Presence Of Long-range Correlations Research Articles

Search for Long-Range Correlations in Relativistic Heavy-Ion Collisions at SPS Energies

Long-range correlations are searched for by analysing the experimental data on16O-AgBr and32S-AgBr collisions at 200 A GeV/c and the results are compared with the predictions of a multi phase transport (AMPT) model. The findings reveal that the observed forward-backward (F-B) multiplicity correlations are mainly of short range in nature. The range of F-B correlations are observed to extend with increasing projectile mass. The observed extended range of F-B correlations might be due to overall multiplicity fluctuations arising because of nuclear geometry. The findings are not sufficient for making any definite conclusions regarding the presence of long-range correlations.

Forward--Backward Multiplicity Correlations in Relativistic Heavy-ion Collisions

Forward-backward multiplicitycorrelations are investigated by analyzing the experimental data on O-AgBr collisions at 14.5A, 60A and 200A GeV/c and the findings are compared with the predictions of Monte Carlo model, hIJING. the findings indicate that the observed correlations are mainly of short-range in nature which arise due to the decay of clusters and (or) resonances produced in the central rapidity region. the result reveal that the range of F-B correlations extend to rather longer range with increasing beam energy which might be due to overall multiplicity fluctuations arising because of nuclear geometry. however, there is no evidence for the presence of long-range correlations even at the highest beam energy considered.

Deformation patterns and surface morphology in a minimal model of amorphous plasticity

We investigate a minimal model of the plastic deformation of amorphous materials. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is considered in terms of random variations of the local yield stresses. Using a finite element implementation of this simple model, we simulate the plane strain deformation of long thin rods loaded in tension. The resulting strain patterns are statistically characterized in terms of their spatial correlation functions. Studies of the corresponding surface morphology reveal a non-trivial Hurst exponent H ≈ 0.8, indicating the presence of long-range correlations in the deformation patterns. The simulated deformation patterns and surface morphology exhibit persistent features which emerge already at the very onset of plastic deformation, while subsequent evolution is characterized by growth in amplitude without major morphology changes. The findings are compared to experimental observations.

Multifractality due to long-range correlation in the L-band ionospheric scintillation S 4 index time series

The earth's ionosphere is well recognized as a dynamical system and non-linearly coupled with the magnetosphere above and natural atmosphere below.The shape and time variability of the ionosphere indeed shows chaos, pattern formation, random behavior and self-organization. The present paper studies the propriety of Multifractal Detrended Fluctuation Analysis (MF-DFA) technique for the ionospheric scintillation index time series. MF-DFA is used to identify the scaling behavior of the ionospheric scintillation time-series data of two different nature.The obtained results show the robustness and the relevancy of the MF-DFA technique for the ionospheric scintillation index time series. The comparison of the MF-DFA results of original data to those of shuffled and surrogate series shows that the multifractal nature of considered time series is almost due to long-range correlations. Subsequently, the Hurst exponents derived from two parallel methods namely Re-scaled range analysis (R/S) and Auto Correlation Function (ACF) are also suggesting the presence of long range correlation. The presented results in this work may be of assistance for future modeling and simulation studies.

A numerical renormalisation group method for the analysis of critical spreading activity in spiking neural networks

In recent years criticality has been used as a mechanism for understanding the presence of long-range correlations and intermittence in macroscopic neural activity. Little work has been done to demonstrate the usefulness of this paradigm for understanding the statistics and dynamics of neural networks. The explanation for self-similarity and universality is grounded in the renormalisation group (RG) theory of critical phenomena [1]. Until recently [2], this theory has not been leveraged for the inspection and understanding of neural network models or in neural data analysis. Here, we present a range of statistics derived from a dynamic renormalisation group theory [3], shown to elucidate the nature of self-organised criticality in sandpile models, which we have operationalised for the numeric data analysis of spike trains. The relationship between universality via self-similarity, the power-law exponents and a set of renormalised parameters is explored in the case of two automata models to demonstrate the application of the RG. In particular, we focus on the temporal profile of avalanches, the branching ratio and the avalanche size distribution and how these can be related to the renormalised parameters we study in these systems. Next, the same statistics are used to investigate the universality of a simplified integrate-and-fire model. Finally we use these methods to assess the critical state on a number of generic neural network models which are used to study the balanced state of neocortex.

