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We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z ? 1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z ≃ 2. [ABSTRACT FROM AUTHOR]

Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socioeconomic changes and climate transitions between ice ages and warm ages. From bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations. The consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition. However, especially in the presence of noise, it is not clear whether these changes in observation variables are statistically relevant such that they could be used as indicators for critical transitions. In this contribution we investigate the predictability of critical transitions in conceptual models. We study the quadratic integrate-and-fire model and the van der Pol model under the influence of external noise. We focus especially on the statistical analysis of the success of predictions and the overall predictability of the system. The performance of different indicator variables turns out to be dependent on the specific model under study and the conditions of accessing it. Furthermore, we study the influence of the magnitude of transitions on the predictive performance. [ABSTRACT FROM AUTHOR]

The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example. [ABSTRACT FROM AUTHOR]

The momentum or velocity autocorrelation function C(t) for a tagged oscillator in a finite harmonic system decays like that of an infinite system for short times, but exhibits erratic behavior at longer time scales. We introduce the autocorrelation function of the long-time noisy tail of C(t) ("a correlation of the correlation"), which characterizes the distribution of recurrence times. Remarkably, for harmonic systems with same-mass particles this secondary correlation may coincide with the primary correlation C(τ) (when both functions are normalized) either exactly, or over a significant initial time interval. When the tagged particle is heavier than the rest, the equality does not hold, correlations show nonrandom long-time scale pattern, and higher-order correlations converge to the lowest normal mode. [ABSTRACT FROM AUTHOR]

We study the occurrence of anticipated synchronization in two complex Ginzburg-Landau systems coupled in a master-slave configuration. Master and slave systems are ruled by the same autonomous function, but the slave system receives the injection from the master and is subject to a negative delayed self-feedback loop. We give evidence that the magnitude of the largest anticipation time, obtained for complex-valued coupling constants, depends on the dynamical regime where the system operates (defect turbulence, phase turbulence, or bichaos) and scales with the linear autocorrelation time of the system. We also provide analytical conditions for the stability of the anticipated synchronization manifold that are in qualitative agreement with those obtained numerically. Finally, we report on the existence of anticipated synchronization in coupled two-dimensional complex Ginzburg-Landau systems. [ABSTRACT FROM AUTHOR]

We present a composite generalized Langevin equation as a unified framework for bridging the hydrodynamic, Brownian, and adhesive spring forces associated with a nanoparticle at different positions from a wall, namely, a bulklike regime, a near-wall regime, and a lubrication regime. The particle velocity autocorrelation function dictates the dynamical interplay between the aforementioned forces, and our proposed methodology successfully captures the well-known hydrodynamic long-time tail with context-dependent scaling exponents and oscillatory behavior due to the binding interaction. Employing the reactive flux formalism, we analyze the effect of hydrodynamic variables on the particle trajectory and characterize the transient kinetics of a particle crossing a predefined milestone. The results suggest that both wall-hydrodynamic interactions and adhesion strength impact the particle kinetics. [ABSTRACT FROM AUTHOR]

Random packing of surfaceless starlike particles built of 3 to 50 line segments was studied using random sequential adsorption algorithm. Numerical simulations allow us to determine saturated packing densities as well as the first two virial expansion coefficients for such objects. Measured kinetics of the packing growth supports the power law known to be valid for particles with a finite surface; however, the dependence of the exponent in this law on the number of star arms is unexpected. The density autocorrelation function shows fast superexponential decay as for disks, but the typical distance between closest stars is much smaller than between disks of the similar size, especially for a small number of arms [ABSTRACT FROM AUTHOR]

We revisit the relation between the shear-stress relaxation modulus G(t), computed at finite shear strain 0 < ɣ ≪ 1, and the shear-stress autocorrelation functions C(t)|ɣ and C(t)|τ computed, respectively, at imposed strain ɣ and mean stress τ. Focusing on permanent isotropic spring networks it is shown theoretically and computationally that in general G(t) = C(t)|τ = C(t)|ɣ + Geq for t > 0 with Geq being the static equilibrium shear modulus. G(t) and C(t)|ɣ thus must become different for solids and it is impossible to obtain Geq alone from C(t)|ɣ as often assumed. We comment briefly on self-assembled transient networks where Geq(ƒ) must vanish for a finite scission-recombination frequency ƒ. We argue that G(t) = C(t)|τ = C(t)|ɣ should reveal an intermediate plateau set by the shear modulus Geq(ƒ = 0) of the quenched network. [ABSTRACT FROM AUTHOR]

