Higher homotopy operations and cohomology

We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams.Comment: 28 page

On local-to-global spectral sequences for the cohomology of diagrams

The aim of this paper is to construct and examine three candidates for local-to-global spectral sequences for the cohomology of diagrams of algebras with directed indexing. In each case, the $E^2$ -terms can be viewed as a type of local cohomology relative to a map or an object in the diagram.Comment: 27 pages; incorporated corrections based on referee's report and added a few reference

A Godunov Method for Multidimensional Radiation Magnetohydrodynamics based on a variable Eddington tensor

We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. This algorithm solves the radiation moment equations in the mixed frame, without invoking any diffusion-like approximations. The moment equations are closed using a variable Eddington tensor whose components are calculated from a formal solution of the transfer equation at a large number of angles using the method of short characteristics. We use a comprehensive test suite to verify the algorithm, including convergence tests of radiation-modified linear acoustic and magnetosonic waves, the structure of radiation modified shocks, and two-dimensional tests of photon bubble instability and the ablation of dense clouds by an intense radiation field. These tests cover a very wide range of regimes, including both optically thick and thin flows, and ratios of the radiation to gas pressure of at least 10^{-4} to 10^{4}. Across most of the parameter space, we find the method is accurate. However, the tests also reveal there are regimes where the method needs improvement, for example when both the radiation pressure and absorption opacity are very large. We suggest modifications to the algorithm that will improve accuracy in this case. We discuss the advantages of this method over those based on flux-limited diffusion. In particular, we find the method is not only substantially more accurate, but often no more expensive than the diffusion approximation for our intended applications.Comment: 42 pages, 22 figures, 2 tables, accepted by ApJ

Mixing of Supersonic Streams

The Strutjet approach to Rocket Based Combined Cycle (RBCC) propulsion depends upon fuel-rich flows from the rocket nozzles and turbine exhaust products mixing with the ingested air for successful operation in the ramjet and scramjet modes. A model of the Strutjet device has been built and is undergoing test to investigate the mixing of the streams as a function of distance from the Strutjet exit plane. Initial cold flow testing of the model is underway to determine both, the behavior of the ingested air in the duct and to validate the mixing diagnostics. During the tests, each of the two rocket nozzles ejected up to two pounds mass per second into the 13.6 square inch duct. The tests showed that the mass flow of the rockets was great enough to cause the entrained air to go sonic at the strut, which is the location of the rocket nozzles. More tests are necessary to determine whether the entrained air chokes due to the reduction in the area of the duct at the strut (a physical choke), or because of the addition of mass inside the duct at the nozzle exit (a Fabri choke). The initial tests of the mixing diagnostics are showing promise

Structure and dynamics of iron pentacarbonyl

The dynamics of CO ligand scrambling in Fe(CO)5 has been investigated by linear infrared spectroscopy in supercritical xenon solution. The activation barrier for the Berry pseudorotation in Fe(CO)5 was determined experimentally to be Ea = 2.5 ± 0.4 kcal mol–1 by quantitative analysis of the temperature-dependent spectral line shape. This compares well with the range of Ea/(kcal mol–1) = 2.0 to 2.3 calculated by various DFT methods and the value of 1.6 ± 0.3 previously obtained from 2D IR measurements by Harris et al. ( Science 2008, 319, 1820). The involvement of Fe(CO)5···Xe interactions in the ligand scrambling process was tested computationally at the BP86-D3/AE2 level and found to be negligible

On realizing diagrams of Pi-algebras

Given a diagram of Pi-algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized Pi-algebras. This extends a program begun in [J. Pure Appl. Alg. 103 (1995) 167-188] and [Topology 43 (2004) 857-892] to study the realization of a single Pi-algebra. In particular, we explicitly analyze the simple case of a single map, and provide a detailed example, illustrating the connections to higher homotopy operations.Comment: This is the version published by Algebraic & Geometric Topology on 21 June 200