Shape of a wave front in a heterogenous medium

Wave propagation in a heterogeneous medium, characterized by a distribution of local elastic moduli, is studied. Both acoustic and elastic waves are considered, as are spatially random and power-law correlated distributions of the elastic moduli with nondecaying correlations. Three models--a continuum scalar model, and two discrete models--are utilized. Numerical simulations indicate the existence, at all times, of the relation, alpha = H, where alpha is the roughness exponent of the wave front in the medium, and H is the Hurst exponent that characterizes the spatial correlations in the distribution of the local elastic moduli. Hence, a direct relation between the static morphology of an inhomogeneous correlated medium and its dynamical properties is established. In contrast, for a wave front in random media, alpha = 0 (logarithmic growth) at short times, followed by a crossover to the classical value, alpha = 1/2, at long times.     

Quantum error correction in spatially correlated quantum noise

We consider quantum error correction of quantum noise that is created by a local interaction of qubits with a common bosonic bath. The possible exchange of bath bosons between qubits gives rise to spatial and temporal correlations in the noise. We find that these kinds of noise correlations have a strong negative impact on quantum error correction.     

Scaling behavior of earthquakes’ inter-events time series

In this paper, we investigate the statistical and scaling properties of the California earthquakes’ inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events.      

Noise correlations in one-dimensional systems of ultracold fermions

Time of flight images reflect the momentum distribution of the atoms in the trap, but the spatial noise in the image holds information on more subtle correlations. Using bosonization, we study such correlations in generic 1D systems of ultracold fermions. We show how pairing as well as spin and charge density wave correlations may be identified and extracted from time of flight images. These incipient orders manifest themselves as power-law singularities in the noise correlations, that depend on the Luttinger parameters, which suggests a general experimental technique to obtain them.     

Self-Similarity of Edge Plasma Fluctuations in TEXTOR

In TEXTOR the long-range time dependence of edge plasma fluctuations has been investigated. The results indicate that the tail of the autocorrelation function decays as a power law for time lags longer than the local decorrelation time. The frequency spectra of the fluctuations show similar features to those obtained in "sandpile" models. Using rescaled range (R/S) analysis techniques the self-similarity parameters have been estimated for the potential fluctuation data detected by Langmuir probes. The results show that the Hurst exponents are well above 0.5 over the self-similarity range at all the measured radial locations. All these facts reveal the self-similar character of the electrostatic fluctuations at the plasma edge of TEXTOR, consistent with plasma transport as characterized by self-organized criticality (SOC). Furthermore, we have analyzed in this respect discharges in which an edge transport barrier was created by means of edge biasing, hitherto limited to floating potential measurements in the scrape off layer outside the barrier region. The results show a decrease of fluctuating amplitudes, a reduction of decorrelation time of local turbulence and, surprisingly, a concomitant increase of the Hurst exponent. This result implies that the mechanisms governing the decorrelation of local turbulence may differ from those governing the decorrelation of SOC transport events.     

Inhibitory effect induced by fractional Gaussian noise in neuronal system

We discover a phenomenon of inhibition effect induced by fractional Gaussian noise in a neuronal system. Firstly, essential properties of fractional Brownian motion (fBm) and generation of fractional Gaussian noise (fGn) are presented, and representative sample paths of fBm and corresponding spectral density of fGn are discussed at different Hurst indexes. Next, we consider the effect of fGn on neuronal firing, and observe that neuronal firing decreases first and then increases with increasing noise intensity and Hurst index of fGn by studying the time series evolution. To further quantify the inhibitory effect of fGn, by introducing the average discharge rate, we investigate the effects of noise and external current on neuronal firing, and find the occurrence of inhibitory effect about noise intensity and Hurst index of fGn at a certain level of current. Moreover, the inhibition effect is not easy to occur when the noise intensity and Hurst index are too large or too small. In view of opposite action mechanism compared with stochastic resonance, this suppression phenomenon is called inverse stochastic resonance (ISR). Finally, the inhibitory effect induced by fGn is further verified based on the inter-spike intervals (ISIs) in the neuronal system. Our work lays a solid foundation for future study of non-Gaussian-type noise on neuronal systems.     

EXPERIMENTAL EVIDENCE OF THE SELF-SIMILARITY AND LONG-RANGE CORRELATIONS OF THE EDGE FLUCTUATIONS IN HT-6M TOKAMAK

To better understand long-time-scale transport dynamics, the rescaled range analysis techniques, the autocorrelation function (ACF) and the probability distribution function (PDF) are used to investigate long-range dependences in edge plasma fluctuations in HT-6M tokamak. The results reveal the self-similar characters of the electrostatic fluctuations with self-similarity parameters (Hurst exponent) ranging from 0.64 to 0.79, taking into consideration the {\vec E}_r×{\vec B} rotation-sheared effect. Fluctuation ACFs of both the ion saturation current and the floating potential, as well as PDF of the turbulence-induced particle flux, have two distinct time scales. One corresponds to the decorrelation time scale of local fluctuations (μs) and the other lasts to the order of the confinement time (ms). All these experimental results suggest that some of the mechanisms of the underlying turbulence are consistent with plasma transport as characterized by self-organized criticality(SOC).     

