arXiv subjects

Shlomo Havlin

Publications and source records attributed to Shlomo Havlin.

At least 289 records · Page 16Linked to original sources

arXiv2001

Correlation Differences in Heartbeat Fluctuations During Rest and Exercise

We study the heartbeat activity of healthy individuals at rest and during exercise. We focus on correlation properties of the intervals formed by successive peaks in the pulse wave and find significant scaling differences between rest and exercise. For exercise the interval series is anticorrelated at short time scales and correlated at intermediate time scales, while for rest we observe the opposite crossover pattern -- from strong correlations in the short-time regime to weaker correlations at larger scales. We suggest a physiologically motivated stochastic scenario to explain the scaling differences between rest and exercise and the observed crossover patterns.

cond-mat.stat-mech↗

arXiv2001

Optimization of congested traffic flow in systems with a localized periodic inhomogeneity

We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's frequency. By studying the wavelength dependence of the flux in stop-and-go traffic states, and exploring their stability, we are able to explain the optimization process. A general conclusion drawn from this study is, that the fundamental diagram of traffic (density flux relation) has to be generalized to include the influence of wavelength on the flux, for the stop-and-go traffic. Projecting the generalized fundamental diagram on the density-flux plane yields a 2D region, qualitatively similar to that found empirically [B. S. Kerner, Phys. Rev. Lett. {\bf 81}, 3797 (1998)] in synchronized flow.

cond-mat.stat-mech↗

arXiv2001

Breakdown of the Internet under intentional attack

We study the tolerance of random networks to intentional attack, whereby a fraction p of the most connected sites is removed. We focus on scale-free networks, having connectivity distribution of P(k)~k^(-a) (where k is the site connectivity), and use percolation theory to study analytically and numerically the critical fraction p_c needed for the disintegration of the network, as well as the size of the largest connected cluster. We find that even networks with a<=3, known to be resilient to random removal of sites, are sensitive to intentional attack. We also argue that, near criticality, the average distance between sites in the spanning (largest) cluster scales with its mass, M, as sqrt(M), rather than as log_k M, as expected for random networks away from criticality. Thus, the disruptive effects of intentional attack become relevant even before the critical threshold is reached.

cond-mat.dis-nn↗

arXiv2001

Magnitude and Sign Correlations in Heartbeat Fluctuations

We propose an approach for analyzing signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and analyzing their scaling properties. We show that signals with identical long-range correlations can exhibit different time organization for the magnitude and sign. We find that the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties. We apply our approach to the heartbeat interval series and find that the magnitude series is long-range correlated, while the sign series is anticorrelated and that both magnitude and sign series may have clinical applications.

cond-mat.stat-mech↗

arXiv2001

`Generalized des Cloizeaux' exponent for self-avoiding walks on the incipient percolation cluster

We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability distribution function for the end-to-end distance r of an N step SAW behaves as a power law for r -> 0. In this work, we determine the corresponding exponent using scaling arguments, and show that our suggested `generalized des Cloizeaux' expression for the exponent is in excellent agreement with exact enumeration results in two and three dimensions.

cond-mat.dis-nn↗

arXiv2001

Detecting Long-range Correlations with Detrended Fluctuation Analysis

We examine the Detrended Fluctuation Analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling that appear at small time scales become stronger in higher orders of DFA, and suggest a modified DFA method to remove them. The improvement is necessary especially for short records that are affected by non-stationarities. Furthermore, we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of DFA.

cond-mat.stat-mech↗

arXiv2000

No indications of metal-insulator transition for systems of interacting electrons in two dimensions

The influence of Coulomb interaction on transport properties of spinless electrons in small disordered two dimensional systems is studied within a tight binding model. Spatial correlations, inverse participation ratio, and multifractal spectrum of the zero temperature local tunneling amplitude as well as the DC Kubo conductance are traced as function of the interaction strength $U$. When $U$ is increased, all of the above quantities are shifted rather smoothly towards localized behavior, indicating the absence of an interaction driven insulator-metal transition.

