arXiv subjects

S. Redner

Publications and source records attributed to S. Redner.

At least 181 records · Page 10Linked to original sources

arXiv1999

Does Good Mutation Help You Live Longer?

We study the dynamics of an age-structured population in which the life expectancy of an offspring may be mutated with respect to that of its parent. When advantageous mutation is favored, the average fitness of the population grows linearly with time $t$, while in the opposite case the average fitness is constant. For no mutational bias, the average fitness grows as t^{2/3}. The average age of the population remains finite in all cases and paradoxically is a decreasing function of the overall population fitness.

cond-mat.stat-mech↗

arXiv1999

Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey

We study the capture of a diffusing "lamb" by diffusing "lions" in one dimension. The capture dynamics is exactly soluble by probabilistic techniques when the number of lions is very small, and is tractable by extreme statistics considerations when the number of lions is very large. However, the exact solution for the general case of three or more lions is still not known.

cond-mat.stat-mech↗

arXiv1999

Coarsening in a Driven Ising Chain with Conserved Dynamics

We study the low-temperature coarsening of an Ising chain subject to spin-exchange dynamics and a small driving force. This dynamical system reduces to a domain diffusion process, in which entire domains undergo nearest-neighbor hopping, except for the shortest domains -- dimers -- which undergo long-range hopping. This system is characterized by two independent length scales: the average domain length L(t)~t^{1/2} and the average dimer hopping distance l(t)~ t^{1/4}. As a consequence of these two scales, the density C_k(t) of domains of length k does not obey scaling. This breakdown of scaling also leads to the density of short domains decaying as t^{-5/4}, instead of the t^{-3/2} decay that would arise from pure domain diffusion.

cond-mat.stat-mech↗

arXiv1998

Influence of Island Diffusion on Submonolayer Epitaxial Growth

We investigate the kinetics of submonolayer epitaxial growth which is driven by a fixed flux of monomers onto a substrate. Adatoms diffuse on the surface, leading to irreversible aggregation of islands. We also account for the effective diffusion of islands, which originates from hopping processes of their constituent adatoms, on the kinetics. When the diffusivity of an island of mass k scales as k^{-mu}, the (mean-field) Smoluchowski rate equations predicts steady behavior for 0<=mu<1, with the concentration c_k of islands of mass k varying as k^{-(3-mu)/2}. For mu>=1, a quasi-static approximation to the rate equations predicts slow continuous evolution in which the island density increases as ln t^{mu/2}. A more refined matched asymptotic expansion reveals unusual multiple-scale mass dependence for the island size distribution. Our theory also describes basic features of epitaxial growth in a more faithful model of growing circular islands. For epitaxial growth in an initial population of monomers and no external flux, a scaling approach predicts power-law island growth and a mass distribution with a behavior distinct from that of the non-zero flux system. Finally, we extend our results to one- and two-dimensional substrates. The physically-relevant latter case exhibits only logarithmic corrections compared to the mean-field predictions.

cond-mat.stat-mech↗

arXiv1998

Slow Coarsening in an Ising Chain with Competing Interactions

We investigate the zero-temperature coarsening dynamics of a chain of Ising spins with a nearest-neighbor ferromagnetic and an nth-neighbor antiferromagnetic interactions. For sufficiently large antiferromagnetic interaction, the ground state consists of $n$ consecutive up spins followed by n down spins, etc. We show that the asymptotic coarsening into this ground state is governed by a multispecies reactive gas of elementary excitations. The basic elementary excitations are identified and each decays at a different power-law rate in time. The dominant excitations are domains of n+1 spins which diffuse freely and disappear through processes which are effectively governed by (n+1)-particle annihilation. This implies that the ground state is approached slowly with time, as t^{-1/n}.

cond-mat.stat-mech↗

arXiv1998

How Popular is Your Paper? An Empirical Study of the Citation Distribution

Numerical data for the distribution of citations are examined for: (i) papers published in 1981 in journals which are catalogued by the Institute for Scientific Information (783,339 papers) and (ii) 20 years of publications in Physical Review D, vols. 11-50 (24,296 papers). A Zipf plot of the number of citations to a given paper versus its citation rank appears to be consistent with a power-law dependence for leading rank papers, with exponent close to -1/2. This, in turn, suggests that the number of papers with x citations, N(x), has a large-x power law decay N(x)~x^{-alpha}, with alpha approximately equal to 3.

cond-mat.stat-mech↗

arXiv1998

Gradient Clogging in Depth Filtration

We investigate clogging in depth filtration, in which a dirty fluid is ``cleaned'' by the trapping of dirt particles within the pore space during flow through a porous medium. This leads to a gradient percolation process which exhibits a power law distribution for the density of trapped particles at downstream distance x from the input. To achieve a non-pathological clogging (percolation) threshold, the system length L should scale no faster than a power of ln w, where w is the width. Non-trivial behavior for the permeability arises only in this extreme anisotropic geometry.

