behavior of the system not only depends crucially on the ratio of the aggregation rate I to the annihilation rate J, but also has relation with the initial concentration of each species and the species number's odevity. We find that the cluster-mass distribution of each species obeys always a scaling law. The scaling exponents may strongly depend on the reaction rates for most cases, however, for the case in which the ratio of the aggregation rate to the annihilation rate is equal to a certain value, the scaling exponents are only dependent on the initial concentrations of the reactants.     

Clustering by mixing flows

We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in epsilon, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Padé-Borel summation. Our results prove that particles suspended in an incompressible random mixing flow can show pronounced clustering when the Stokes number is large and we characterize two distinct clustering effects which occur in that limit.     

Enhancement Factor in the Light Backscattered by Fractal Aggregated Media

We investigate the phenomenon of the enhanced backscattering of light from soft sediments of fractal clusters. The clusters consist of spherical PMMA particles with the diameter of 0.4 μ, aggregated in aqueous solutions of NaCl. We found that the kinetics of aggregation, which determines the average cluster size in sediments, is controlled by the salt concentration and that the sediments are mutually self-similar media. In comparison to uniform random media, specific features for the enhancement peaks are revealed. It is found that the peak line-shape reflects the particularities of the density of scatterers in a fractal-like medium. It is shown experimentally that the enhancement factor in the light backscattered by fractal aggregated media is sensitive to the average cluster size. On this basis, we suggest a possible way to distinguish between mutually self-similar media.     

面向自组装结构精确控制的聚集结构定量计算及表征方法

在自组装结构形成过程中,热涨落会导致出现多种无定形结构及转化路径. 这些无定型结构对应着不同的粒子聚集程度,但是目前缺乏描述它们的定量方法. 为了实现对自组装结构的精确控制,其中重要的一步是定量描述和分析在自组装结构形成过程中出现的不同聚集结构. 本文提出了一种直接计算以及定量对比不同聚集结构的方法,进一步给出了几个案例研究用来评估聚集结构如何受外界控制因素(如相互作用范围、强度、以及吸引作用的各向异性)的影响.     

排名聚合算法在少量长列表聚合中的性能比较分析

排名聚合将多个排名列表聚合成一个综合排名列表,可应用于推荐系统、链路预测、元搜索、提案评选等.当前已有工作从不同角度对不同排名聚合算法进行了综述、比较,但存在算法种类较少、数据统计特性不清晰、评价指标不够合理等局限性.不同排名聚合算法在提出时均声称优于已有算法,但是用于比较的方法不同,测试的数据不同,应用的场景不同,因此何种算法最能适应某一任务在很多情况下仍不甚清楚.本文基于Mallows模型,提出一套生成统计特性可控的不同类型的排名列表的算法,使用一个可应用于不同类型排名列表的通用评价指标,介绍9种排名聚合算法以及它们在聚合少量长列表时的表现.结果发现启发式方法虽然简单,但是在排名列表相似度较高、列表相对简单的情况下,能够接近甚至超过一些优化类方法的结果;列表中平局数量的增长会降低聚合排名的一致性并增加波动;列表数量的增加对聚合效果的影响呈现非单调性.整体而言,基于距离优化的分支定界方法 (FAST)优于其他各类算法,在不同类型的排名列表中表现非常稳定,能够很好地完成少量长列表的排名聚合.     

A Diffusion Model of Field-Induced Aggregation in Ferrofluid Film

By introducing Arrhenius behaviour to the ferroparticles on the surface of the aggregated columnar structure in a diffusion model, equilibrium equations are set up. The solution of the equations shows that to keep the aggregated structures stable, a characteristic field is needed. The aggregation is enhanced by magnetic fields, yet suppressed as the temperature increases. Analysing the influence of the magnetic field on the interaction energy between the dipolar particles, we estimate the portion of the diffusing particles, and provide the agreeable ratio of the column radius over the centre-to-centre spacing between columns in a hexagonal columnar structure formed under a perpendicular magnetic field.     

Monte Carlo simulation and theory of proton NMR transverse relaxation induced by aggregation of magnetic particles used as MRI contrast agents

Superparamagnetic particles are widely used in MRI as R2 contrast agents. In this last decade, different studies have focused on aggregation of superparamagnetic particles for important applications such as multimodal agents. A complete study--via simulations--of the influence of aggregation on the MR efficiency of these particles at high magnetic field is presented here. First, an empirical expression is proposed for R2 in the presence of uniformly distributed nanoparticles, taking into account two regimes at once (motional averaging and slow motion regimes). Three cluster shapes are simulated: Sphere, shell and line. An analytical model is proposed to understand water transverse relaxation induced by spherical and shell aggregates. Simulations lead to the conclusion that, in the motional averaging regime, the most efficient aggregate contrast agent is the densest sphere or shell.     

Nanoparticle formation during laser ablation of metals at different pressures of surrounding noble gases

We demonstrate that the nanoparticle formation during laser ablation of metals by short (of a few tens of ps) laser pulses strongly depends on the concentration of surrounding gas. While, at vacuum conditions, nanoparticle formation shows very “sharp” atomic force microscope images of aggregated clusters, following with clear appearance of plasmon resonance on the absorption spectra of deposited films, an addition of gas particles starts to decrease the probability of cluster formation. This process shows a threshold for both helium (33 torr) and xenon (12 torr) above which no surface plasmon resonance and correspondingly no observable nanoparticles on the deposited surfaces were detected. The destruction of nanoparticle formation was attributed to the negative influence of surrounding gas particles on ablated particles aggregation.     