Detection of areas with viable remnant tumor in postchemotherapy patients with Ewing's sarcoma by dynamic contrast-enhanced MRI using pharmacokinetic modeling

An approach is presented for monitoring the effects of neoadjuvant chemotherapy in patients with Ewing's sarcoma using dynamic contrast-enhanced perfusion magnetic resonance (MR) images. For that purpose, we modify the three-compartment pharmacokinetic permeability model introduced by Tofts et al. (Magn Reson Med 1991;17:357-67) to a two-compartment model. Perfusion MR images acquired using an intravenous injection with Gadolinium (Gd-DTPA) are analyzed with this two-compartment pharmacokinetic model as well as the with an extended pharmacokinetic model that includes the (local) arrival time t(0) of the tracer as an endogenous (estimated) parameter. For each MR section, a wash-in parameter associated with each voxel is estimated twice by fitting each of the two pharmacokinetic models to the dynamic MR signal. A comparison of the two wash-in parametric images (global versus local arrival time) with matched histologic macroslices demonstrates a good correspondence between areas with viable remnant tumor and a high wash-in rate. This can be explained by the high number and permeability of the (leaking) capillaries in viable tumor tissue. The novel pharmacokinetic model based on a local arrival time of tracer results in the best fit of the wash-in rate, the most important factor discerning viable from nonviable tumor components. However, parameter estimates obtained with this model are also more sensitive to noise in the MR signal. The novel pharmacokinetic model resulted in a sensitivity between 0.22 and 0.60 and a specificity between 0.61 and 1. The model based on a global arrival time gave sensitivities between 0.33 and 0.77 and specificities between 0.58 and 0.99. Both statistics are computed as the fraction of correctly labeled voxels (viable or nonviable tumor) within a specified ROI, which delineates the tumor. We conclude that the added value of estimating the local arrival time of tracer first manifests itself for moderate noise levels in the MR signal. The novel pharmacokinetic model should moreover be preferred when pharmacokinetic modeling is applied on the average signal intensity within a ROI, where noise has less effect on the fitted parameters.     

Geometry of crumpled paper

We measure the geometry of a crumpled sheet of paper with laser-aided topography and discuss its statistical properties. The curvature of an elastoplastic fold scales linearly with applied force. The curvature distribution follows an exponential form with regions of high curvature localized along ridges. The measured ridge length distribution is consistent with a hierarchical model for ridge breaking during crumpling. A large fraction of the ridges are observed to terminate without bifurcating, and the ridge network connectedness is not as complete as anticipated. The self-affinity of the surface is characterized by a Hurst exponent of 0.71+/-0.01 in contrast with previous results.     

风沙流对高压绝缘子电位和电场分布的影响

研究风沙流对高压绝缘子电位和电场分布的影响,基于有限体积法建立绝缘子风沙气固两相流模型和风沙天气下绝缘子的风-沙-电耦合场模型,计算不同风沙天气下绝缘子表面沙尘的空间分布和沉积及其对绝缘子沿面电位和电场的影响,结果表明：风沙天气下绝缘子沿面电位和电场畸变受风速和粒径影响显著,电位的畸变幅度随风速和粒径的增加而升高,电场的畸变幅度随风速和粒径的增大而减少;风沙天气下绝缘子表面不同的沙尘空间分布和沉积导致绝缘子不同位置沿面电位和电场畸变不同.     

Spatial distribution of the intensity noise of a vertical-cavity surface-emitting semiconductor laser

We studied anticorrelated quantum fluctuations between the TEM(00) and the TEM(01) transverse modes of a vertical-cavity surface-emitting semiconductor laser by measuring the transverse spatial distribution of the laser beam intensity noise. Our experimental results are found to be in good agreement with the predictions of a phenomenological model that accounts for quantum correlations between transverse modes in a light beam.     

Impact of perturbations on watersheds

We find that watersheds in real and artificial landscapes can be strongly affected by small, local perturbations like landslides or tectonic motions. We observe power-law scaling behavior for both the distribution of areas enclosed by the original and the displaced watershed as well as the probability density to induce, after perturbation, a change at a given distance. Scaling exponents for real and artificial landscapes are determined, where in the latter case the exponents depend linearly on the Hurst exponent of the applied fractional Brownian noise. The obtained power laws are shown to be independent on the strength of perturbation. Theoretical arguments relate our scaling laws for uncorrelated landscapes to properties of invasion percolation.     

