Cohomological characterization of vector bundles on multiprojective spaces

We show that Horrock's criterion for the splitting of vector bundles on \PP^n can be extended to vector bundles on multiprojective spaces and to smooth projective varieties with the weak CM property (see Definition 3.11). As a main tool we use the theory of $n$-blocks and Beilinson's type spectral sequences. Cohomological characterizations of vector bundles are also showed

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