Quantum n-Vector Anharmonic Crystal II: Displacement Fluctuations

Based on the 1/n-expansion derived in a previous paper, the displacement fluctuations are analyzed in a quantum n-vector model of anharmonic crystal in the large n regime. It is shown that in the ferroelectric phase the n limit of the local fluctuation field has faster large-distance correlation decay than its Hartree–Fock approximation. Also, the critical exponent of the global displacement fluctuation is strictly smaller there than the Hartree–Fock exponent. In particular, the displacement fluctuations may be normal in the ferroelectric phase in spite of the Hartree–Fock prediction.     

Visibility graph network analysis of gold price time series

Mapping time series into a visibility graph network, the characteristics of the gold price time series and return temporal series, and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory. The network degree distribution characters, which change from power law to exponent law when the series was shuffled from original sequence, and the average path length characters, which change from L∼lnN$L\sim lnN$ into lnL∼lnN$lnL\sim lnN$ as the sequence was shuffled, demonstrate that price series and return series are both long-rang dependent fractal series. The relations of Hurst exponent to the power-law exponent of degree distribution demonstrate that the logarithmic price series is a fractal Brownian series and the logarithmic return series is a fractal Gaussian series. Power-law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series. The Power-law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network. The hierarchy character, in light of the correspondence of graph to price fluctuation, means that gold price fluctuation is a hierarchy structure, which appears to be in agreement with Elliot’s experiential Wave Theory on stock price fluctuation, and the local-rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent, short term factors, such as short term speculation.     

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.     

Dynamical properties of colloidal systems: II. Correlation- and response functions

For systems of interacting Brownian particles a Fokker-Planck equation is derived for the probability distribution function of the concentration fluctuations, using assumption of a Gaussian static distribution function. The drift- and the diffusion term are determined by static correlation functions. By this approach specific properties of different systems as e.g., suspensions of charged spherical particles or chain polymers are taken into account. Although the diffusion term is fluctuation dependent the properties of detailed balance and both fluctuation dissipation theorems are satisfied. Using the formalism of Martin, Siggia and Rose, Dyson- and vertex-equations for the two-particle correlation functions are derived. An explicit calculation of these functions, together with related quantities as the dynamic structure factor, and of the diffusion coefficients, is given in a mean-field approximation. The results are compared with several earlier theories, which were developed for specific systems.     

The influence of random fluctuations on the behaviour of an aerosol

The purpose of the paper is to assess in a general manner the influence of random fluctuations in the local velocity, deposition rate, growth rate and coagulation constant on the behaviour of an aerosol. Using stochastic methods of probability theory we have shown that fluctuations in the local velocity lead to a broadening of the volume distribution which increases with time. The fluctuation in the deposition rate has a destabilizing effect and reduces the deterministically calculated rate of decay. Fluctuations in growth rate lead to the broadening of an initially monodisperse distribution and allow for evaporation and condensation. The rate of increase of suspended mass arising from this condensation-evaporation process is greater than the corresponding deterministic value.The effect of fluctuations in the coagulation constant leads to a decrease in the usual rate of removal of particles, although this is a small effect.The fluctuations are assumed to be stationary, random functions of time or position and in most cases are taken to be Gaussian variables. However, it is found that the infinite range of the Gaussian can lead to certain unphysical results and other distributions are examined.     

On the detection of trends in long-term correlated records

We use the Detrended Fluctuation Analysis (DFA) to quantify underlying trends in long-term correlated records. Our approach is based on the fact that different orders of DFA are affected differently by trends. For a given instrumental record of length N, we compare the fluctuation exponent α₀ of DFA0 where trends are not being eliminated, with the fluctuation exponent α₂ of DFA2 where possible linear trends in the instrumental record are being eliminated. From this we deduce numerically the probability density p(A) that in the considered long-term correlated record, a linear trend with a slope between A and occurs. Without loss of generality we focus on Gaussian distributed data. As an example, we apply our analysis to several long temperature records (Melbourne, Oxford, Prague, Pusan, Uppsala, and Vienna), where we discuss the trends within the last 90 years, which may originate from both, urban and global warming.     

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, , is λ=1.17±0.04 which is almost similar for all underlying rivers at 1σ confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are λ∈(0.76,0.85) and γ_×∈(0.30,0.48), respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), is confirmed.     