cond-mat.mes-hall↗

arXiv2000

Universality of the Directed Polymer Model

The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the non-Gaussian cases the \emph{finite size} estimates of the energy exponents are below the persumed universal values, these estimates \emph{increase} with the system size, and the further they are below the universal values, the higher is their rate of increase. The results are explained in terms of the efficiency of variance reduction during the optimization process.

cond-mat.dis-nn↗

arXiv2000

Entropy fluctuations for directed polymers in 2+1 dimensions

We find numerically that the sample to sample fluctuation of the entropy, $ΔS$, is a tool more sensitive in distinguishing how from high temperature behaviors, than the corresponding fluctuation in the free energy. In 1+1 dimensions we find a single phase for all temperatures since $(ΔS)^{2}$ is always extensive. In 2+1 dimensions we find a behavior may look at first sight as a transition from a low temperature phase where $(ΔS)^{2}$ is extensive to a high temperature phase where it is subextensive. This is observed in spite of the relatively large system we use. The observed behavior is explained not as a phase transition but as a strong crossover behavior. We use an analytical agreement to obtain $(ΔS)^{2}$ for high temperature and find that while it is always extensive it is also extremly small and the leading extensive part decays very fast to zero as temperature is increased.

cond-mat.dis-nn↗

arXiv2000

Resilience of the Internet to random breakdowns

A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k)=ck^-a. We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, p_c, that need to be removed before the network disintegrates. We show that for a<=3 the transition never takes place, unless the network is finite. In the special case of the Internet (a=2.5), we find that it is impressively robust, where p_c is approximately 0.99.

cond-mat.dis-nn↗

arXiv2000

Flow Between Two Sites on a Percolation Cluster

We study the flow of fluid in porous media in dimensions $d=2$ and 3. The medium is modeled by bond percolation on a lattice of $L^d$ sites, while the flow front is modeled by tracer particles driven by a pressure difference between two fixed sites (``wells'') separated by Euclidean distance $r$. We investigate the distribution function of the shortest path connecting the two sites, and propose a scaling {\it Ansatz} that accounts for the dependence of this distribution (i) on the size of the system, $L$, and (ii) on the bond occupancy probability, $p$. We confirm by extensive simulations that the {\it Ansatz} holds for $d=2$ and 3, and calculate the relevant scaling parameters. We also study two dynamical quantities: the minimal traveling time of a tracer particle between the wells and the length of the path corresponding to the minimal traveling time ``fastest path'', which is not identical to the shortest path. A scaling {\it Ansatz} for these dynamical quantities also includes the effect of finite system size $L$ and off-critical bond occupation probability $p$. We find that the scaling form for the distribution functions for these dynamical quantities for $d=2$ and 3 is similar to that for the shortest path but with different critical exponents. The scaling form is represented as the product of a power law and three exponential cutoff functions. We summarize our results in a table which contains estimates for all parameters which characterize the scaling form for the shortest path and the minimal traveling time in 2 and 3 dimensions; these parameters are the fractal dimension, the power law exponent, and the constants and exponents that characterize the exponential cutoff functions.

cond-mat.stat-mech↗

arXiv2000

Presence of Many Stable Nonhomogeneous States in an Inertial Car-Following Model

A new single lane car following model of traffic flow is presented. The model is inertial and free of collisions. It demonstrates experimentally observed features of traffic flow such as the existence of three regimes: free, fluctuative (synchronized) and congested (jammed) flow; bistability of free and fluctuative states in a certain range of densities, which causes the hysteresis in transitions between these states; jumps in the density-flux plane in the fluctuative regime and gradual spatial transition from synchronized to free flow. Our model suggests that in the fluctuative regime there exist many stable states with different wavelengths, and that the velocity fluctuations in the congested flow regime decay approximately according to a power law in time.