cond-mat.stat-mech↗

arXiv1997

Logarithmic Clustering in Submonolayer Epitaxial Growth

We investigate submonolayer epitaxial growth with a fixed monomer flux and irreversible aggregation of adatom islands due to their effective diffusion. When the diffusivity D_k of an island of mass k is proportional to k^{-μ}, a Smoluchowski rate equation approach predicts steady behavior for 0<μ<1, with the concentration c_k of islands of mass k varying as k^{-(3-μ)/2}. For μ>1, continuous evolution occurs in which c_k(t)~(\ln t)^{-(2k-1)μ/2}, while the total island density increases as N(t)~(\ln t)^{μ/2}. Monte Carlo simulations support these predictions.

cond-mat.stat-mech↗

arXiv1997

Alternating Kinetics of Annihilating Random Walks Near a Free Interface

The kinetics of annihilating random walks in one dimension, with the half-line x>0 initially filled, is investigated. The survival probability of the nth particle from the interface exhibits power-law decay, S_n(t)~t^{-alpha_n}, with alpha_n approximately equal to 0.225 for n=1 and all odd values of n; for all n even, a faster decay with alpha_n approximately equal to 0.865 is observed. From consideration of the eventual survival probability in a finite cluster of particles, the rigorous bound alpha_1<1/4 is derived, while a heuristic argument gives alpha_1 approximately equal to 3 sqrt{3}/8 = 0.2067.... Numerically, this latter value appears to be a stringent lower bound for alpha_1. The average position of the first particle moves to the right approximately as 1.7 t^{1/2}, with a relatively sharp and asymmetric probability distribution.

cond-mat.stat-mech↗

arXiv1997

Wealth Distributions in Models of Capital Exchange

A dynamical model of capital exchange is introduced in which a specified amount of capital is exchanged between two individuals when they meet. The resulting time dependent wealth distributions are determined for a variety of exchange rules. For ``greedy'' exchange, an interaction between a rich and a poor individual results in the rich taking a specified amount of capital from the poor. When this amount is independent of the capitals of the two traders, a mean-field analysis yields a Fermi-like scaled wealth distribution in the long-time limit. This same distribution also arises in greedier exchange processes, where the interaction rate is an increasing function of the capital difference of the two traders. The wealth distribution in multiplicative processes, where the amount of capital exchanged is a finite fraction of the capital of one of the traders, are also discussed. For random multiplicative exchange, a steady state wealth distribution is reached, while in greedy multiplicative exchange a non-steady power law wealth distribution arises, in which the support of the distribution continuously increases. Finally, extensions of our results to arbitrary spatial dimension and to growth processes, where capital is created in an interaction, are presented.

cond-mat.stat-mech↗

arXiv1996

Slowly Divergent Drift in the Field-Driven Lorentz Gas

The dynamics of a point charged particle which is driven by a uniform external electric field and moves in a medium of elastic scatterers is investigated. Using rudimentary approaches, we reproduce, in one dimension, the known results that the typical speed grows with time as t^{1/3} and that the leading behavior of the velocity distribution is exp(-|v|^3/t). In spatial dimension d>1, we develop an effective medium theory which provides a simple and comprehensive description for the motion of a test particle. This approach predicts that the typical speed grows as t^{1/3} for all d, while the speed distribution is given by the scaling form P(u,t)= ^{-1}f(u/ ), where u=|v|^{3/2}, ~t^{1/2}, and f(z) is proportional to z^{(d-1)/3}exp(-z^2/2). For a periodic Lorentz gas with an infinite horizon, e. g., for a hypercubic lattice of scatters, a logarithmic correction to the effective medium result is predicted; in particular, the typical speed grows as (t ln t)^{1/3}.

cond-mat.stat-mech↗

arXiv1996

Aging and its Distribution in Coarsening Processes

We investigate the age distribution function P(tau,t) in prototypical one-dimensional coarsening processes. Here P(tau,t) is the probability density that in a time interval (0,t) a given site was last crossed by an interface in the coarsening process at time tau. We determine P(tau,t) analytically for two cases, the (deterministic) two-velocity ballistic annihilation process, and the (stochastic) infinite-state Potts model with zero temperature Glauber dynamics. Surprisingly, we find that in the scaling limit, P(tau,t) is identical for these two models. We also show that the average age, i. e., the average time since a site was last visited by an interface, grows linearly with the observation time t. This latter property is also found in the one-dimensional Ising model with zero temperature Glauber dynamics. We also discuss briefly the age distribution in dimension d greater than or equal to 2.

