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.     

不同能区核-核碰撞实验中高多重数,大起伏的事件性质的分析-与物理模型无关的统计分析

报道了用不依赖于任何物理模型的纯数理统计的方法对EMU01实验组200A GeV的³²S与固定的Au靶碰撞中较高多重数和较大起伏事例的数据和STAR实验组在核-核质量中心能量为\sqrt{s_{_{\rm NN}}}=200GeV的Au+Au碰撞中较高多重数和较大起伏事例的数据所做的分析. 对3个相差很远的能区——固定靶加速器能区, 核-核对撞机能区以及宇宙线能区所得的分析结果进行了比较, 并对所得的结果进行了讨论.     

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.     

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.     

Molecular dynamics simulations of aggregation of copper nanoparticles with different heating rates

Molecular dynamics simulations were employed to investigate the heating rates’ effect on aggregation of two copper nanoparticles. The aggregation can be distinguished into three distinct regimes by the contacting and melting of nanoparticles. The nanoparticles contacting at a lower temperature during the sintering with lower heating rate, meanwhile, some temporary stacking fault exists at the contacting neck. The aggregation properties of the system, i.e. neck diameter, shrinkage ratio, potential energy, mean square displacement (MSD) and relative gyration radius, experience drastic changes due to the free surface annihilation. After the nanoparticles coalesced for a stable period, the shrinkage ratio, MSD, relative gyration radius and neck diameter of the system are dramatically changed during the melting process. It is shown that the shrinkage ratio and MSD have relative larger increasing ratio for a lower heating rate. While the evolution of the relative gyration radius and neck diameter is only sensitive to the temperature.     

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.     

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.     

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.     

Simple off-lattice model to study the folding and aggregation of peptides

We present a numerical study of a new protein model. This off-lattice model takes into account both the hydrogen bonds and the amino-acid interactions. It reproduces the folding of a small protein (peptide): morphological analysis of the conformations at low temperature shows two well-known substructures α-helix and β-sheet depending on the chosen sequence. The folding pathway in the scope of this model is studied through a free-energy analysis. We then study the aggregation of proteins. Proteins in the aggregate are mainly bound via hydrogen bonds. Performing a free-energy analysis we show that the addition of a peptide to such an aggregate is not favourable. We qualitatively reproduce the abnormal aggregation of proteins in prion diseases.     

具有幂率度分布的因特网平均最短路径长度估计

针对具有幂律度分布的复杂网络的平均最短路径长度进行了研究.给出了一个计算因特网平 均最短路径长度的公式.提出因特网的整体构造实质是以最小代价换取最大收益，从此出 发通过对因特网这类复杂网络平均最短路径长度影响因素分析，推断出网络最短路径长度分 布P(l)的基本性质，进而构造了一个只含参数α的P(l)的简洁形式，直接打通了拓扑具有幂 律度分布的因特网的度分布P(k)与网络最短路径长度分布P(l)之间的关系.然后说明了导出 的公式的物理意义，即参数α代表网络节点连接方式和网络的总边数对平均最短路径长 度的影响.此公式意味着只要掌握幂律P(k)～k-α中α值，就可以直接计算相应网 络的平均最短路径长度.通过对已知数据的计算，验证了公式的有效性.阐明了参数 α对网络设计的重要性和对网络功能的影响. 关键词： 复杂网络 幂律 度分布 平均最短路径长度     

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.     

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.