Nuclear multifragmentation, percolation, and the fisher droplet model: common features of reducibility and thermal scaling

It is shown that the Fisher droplet model, percolation, and nuclear multifragmentation share the common features of reducibility (stochasticity in multiplicity distributions) and thermal scaling (one-fragment production probabilities are Boltzmann factors). Barriers obtained, for cluster production on percolation lattices, from the Boltzmann factors show a power-law dependence on cluster size with an exponent of 0.42+/-0.02. The EOS Collaboration Au multifragmentation data yield barriers with a power-law exponent of 0.68+/-0.03. Values of the surface energy coefficient of a low density nuclear system are also extracted.     

典型类型气溶胶吸收光学厚度的定标规律

利用云和气溶胶粒子的光学特性软件包(OPAC)对陆地型、海洋型、沙漠型和极地型四种典型类型气溶胶的吸收光学厚度进行了计算统计分析,根据每一种类型气溶胶成分的差异,分析了气溶胶吸收光学厚度随波长及相对湿度变化的规律,建立了四种典型类型气溶胶吸收光学厚度与波长、相对湿度的定标关系。气溶胶吸收光学厚度随波长的幂指数衰减规律并不是在所有波长范围内均满足,不同类型的气溶胶,其适用的范围不同;气溶胶吸收光学厚度随波长和相对湿度的变化主要受气溶胶成分影响,相对湿度的增大会导致气溶胶吸收特性的降低,并会对吸收Angstrom指数造成影响。根据建立的气溶胶吸收光学厚度的定标关系,可由气溶胶激光雷达等设备实测的某一波长的光学参量计算光电系统对应波长、不同相对湿度情况下的光学特性。     

典型类型气溶胶吸收光学厚度的定标规律

利用云和气溶胶粒子的光学特性软件包（OPAC）对陆地型、海洋型、沙漠型和极地型四种典型类型气溶胶的吸收光学厚度进行了计算统计分析,根据每一种类型气溶胶成分的差异,分析了气溶胶吸收光学厚度随波长及相对湿度变化的规律,建立了四种典型类型气溶胶吸收光学厚度与波长、相对湿度的定标关系。气溶胶吸收光学厚度随波长的幂指数衰减规律并不是在所有波长范围内均满足,不同类型的气溶胶,其适用的范围不同;气溶胶吸收光学厚度随波长和相对湿度的变化主要受气溶胶成分影响,相对湿度的增大会导致气溶胶吸收特性的降低,并会对吸收Angstrom指数造成影响。根据建立的气溶胶吸收光学厚度的定标关系,可由气溶胶激光雷达等设备实测的某一波长的光学参量计算光电系统对应波长、不同相对湿度情况下的光学特性。     

Decoherence dynamics in low-dimensional cold atom interferometers

We report on a study of the dynamics of decoherence of a matter-wave interferometer, consisting of a pair of low-dimensional cold atom condensates at finite temperature. We identify two distinct regimes in the time dependence of the coherence factor of the interferometer: quantum and classical. Explicit analytical results are obtained in both regimes. In particular, in the two-dimensional case in the classical (long time) regime, we find that the dynamics of decoherence is universal, exhibiting a power-law decay with an exponent, proportional to the ratio of the temperature to the Kosterlitz-Thouless temperature of a single 2D condensate. In the one-dimensional case in the classical regime we find a universal nonanalytic time dependence of decoherence, which is a consequence of the nonhydrodynamic nature of damping in 1D liquids.     

Bose-Einstein condensation of S = 1 nickel spin degrees of freedom in NiCl2-4SC(NH2)2

It has recently been suggested that the organic compound NiCl2-4SC(NH2)2 (DTN) undergoes field-induced Bose-Einstein condensation (BEC) of the Ni spin degrees of freedom. The Ni S = 1 spins exhibit three-dimensional XY antiferromagnetism above a critical field H(c1) approximately 2 T. The spin fluid can be described as a gas of hard-core bosons where the field-induced antiferromagnetic transition corresponds to Bose-Einstein condensation. We have determined the spin Hamiltonian of DTN using inelastic neutron diffraction measurements, and we have studied the high-field phase diagram by means of specific heat and magnetocaloric effect measurements. Our results show that the field-temperature phase boundary approaches a power-law H - H(c1) proportional variant T(alpha)(c) near the quantum critical point, with an exponent that is consistent with the 3D BEC universal value of alpha = 1.5.     