We study a nonlinear Langevin equation describing the dynamic variable X(t), the mean field (order parameter) of a finite size complex network at criticality. The conditions under which the autocorrelation function of X shows any direct connection with criticality are discussed. We find that if the network is prepared in a state far from equilibrium, X(0) = 1, the autocorrelation function is characterized by evident signs of critical slowing down as well as by significant aging effects, while the preparation X(0) = 0 does not generate evident signs of criticality on X(t), in spite of the fact that the same initial state makes the fluctuating variable η(t) = sgn(X(f)) yield significant aging effects. These latter effects arise because the dynamics of η(t) are directly dependent on crucial events, namely the re-crossings of the origin, which undergo a significant aging process with the preparation X(0) = 0. The time scale dominated by temporal complexity, aging, and ergodicity breakdown of η(t) is properly evaluated by adopting the method of stochastic linearization which is used to explain the exponential-like behavior of the equilibrium autocorrelation function of X(t). [ABSTRACT FROM AUTHOR]

Effects of the presence of ions, at moderate to high concentrations, on dynamical properties of water molecules are investigated through classical molecular dynamics simulations using two well-known nonpolarizable water models. Simulations reveal that the presence of magnesium chloride (MgCl2) induces perturbations in the hydrogen bond network of water leading to the formation of bulklike domains with "defect sites" on boundaries of such domains: water molecules at such defect sites have less number of hydrogen bonds than those in bulk water. Reorientational autocorrelation functions for dipole vectors of such defect water molecules are computed at different concentrations of ions and compared with system of pure water. Earlier experimental and simulation studies indicate significant differences in reorientational dynamics for water molecules in the first hydration shell of many dissolved ions. Results of this study suggest that defect water molecules, which are beyond the first hydration shells of ions, also experience significant slowing of reorientation times as a function of concentration in the case of MgCl2. However, addition of cesium chloride (CsCl) to water does not perturb the hydrogen bond network of water significantly even at higher concentrations. This difference in behavior between MgCl2 and CsCl is consistent with the well-known Hofmeister series. [ABSTRACT FROM AUTHOR]

We present a detailed experimental characterization of the autocorrelation properties of a delayed feedback semiconductor laser for different dynamical regimes. We show that in many cases the autocorrelation function of laser intensity dynamics can be approximated by the analytically derived autocorrelation function obtained from a linear stochastic model with delay. We extract a set of dynamic parameters from the fit with the analytic solutions and discuss the limits of validity of our approximation. The linear model captures multiple fundamental properties of delay systems, such as the shift and asymmetric broadening of the different delay echoes. Thus, our analysis provides significant additional insight into the relevant physical and dynamical properties of delayed feedback lasers. [ABSTRACT FROM AUTHOR]

We employ Monte Carlo simulations to investigate the nonequilibrium relaxation properties of the two- and three-dimensional Coulomb glass with different long-range repulsive interactions. Specifically, we explore the aging scaling laws in the two-time density autocorrelation function. We find that, in the time window and parameter range accessible to us, the scaling exponents are not universal, depending on the filling fraction and temperature: As either the temperature decreases or the filling fraction deviates more from half filling, the exponents reflect markedly slower relaxation kinetics. In comparison with a repulsive Coulomb potential, appropriate for impurity states in strongly disordered semiconductors, we observe that, for logarithmic interactions, the soft pseudogap in the density of states is considerably broader, and the dependence of the scaling exponents on external parameters is much weaker. The latter situation is relevant for flux creep in the disorder-dominated Bose glass phase of type-II superconductors subject to columnar pinning centers. [ABSTRACT FROM AUTHOR]

We demonstrate diffusing-wave spectroscopy (DWS) in a localized region of a viscoelastically inhomogeneous object by measurement of the intensity autocorrelation [g2(τ)] that captures only the decay introduced by the temperature-induced Brownian motion in the region. The region is roughly specified by the focal volume of an ultrasound transducer which introduces region specific mechanical vibration owing to insonification. Essential characteristics of the localized non-Markovian dynamics are contained in the decay of the modulation depth [M(τ)], introduced by the ultrasound forcing in the focal volume selected, on g2(τ). The modulation depth M(τi) at any delay time τi can be measured by short-time Fourier transform of g2(τ) and measurement of the magnitude of the spectrum at the ultrasound drive frequency. By following the established theoretical framework of DWS, we are able to connect the decay in M(τ) to the mean-squared displacement (MSD) of scattering centers and the MSD to G*(ω), the complex viscoelastic spectrum. A two-region composite polyvinyl alcohol phantom with different viscoelastic properties is selected for demonstrating local DWS-based recovery of G*(ω) corresponding to these regions from the measured region specific M(τi)vsτi. The ultrasound-assisted measurement of MSD is verified by simulating, using a generalized Langevin equation (GLE), the dynamics of the particles in the region selected as well as by the usual DWS experiment without the ultrasound. It is shown that whereas the MSD obtained by solving the GLE without the ultrasound forcing agreed with its experimental counterpart covering small and large values of τ, the match was good only in the initial transients in regard to experimental measurements with ultrasound. [ABSTRACT FROM AUTHOR]

