Continuity for self-destructive percolation in the plane

A few years ago two of us introduced, motivated by the study of certain forest-fireprocesses, the self-destructive percolation model (abbreviated as sdp model). A typical configuration for the sdp model with parameters p and delta is generated in three steps: First we generate a typical configuration for the ordinary percolation model with parameter p. Next, we make all sites in the infinite occupied cluster vacant. Finally, each site that was already vacant in the beginning or made vacant by the above action, becomes occupied with probability delta (independent of the other sites). Let theta(p, delta) be the probability that some specified vertex belongs, in the final configuration, to an infinite occupied cluster. In our earlier paper we stated the conjecture that, for the square lattice and other planar lattices, the function theta has a discontinuity at points of the form (p_c, delta), with delta sufficiently small. We also showed remarkable consequences for the forest-fire models. The conjecture naturally raises the question whether the function theta is continuous outside some region of the above mentioned form. We prove that this is indeed the case. An important ingredient in our proof is a (somewhat stronger form of a) recent ingenious RSW-like percolation result of Bollob\'{a}s and Riordan

Parametric analysis of closed cycle magnetohydrodynamic (MHD) power plants

A parametric analysis of closed cycle MHD power plants was performed which studied the technical feasibility, associated capital cost, and cost of electricity for the direct combustion of coal or coal derived fuel. Three reference plants, differing primarily in the method of coal conversion utilized, were defined. Reference Plant 1 used direct coal fired combustion while Reference Plants 2 and 3 employed on site integrated gasifiers. Reference Plant 2 used a pressurized gasifier while Reference Plant 3 used a ""state of the art' atmospheric gasifier. Thirty plant configurations were considered by using parametric variations from the Reference Plants. Parametric variations include the type of coal (Montana Rosebud or Illinois No. 6), clean up systems (hot or cold gas clean up), on or two stage atmospheric or pressurized direct fired coal combustors, and six different gasifier systems. Plant sizes ranged from 100 to 1000 MWe. Overall plant performance was calculated using two methodologies. In one task, the channel performance was assumed and the MHD topping cycle efficiencies were based on the assumed values. A second task involved rigorous calculations of channel performance (enthalpy extraction, isentropic efficiency and generator output) that verified the original (task one) assumptions. Closed cycle MHD capital costs were estimated for the task one plants; task two cost estimates were made for the channel and magnet only

Morse theory on spaces of braids and Lagrangian dynamics

In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces. Parabolic flows, a type of one-dimensional lattice dynamics, evolve singular braid diagrams in such a way as to decrease their topological complexity; algebraic lengths decrease monotonically. This topological invariant is derived from a Morse-Conley homotopy index and provides a gloablization of `lap number' techniques used in scalar parabolic PDEs. In the second half of the paper we apply this technology to second order Lagrangians via a discrete formulation of the variational problem. This culminates in a very general forcing theorem for the existence of infinitely many braid classes of closed orbits.Comment: Revised version: numerous changes in exposition. Slight modification of two proofs and one definition; 55 pages, 20 figure

A Pulsed Synchrotron for Muon Acceleration at a Neutrino Factory

A 4600 Hz pulsed synchrotron is considered as a means of accelerating cool muons with superconducting RF cavities from 4 to 20 GeV/c for a neutrino factory. Eddy current losses are held to less than a megawatt by the low machine duty cycle plus 100 micron thick grain oriented silicon steel laminations and 250 micron diameter copper wires. Combined function magnets with 20 T/m gradients alternating within single magnets form the lattice. Muon survival is 83%.Comment: 4 pages, 1 figures, LaTeX, 5th International Workshop on Neutrino Factories and Superbeams (NuFact 03), 5-11 Jun 2003, New Yor

Frequency Dependent Viscosity Near the Critical Point: The Scale to Two Loop Order

The recent accurate measurements of Berg, Moldover and Zimmerli of the viscoelastic effect near the critical point of xenon has shown that the scale factor involved in the frequency scaling is about twice the scale factor obtained theoretically. We show that this discrepancy is a consequence of using first order perturbation theory. Including two loop contribution goes a long way towards removing the discrepancy.Comment: No of pages:7,Submitted to PR-E(Rapid Communication),No of EPS files:

Constrained Orthogonal Polynomials

We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study of density fluctuations in centrifuges. We give explicit properties of such polynomial sets, generalizing Laguerre and Legendre polynomials. The nature of the dimension 1 subspace completing such sets is described. A numerical example illustrates the use of such polynomials.Comment: 11 pages, 10 figure