Mapping of the roughness exponent for the fuse model for fracture

The roughness exponent for fracture surfaces in the fuse model has been thought to be universal for narrow threshold distributions and has been important in the numerical studies of fracture roughness. We show that the fuse model gives a disorder dependent roughness exponent for narrow disorders when the lattice is influencing the fracture growth. When the influence of the lattice disappears, the local roughness exponent approaches zeta(local)=0.65+/-0.03 for distribution with a tail toward small thresholds, but with large jumps in the profiles giving corrections to scaling on small scales. For very broad disorders the distribution of jumps becomes a Lévy distribution and the Lévy characteristics contribute to the local roughness exponent.     

Acoustic emission from paper fracture

We report tensile failure experiments on paper sheets. The acoustic emission energy and the waiting times between acoustic events follow power-law distributions. This remains true while the strain rate is varied by more than 2 orders of magnitude. The energy statistics has the exponent beta approximately 1.25+/-0.10 and the waiting times the exponent tau approximately 1.0+/-0.1, in particular, for the energy roughly independent of the strain rate. These results do not compare well with fracture models, for (brittle) disordered media, which as such exhibit criticality. One reason may be residual stresses, neglected in most theories.     

自对耦无序分布随机链Potts模型的临界普适性研究

以蒙特卡罗模拟方法对自对耦分布二维随机链q态Potts模型的短时临界行为进行了数值研究.利用初始非平衡演化阶段存在的普适幂指数和有限体积标度行为，数值模拟了在不同形式随机分布时q＝3和q＝8态Potts模型磁临界指数η和动力学临界指数z.计算结果发现η不依赖于自对偶无序分布的具体形式， 从而以数值方法给出了一个关于淬火掺杂自旋系统的临界普适行为的验证. 关键词： 随机链Potts模型 动力学蒙特卡罗模拟 临界普适性     

Environment-dependent blinking of single semiconductor nanocrystals and statistical aging of ensembles

We compare decreasing fluorescence signals from ensembles with the blinking statistics of individual nanocrystals in various environments. For most substrates, the ensemble decay follows a power-law of time, the exponent being the difference of the power-law exponents of on- and off-time distributions. The decay exponent is also found to depend on substrate. We discuss possible mechanisms for this dependence, in conjunction with previously published models.     

An estimation formula for the average path length of scale-free networks

A universal estimation formula for the average path length of scale free networks is given in this paper. Different from other estimation formulas, most of which use the size of network, $N$, as the only parameter, two parameters including $N$ and a second parameter $\alpha $ are included in our formula. The parameter $\alpha $ is the power-law exponent, which represents the local connectivity property of a network. Because of this, the formula captures an important property that the local connectivity property at a microscopic level can determine the global connectivity of the whole network. The use of this new parameter distinguishes this approach from the other estimation formulas, and makes it a universal estimation formula, which can be applied to all types of scale-free networks. The conclusion is made that the small world feature is a derivative feature of a scale free network. If a network follows the power-law degree distribution, it must be a small world network. The power-law degree distribution property, while making the network economical, preserves the efficiency through this small world property when the network is scaled up. In other words, a real scale-free network is scaled at a relatively small cost and a relatively high efficiency, and that is the desirable result of self-organization optimization.     

Universal local versus unified global scaling laws in the statistics of seismicity

The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power law governs short times, but with an exponent that may change from one area to another. This is in contrast with a local, time-homogenized version of Bak et al.'s procedure, which seems to present a universal scaling behavior.     