We propose a "phase diagram" for particulate systems with purely repulsive contact forces, such as granular media and colloids. We characterize two classes of behavior as a function of the input kinetic energy per degree of freedom T0 and packing fraction deviation from jamming onset ΔΦ = Φ -- ΦJ using simulations of frictionless disks. Isocoordinated solids (ICS) exist above jamming; they possess an average contact number equal to the isostatic value ziso. ICS display "strict" harmonic response, where the density of vibrational modes from the Fourier transform of the velocity autocorrelation function is a set of sharp peaks at eigenfrequencies ωkd of the dynamical matrix. In contrast, hypocoordinated solids (HCS) occur above and below jamming and possess fluctuating networks of interparticle contacts but do not undergo cage-breaking particle rearrangements. The density of vibrational frequencies for the HCS is not a collection of sharp peaks at ωkd, but it does possess a common form over a range of ΔΦ and T0. [ABSTRACT FROM AUTHOR]

Over the last 15 years, x-ray microtomography has become a useful technique to obtain morphological, structural, and topological information on materials. Moreover, these three-dimensional (3D) images can be used as input data to assess certain properties (e.g., permeability) or to simulate phenomena (e.g., transfer properties). In order to capture all the features of interest, high spatial resolution is required. This involves imaging small samples, raising the question of the representativity of the data sets. In this article, we (i) present a methodology to analyze the microstructural properties of complex porous media from 3D images, (ii) assess statistical representative elementary volumes (REVs) for such materials; and (iii) establish criteria to delimit these REVs. In the context of cultural heritage conservation, a statistical study was done on 30 quarry samples for three sorts of stones. We first present the principles of x-ray microtomography experiments and emphasize the care that must be taken in the 3D image segmentation steps. Results show that statistical REVs exist for these media and are reached for the image sizes studied (1300 x 1300 x 1000 voxels) for two characteristics: porosity and chord length distributions. Furthermore, the estimators used (porosity, autocorrelation function, and chord length distributions) are sufficiently sensitive to quantitatively distinguish these three porous media from each other. Lastly, this study puts forward criteria based on the above-mentioned estimators to evaluate the REVs. These criteria avoid having to repeat the statistical study for each new material studied. This is particularly relevant to quantitatively monitor the modifications in materials (weathering, deformation ... ) or to determine the smallest 3D volume for simulation in order to reduce computing time. [ABSTRACT FROM AUTHOR]

Saturated random packing of particles built of two identical, relatively shifted spheres in two- and three-dimensional flat and homogeneous space was studied numerically using a random sequential adsorption algorithm. The shift between centers of spheres varied from 0.0 to 8.0 sphere diameters. Numerical simulations allowed the determination of random sequential adsorption kinetics, the saturated random coverage ratio, as well as the available surface function and density autocorrelation function. [ABSTRACT FROM AUTHOR]

We review ideas on temporal dependencies and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework to study nonlinear time dependencies and related concepts--like aftershocks, Omori law, recurrences, and waiting times. We also critically argue, using this global approach, that previous phenomenological attempts involving only a long-ranged autocorrelation function lacked complexity in that they were essentially monoscale. [ABSTRACT FROM AUTHOR]

We investigate the effect of an external magnetic field on the velocity autocorrelation function and the "caging" of the particles in a two-dimensional strongly coupled Yukawa liquid, via numerical simulations. The influence of the coupling strength on the position of the dominant peak in the frequency spectrum of the velocity autocorrelation function confirms the onset of a joint effect of the magnetic field and strong correlations at high coupling. Our molecular dynamics simulations quantify the decorrelation of the particles' surroundings: the magnetic field is found to increase significantly the caging time, which reaches values well beyond the time scale of plasma oscillations. The observation of the increased caging time is in accordance with findings that the magnetic field decreases diffusion in similar systems. [ABSTRACT FROM AUTHOR]

Extended dynamical simulations have been performed on a (2 + l)-dimensional driven dimer lattice-gas model to estimate aging properties. The autocorrelation and the autoresponse functions are determined and the corresponding scaling exponents are tabulated. Since this model can be mapped onto the (2 + l)-dimensional Kardar-Parisi-Zhang surface growth model, our results contribute to the understanding of the universality class of that basic system. [ABSTRACT FROM AUTHOR]

