The plasma in high-current pseudospark switches

The discharge behavior and the erosion rate of pseudospark switches for high currents (50-150 kA) and pulse lengths of several microseconds were investigated for different electrode materials. A capacitor discharge (3.3 μF) without any load was used at a maximum voltage of 30 kV. Side-on optical investigations were performed either with a streak camera or a fast shutter camera. Using metal electrodes, the discharge ignites on axis, then widens up radially and burns homogeneously at the edge of the central apertures. After about 500 ns, a stable anode spot is observed on the plane electrode surface (at currents exceeding 45 kA), the location of which is statistical. The discharge is transformed to a metal vapor are discharge and the erosion rate increases by more than one order of magnitude. With semiconductor electrodes (i.e., silicon carbide), a different discharge behavior is observed, After ignition on axis, the discharge burns homogeneously on the whole carbide surface. No contraction to a small area occurs in comparison to metal electrodes. The reignition of later current half cycles starts at the triple point metal-carbide-gas. Then the discharge again spreads homogeneously over the total carbide surface. The erosion rate is about two magnitudes lower in comparison to metals. We assume that the current is conducted in a thin surface sheath which is heated to more than 2000 K     

Mixing times of the biased card shuffling and the asymmetric exclusion process

Consider the following method of card shuffling. Start with a deck of cards numbered 1 through . Fix a parameter between 0 and 1. In this model a ``shuffle' consists of uniformly selecting a pair of adjacent cards and then flipping a coin that is heads with probability . If the coin comes up heads, then we arrange the two cards so that the lower-numbered card comes before the higher-numbered card. If the coin comes up tails, then we arrange the cards with the higher-numbered card first. In this paper we prove that for all , the mixing time of this card shuffling is , as conjectured by Diaconis and Ram (2000). Our result is a rare case of an exact estimate for the convergence rate of the Metropolis algorithm. A novel feature of our proof is that the analysis of an infinite (asymmetric exclusion) process plays an essential role in bounding the mixing time of a finite process.

     

The generalized almost resolvable cycle system problem

Let (X, C) be a k-cycle system of order n, with vertex set X (of cardinality n) and collection of k-cycles C. Suppose n=kq+r where r<k. An almost parallel class of C is a collection of q=(n−r)/k pairwise vertex-disjoint k-cycles of C. Each almost parallel class thus will miss r of the n vertices in X. The k-cycle system (X,C) is said to be almost resolvable if C can be partitioned into almost parallel classes such that the remaining k-cycles are vertex disjoint. (These remaining k-cycles are referred to as a short parallel class.)     

Pseudozeros of multivariate polynomials

The pseudozero set of a system of polynomials in complex variables is the subset of which is the union of the zero-sets of all polynomial systems that are near to in a suitable sense. This concept is made precise, and general properties of pseudozero sets are established. In particular it is shown that in many cases of natural interest, the pseudozero set is a semialgebraic set. Also, estimates are given for the size of the projections of pseudozero sets in coordinate directions. Several examples are presented illustrating some of the general theory developed here. Finally, algorithmic ideas are proposed for solving multivariate polynomials.

     

ChemInform Abstract: Three Lowest-Lying Electronic States of NH2.

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