cond-mat↗

arXiv1996

Two-Scale Annihilation

The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between convection and diffusion leads to a decay of the density which is proportional to $t^{-3/4}$. At long times, the reactants organize into domains of right- and left-moving particles, with the typical distance between particles in a single domain growing as $t^{3/4}$, and the distance between domains growing as $t$. The probability that an arbitrary particle reacts with its $n^{\rm th}$ neighbor is found to decay as $n^{-5/2}$ for same-velocity pairs and as $n^{-7/4}$ for $+-$ pairs. These kinetic and spatial exponents and their interrelations are obtained by scaling arguments. Our predictions are in excellent agreement with numerical simulations.

cond-mat↗

arXiv1996

Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions

The survival probability, S_N(t), of a diffusing prey (``lamb'') in the proximity of N diffusing predators (a ``pride of lions'') in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, S_N(t) is proportional to t^{-beta_N}, with the decay exponent beta_N proportional to ln N. The crossover behavior as a function of the relative diffusivities of the lions and the lamb is also discussed. When N--->oo, the lamb survival probability exhibits a log-normal decay, exp(-ln^2 t).

cond-mat↗

arXiv1996

On War: The Dynamics of Vicious Civilizations

The dynamics of ``vicious'', continuously growing civilizations (domains), which engage in ``war'' whenever two domains meet, is investigated. In the war event, the smaller domain is annihilated, while the larger domain is reduced in size by a fraction $\e$ of the casualties of the loser. Here $\e$ quantifies the fairness of the war, with $\e=1$ corresponding to a fair war with equal casualties on both side, and $\e=0$ corresponding to a completely unfair war where the winner suffers no casualties. In the heterogeneous version of the model, evolution begins from a specified initial distribution of domains, while in the homogeneous system, there is a continuous and spatially uniform input of point domains, in addition to the growth and warfare. For the heterogeneous case, the rate equations are derived and solved, and comparisons with numerical simulations are made. An exact solution is also derived for the case of equal size domains in one dimension. The heterogeneous system is found to coarsen, with the typical cluster size growing linearly in time $t$ and the number density of domains decreases as $1/t$. For the homogeneous system, two different long-time behaviors arise as a function of $\e$. When $1/2<\e\leq 1$ (relatively fair wars), a steady state arises which is characterized by egalitarian competition between domains of comparable size. In the limiting case of $\e=1$, rate equations which simultaneously account for the distribution of domains and that of the intervening gaps are derived and solved. The steady state is characterized by domains whose age is typically much larger than their size. When $0\leq\e<1/2$ (unfair wars), a few ``superpowers'' ultimately dominate. Simulations indicate that this coarsening process is characterized by power-law temporal behavior, with non-universal

cond-mat↗

arXiv1995

Heterogeneous Catalysis on a Disordered Surface

We introduce a simple model of heterogeneous catalysis on a disordered surface which consists of two types of randomly distributed sites with different adsorption rates. Disorder can create a reactive steady state in situations where the same model on a homogeneous surface exhibits trivial kinetics with no steady state. A rich variety of kinetic behaviors occur for the adsorbate concentrations and catalytic reaction rate as a function of model parameters.

cond-mat↗

arXiv1995

Life and Death at the Edge of a Windy Cliff

The survival probability of a particle diffusing in the two dimensional domain $x>0$ near a ``windy cliff'' at $x=0$ is investigated. The particle dies upon reaching the edge of the cliff. In addition to diffusion, the particle is influenced by a steady ``wind shear'' with velocity $\vec v(x,y)=v\,{\rm sign}(y)\,\hat x$, \ie, no average bias either toward or away from the cliff. For this semi-infinite system, the particle survival probability decays with time as $t^{-1/4}$, compared to $t^{-1/2}$ in the absence of wind. Scaling descriptions are developed to elucidate this behavior, as well as the survival probability within a semi-infinite strip of finite width $|y|<w$ with particle absorption at $x=0$. The behavior in the strip geometry can be described in terms of Taylor diffusion, an approach which accounts for the crossover to the $t^{-1/4}$ decay when the width of the strip diverges. Supporting numerical simulations of our analytical results are presented.

cond-mat↗

arXiv1995

Kinetics of A+B--->0 with Driven Diffusive Motion

We study the kinetics of two-species annihilation, A+B--->0, when all particles undergo strictly biased motion in the same direction and with an excluded volume repulsion between same species particles. It was recently shown that the density in this system decays as t^{-1/3}, compared to t^{-1/4} density decay in A+B--->0 with isotropic diffusion and either with or without the hard-core repulsion. We suggest a relatively simple explanation for this t^{-1/3} decay based on the Burgers equation. Related properties associated with the asymptotic distribution of reactants can also be accounted for within this Burgers equation description.

cond-mat↗