Migration-driven aggregation behaviors in job markets with direct foreign immigration

This Letter introduces a new set of rate equations describing migration-driven aggregation behaviors in job markets with direct foreign immigration. We divide the job market into two groups: native and immigrant. A reversible migration of jobs exists in both groups. The interaction between two groups creates a birth and death rate for the native job market. We find out that regardless of initial conditions or the rates, the total number of cities with either job markets decreases. This indicates a more concentrated job markets for both groups in the future. On the other hand, jobs available for immigrants increase over time but the ones for natives are uncertain. The native job markets can either expand or shrink or remain constant due to combined effects of birth and death rates. Finally, we test our analytical results with the population data of all counties in the US from 2000 to 2011.     

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.     

Statistical mechanics of red blood cell aggregation: The distribution of rouleaux in thermal equilibrium

When placed in suspension red blood cells adhere face-to-face and form long, cylindrical, and sometimes branched structures called rouleaux. We use methods developed in statistical mechanics to compute various statistical properties describing the size and shape of rouleaux in thermodynamic equilibrium. This leads to analytical expressions for (1) the average number of rouleaux consisting ofn cells and havingm branch points; (2) the average number of cells per rouleau; (3) the average number of branch points per rouleau; and (4) the number of rouleaux withn cells in a system containing a total ofN cells. We also derive asymptotic formulas that simplify these analytic expressions, and present numerical comparisons of the exact and asymptotic results.     

Effect of solvent-controlled aggregation on the intrinsic emission properties of PAMAM dendrimers

Solvent-induced aggregation and its effect on the intrinsic emission properties of amine, hydroxy and carboxylate terminated, poly(amidoamine) (PAMAM) dendrimers have been investigated in glycerol, ethylene glycol, methanol, ethylene diamine and water. Altering the solvent medium induces remarkable changes in the intrinsic emission properties of the PAMAM dendrimers at identical concentration. Upon excitation at 370 nm, amine terminated PAMAM dendrimer exhibits an intense emission at 470 nm in glycerol, ethylene glycol as well as glycerol-water mixtures. Conversely, weak luminescence is observed for hydroxy and carboxylate terminated PAMAM dendrimers in the same solvent systems. When the solvent is changed to ethylene diamine, hydroxy terminated PAMAM exhibits intense blue emission at 425 nm. While the emission intensity is varied when the solvent milieu is changed, excited state lifetime values of PAMAM dendrimers remain independent of the solvent used. UV-visible absorption and dynamic light scattering (DLS) experiments confirm the formation of solvent-controlled dendrimer aggregates in the systems. Comparison of the fluorescence and DLS data reveals that the size distribution of the dendrimer aggregates in each solvent system is distinct, which control the intrinsic emission intensity from PAMAM dendrimers. The experimental results suggest that intrinsic emission intensity from PAMAM dendrimers can be regulated by proper selection of solvents at neutral conditions and room temperature.     

A joint volume-surface model of soot aggregation with the method of moments

In this work, a bivariate model of soot aggregation is formulated within the framework of the Method of Moments with Interpolative Closure (MOMIC). In the bivariate model, soot particles are represented by two independent variables: their volume and surface area. This joint formulation also allows for the blending of aggregation and coalescence with the two as limits. The new formulation is compared to the old formulation with the univariate model as well as both the Direct Quadrature Method of Moments (DQMOM) and Direct Simulation Monte Carlo (DSMC) for a laminar premixed ethylene flame. With the bivariate model, MOMIC is shown to predict volume fraction and number density very accurately and gives some insight into the properties of the aggregates.     

Statistical properties of one-dimensional binary sequences with power-law power spectrum

By the Fourier filtering method, we generate one-dimensional binary sequences from coarse-grained continuous sequences with preset exponents α₀. Using the spectrum analysis, we find that the corresponding binary sequences have pure 1/f^α power spectrum and spectrum exponents α∈[0.0,2.0], where f is the frequency. We evaluate numerically the relation between α and α₀. Using the autocorrelation function analysis, the detrended fluctuation analysis, the duration time analysis and the entropy analysis, we investigate extensively the statistical properties of such binary sequences. We find that the statistical properties are basically different for α<1 and α>1, and binary sequences become more and more ordered as α increases.     

On the equivalence of the parallel channel and the correlated cluster relaxation models

The question of the origins of nonexponential relaxation is addressed in terms of the probabilistic approach to relaxation. The interconnection between two differently rooted probabilistic models, i.e., between the parallel channel and the correlated cluster models, is presented. We show that clearly different probabilistic origins yield in both approaches a well-defined class of universally valid two-power-law responses with the stretched-exponential and exponential decay laws as special cases. The equivalence of both models indicates that variations in the local environment of the relaxing configurational units (parallel channel relaxation) can provide a basis for self-similar relaxation dynamics without the need for hierarchically constrained dynamics (correlated clusters relaxation).     

Constant flux relation for aggregation models with desorption and fragmentation

We study mass fluxes in aggregation models where mass transfer to large scales by aggregation occurs alongside desorption or fragmentation. Two models are considered: (1) a system of diffusing, aggregating particles with influx and outflux of particles (in-out model); and (2) a system of diffusing aggregating particles with fragmentation (chipping model). Both these models can exist in phases where probability distributions are power laws. In these power law phases, we argue that the two point correlation function should have a certain homogeneity exponent. These arguments are based on the exact constant flux scaling valid for simple aggregation with input. Predictions are compared with Monte Carlo simulations.     