Tuning Effect in Particle Masses, Nuclear Data and Standard Model Parameters

Recent determination of the scalar boson mass and results of the analysis of nuclear excitations collected in the new nuclear data compilation confirmed the presence of a common tuning effect in particle masses, in parameters of the Standard Model and in nuclear data. This tuning effect includes the distinguished character of estimates of constituent quark masses and the presence of long-range correlations in nucleon masses and nuclear data with the parameters close to (or rational to) the electromagnetic mass splitting of the electron and the nucleon. One of SM-parameters of the tuning effect is the QED radiative correction. Its value coincides with the ratios between masses of both leptons and masses of the constituent quark and Z-boson. It means that the lepton ratio (L=mµ/me=MZ/Mq with Mq=441 MeV) has the universal character.

Revisiting polymer statistical physics to account for the presence of long-range-correlated structural disorder in 2D DNA chains

We elaborate on a generalization of the 2D wormlike chain (WLC) model that accounts for the presence of long-range correlations (LRC) in the intrinsic curvature distribution of eukaryotic DNA. This model predicts some decrease of the DNA persistence length resulting from some large-scale intrinsic curvature induced by sequence-dependent persistent random distribution of local bending sites. When assisting exact analytical calculations by numerical DNA simulations, we show that the conjugated contributions of i) the thermal curvature fluctuations characterized by the "dynamic" persistence length ℓ(p)(d) = 2A, where A is the elastic bending modulus, and ii) the intrinsic LRC curvature disorder of amplitude σ(o) and Hurst exponent H > 1/2, characterized by a "static" persistence length ℓ(p)(H) = A(1/2H)σ(o)(-1/H) Γ(1/2H + 1), can be described by a continuum of generalized WLC (GWLC) models parametrized by the LRC exponent H. We use perturbation analysis to investigate the two limiting cases of weak static disorder (w(H) << 1 and weak dynamical fluctuations (1/w (H) << 1), where w(H) = l(p)(d)/l(p)(H) is a dimensionless parameter. From a quantitative point of view, our study demonstrates that even for a small value of the LRC (H approximately equal 0.6-0.8) static disorder amplitude σ(o) ~ 10(-2), as previously reported for genomic DNA, the decrease of the persistence length from the WLC prediction l(p)(d) can be very significant, up to twofold. The implications of these results on the first steps of compaction of DNA in eukaryotic cells are discussed.

A theoretical study of a strongly correlated linear H50 chain

We have investigated the strong correlation effects which are present in a chain model exclusively composed of hydrogen atoms, upon concerted dissociation of all of them, via different cost-effective methods based on DFT or scaled variants of MP2 theory. The presence of long-range correlation along bond breaking in an approximate exchange density functional (OPTX) is highlighted, although the corresponding decrease in energy does not suffice to completely describe the dissociation process. The influence of the scaling parameters in SCS-MP2, and related theories, is also thoroughly considered with however limited success.

Relativistic hydrodynamical model in the presence of long-range correlations

Effects of dynamical long-range correlations over a fluid cell size scale on a relativistic fluid are discussed. It is shown that such correlations among the fluid elements introduced into hydrodynamical model induce some weak dissipation and viscosity into the fluid. The influence of the long-range correlations on the entropy current is also discussed.

STATISTICAL ANALYSIS OF MAGNETIC FIELD REVERSALS IN LABORATORY DYNAMO AND IN PALEOMAGNETIC MEASUREMENTS

Statistical properties of the temporal distribution of polarity reversals of the geomagnetic field are commonly assumed to be a realization of a renewal Poisson process with a variable rate. However, it has been recently shown that the polarity reversals strongly depart from a local Poisson statistics, because of temporal clustering. Such clustering arises from the presence of long-range correlations in the underlying dynamo process. Recently achieved laboratory dynamo also shows reversals. It is shown here that laboratory and paleomagnetic data are both characterized by the presence of long-range correlations.

ENERGY DEPENDENCE OF SHORT AND LONG-RANGE MULTIPLICITY CORRELATIONS IN Au+Au COLLISIONS FROM STAR

A general overview of the measurement of long-range multiplicity correlations measured by the STAR experiment in Au + Au collisions at RHIC is presented. The presence of long-range correlations can provide insight into the early stages, and the type of matter produced in, these collisions. These measurements have been made in Au + Au collisions at [Formula: see text] and 62.4 GeV. These results indicate a relatively large long-range correlation is produced in Au + Au collisions compared to a pp baseline at [Formula: see text]. A weaker long-range correlation is seen as a function of incident energy. Further, comparison of the onset of the long-range correlation to the calculated percolation density parameter at [Formula: see text] is presented.

