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Full-Text Articles in Physical Sciences and Mathematics
Efficiency Of Competitions, E. Ben-Naim, N.W. Hengartner
Efficiency Of Competitions, E. Ben-Naim, N.W. Hengartner
Eli Ben-Naim
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 …
Kinetic Theory Of Random Graphs: From Paths To Cycles, E. Ben-Naim, P.L. Krapivsky
Kinetic Theory Of Random Graphs: From Paths To Cycles, E. Ben-Naim, P.L. Krapivsky
Eli Ben-Naim
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.
Stationary States And Energy Cascades In Inelastic Gases, E. Ben-Naim, J. Machta
Stationary States And Energy Cascades In Inelastic Gases, E. Ben-Naim, J. Machta
Eli Ben-Naim
We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transfered from large velocity scales to small velocity scales. These steady-states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v) ~ v^{-sigma}. The exponent sigma is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high …
The Inelastic Maxwell Model, E. Ben-Naim, P.L. Krapivsky
The Inelastic Maxwell Model, E. Ben-Naim, P.L. Krapivsky
Eli Ben-Naim
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 …
Knots And Random Walks In Vibrated Granular Chains, E. Ben-Naim, Z.A. Daya, P. Vorobieff, R.E. Ecke
Knots And Random Walks In Vibrated Granular Chains, E. Ben-Naim, Z.A. Daya, P. Vorobieff, R.E. Ecke
Eli Ben-Naim
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.
Shock-Like Dynamics Of Inelastic Gases, E. Ben-Naim, S.Y. Chen, G.D. Doolen
Shock-Like Dynamics Of Inelastic Gases, E. Ben-Naim, S.Y. Chen, G.D. Doolen
Eli Ben-Naim
No abstract provided.
Density Fluctuations In Vibrated Granular Materials , E.R. Nowak, J.B. Knight, E. Ben-Naim, H.M Jaeger, S.R. Nagel
Density Fluctuations In Vibrated Granular Materials , E.R. Nowak, J.B. Knight, E. Ben-Naim, H.M Jaeger, S.R. Nagel
Eli Ben-Naim
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 …
Towards Granular Hydrodynamics In Two-Dimensions, E.L. Grossman, T. Zhou, E. Ben-Naim
Towards Granular Hydrodynamics In Two-Dimensions, E.L. Grossman, T. Zhou, E. Ben-Naim
Eli Ben-Naim
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.
Coarsening And Persistence In The Voter Model, E. Ben-Naim, L. Frachebourg, P.L. Krapivsky
Coarsening And Persistence In The Voter Model, E. Ben-Naim, L. Frachebourg, P.L. Krapivsky
Eli Ben-Naim
No abstract provided.
Kinetics Of Clustering In Traffic Flows, E. Ben-Naim, P. L. Krapivsky, S. Redner
Kinetics Of Clustering In Traffic Flows, E. Ben-Naim, P. L. Krapivsky, S. Redner
Eli Ben-Naim
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 …