Copyright (c) 2008 All rights reserved. http://works.bepress.com/ebn Recent documents in Eli Ben-Naim en-us Wed, 02 Jan 2008 23:16:31 PST 3600 http://works.bepress.com/ebn/13 http://works.bepress.com/ebn/13 Sat, 23 Dec 2006 13:05:22 PST League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest number of wins is declared to be the champion. The total number of games needed for the best team to win the championship with high certainty, T, grows as the cube of the number of teams, N, i.e., T ~ N^3. This number can be substantially reduced using preliminary rounds where teams play a small number of games and subsequently, only the top teams advance to the next round. When there are k rounds, the total number of games needed for the best team to emerge as champion, T_k, scales as follows, T_k ~N^(\gamma_k) with gamma_k=1/[1-(2/3)^(k+1)]. For example, gamma_k=9/5,27/19,81/65 for k=1,2,3. These results suggest an algorithm for how to infer the best team using a schedule that is linear in N. We conclude that league format is an ineffective method of determining the best team, and that sequential elimination from the bottom up is fair and efficient. E. Ben-Naim Complex Systems http://works.bepress.com/ebn/12 http://works.bepress.com/ebn/12 Sat, 23 Dec 2006 13:01:43 PST Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically. At the gelation point, the typical length of paths and cycles, l, scales with the component size k as l ~ k^{1/2}. Dynamic and finite-size scaling laws for the behavior at and near the gelation point are obtained. Finite-size scaling laws are verified using numerical simulations. E. Ben-Naim Kinetic Theory http://works.bepress.com/ebn/11 http://works.bepress.com/ebn/11 Thu, 14 Dec 2006 21:06:45 PST We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions compare well with numerical simulations in the nearly elastic limit. It is also seen that the system can achieve a nonequilibrium steady-state with asymmetric velocity distributions, and we discuss the conditions under which such situations occur. E.L. Grossman Granular Materials http://works.bepress.com/ebn/10 http://works.bepress.com/ebn/10 Thu, 14 Dec 2006 21:01:45 PST We report systematic measurements of the density of a vibrated granular material as a function of time. Monodisperse spherical beads were confined to a cylindrical container and shaken vertically. Under vibrations, the density of the pile slowly reaches a final steady-state value about which the density fluctuates. We have investigated the frequency dependence and amplitude of these fluctuations as a function of vibration intensity Γ. The spectrum of density fluctuations around the steady state value provides a probe of the internal relaxation dynamics of the system and a link to recent thermodynamic theories for the settling of granular material. In particular, we propose a method to evaluate the compactivity of a powder, first put forth by Edwards and co-workers, that is the analog to temperature for a quasistatic powder. We also propose a stochastic model based on free volume considerations that captures the essential mechanism underlying the slow relaxation. We compare our experimental results with simulations of a one-dimensional model for random adsorption and desorption. E.R. Nowak Granular Materials http://works.bepress.com/ebn/9 http://works.bepress.com/ebn/9 Thu, 14 Dec 2006 20:54:42 PST E. Ben-Naim Granular Materials http://works.bepress.com/ebn/8 http://works.bepress.com/ebn/8 Thu, 14 Dec 2006 20:49:14 PST Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy dissipation leads to a significant departure from the elastic case. Specifically, the velocity distributions have overpopulated high energy tails and different velocity components are correlated. In the freely cooling case, the velocity distribution develops an algebraic high-energy tail, with an exponent that depends sensitively on the dimension and the degree of dissipation. Moments of the velocity distribution exhibit multiscaling asymptotic behavior, and the autocorrelation function decays algebraically with time. In the forced case, the steady state velocity distribution decays exponentially at large velocities. An impurity immersed in a uniform inelastic gas may or may not mimic the behavior of the background, and the departure from the background behavior is characterized by a series of phase transitions. E. Ben-Naim Kinetic Theory http://works.bepress.com/ebn/7 http://works.bepress.com/ebn/7 Thu, 14 Dec 2006 20:41:07 PST We model the dynamics of social structure by a simple interacting particle system. The social standing of an individual agent is represented by an integer-valued fitness that changes via two offsetting processes. When two agents interact one advances: the fitter with probability p and the less fit with probability 1-p. The fitness of an agent may also decline with rate r. From a scaling analysis of the underlying master equations for the fitness distribution of the population, we find four distinct social structures as a function of the governing parameters p and r. These include: (i) a static lower-class society where all agents have finite fitness; (ii) an upwardly-mobile middle-class society; (iii) a hierarchical society where a finite fraction of the population belongs to a middle class and a complementary fraction to the lower class; (iv) an egalitarian society where all agents are upwardly mobile and have nearly the same fitness. We determine the basic features of the fitness distributions in these four phases. E. Ben-Naim Complex Systems http://works.bepress.com/ebn/6 http://works.bepress.com/ebn/6 Thu, 14 Dec 2006 18:19:15 PST E. Ben-Naim Complex Systems http://works.bepress.com/ebn/5 http://works.bepress.com/ebn/5 Thu, 14 Dec 2006 18:15:02 PST 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. E. Ben-Naim Granular Materials http://works.bepress.com/ebn/4 http://works.bepress.com/ebn/4 Thu, 14 Dec 2006 18:09:58 PST We study a simple aggregation model that mimics the clustering of traffic on a one-lane roadway. In this model, each ``car'' moves ballistically at its initial velocity until it overtakes the preceding car or cluster. After this encounter, the incident car assumes the velocity of the cluster which it has just joined. The properties of the initial distribution of velocities in the small velocity limit control the long-time properties of the aggregation process. For an initial velocity distribution with a power-law tail at small velocities, $\pvim$ as $v \to 0$, a simple scaling argument shows that the average cluster size grows as $n \sim t^{\va}$ and that the average velocity decays as $v \sim t^{-\vb}$ as $t\to \infty$. We derive an analytical solution for the survival probability of a single car and an asymptotically exact expression for the joint mass-velocity distribution function. We also consider the properties of spatially heterogeneous traffic and the kinetics of traffic clustering in the presence of an input of cars. E. Ben-Naim Kinetic Theory