Statistical dynamics of early river networks

Based on local erosion rule and fluctuations in rainfall, geology and parameters of a river channel, a generalized Langevin equation is proposed to describe the random prolongation of a river channel. This equation is transformed into the Fokker–Plank equation to follow the early evolution of a river network and the variation of probability distribution of channel lengths. The general solution of the equation is in the product form of two terms. One term is in power form and the other is in exponent form. This distribution shows a complete history of a river network evolving from its infancy to “adulthood”). The infancy is characterized by the Gaussian distribution of the channel lengths, while the adulthood is marked by a power law distribution of the channel lengths. The variation of the distribution from the Gaussian to the power law displays a gradual developing progress of the river network. The distribution of basin areas is obtained by means of Hack’s law. These provide us with new understandings towards river networks.     

Anomalous aggregation of squaraine dyes in confined solutions

Enhanced aggregation of squaraine (SQ) dyes in solution capillary layers in contrast to the monomer behavior of the bulk solutions has been observed through differences in electronic absorption spectra of the capillary and bulk SQ solutions of the same concentration. The spectra of the capillary solutions were also different from spectra of SQ condensed films. The spectral differences were dependent on both chemical structure of the dye used and the solvent. It was found that aggregation was stronger in dimethylformamide (DMFA) capillary solutions when compared to the chloroform capillary solutions where aggregation was negligible. It is proposed that the driven force of the observed phenomena is enhanced adsorption of SQ molecules and formation of a liquid crystalline state of the solution near the liquid/solid interface.     

Statistical properties of the yuan exchange rate index

We choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after China’s exchange rate system reform on the 21st July 2005. After dividing the time series into two parts according to the change in the yuan exchange rate regime in July 2008, we compare the statistical properties of the yuan exchange rate index during these two periods. We find that the distribution of the two return series has the exponential form. We also perform the detrending moving average analysis (DMA) and the multifractal detrending moving average analysis (MFDMA). The two periods possess different degrees of long-range correlations, and the multifractal nature is also unveiled in these two time series. Significant difference is found in the scaling exponents τ(q)$\tau \left(q\right)$ and singularity spectra f(α)$f\left(\alpha \right)$ of the two periods obtained from the MFDMA analysis. Besides, in order to detect the sources of multifractality, shuffling and phase randomization procedures are applied to destroy the long-range temporal correlation and fat-tailed distribution of the yuan exchange rate index respectively. We find that the fat-tailedness plays a critical role in the sources of multifractality in the first period, while the long memory is the major cause in the second period. The results suggest that the change in China’s exchange rate regime in July 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods, and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st July 2005.     

简并参量下转换光场的统计性质

通过经(?)泵浦场的简并参量下转换过程的薛定谔方程的解,讨论了简并参量下转换光场的统计性质.     

Maximum-Entropy and Stability in Statistics and Thermodynamics

The object of the present paper is first to study the role of maximum-entropy principle based on Shannon's entropy in generating stable distribution in statistics and characterizing stable thermal equilibrium state in thermodynamics. The second is to show the nonuniqueness of Shannon's entropy in the study of the stable distribution in statistics and stable equilibrium state in thermodynamics.     

Statistical analysis of aggregation in freeway traffic

We restudy the master-equation approach to aggregation in freeway traffic based on the theory of birth--death process, in which the clustering behaviour in one-lane freeway traffic model is investigated. The transition probabilities for the jump processes are reconstructed by using Greenshields' model, and the equation of the mean size of the cluster at any time t is derived from the birth--death equation. Numerical experiments show the clustering behaviours varying with time very well.     

基于选择模式的幂律生成机制

自然界与社会生活中存在多种性质迥异的幂律分布现象,因而对它们的研究具有广泛而深远的意义．研究了一类由于人类的选择行为而产生的幂律现象,提出了人类选择行为的两个特性：理性与自利．据此,通过小球选择试验构建了模型．研究发现,这类幂律现象中随机变量服从一种近似于Zipf分布的分布．此分布为首次提出的一种新分布,将它命名为偏序分布．网络中已有的统计数据表明,偏序分布比Zipf分布更真实的反应了网络中统计变量服从的分布．文中对偏序分布进行了理论分析,并通过约束条件的改变,生成了Yule分布;表述了Yule分布的物理意义,并构造了比Yule分布更具现实意义的分布．说明了选择理论在解释幂律现象方面的普遍适用性及模型的可扩展性．文中在幂律现象的成因上支持还原论,即简单的人类选择行为导致了普遍的幂律现象．关键词：选择行为幂律分布偏序分布Yule分布     

A microscopic aggregation model of droplet dynamics in warm clouds

A microscopic model of warm clouds involving input of water droplets, dropletdroplet aggregation, droplet breakup, and precipitation is presented. Numerical simulations and analytical arguments indicate that after the stage of growth and just before precipitation sets in, a warm cloud is characterized by a droplet-size distribution which follows from an inverse power law as a function of the droplet size. When precipitation is taken into account, the above distribution is transformed into a distribution decaying exponentially with the droplet size, in agreement with field observations. It is suggested that the initiation of rainfall in a precipitating warm cloud can be viewed as an instability triggered by the presence of a power-law distribution.     

Statistical properties of dynamical systems with singularities

We prove statistical properties of two-dimensional hyperbolic dynamical systems with singularities. Bunimovich, Sinai, and Chernov proved a theorem on the subexponential decay of correlations and a central limit theorem for billiard systems. In this paper we use their techniques to prove the same results for abstract systems.     

用三个分布律整合气体动理论的教学

用麦克斯韦速度分布律、玻耳兹曼分布律、自由程分布律整合了气体动理论的教学．