In a plane Couette cell a thin fluid layer consisting of water is sheared between the sides of a transparent band at Reynolds numbers ranging from 300 to 1400. The length of the cell's flow channel is large compared to the film separation. To extract the flow velocity in the experiments, a correlation image velocimetry method is used on pictures recorded with a high-speed camera. The flow is recorded at a resolution that allows us to analyze flow patterns similar in size to the film separation. The fluid flow is then studied by calculating flow velocity autocorrelation functions. The turbulent patterns that arise on this scale above a critical Reynolds number of Re = 360 display characteristic patterns that are proven by use of the calculated velocity autocorrelation functions. The patterns are metastable and reappear at different positions and times throughout the experiments. Typically these patterns are turbulent rolls which are elongated in the stream direction, which is the direction in which the band is moving. Although the flow states are metastable they possess similarities to the steady Taylor vortices known to appear in circular Taylor Couette cells. [ABSTRACT FROM AUTHOR]

We consider a generalized Langevin equation that can be used to describe thermal motion of a tracer in a viscoelastic medium by accounting for inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. We derive a Laplace-type integral representation for the linear response function that governs the diffusive dynamics. This representation is particularly well suited for rapid numerical computation and theoretical analysis. In particular, we deduce explicit formulas for the mean and variance of the time averaged (TA) mean square displacement (MSD) and velocity autocorrelation function (VACF). The asymptotic behavior of the TA MSD and TA VACF is investigated at different time scales. Some biophysical and microrheological applications are discussed, with an emphasis on the statistical analysis of optical tweezers' single-particle tracking experiments in polymer networks and living cells. [ABSTRACT FROM AUTHOR]

We derive exact expressions for the autocorrelation and cross-correlation functions of wave forms generated by two exactly solvable chaotic systems. For each system, an analytic expression exists for chaotic solutions, which we use to evaluate correlation integrals explicitly. For some specific parameter values, we calculate the mean and variance of the correlation functions averaged over all possible solutions. The mean autocorrelation is shown to decay at a rate equal to the Kolmogorov-Sinai entropy. All derived results are shown to agree with numerical calculations of the corresponding quantities. [ABSTRACT FROM AUTHOR]

We study statistics of entanglement generated by quantum chaotic dynamics. Using an ensemble of the very large number (≲107) of quantum states obtained from the temporally evolving coupled kicked tops, we verify that the estimated one-body distribution of the squared Schmidt eigenvalues for the quantum chaotic dynamics can agree surprisingly well with the analytical one for the universality class of the random matrices described by the fixed trace ensemble (FTE). In order to quantify this agreement, we introduce the V norm of the difference between the one-body distributions for the quantum chaos and FTE and use it as an indicator of the dynamical randomness. As we increase the scaled coupling constant, the L¹ difference decreases. When the effective Planck constant is not small enough, the decrease saturates, which implies quantum suppression of dynamical randomness. On the other hand, when the effective Planck constant is small enough, the decrease of the L¹ difference continues until it is masked by statistical fluctuation due to finiteness of the ensemble. Furthermore, we carry out two statistical analyses, the x² goodness of fit test and an autocorrelation analysis, on the difference between the distributions to seek for dynamical remnants buried under the statistical fluctuation. We observe that almost all fluctuating deviations are statistical. However, even for well-developed quantum chaos, unexpectedly, we find a slight nonstatistical deviation near the largest Schmidt eigenvalue. In this way, the statistics of Schmidt eigenvalues enables us to measure dynamical randomness of quantum chaos with reference to the random matrix theory of FTE. [ABSTRACT FROM AUTHOR]

We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A 392,2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R2 of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible. [ABSTRACT FROM AUTHOR]

A generalization of the Faxén's theorem to the nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow is presented. From this result, expressions for the velocity autocorrelation function (VAF) and the time-dependent diffusion coefficient of the particle can be obtained. We analyze the behavior of the VAF and the time-dependent diffusion coefficient for different physical regimes of the suspending fluid. The relevance of the theorem to microrheology is discussed. [ABSTRACT FROM AUTHOR]

We use state-of-the-art molecular dynamics simulations to study hydrodynamic effects on aging during kinetics of phase separation in a fluid mixture. The domain growth law shows a crossover from a diffusive regime to a viscous hydrodynamic regime. There is a corresponding crossover in the autocorrelation function from a power-law behavior to an exponential decay. While the former is consistent with theories for diffusive domain growth, the latter results as a consequence of faster advective transport in fluids for which an analytical justification has been provided. [ABSTRACT FROM AUTHOR]

The momentum relaxation of a relativistic Brownian particle immersed in a fluid is studied on the basis of the Fokker-Planck equation for the relativistic Ornstein-Uhlenbeck process. An analytical expression is derived for the short-time relaxation rate. The relaxation spectrum has both discrete and continuum components. It is shown that the Fokker-Planck equation under consideration is closely related to the Schrodinger equation for the hydrogen atom. Hence it follows that there is an infinite number of discrete states. The momentum autocorrelation function is calculated numerically for a strongly relativistic particle. [ABSTRACT FROM AUTHOR]