Controlling Polarization Dynamics in a Liquid Environment: From Localized to Macroscopic Switching in Ferroelectrics

The effect of disorder on polarization switching in ferroelectric materials is studied using piezoresponse force microscopy in a liquid environment. The spatial extent of the electric field created by a biased tip is controlled by the choice of medium, resulting in a transition from localized switching dictated by tip radius, to uniform switching across the film. In the localized regime, the formation of fractal domains has been observed with dimensionality controlled by the length scale of the frozen disorder. In the nonlocal regime, preferential nucleation at defect sites and the presence of long-range correlations has been observed.

Walking speed influences on gait cycle variability

The purpose of this study was to investigate the influence of walking speed on the amount and structure of the stride-to-stride fluctuations of the gait cycle. Based on previous findings for both walking [Hausdorff JM, Purdon PL, Peng CK, Ladin Z, Wei JY, Goldberger AL. Fractal dynamics of human gait: stability of long-range correlations in stride interval fluctuations. J Appl Physiol 1996;80:1448–57], and running [Jordan K, Challis JH, Newell KM. Long range correlations in the stride interval of running. Gait Posture 2006;24:120–5] it was hypothesized that the fractal nature of human locomotion is a reflection of the attractor dynamics of human locomotion. Female participants walked for 12 min trials at 80%, 90%, 100%, 110% and 120% of their preferred walking speed. Eight gait cycle variables were investigated: stride interval and length, step interval and length, and from the vertical ground reaction force profile the impulse, first and second peak forces, and the trough force. Detrended fluctuation analysis (DFA) revealed the presence of long range correlations in all gait cycle variables investigated. Speed related U-shaped functions occurred in five of the eight variables, with the minima of these curves falling between 100% and 110% of the preferred walking speed. These findings are consistent with those previously shown in running studies and support the hypothesis that reduced strength of long range correlations at preferred locomotion speeds is reflective of enhanced stability and adaptability at these speeds.

Distance traveled by random walkers before absorption in a random medium

We consider the penetration length l of random walkers diffusing in a medium of perfect or imperfect absorbers of number density rho. We solve this problem on a lattice and in the continuum in all dimensions D, by means of a mean-field renormalization group. For a homogeneous system in D > 2, we find that l is similar to max(xi,rho(-1/2)), where is the absorber density correlation length. The cases of D = 1 and D = 2 are also treated. In the presence of long-range correlations, we estimate the temporal decay of the density of random walkers not yet absorbed. These results are illustrated by exactly solvable toy models, and extensive numerical simulations on directed percolation, where the absorbers are the active sites. Finally, we discuss the implications of our results for diffusion limited aggregation (DLA), and we propose a more effective method to measure l in DLA clusters.

Formation and positioning of nucleosomes: Effect of sequence-dependent long-range correlated structural disorder

The understanding of the long-range correlations (LRC) observed in DNA sequences is still an open and very challenging problem. In this paper, we start reviewing recent results obtained when exploring the scaling properties of eucaryotic, eubacterial and archaeal genomic sequences using the space-scale decomposition provided by the wavelet transform (WT). These results suggest that the existence of LRC up to distances approximately 20-30 kbp is the signature of the nucleosomal structure and dynamics of the chromatin fiber. Actually the LRC are mainly observed in the DNA bending profiles obtained when using some structural coding of the DNA sequences that accounts for the fluctuations of the local double-helix curvature within the nucleosome complex. Because of the approximate planarity of nucleosomal DNA loops, we then study the influence of the LRC structural disorder on the thermodynamical properties of 2D elastic chains submitted locally to mechanical/topological constraint as loops. The equilibrium properties of the one-loop system are derived numerically and analytically in the quite realistic weak-disorder limit. The LRC are shown to favor the spontaneous formation of small loops, the larger the LRC, the smaller the size of the loop. We further investigate the dynamical behavior of such a loop using the mean first passage time (MFPT) formalism. We show that the typical short-time loop dynamics is superdiffusive in the presence of LRC. For displacements larger than the loop size, we use large-deviation theory to derive a LRC-dependent anomalous-diffusion rule that accounts for the lack of disorder self-averaging. Potential biological implications on DNA loops involved in nucleosome positioning and dynamics in eucaryotic chromatin are discussed.

