arXiv subjects

E. Ben-Naim

Publications and source records attributed to E. Ben-Naim.

At least 91 records · Page 5Linked to original sources

arXiv2002

Impurity in a Granular Fluid

We investigate velocity statistics of an impurity immersed in a uniform granular fluid. An analytic solution of the inelastic Maxwell model shows that a phase transition occurs in the cooling case. Light impurities have similar velocity statistics as the fluid background, although their temperature is generally different. Asymptotically, the temperature ratio increases with the impurity mass, and it diverges at some critical mass. Impurities heavier than this critical mass essentially scatter of a static fluid background. The impurity velocity distribution is generally characterized by multiscaling asymptotic behavior of its moments. Additionally, in the heavy impurity phase, it consists of modified replicas of the initial distribution.

cond-mat.stat-mech↗

arXiv2002

Kinetic Theory of Traffic Flows

We describe traffic flows in one lane roadways using kinetic theory, with special emphasis on the role of quenched randomness in the velocity distributions. When passing is forbidden, growing clusters are formed behind slow cars and the cluster velocity distribution is governed by an exact Boltzmann equation which is linear and has an infinite memory. The distributions of the cluster size and the cluster velocity exhibit scaling behaviors, with exponents dominated solely by extremal characteristics of the intrinsic velocity distribution. When passing is allowed, the system approaches a steady state, whose nature is determined by a single dimensionless number, the ratio of the passing time to the collision time, the two time scales in the problem. The flow exhibits two regimes, a laminar flow regime, and a congested regime where large slow clusters dominate the flow. A phase transition separates these two regimes when only the next-to-leading car can pass.

cond-mat.stat-mech↗

arXiv2002

Scaling, Multiscaling, and Nontrivial Exponents in Inelastic Collision Processes

We investigate velocity statistics of homogeneous inelastic gases using the Boltzmann equation. Employing an approximate uniform collision rate, we obtain analytic results valid in arbitrary dimension. In the freely evolving case, the velocity distribution is characterized by an algebraic large velocity tail, P(v,t) ~ v^{-sigma}. The exponent sigma(d,epsilon), a nontrivial root of an integral equation, varies continuously with the spatial dimension, d, and the dissipation coefficient, epsilon. Although the velocity distribution follows a scaling form, its moments exhibit multiscaling asymptotic behavior. Furthermore, the velocity autocorrelation function decays algebraically with time, A(t)= ~ t^{-alpha}, with a non-universal dissipation-dependent exponent alpha=1/epsilon. In the forced case, the steady state Fourier transform is obtained via a cumulant expansion. Even in this case, velocity correlations develop and the velocity distribution is non-Maxwellian.

cond-mat.stat-mech↗

arXiv2001

Nontrivial Velocity Distributions in Inelastic Gases

We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In the freely evolving case, we find that the velocity distribution decays algebraically, P(v,t) ~ v^{-sigma} for sufficiently large velocities. We derive the exponent sigma(d,epsilon), which exhibits nontrivial dependence on both d and epsilon, exactly. In the forced case, the velocity distribution approaches a steady-state with a Gaussian large velocity tail.

cond-mat.stat-mech↗

arXiv2001

Entropic Tightening of Vibrated Chains

We investigate experimentally the distribution of configurations of a ring with an elementary topological constraint, a ``figure-8'' twist. Using vibrated granular chains, which permit controlled preparation and direct observation of such a constraint, we show that configurations where one of the loops is tight and the second is large are strongly preferred. This agrees with recent predictions for equilibrium properties of topologically-constrained polymers. However, the dynamics of the tightening process weakly violate detailed balance, a signature of the nonequilibrium nature of this system.

cond-mat.soft↗

arXiv2001

Stable Distributions in Stochastic Fragmentation

We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail. Furthermore, the entire range of acceptable values of decay exponent consistent with the length conservation can be realized. We show that the stochastic fragmentation process is non-self-averaging as moments exhibit significant sample-to-sample fluctuations. Additionally, we find that the distributions of the moments and of extremal characteristics possess an infinite set of progressively weaker singularities.

cond-mat.stat-mech↗

arXiv2001

Parity and Ruin in a Stochastic Game

We study an elementary two-player card game where in each round players compare cards and the holder of the smallest card wins. Using the rate equations approach, we treat the stochastic version of the game in which cards are drawn randomly. We obtain an exact solution for arbitrary initial conditions. In general, the game approaches a steady state where the card densities of the two players are proportional to each other. The leading small size behavior of the initial card densities determines the corresponding proportionality constant, while the next correction governs the asymptotic time dependence. The relaxation towards the steady state exhibits a rich behavior, e.g., it may be algebraically slow or exponentially fast. Moreover, in ruin situations where one player eventually wins all cards, the game may even end in a finite time.