The emergent fluctuating hydrodynamics of the multiparticle collision dynamics (MPC) approach, a particle-based mesoscale simulation technique for fluid dynamics, is analyzed theoretically and numerically. We focus on the stochastic rotation dynamics implementation of the MPC method. The fluid is characterized by its longitudinal and transverse velocity correlation functions in Fourier space and velocity autocorrelation functions in real space. Particular attention is paid to the role of sound, which leads to piecewise negative correlation functions. Moreover, finite system-size effects are addressed with an emphasis on the role of sound. Analytical expressions are provided for the transverse and longitudinal velocity correlations, which are derived from the linearized Landau-Lifshitz Navier-Stokes equation adopted for an isothermal MPC fluid. The comparison of-the analytical results with simulations shows excellent agreement above a minimal length scale. The simulations indicate a breakdown in hydrodynamics on length scales smaller than this minimal length. This demonstrates that we have an excellent analytical description and understanding of the MPC method and its limitations in terms of time and length scales. [ABSTRACT FROM AUTHOR]

Thermostats for homogeneous nonequilibrium molecular dynamics simulations are usually designed to control the kinetic temperature, but it is now possible control any combination of many different types of temperature, including the configurational and kinetic temperatures and their directional components. It is well known that these temperatures can become unequal in homogeneously thermostatted shearing steady states. The microscopic expressions for these temperatures are all derived from equilibrium distribution functions, and it is pertinent to ask, what are the consequences of using these equilibrium microscopic expressions for temperature in thermostats for shearing nonequilibrium steady states? Here we show that the answer to this question depends on which properties are being investigated. We present numerical results showing that the value of the zero shear rate viscosity obtained by extrapolating results of nonequilibrium molecular dynamics simulations of shearing steady states is the same, regardless of the type of temperature that is controlled. It also agrees with the value obtained from the equilibrium stress autocorrelation function via the Green-Kubo relation. However, the values of the limiting zero shear rate first normal stress coefficient obtained from nonequilibrium molecular dynamics simulations of shearing steady states are strongly dependent on the choice of temperature being controlled. They also differ from the value of the first normal stress coefficient that is calculated from the equilibrium stress autocorrelation function. We show that even when all of the directional components of the kinetic and configurational temperatures are simultaneously controlled to the same value, the agreement with the result obtained from the equilibrium stress autocorrelation function is poor. [ABSTRACT FROM AUTHOR]

Using Monte Carlo simulations, we show that the autocorrelation function C(t) in the d = 3 Ising model with a plaquette interaction has a stretched-exponential decay in a supercooled liquid phase. Such a decay characterizes also some ground-state probability distributions obtained from the numerically exact counting of up to 10450 configurations. A related model with a strongly degenerate ground state but lacking glassy features does not exhibit such a decay. Although the stretched exponential decay of C(t) in the three-dimensional supercooled liquid is inconsistent with the droplet model, its modification that considers tensionless droplets might explain such a decay. An indication that tensionless droplets might play some role comes from the analysis of low-temperature domains that compose the glassy state. It shows that the energy of a domain of size l scales as l1.15, hence these domains are indeed tensionless. [ABSTRACT FROM AUTHOR]

For many real-world networks only a small "sampled" version of the original network may be investigated; those results are then used to draw conclusions about the actual system. Variants of breadth-first search (BFS) sampling, which are based on epidemic processes, are widely used. Although it is well established that BFS sampling fails, in most cases, to capture the IN component(s) of directed networks, a description of the effects of BFS sampling on other topological properties is all but absent from the literature. To systematically study the effects of sampling biases on directed networks, we compare BFS sampling to random sampling on complete large-scale directed networks. We present new results and a thorough analysis of the topological properties of seven complete directed networks (prior to sampling), including three versions of Wikipedia, three different sources of sampled World Wide Web data, and an Internet-based social network. We detail the differences that sampling method and coverage can make to the structural properties of sampled versions of these seven networks. Most notably, we find that sampling method and coverage affect both the bow-tie structure and the number and structure of strongly connected components in sampled networks. In addition, at a low sampling coverage (i.e., less than 40%), the values of average degree, variance of out-degree, degree autocorrelation, and link reciprocity are overestimated by 30% or more in BFS-sampled networks and only attain values within 10% of the corresponding values in the complete networks when sampling coverage is in excess of 65%. These results may cause us to rethink what we know about the structure, function, and evolution of real-world directed networks. [ABSTRACT FROM AUTHOR]

