Homological Domination in Large Random Simplicial Complexes

In this paper we state the homological domination principle for random multi-parameter simplicial complexes, claiming that the Betti number in one specific dimension (which is explicitly determined by the probability multi-parameter) significantly dominates the Betti numbers in all other dimensions. We also state and discuss evidence for two interesting conjectures which would imply a stronger version of the homological domination principle, namely that generically homology of a random simplicial complex coincides with that of a wedges of k-dimensional spheres. These two conjectures imply that under an additional assumption (specified in the paper) a random simplicial complex collapses to a k-dimensional complex homotopy equivalent to a wedge of spheres of dimension k.Comment: 8 pages, 1 figur

Monte Carlo Study of the Spin-1 Baxter-Wu Model

The two-dimensional spin-1 Baxter-Wu model is studied by using Monte Carlo simulations. The standard single-spin-flip Metropolis algorithm is used to generate the configurations from which the order parameter, specific heat and magnetic susceptibility are measured. The finite-size scaling procedure is employed in order to get the critical behavior. The extensive simulations shown that the critical exponents are different from those of the spin-1/2 model suggesting that the spin-1 model is in a different universality class.Comment: 3 pages, 3 figures, 1 tabl

Discontinuous Transition in a Boundary Driven Contact Process

The contact process is a stochastic process which exhibits a continuous, absorbing-state phase transition in the Directed Percolation (DP) universality class. In this work, we consider a contact process with a bias in conjunction with an active wall. This model exhibits waves of activity emanating from the active wall and, when the system is supercritical, propagating indefinitely as travelling (Fisher) waves. In the subcritical phase the activity is localised near the wall. We study the phase transition numerically and show that certain properties of the system, notably the wave velocity, are discontinuous across the transition. Using a modified Fisher equation to model the system we elucidate the mechanism by which the the discontinuity arises. Furthermore we establish relations between properties of the travelling wave and DP critical exponents.Comment: 14 pages, 9 figure

The synthesis of the light Mo and Ru isotopes: how now, no need for an exotic solution ?

The most detailed calculations of the p-process call for its development in the O/Ne layers of Type II supernovae. In spite of their overall success in reproducing the solar system content of p-nuclides, they suggest a significant underproduction of the light Mo and Ru isotopes. On grounds of a model for the explosion of a 25 solar mass star with solar metallicity, we demonstrate that this failure might just be related to the uncertainties left in the rate of the 22Ne(alpha,n)25Mg neutron producing reaction. The latter indeed have a direct impact on the distribution of the s-process seeds for the p-process.Comment: 4 pages, 4 figures. LaTex2e with aa.cls. A&A Letters, in pres