On-lattice coalescence and annihilation of immobile reactants in loopless lattices and beyond.
We study the behavior of the chemical reactions A+A-->A+S and A+A-->S+S (where the reactive species A and the inert species S are both assumed to be immobile) embedded on Bethe lattices of arbitrary coordination number z and on a two-dimensional (2D) square lattice. For the Bethe lattice case, exact solutions for the coverage in the A species in terms of the initial condition are obtained. In particular, our results hold for the important case of an infinite one-dimensional (1D) lattice (z=2). The method is based on an expansion in terms of conditional probabilities which exploits a Markovian property of these systems. Along the same lines, an approximate solution for the case of a 2D square lattice is developed. The effect of dilution in a random initial condition is discussed in detail, both for the lattice coverage and for the spatial distribution of reactants.
Yard-Sale exchange on networks: wealth sharing and wealth appropriation
Yard Sale (YS) is a stochastic multiplicative wealth exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1D rings, 2D square lattices, and random graphs with variable average coordination, comparing its properties with those in mean field (MF). Equilibrium properties in the stable phase are almost unaffected by the introduction of a network. Measurement of decorrelation times in the stable phase allows us to determine the critical interface with very good precision, and it turns out to be the same, for all networks analyzed, as the one that can be analytically derived in MF. In the unstable phase, on the other hand, dynamical as well as asymptotic properties are strongly network dependent. Wealth no longer condenses on a single agent, as in MF, but onto an extensive set of agents, the properties of which depend on the network. Connections with previous studies of coalescence of immobile reactants are discussed, and their analytic predictions are successfully compared with our numerical results.
Can Centauros or Chirons BE the First Observations of Evaporating Mini Black Holes
We argue that the signals expected from the evaporation of mini black holes — predicted in TeV-gravity models with large extra dimensions, and possibly produced in ultrahigh energy collisions in the atmosphere — are quite similar to the characteristics of the Centauro events, an old mystery of cosmic-ray physics.