The interaction of two diffusing particles is strongly influenced by their hydrodynamic coupling. At a tracking rate of 10 kHz we are able to measure the 3D trajectories of two colloidal spheres in a single harmonic potential, which was generated by scanning line optical tweezers. This common potential enables tilting, rotational, and translational dynamics of the spheres, which we analyzed via the spheres position cross-correlations C(τ) over a time range of 10-4-2 s. We found that the dynamic interaction of the colloids is controlled by short-range surface forces Fs, which are attractive in one direction and repulsive in the other two directions. This unexpected behavior is supported by a theoretical model using two Langevin equations, which decouple for linear Fs, allowing a description with autocorrelation functions for collective and relative motions. We further demonstrate that variations in salt concentration and reaction volumes significantly influence C(τ) and the mean contact times between the particles, which may offer new insights into biological particle interaction. [ABSTRACT FROM AUTHOR]

This article presents the study of the generic behavior of viscosity of liquids based on some simple theoretical models, the soft-spheres and Lennard-Jones systems. The use of these simple models allows us to investigate in detail the viscosity behavior in a wide range of temperatures and pressures including the high-temperature-high- pressure limits. Based on the simulation results, we discuss the shape of isoviscosity lines and analyze the glass transition at high temperatures and high pressures. Despite the fact that the viscosity drastically increases in the limit of high temperatures and high pressures along the melting line, the relaxation time rapidly decreases `in this region, and the system becomes further from the glass transition. [ABSTRACT FROM AUTHOR]

We study the effect of, noise recycling on nonequilibrium escape dynamics in a bistable system. For small noise, the non-Markovian problem is reduced to a two-state model with the master equation depending on not only the current state but also the earlier state, based on which we are able to derive the analytical formulas for the switching rate, the autocorrelation function, and the power spectrum density (PSD). Both the theoretical and the numerical results show that, with modulating the time delay in noise recycling, a monotonie PSD may switch to a nonmonotonic one; the amplitude of PSD at resonance frequency exhibits a pronounced maximum at a certain noise level, declaring the onset of stochastic resonance (SR) in the absence of a weak periodic signal. Further, we also demonstrate that the linear response to the external periodic force displays a maximum at a certain level of time delay, displaying the signature of SR. [ABSTRACT FROM AUTHOR]

We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (cm.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The cm. velocity autocorrelation function (cm. VAF) exhibits a slow power law relaxation in the time range between the monomer time t1 and the Rouse relaxation time tN. We obtain an analytical expression for the cm. VAF in terms of molecular parameters. In particular, the cm. VAF scales as -- N-1t5/4 (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted --t5/4 dependence of the cm. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper]. [ABSTRACT FROM AUTHOR]

A mode-coupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [Farago, Meyer, and Semenov, Phys. Rev. Lett. 107, 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the density-based MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the center-of-mass velocity autocorrelation function (cm. VAF). We show that in most cases the VHI mechanism is domiijant; for long chains and prediffusive times it yields a negative tail ∝--N-1/2t-3/2 for the cm. VAF. The case of non-momentum-conserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first --N-15/4t-5/4 (as in the dMCT approach), then --N-1/2t-3/2. Both the amplitude and the duration of the first t-5/4 stage crucially depend on the Langevin friction parameter y. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the cm. VAF, thus account for the anomalous subdiffusive regime of the cm. mean square displacement widely observed in numerical and experimental works. [ABSTRACT FROM AUTHOR]

We present a method for the testing of significance when evaluating the coherence of two oscillatory time series that may have variable amplitude and frequency. It is based on evaluating the self-correlations of the time series. We demonstrate our approach by the application of wavelet-based coherence measures to artificial and physiological examples. Because coherence measures of this kind are strongly biased by the spectral characteristics of the time series, we evaluate significance by estimation of the characteristics of the distribution of values that may occur due to chance associations in the data. The expectation value and standard deviation of this distribution are shown to depend on the autocorrelations and higher order statistics of the data. Where the coherence value falls outside this distribution, we may conclude that there is a causal relationship between the signals regardless of their spectral similarities or differences. [ABSTRACT FROM AUTHOR]

We analyze the dissipative dynamics of a particle governed by a two-dimensional generalized Langevin equation with coupled fractional Gaussian noise and white noise in its respective coordinates, assuming the lowest-order coupling form. Two situations are studied: In the first the particle is free from external force and in the second the particle is subject to a two-dimensional harmonic potential. We derive the general expressions for the mean values, variances, and velocity autocorrelation function and evaluate their temporal evolutions via the numerical Laplace inversion technique. Through the analytical results of the short-time and long-time behaviors, we also explicitly elucidate the effects of fluctuation correlation coupling and interoscillator coupling on the dynamic behaviors of the particle. It is shown that in both situations the couplings do not affect the short-time behavior of self-diffusions in each coordinate, and the subdiffusive and normal diffusive features of these processes resemble those in a one-dimensional system with fractional Gaussian noise and white noise, respectively. However, over a long time period, the fluctuation correlation extends the characteristic time scales for the self-diffusions of a free particle; while only the interoscillator coupling induces a retardation of the relaxation processes of a bounded particle toward equilibrium. Moreover, both couplings generate a cross diffusion, whose long-time approximation has two possible forms, the selection of which depends on the relevant time scales of self-diffusions in each coordinate. [ABSTRACT FROM AUTHOR]

