83,928 research outputs found
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
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
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
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