nlin.AO↗

arXiv2001

Extremal properties of random trees

We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights approaches a traveling wave form. The wave front in the minimal case is governed by the small-extremal-height tail of the distribution, and conversely, the front in the maximal case is governed by the large-extremal-height tail of the distribution. We determine several statistical characteristics of the extremal height distribution analytically. In particular, the expected minimal and maximal heights grow logarithmically with the tree size, N, hmin ~ vmin ln N, and hmax ~ vmax ln N, with vmin=0.373365 and vmax=4.31107, respectively. Corrections to this asymptotic behavior are of order O(ln ln N).

cond-mat.stat-mech↗

arXiv2000

Knots and Random Walks in Vibrated Granular Chains

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with the theoretical values.

cond-mat.soft↗

arXiv2000

Fragmentation with a Steady Source

We investigate fragmentation processes with a steady input of fragments. We find that the size distribution approaches a stationary form which exhibits a power law divergence in the small size limit, P(x) ~ x^{-3}. This algebraic behavior is robust as it is independent of the details of the input as well as the spatial dimension. The full time dependent behavior is obtained analytically for arbitrary inputs, and is found to exhibit a universal scaling behavior.

cond-mat.stat-mech↗

arXiv2000

Stochastic Aggregation: Rate Equations Approach

We investigate a class of stochastic aggregation processes involving two types of clusters: active and passive. The mass distribution is obtained analytically for several aggregation rates. When the aggregation rate is constant, we find that the mass distribution of passive clusters decays algebraically. Furthermore, the entire range of acceptable decay exponents is possible. For aggregation rates proportional to the cluster masses, we find that gelation is suppressed. In this case, the tail of the mass distribution decays exponentially for large masses, and as a power law over an intermediate size range.

cond-mat.stat-mech↗

arXiv2000

Stochastic Aggregation: Scaling Properties

We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents corresponding to the survival probability of particles and monomers. The overall behavior agrees qualitatively with the mean-field theory. This theory also provides a useful approximation for the decay exponents, as well as the limiting mass distribution.

cond-mat.stat-mech↗

arXiv1999

Dynamics of Vibrated Granular Monolayers

We study statistical properties of vibrated granular monolayers using molecular dynamics simulations. We show that at high excitation strengths, the system is in a gas state, particle motion is isotropic, and the velocity distributions are Gaussian. As the vibration strength is lowered the system's dimensionality is reduced from three to two. Below a critical excitation strength, a gas-cluster phase occurs, and the velocity distribution becomes bimodal. In this phase, the system consists of clusters of immobile particles arranged in close-packed hexagonal arrays, and gas particles whose energy equals the first excited state of an isolated particle on a vibrated plate.

cond-mat.soft↗

arXiv1999

Scale Invariance and Lack of Self-Averaging in Fragmentation

We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d dimensions, the volume distribution diverges algebraically in the small fragment limit, P(V)\sim V^{-γ} with γ=2p^{1/d}. Hence, the entire range of exponents allowed by mass conservation is realized. We demonstrate that this fragmentation process is non-self-averaging. Specifically, the moments Y_α=\sum_i x_i^α exhibit significant fluctuations even in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv1999

Shock-Like Dynamics of Inelastic Gases

We provide a simple physical picture which suggests that the asymptotic dynamics of inelastic gases in one dimension is independent of the degree of inelasticity. Statistical characteristics, including velocity fluctuations and the velocity distribution are identical to those of a perfectly inelastic sticky gas, which in turn is described by the inviscid Burgers equation. Asymptotic predictions of this continuum theory, including the t^{-2/3} temperature decay and the development of discontinuities in the velocity profile, are verified numerically for inelastic gases.

cond-mat.stat-mech↗

arXiv1999

Multiscaling in Infinite Dimensional Collision Processes

We study relaxation properties of two-body collisions in infinite spatial dimension. We show that this process exhibits multiscaling asymptotic behavior as the underlying distribution is characterized by an infinite set of nontrivial exponents. These nonequilibrium relaxation characteristics are found to be closely related to the steady state properties of the system.

cond-mat.stat-mech↗

arXiv1999

Comment on ``Dynamic Scaling in the Spatial Distribution of Persistent Sites''

In a recent paper (cond-mat/9901130), the spatial distribution of unvisited sites in the one-dimensional single-species annihilation process was investigated. It was claimed that this distribution is characterized by a new length scale, and that the corresponding dynamical exponent depends upon the initial concentration. We show numerically that this assertion is erroneous. Regardless of the initial concentration, this spatial distribution is characterized by the diffusive length scale.

cond-mat.stat-mech↗

arXiv1998

Genetic Correlations in Mutation Processes

We study the role of phylogenetic trees on correlations in mutation processes. Generally, correlations decay exponentially with the generation number. We find that two distinct regimes of behavior exist. For mutation rates smaller than a critical rate, the underlying tree morphology is almost irrelevant, while mutation rates higher than this critical rate lead to strong tree-dependent correlations. We show analytically that identical critical behavior underlies all multiple point correlations. This behavior generally characterizes branching processes undergoing mutation.

cond-mat.stat-mech↗