Anomalous diffusion of a particle in a cosine periodic potential is treated using fractional diffusion equations in both phase and configuration space. Exact solutions of two distinct forms of the fractional Klein-Kramers (Fokker-Planck) equation for the distribution function in phase space are obtained via matrix continued fractions yielding the average velocity, the velocity autocorrelation function, its spectrum, etc. In the overdamped limit, the results yielded by both equations agree with those from a fractional probability density diffusion equation in configuration space. A simple analytic solution for the spectrum of the velocity correlation function is also given using the effective eigenvalue approximation. The results represent generalizations of the conventional solutions for the normal diffusion of a Brownian particle in a cosine potential to fractional dynamics (giving rise to anomalous diffusion). [ABSTRACT FROM AUTHOR]

The population activity of random networks of excitatory and inhibitory leaky integrate-and-fire neurons has been studied extensively. In particular, a state of asynchronous activity with low firing rates and low pairwise correlations emerges in sparsely connected networks. We apply linear response theory to evaluate the influence of detailed network structure on neuron dynamics. It turns out that pairwise correlations induced by direct and indirect network connections can be related to the matrix of direct linear interactions. Furthermore, we study the influence of the characteristics of the neuron model. Interpreting the reset as self-inhibition, we examine its influence, via the spectrum of single-neuron activity, on network autocorrelation functions and the overall correlation level. The neuron model also affects the form of interaction kernels and consequently the time-dependent correlation functions. We find that a linear instability of networks with Erdös-Rényi topology coincides with a global transition to a highly correlated network state. Our work shows that recurrent interactions have a profound impact on spike train statistics and provides tools to study the effects of specific network topologies. [ABSTRACT FROM AUTHOR]

We consider two complementary polymer strands of length L attached by a common-end monomer. The two strands bind through complementary monomers and at low temperatures form a double-stranded conformation (zipping), while at high temperature they dissociate (unzipping). This is a simple model of DNA (or RNA) hairpin formation. Here we investigate the dynamics ofthe strands at the equilibrium critical temperature T = Tc using Monte Carlo Rouse dynamics. We find that the dynamics is anomalous, with a characteristic time scaling as &tgr; ∼ L2.26(2), exceeding the Rouse time ∼L2.18. We investigate the probability distribution function, velocity autocorrelation function, survival probability, and boundary behavior ofthe underlying stochastic process. These quantities scale as expected from a fractional Brownian motion with a Hurst exponent H = 0.44(1). We discuss similarities to and differences from unbiased polymer translocation. [ABSTRACT FROM AUTHOR]

The autocorrelation function of pattern fluctuation is used to study soft-mode turbulence (SMT), a spatiotemporal chaos observed in homeotropic nematics. We show that relaxation near the electroconvection threshold deviates from the exponential. To describe this relaxation, we propose a compressed exponential appearing in dynamics of glass-forming liquids. Our findings suggest that coherent motion contributes to SMT dynamics. We also confirmed that characteristic time is inversely proportional to electroconvection's control parameter. [ABSTRACT FROM AUTHOR]

We show that an exact solution of the generalized Langevin equation (GLE) for the autocorrelations of a many-body classical system can be given in an exponential functionality (EF) form. As a consequence, the power spectrum of the correlation has a Lorentzian functionality, i.e., is represented by an infinite sum of Lorentzian functions corresponding to the eigenmodes of the considered correlation. By means of the simple derivation of the GLE by M. H. Lee [Phys. Rev. B 26, 2547 (1982)], we also show that, in practical cases of interest to experimental spectroscopies, possible approximations of the EF are related to a reduction of the relevant dynamical variables via a restriction of the dimensions of the orthogonalized space onto which the dynamics of the system is projected. [ABSTRACT FROM AUTHOR]