Model for folding and aggregation in RNA secondary structures

We study the statistical mechanics of RNA secondary structures designed to have an attraction between two different types of structures as a model system for heteropolymer aggregation. The competition between the branching entropy of the secondary structure and the energy gained by pairing drives the RNA to undergo a "temperature independent" second order phase transition from a molten to an aggregated phase. The aggregated phase thus obtained has a macroscopically large number of contacts between different RNAs. The partition function scaling exponent for this phase is theta approximately 1/2 and the crossover exponent of the phase transition is nu approximately 5/3. The relevance of these calculations to the aggregation of biological molecules is discussed.     

Power spectra of the total occupancy in the totally asymmetric simple exclusion process

As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of nonequilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a 1-dimensional open lattice and its power spectrum. Using both Monte Carlo simulations and analytic methods, we explore its behavior in different characteristic regimes. In the maximal current phase and on the coexistence line (between high and low density phases), the power spectrum displays algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the high and low density phases, we find pronounced oscillations, which damp into power laws. This behavior can be understood in terms of driven biased diffusion with conserved noise in the bulk.     

Statistical models of diffusion and aggregation for coke formation in a catalyst pore

We simulated models of diffusion and aggregation in long pores of small widths in order to represent the basic mechanisms of coke deposition in catalysts’ pores. Coke precursors are represented by particles injected at the pore entrance. Knudsen diffusion, which is usually expected inside the pores, is modeled by ballistic motion of those particles. The regime of molecular diffusion is also analyzed via models of lattice random walks biased along the pores. The aggregation at the surface or near previously aggregated particles was modeled by different probabilistic rules, accounting for the possibilities of more compact or more ramified deposits. In the model of Knudsen diffusion and in some cases of molecular diffusion, there is an initial regime of uniform deposition along the pore, after which the deposits acquire an approximately wedge shape, with the pore plugging near its entrance. After the regime of uniform deposition and before that of critical pore plugging, the average aggregation position slowly decreases with the number N of deposited particles approximately as N^-0.25. The apparently universal features of deposits generated by microscopic models are compared with those currently adopted in continuum models.     

Structure of a collisionless shock front with relativistically accelerated particles

A nonlinear self-consistent analytic theory is developed to describe the front structure of a strong magnetohydrodynamic (MHD) collisionless shock wave that generates accelerated particles (including ultrarelativistic particles). The theory is used to predict the degree of compression of matter at the plane front of such a wave, which can greatly exceed compression at an ordinary gas-dynamic front, and also the velocity, density, and pressure profiles. The energy spectrum of the accelerated particles, which is produced by the complex velocity profile at the shock transition, is determined self-consistently. New nonlinear effects are predicted that have not been discussed previously in the literature: a strong dependence of the particle acceleration regimes on the rate of injection; the existence of several regimes within a certain range of injected powers with differing spectra of accelerated particles, shapes of the shock transition profile, and magnitudes of compression of the medium; and the possibility of spontaneous jumps between different states of the shock transition. The question of stability of these states is discussed. For the values of the system parameters used here, the nonlinear regimes correspond to extremely low injection rates, of order 10⁻²–10⁻¹⁰ of the plasma flux density advancing into the front, and to exponents of the power-law spectra of accelerated particles between 5 and 3. Zh. éksp. Teor. Fiz. 112, 1584–1602 (November 1997)     

On finite-size Lyapunov exponents in multiscale systems

We study the effect of regime switches on finite size Lyapunov exponents (FSLEs) in determining the error growth rates and predictability of multiscale systems. We consider a dynamical system involving slow and fast regimes and switches between them. The surprising result is that due to the presence of regimes, the error growth rate can be a non-monotonic function of initial error amplitude. In particular, troughs in the large scales of FSLE spectra are shown to be a signature of slow regimes, whereas fast regimes are shown to cause large peaks in the spectra where error growth rates far exceed those estimated from the maximal Lyapunov exponent. We present analytical results explaining these signatures and corroborate them with numerical simulations. We show further that these peaks disappear in stochastic parametrizations of the fast chaotic processes, and the associated FSLE spectra reveal that large scale predictability properties of the full deterministic model are well approximated, whereas small scale features are not properly resolved.     

The effect of particle aggregation on the absorption and emission properties of mono- and polydisperse soot aggregates

This study concerns the effect of soot-particle aggregation on the soot temperature derived from the signal ratio in two-color laser-induced incandescence measurements. The emissivity of aggregated fractal soot particles was calculated using both the commonly used Rayleigh–Debye–Gans fractal-aggregate theory and the generalized Mie-solution method in conjunction with numerically generated fractal aggregates of specified fractal parameters typical of flame-generated soot. The effect of aggregation on soot temperature was first evaluated for monodisperse aggregates of different sizes and for a lognormally distributed aggregate ensemble at given signal ratios between the two wavelengths. Numerical calculations were also conducted to account for the effect of aggregation on both laser heating and thermal emission at the two wavelengths for determining the effective soot temperature of polydisperse soot aggregates. The results show that the effect of aggregation on laser energy absorption is important at low fluences. The effect of aggregation on soot emissivity is relatively unimportant in LII applications to typical laminar diffusion flames at atmospheric pressure, but it can become more important in flames at high pressures due to larger primary particles and wider aggregate distributions associated with enhanced soot loading.     

Lyapunov exponents and kolmogorov-sinai entropy for a high-dimensional convex billiard

We compute the Lyapunov exponents and the Kolmogorov-Sinai (KS) entropy for a self-bound N-body system that is realized as a convex billiard. This system exhibits truly high-dimensional chaos, and 2N-4 Lyapunov exponents are found to be positive. The KS entropy increases linearly with the numbers of particles. We examine the chaos generating defocusing mechanism and investigate how high-dimensional chaos develops in this system with no dispersing elements.