Roughness of stylolites: implications of 3D high resolution topography measurements

Stylolites are natural pressure-dissolution surfaces in sedimentary rocks. We present 3D high resolution measurements at laboratory scales of their complex roughness. The topography is shown to be described by a self-affine scaling invariance. At large scales, the Hurst exponent is zeta(1) approximately 0.5 and very different from that at small scales where zeta(2) approximately 1.2. A crossover length scale at around L(c)=1 mm is well characterized. Measurements are consistent with a Langevin equation that describes the growth of a stylolitic interface as a competition between stabilizing long range elastic interactions at large scales or local surface tension effects at small scales and a destabilizing quenched material disorder.     

Comparison of the Hurst and DEA exponents between the catalogue and its clusters: The California case

In this work, we analyse the long-run correlations of the seismic catalogue and of its clusters, by means of the Diffusion Entropy Analysis (DEA) and the value of the Hurst exponent. First we calculate the values for the whole catalogue, for the rate and the inter-event times and distance distribution over time, and subsequently we calculate the values for the declustered catalogue and the main clusters. We find a wide variety of behaviours, which depart from the Poisson statistics.     

New class of level statistics in correlated disordered chains

We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated-disordered systems), and above which the level statistics is described by a new class of distribution functions. At the threshold, we find that with increasing system size, the standard deviation of the function describing the level statistics converges to the standard deviation of the Poissonian distribution as a power law. Above the threshold we find that the level statistics is characterized by different functional forms for different degrees of correlations.     

Analysis of the efficiency of the Shanghai stock market: A volatility perspective

By applying the rolling window method, we investigate the efficiency of the Shanghai stock market through the dynamic changes of local Hurst exponents based on multifractal detrended fluctuation analysis. We decompose the realized volatility into continuous sample paths and jump components and analyze their long-range correlations of decomposing components. Our results reveal that the efficiency of the Shanghai stock market improved greatly based on the time-varying Hurst exponents.     

Stochastic resonance phenomena in spin chains

We discuss stochastic resonance-like effects in the context of coupled quantum spin systems. We focus here on an information-theoretic approach and analyze the steady state quantum correlations (entanglement) as well as the global correlations in the system when subject to different forms of local decoherence. In the presence of decay, it has been shown that the system displays quantum correlations only when the noise strength is above a certain threshold. We extend this result to the case of a Heisenberg XYZ exchange interaction and revise and clarify the mechanisms underlying this behaviour. In the presence of pure dephasing, we show that the system always remains separable in the steady state. When both types of noise are present, we show that the system can still exhibit entanglement for long times, provided that the pure dephasing rate is not too large.     

The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange

The local properties of the time series of the evolution of share prices of 126 significant companies traded on the Warsaw Stock Exchange during the period between 1991-2008 have been investigated. The analysis was applied to daily financial returns. I have used the local DFA to obtain the Hurst exponent (diffusion coefficient) while searching for negative correlations by which changes of long-term trends would be effected. A certain evidence, proving that after the signature of anti-correlation-the drop in the Hurst exponent-the change in the trend and in the return rate of an investment is probable, was pointed out. Hence after further investigation this method may be useful as a part of an investment strategy. As the Warsaw Stock Exchange is relatively smaller and younger than other significant world Stock Exchanges-and as the developing market is less efficient-the generalization for others markets needs further investigation.     

Spatial Density Distributions and Correlations in a Quasi-one-Dimensional Polydisperse Granular Gas

By Monte Carlo simulations, the effect of the dispersion of particle size distribution on the spatial density distributions and correlations of a quasi one-dimensional polydisperse granular gas with fractal size distribution is investigated in the same inelasticity. The dispersive degree of the particle size distribution can be measured by a fractal dimension dr, and the smooth particles are constrained to move along a circle of length L, colliding inelastically with each other and thermalized by a viscosity heat bath. When the typical relaxation time τ of the driving Brownian process is longer than the mean collision time To, the system can reach a nonequilibrium steady state. The average energy of the system decays exponentially with time towards a stable asymptotic value, and the energy relaxation time τB to the steady state becomes shorter with increasing values of df. In the steady state, the spatial density distribution becomes more clusterized as df increases, which can be quantitatively characterized by statistical entropy of the system. Furthermore, the spatial correlation functions of density and velocities are found to be a power-law form for small separation distance of particles, and both of the correlations become stronger with the increase of df. Also, tile density clusterization is explained from the correlations.