The dynamic modulus G* of a viscoelastic medium is often measured by following the trajectory of a small bead subject to Brownian motion in a method called "passive microbead rheology." This equivalence between the positional autocorrelation function of the tracer bead and G* is assumed via the generalized Stokes-Einstein relation (GSER). However, inertia of both bead and medium are neglected in the GSER so that the analysis based on the GSER is not valid at high frequency where inertia is important. In this paper we show how to treat both contributions to inertia properly in one-bead passive microrheological analysis. A Maxwell fluid is studied as the simplest example of a viscoelastic fluid to resolve some apparent paradoxes of eliminating inertia. In the original GSER, the mean-square displacement (MSD) of the tracer bead does not satisfy the correct initial condition. If bead inertia is considered, the proper initial condition is realized, thereby indicating an importance of including inertia, but the MSD oscillates at a time regime smaller than the relaxation time of the fluid. This behavior is rather different from the original result of the GSER and what is observed. What is more, the discrepancy from the GSER result becomes worse with decreasing bead mass, and there is an anomalous gap between the MSD derived by naively taking the zero-mass limit in the equation of motion and the MSD for finite bead mass as indicated by McKinley et al. [J. Rheol. 53, 1487 (2009)]. In this paper we show what is necessary to take the zero-mass limit of the bead safely and correctly without causing either the inertia] oscillation or the anomalous gap, while obtaining the proper initial condition. The presence of a very small purely viscous element can be used to eliminate bead inertia safely once included in the GSER. We also show that if the medium contains relaxation times outside the window where the single-mode Maxwell behavior is observed, the oscillation can be attenuated inside the window. This attenuation is realized even in the absence of a purely viscous element. Finally, fluid inertia also affects the bead autocorrelation through the Basset force and the fluid dragged around with the bead. We show that the Basset force plays the same role as the purely viscous element in high-frequency regime, and the oscillation of MSD is suppressed if fluid density and bead density are comparable. [ABSTRACT FROM AUTHOR]

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image reconstruction and statistical inference. Here, methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals. In particular, the generalized Wiener filter methodology, as developed within information field theory, is shown to significantly improve estimates based on only a few sampling probes, in cases in which some form of continuity of the solution can be assumed. The strength, length scale, and precise functional form of the exploited autocorrelation function of the matrix diagonal is determined from the probes themselves. The developed algorithm is successfully applied to mock and real world problems. These performance tests show that, in situations where a matrix diagonal has to be calculated from only a small number of computationally expensive probes, a speedup by a factor of 2 to 10 is possible with the proposed method. [ABSTRACT FROM AUTHOR]

We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow. [ABSTRACT FROM AUTHOR]

In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics, but also on the length of the observation window over which the correlation is calculated. In this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales, a quantity that provides a convenient proxy for the spike count correlation. Over short time scales, we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference. Our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales. We also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales. These analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type I oscillators transfer correlations more faithfully than do type II over long time scales, while the reverse holds true for the better understood case of short time scales. [ABSTRACT FROM AUTHOR]

We consider a particle immersed in a thermal reservoir and simultaneously subjected to an external random force that drives the system to a nonequilibrium situation. Starting from a Langevin equation description, we derive exact expressions for the mean-square displacement and the velocity autocorrelation function of the diffusing particle. An effective temperature is introduced to characterize the deviation from the internal equilibrium situation. Using a power-law force autocorrelation function, the mean-square displacement and the velocity autocorrelation function are analytically obtained in terms of Mittag-Leffler functions. In this case, we show that the present model exhibits a superdiffusive regime as a consequence of the competition between passive and active processes. [ABSTRACT FROM AUTHOR]

The predictions of the mode-coupling theory (MCT) for the dynamical arrest scenarios in a partly pinned (PP) fluid system are reported. The corresponding dynamical phase diagram is found to be very similar to that of a related quenched-annealed (QA) system. The only significant qualitative difference lies in the shape of the diffusion-localization lines at high matrix densities, with a reentry phenomenon for the PP system but not for the QA model, in full agreement with recent computer simulation results. This finding clearly lends support to the predictive power of the MCT for fluid-matrix systems. In addition, the predictions of the MCT are shown to be in stark contrast with those of the random first-order transition theory. The PP systems are thus confirmed as very promising models for differentiating tests of theories of the glass transition. [ABSTRACT FROM AUTHOR]

We investigate hydrodynamic fluctuations in a two-dimensional granular fluid excited by a vibrating base and in the presence of gravity, focusing on the transverse velocity modes. Since the system is inhomogeneous, we measure fluctuations in horizontal layers whose width is smaller than the characteristic hydrodynamic lengths: they can be considered as almost-homogeneous subsystems. The large time decay of the autocorrelations of modes is exponential and compatible with vorticity diffusion due to shear viscosity, as in equilibrium fluids. The velocity structure factor, which strongly deviates from the equilibrium constant behavior, is well reproduced by an effective fluctuating hydrodynamics described by two noise terms: the first associated with vorticity diffusion and the second with the local energy exchange, which have internal and external character, respectively. [ABSTRACT FROM AUTHOR]