cond-mat.dis-nn↗

arXiv1999

Directed polymers at finite temperatures in 1+1 and 2+1 dimensions

We present systematic numerical simulations for directed polymers at finite temperatures in 1+1 and 2+1 dimensions. The transverse fluctuations and free energy fluctuations tend to the strong coupling limit at any temperature in both 1+1 and 2+1 dimensions for long time t. Two different definitions for energy fluctuations at finite temperatures, which are the ensemble energy fluctuations and the internal energy fluctuations, are investigated. Apart from zero temperature, the behavior of the energy fluctuations and the free energy fluctuations for directed polymers is shown to be different. At finite temperatures, the ensemble energy fluctuations in both 1+1 and 2+1 dimensions and internal energy fluctuations in 1+1 dimensions scale as t^{1/2} where the free energy fluctuations in 1+1 dimensions and 2+1 dimensions scale as t^{1/3} and t^{0.2} respectively. As a consequence of that the specific heat in both 1+1 and 2+1 dimensions scales as t and the entropy fluctuations in 1+1 dimensions scale as t^{1/2} at any finite temperature.

cond-mat.soft↗

arXiv1999

Distribution function of mesoscopic hopping conductance

We study by computer simulation distribution functions (DF) of mesoscopic hopping conductance. The DFs obtained for one-dimensional systems were found to be quite close to the predictions of the theory by Raikh and Ruzin. For D=2, the DFs both for narrow system and thin film look similar (and close to the 1D case).The distribution function for the conductance of the square sample is nearly Gaussian.

cond-mat.mes-hall↗

arXiv1999

Sleep-Wake Differences in Scaling Behavior of the Human Heartbeat: Analysis of Terrestrial and Long-Term Space Flight Data

We compare scaling properties of the cardiac dynamics during sleep and wake periods for healthy individuals, cosmonauts during orbital flight, and subjects with severe heart disease. For all three groups, we find a greater degree of anticorrelation in the heartbeat fluctuations during sleep compared to wake periods. The sleep-wake difference in the scaling exponents for the three groups is comparable to the difference between healthy and diseased individuals. The observed scaling differences are not accounted for simply by different levels of activity, but appear related to intrinsic changes in the neuroautonomic control of the heartbeat.

cond-mat.stat-mech↗

arXiv1999

Dependence of Conductance on Percolation Backbone Mass

On two-dimensional percolation clusters at the percolation threshold, we study $<σ(M_B,r)>$, the average conductance of the backbone, defined by two points separated by Euclidean distance $r$, of mass $M_B$. We find that with increasing $M_B$ and for fixed r, $<σ(M_B,r)>$ asymptotically {\it decreases} to a constant, in contrast with the behavior of homogeneous sytems and non-random fractals (such as the Sierpinski gasket) in which conductance increases with increasing $M_B$. We explain this behavior by studying the distribution of shortest paths between the two points on clusters with a given $M_B$. We also study the dependence of conductance on $M_B$ slightly above the percolation threshold.

cond-mat.stat-mech↗

arXiv1999

Scaling of the distribution of shortest paths in percolation

We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for {\it (i)} the effect of the finite size of the system, and {\it (ii)} the dependence of this distribution on the site occupancy probability $p$. We test the hypothesis for the case of two-dimensional percolation.

cond-mat.stat-mech↗

arXiv1999

Traveling time and traveling length for flow in porous media

We study traveling time and traveling length for tracer dispersion in porous media. We model porous media by two-dimensional bond percolation, and we model flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance $r$. We find that the minimal traveling time $t_{min}$ scales as $t_{min} \sim r^{1.40}$, which is different from the scaling of the most probable traveling time, ${\tilde t} \sim r^{1.64}$. We also calculate the length of the path corresponding to the minimal traveling time and find $\ell_{min} \sim r^{1.13}$ and that the most probable traveling length scales as ${\tilde \ell} \sim r^{1.21}$. We present the relevant distribution functions and scaling relations.

cond-mat.stat-mech↗