S. Redner

Degree distributions of growing networks

The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree). The network is built by (i) creation of new nodes which each immediately attach to a preexisting node, and (ii) creation of new links between preexisting nodes. This process naturally generates correlated in-degree and out-degree distributions. When the node and link creation rates are linear functions of node degree, these distributions exhibit distinct power-law forms. By tuning the parameters in these rates to reasonable values, exponents which agree with those of the web graph are obtained.

SHOCKLIKE 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

Networks: Teasing out the missing links

{t}^{\ensuremath{-}2/3}

Fate of 2D kinetic ferromagnets and critical percolation crossing probabilities.

temperature decay and the development of discontinuities in the velocity profile, are verified numerically for inelastic gases.

Propagation and extinction in branching annihilating random walks.

Focusing on the hierarchical structure inherent in social and biological networks might provide a smart way to find missing connections that are not revealed in the raw data — which could be useful in a range of contexts. Networks are now a ubiquitous tool for representing the structure of complex systems, including the Internet, social networks, food webs, and protein and genetic networks. Unfortunately, the data describing these networks are in many cases incomplete or biased. A new study provides a general technique to divide network vertices into groups and sub-groups. Revealing such underlying hierarchies makes it possible to predict missing links from partial data with higher accuracy than previous methods.

Kinetics of A + B →0 with driven diffusive motion

We present evidence for a deep connection between the zero-temperature coarsening of both the two-dimensional time-dependent Ginzburg-Landau equation and the kinetic Ising model with critical continuum percolation. In addition to reaching the ground state, the time-dependent Ginzburg-Landau equation and kinetic Ising model can fall into a variety of topologically distinct metastable stripe states. The probability to reach a stripe state that winds a times horizontally and b times vertically on a square lattice with periodic boundary conditions equals the corresponding exactly solved critical percolation crossing probability P(a,b) for a spanning path with winding numbers a and b.

Kinetics of heterogeneous single-species annihilation

We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite density wave, or extinction may occur, in which the number of particles vanishes in the long-time limit. The number parity conserving case where 2-offspring are produced in each branching event can be solved exactly for unit reaction probability, from which qualitative features of the transition between propagation and extinction, as well as intriguing parity-specific effects are elucidated. An approximate analysis is developed to treat this transition for general BAW processes. A scaling description suggests that the critical exponents which describe the vanishing of the particle density at the transition are unrelated to those of conventional models, such as Reggeon Field Theory. P. A. C. S. Numbers: 02.50.+s, 05.40.+j, 82.20.-w

War: The dynamics of vicious civilizations.

We study the kinetics of two-species annihilation A+B\ensuremath{\rightarrow}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

Zero-temperature freezing in the three-dimensional kinetic Ising model.

{\mathit{t}}^{\mathrm{\ensuremath{-}}1/3}

Teasing out the missing links

, compared to