Turbulence simulations of blob formation and radial propagation in toroidally magnetized plasmas

Two-dimensional numerical fluid turbulence simulations demonstrating the formation and radial propagation of blob structures in toroidally magnetized plasmas are presented and analysed in detail. A salient feature of the model is a linearly unstable edge plasma region with localized sources of particles and heat, which is coupled to a scrape-off layer with linear damping terms for all dependent variables corresponding to transport along open magnetic field lines. The formation of blob structures is related to profile variations caused by bursting in the global turbulence level, which is due to a dynamical regulation by self-sustained differential rotation of the plasma layer. Radial propagation of the blob structures follows from a vertical charge polarization due to magnetic guiding centre drifts in the toroidally magnetized plasma. Statistical analysis of the particle density, radial electric drift and the radial turbulent particle flux reveals asymmetric conditional waveforms with a steep front and a trailing wake and positively skewed and flattened probability distributions, in agreement with recent experimental investigations. Coarse graining and spectral analysis further indicate the presence of long-range correlations in the particle density fluctuations. Finally, conditional statistics of the particle flux demonstrates the intermittency of the turbulent plasma transport and the quasi-periodic apparency of blob structures due to bursting in the global turbulence level.

Thermodynamics of DNA Loops with Long-Range Correlated Structural Disorder

We study the influence of a structural disorder on the thermodynamical properties of 2D-elastic chains submitted to mechanical/topological constraint as loops. The disorder is introduced via a spontaneous curvature whose distribution along the chain presents either no correlation or long-range correlations (LRC). The equilibrium properties of the one-loop system are derived numerically and analytically for weak disorder. LRC are shown to favor the formation of small loop, larger the LRC, smaller the loop size. We use the mean first passage time formalism to show that the typical short time loop dynamics is superdiffusive in the presence of LRC. Potential biological implications on nucleosome positioning and dynamics in eukaryotic chromatin are discussed.

Long-range temporal correlations in the spontaneous spiking of neurons in the hippocampal-amygdala complex of humans

The spontaneous or background discharge patterns of in vivo single neuron is mostly considered as neuronal noise, which is assumed to be devoid of any correlation between successive inter-spike-intervals (ISI). Such random fluctuations are modeled only statistically by stochastic point process, lacking any temporal correlation. In this study, we have investigated the nature of spontaneous irregular fluctuations of single neurons from human hippocampus-amygdala complex by three different methods: (i) detrended fluctuation analysis (DFA), (ii) multiscale entropy (MSE), (iii) rate estimate convergence. Both the DFA and MSE analysis showed the presence of long-range power-law correlation over time in the ISI sequences. Moreover, we observed that the individual spike trains presented non-random structure on longer time-scales and showed slow convergence of rate estimates with increasing counting time. This power-law correlation and the slow convergence of statistical moments were eliminated by randomly shuffling the ISIs even though the distributions of ISIs were preserved. Thus the power-law relationship arose from long-term correlations among ISIs that were destroyed by shuffling the data. Further, we found that neurons which showed long-range correlations also showed statistically significant correlated firing as measured by correlation coefficient or mutual information function. The presence of long-range correlations indicates the history-effect or memory in the firing pattern by the associative formation of a neuronal assembly.

Metal-insulator transition in two-dimensional systems with long-range correlated disorder

We study the localization properties of electrons in a two-dimensional model with on-site energies exhibiting long-range correlated disorder. The localization length and conductance of the system are calculated by using the finite size scaling method combined with transfer matrix technique. In the presence of long-range correlations, we find that there is a continuous line of fixed points indicating that the system undergoes a disorder driven Kosterlitz-Thouless-type metal-insulator transition.

Universal behavior of the resistance noise across the metal-insulator transition in silicon inversion layers.

Studies of low-frequency resistance noise show that the glassy freezing of the two-dimensional (2D) electron system in the vicinity of the metal-insulator transition occurs in all Si inversion layers. The size of the metallic glass phase, which separates the 2D metal and the (glassy) insulator, depends strongly on disorder, becoming extremely small in high-mobility samples. The behavior of the second spectrum, an important fourth-order noise statistic, indicates the presence of long-range correlations between fluctuators in the glassy phase, consistent with the hierarchical picture of glassy dynamics.