Acoustically derived ice-fracture velocity in central Arctic pack ice

Sounds radiated by fractures in Arctic ice (called acoustic events) are used to estimate fracture velocity. Both speed and orientation are obtained by measuring Doppler shifts induced by source motion. Data from the SIMI experiment of 1994 in the central Arctic are used in the frequency window 10 to 350 Hz. The estimation procedure assumes that each fracture propagates unilaterally, i.e., unidirectionally. Results for a population of 186 events show fracture propagation speed to be mostly subsonic, in the range 100 to 1100 m/s, significantly lower than the Rayleigh wave speed (1700 m/s for sea ice) assumed in previous studies. The wide range of speeds observed indicates either the presence of distinct multiple fractures in each event, or of a single mechanism at different stages in its propagation.     

Path coupling using stopping times and counting independent sets and colorings in hypergraphs

We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q‐colorings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Embeddings of root systems I: Root systems over commutative rings

This paper gives examples of embeddings of root systems of Coxeter groups, including sporadic embeddings of standard real root systems in other standard real root systems, and, for a general Coxeter group, an embedding of its universal symmetric root system over commutative rings into the standard real root system of a simply laced Coxeter group.     

Infrared laser-induced decomposition of 2,2-dimethyloxetane

The unimolecular decomposition of 2,2 dimethyloxetance to give either isobutence and formaldehyde or ethene and acetone induced by a pulsed CO₂ laser has been investigated. Absorption characteristics and fractional decomposition have been studied as a function of laser fluence, irradiation frequency, reactant pressure, and added inert bath gas. Both absorption cross section and fractional decomposition are approximately independent of pressure of 2,2-dimethyloxetane below 50 times; 10^?3 torr and increase with pressure at higher pressures of 2,2-dimethyloxetane. At pressures sufficiently low that collisions are negligible during the laser pulse, added inert gases reduce the amount of decomposition. Calculations of the fractional decomposition have been carried out based on RRKM theory and assuming either a Boltzmann or a Poisson intermolecular energy distribution. Master equation calculations of both absorption and decomposition for 10R20 irradiation have also been performed. Agreement between observed and calculated results for 10R20 irradiation could be obtained only by assuming that most, but not all, of the molecules in the irradiated volume absorb the laser radiation. Differences between the absorptions of the 10R20 and 9P20 lines and in the resulting extents of decomposition indicate that the fraction of irradiated molecules which absorbs 9P20 radiation is smaller than the fraction which absorbs 10R20 radiation.