Superconductivity fluctuations in Bi(Pb) based granular ceramics superconductors: evidence for fractal behavior

We report precise measurements of the electrical resistivity in three different Bi(Pb) based granular ceramics superconductors. We show that a single critical exponent (5/6) describes the superconductivity fluctuations. Such a critical exponent indicates a fractal behavior of the superconducting path. Our results thus indicate a strict two dimensional fluctuation percolation set (below the superconductivity onset temperature 195 K down toT _c), and provide some proof for Tarascon et al. shell conductivity path hypothesis. We estimate the shell thickness to be of the order of 10 Å.     

单峰高斯分布适应面上的误差阈

在Eigen的单峰适应面模型基础上,提出了生物体的适应值为高斯分布的随机适应面模型。 利用系综平均的方法, 计算了在单峰高斯分布适应面上准物种的浓度分布和误差阈。 结果表明, 对于小的适应面涨落, 准物种分布和误差阈与确定情形相比变化极小,误差阈对于小的涨落是稳定的。 然而, 当适应值涨落较大时,从准物种到误差灾变的转变不再明显。 误差阈变宽, 并且在涨落增加时向大的突变率方向移动。 Based on the Eigen model with a single peak fitness landscape, the fitness values of all sequence types are assumed to be random with Gaussian distribution. By ensemble average method, the concentration distribution and error threshold of quasispecies on single peak Gaussian distributed fitness landscapes were evaluated. It is shown that the concentration distribution and error threshold change little in comparing with deterministic case for small fluctuations, which implies that the error threshold is stable against small perturbation. However, as the fluctuation increases, the situation is quite different. The transition from quasi species to error catastrophe is no longer sharp. The error threshold becomes a narrow band which broadens and shifts toward large values of error rate with increasing fluctuation.     

Power spectrum of fluctuation for ultrasonic cavitation process in glycerin

Experiments were carried out on ultrasonic cavitation in glycerin. The zone near the emitter has a structure from interacting gas-vapor bubbles; this structure takes the form of fractal clusters. The photometry of passed laser emission was the tool for studying dynamics of fluctuations. In transitive mode, the power spectrum of fluctuation varies by the law inversely proportional to frequency. Distributions of local fluctuations are different from Gaussian and exhibit the property of scale invariance. The qualitative behavior of the frequency dependence of the spectral fluctuation density was tested while varying the power of the ultrasonic emitter. It was demonstrated that the growth of the high-frequency margin of flicker-type behavior evidences for growing instability and can be considered as a forerunner of possible large-scale outbursts. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 05-08-01320a).     

Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation, and Fragmentation

We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact, and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady-state mass distribution decays exponentially for large mass in one phase. In the other phase, the mass distribution decays as a power law accompanied, in addition, by the formation of an infinite aggregate. The model is solved exactly within a mean-field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time-dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.     

The shear diffusion coefficient for generalized theories of gravity

Near the horizon of a black brane in Anti-de Sitter (AdS) space and near the AdS boundary, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. The gauge–gravity duality then relates the boundary hydrodynamics for generalized gravity to that of gauge theories with large finite values of 't Hooft coupling. We discuss, for this framework, the hydrodynamics of the shear mode in generalized theories of gravity in d+1$d+1$ dimensions. It is shown that the shear diffusion coefficients of the near-horizon and boundary hydrodynamics are equal and can be expressed in a form that is purely local to the horizon. We find that the Einstein-theory relation between the shear diffusion coefficient and the shear viscosity to entropy ratio is modified for generalized gravity theories: Both can be explicitly written as the ratio of a pair of polarization-specific gravitational couplings but implicate differently polarized gravitons. Our analysis is restricted to the shear-mode fluctuations for simplicity and clarity; however, our methods can be applied to the hydrodynamics of all gravitational and matter fluctuation modes.     

Capture-zone scaling in island nucleation: universal fluctuation behavior

In island nucleation and growth, the distribution of capture zones (in essence proximity cells) can be described by a simple expression generalizing the Wigner surmise (power-law rise, Gaussian decay) from random matrix theory that accounts for spacing distributions in a host of fluctuation phenomena. Its single adjustable parameter, the power-law exponent, can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory elucidates the result.     