Power-law distributions in random multiplicative processes with non-Gaussian colored multipliers

One class of universal mechanisms that generate power-law probability distributions is that of random multiplicative processes. In this paper, we consider a multiplicative Langevin equation driven by non-Gaussian colored multipliers. We analytically derive a formula that relates the power-law exponent to the statistics of the multipliers and numerically confirm its validity using multiplicative noise generated by chaotic dynamical systems and by a two-valued Markov process. We also investigate the relationship between our treatment and the large deviation analysis of time series, and demonstrate the appearance of log-periodic fluctuations superimposed on the power-law distribution due to the non-Gaussian nature of the multipliers.     

Cholesteric pitch of cholesteryl decanoate near the smectic-a transition

The temperature dependence of the cholesteric pitch in cholesteryl decanoate has been measured near the smectic-A transition. The data show a power-law divergence with a critical exponent v = 0.67 ± 0.03, in agreement with previous results in cholesteryl nonanoate.     

Modelling conflicts with cluster dynamics in networks

We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study the model in its annealed random graph version, on a fixed network, and on a network evolving through the actions. The sizes of actions are distributed with a power-law tail, however, the exponent is non-universal and depends on the frequency of actions and sparseness of the available connections between units. Allowing the network reconstruction over time in a self-organized manner, e.g., by adding the links based on previous liaisons between units, we find that the power-law exponent depends on the evolution time of the network. Its lower limit is given by the universal value 5/2, derived analytically for the case of random fragmentation processes. In the temporal patterns behind the size of actions we find long-range correlations in the time series of the number of clusters and the non-trivial distribution of time that a unit waits between two actions. In the case of an evolving network the distribution develops a power-law tail, indicating that through repeated actions, the system develops an internal structure with a hierarchy of units.     

Inversion symmetry and exact critical exponents of dissipating waves in the sandpile model

By an inversion symmetry, we show that in the Abelian sandpile model the probability distribution of dissipating waves of topplings that touch the boundary of the system shows a power-law relationship with critical exponent 5/8 and the probability distribution of those dissipating waves that are also last in an avalanche has an exponent of 1. Our extensive numerical simulations not only support these predictions, but also show that inversion symmetry is useful for the analysis of the two-wave probability distributions.     

Defect production in nonlinear quench across a quantum critical point

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.     

Scaling behavior of grain-rotation-induced grain growth

Recent investigations of grain growth in nanocrystalline materials have revealed a new growth mechanism: grain-rotation-induced grain coalescence. Based on a simple model employing a stochastic theory and using computer simulations, here we investigate the coarsening of a polycrystalline microstructure due solely to the grain-rotation coalescence mechanism. Our study demonstrates that this mechanism exhibits power-law growth with a universal scaling exponent. The value of this universal growth exponent is shown to depend on the assumed mechanism by which the grain rotations are accommodated.     

Short-Time Dynamics of Random-Bond Potts Ferromagnet with Continuous Self-Dual Quenched Disorders

We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson-Young self-dual distribution of quenched disorders in two dimensions. By exploring the short-time scaling dynamics, we find the universal power-law critical behavior of the magnetization and Binder cumulant at the critical point, and thus obtain estimates of the dynamic exponent z and magnetic exponent η, as well as the exponent θ. Our special attention is paid to the dynamic process for the q = 8 Potts model.     

Decay of silicon mounds: scaling laws and description with continuum step parameters

The decay of mounds about a dozen layers high on the Si(111)-(7x7) surface has been measured quantitatively by scanning tunneling microscopy and compared with analytic predictions for the power-law dependence on time predicted for a step-mediated decay mechanism. Conformably, we find an exponent 1/4 associated with the (3D) decay of the mound height and exponent 1/3 associated with the (2D) decay of top-layer islands. Using parameters from a continuum step model, we capture the essence of the kinetics. Qualitative features distinguish these mounds from multilayer islands found on metals.     

Exponential decay properties of Wannier functions and related quantities

The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of -3/4 for Wannier functions, -1/2 for the density matrix and for energy matrix elements, and -1/2 or -3/2 for different constructions of nonorthonormal Wannier-like functions.