Lattice models of advection-diffusion

We present a synthesis of theoretical results concerning the probability distribution of the concentration of a passive tracer subject to both diffusion and to advection by a spatially smooth time-dependent flow. The freely decaying case is contrasted with the equilibrium case. A computationally efficient model of advection-diffusion on a lattice is introduced, and used to test and probe the limits of the theoretical ideas. It is shown that the probability distribution for the freely decaying case has fat tails, which have slower than exponential decay. The additively forced case has a Gaussian core and exponential tails, in full conformance with prior theoretical expectations. An analysis of the magnitude and implications of temporal fluctuations of the conditional diffusion and dissipation is presented, showing the importance of these fluctuations in governing the shape of the tails. Some results concerning the probability distribution of dissipation, and concerning the spatial scaling properties of concentration fluctuation, are also presented. Though the lattice model is applied only to smooth flow in the present work, it is readily applicable to problems involving rough flow, and to chemically reacting tracers. (c) 2000 American Institute of Physics.     

Density fluctuations of two-dimensional active-passive mixtures

Dimension-dependent giant density fluctuations are a typical feature of active matter systems. In this work, we study the density fluctuation in two-dimensional mixtures of active and passive particles by Brownian dynamics simulations. The boundary of motility-induced phase separation is determined by the transition from unimodal to bimodal density distribution. A rapid increase of the fluctuation exponent near the boundary of phase separation in the plane of density and Péclet number was observed. When phase separation occurs, the fluctuation exponent is an approximate constant of $0.85.$     

Stochastic theory of ignition processes

We consider a closed gaseous system immersed in a heat bath undergoing a thermal explosion. The effects of instantaneous fluctuations in the temperature on the heat removal mechanism and on the reaction rate are considered. The intensity of the fluctuations in situations far from equilibrium is determined by calculating the temperature self-correlation. This quantity scales with the inverse of an effective volume obtained from generalized fluctuation-dissipation theory. This determines a virtual system corresponding to the localized ignition process, possibly leading to a global runaway. The induction period is identified with the Kramers mean passage time for diffusion across a kinetic barrier. The induction period is thus shown to be dependent on the fluctuation volume . The diffusion process is hastened by the critical fluctuations. The explosive decomposition of ethyl azide was selected to test the theory and the results exhibit very good agreement with experimental data. Our treatment resolves the previous discrepancy between the predictions rooted in the classical Frank-Kamenetsky treatment and the premature ignition observed experimentally.     

Finite correlation time effects in nonequilibrium phase transitions: I. Dynamic equation and steady state properties

We determine an approximate renormalized equation of evolution for an arbitrary nonlinear single-degree-of-freedom system externally driven by Gaussian parametric fluctuations of finite correlation time. The renormalization scheme used here gives a second order equation with a time-and-state-dependent “diffusion coefficient”. We are able to calculate the diffusion coefficient in closed form. The steady-state distribution can easily be obtained from the evolution equation. We are thus able to determine the parameter dependence of the steady-state distribution and, in particular, the influence of a correlation time of the fluctuations, which does not vanish, on the steady-state distribution.     

Probing spatial correlations in the inhomogeneous glassy state of the cuprates by Cu NMR

We discuss the crossover of the form of the Cu Nuclear magnetic resonance (NMR) spin echo decay at the onset of Cu wipeout in lanthanum cuprates. Experimentally, the echo decay undergoes a crossover from Gaussian to exponential form below the temperature where the Cu NMR intensity drops. The wipeout and the change in behavior both arise because the nuclei experience spatially inhomogeneous spin fluctuations at low temperatures. We argue that regions where the spin fluctuations remain fast are localized on length scales of order 1-2 lattice spacings. The inhomogeneity is characterized by the local activation energy E_a(r); we estimate the functional form of E_a(r) for points where E_a>(r)∼0.     

Geometry of intensive scalar dissipation events in turbulence

The maxima of the scalar dissipation rate in turbulence appear in the form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross section extension determines a locally varying diffusion scale of the mixing process and extends the classical Batchelor picture of one mean diffusion scale. The distribution of the local diffusion scales is analyzed for different Reynolds and Schmidt numbers with a fast multiscale technique applied to very high-resolution simulation data. The scales always take values across the whole Batchelor range and beyond. Furthermore, their distribution is traced back to the distribution of the contractive short-time Lyapunov exponent of the flow.     

反应扩散系统中的涨落问题

本文用Master方程导出的带有扩散涨落项的福克-普朗克方程讨论了三个化学模型在不同情况下的涨落问题,文章指出:平衡态附近的无空间关联的涨落,偏离平衡时涨落的关联性,Schlogl三分子模型县有非经典的临界指数,而Schligl双分子模型具有经典的临界指数等多样的情况是由系统的本身性质决定的,用本文的方法能统一地处理这些问题,并且因而澄清了文献[6]中提出的关于临界指数的疑点。 关键词：