Morita cohomology

We consider two categorifications of the cohomology of a topological space X by taking coefficients in the category of differential graded categories. We consider both derived global sections of a constant presheaf and singular cohomology and find the resulting dg-categories are quasi-equivalent and moreover quasi-equivalent to representations in perfect complexes of chains on the loop space of X.Comment: 33 page

Moths and How to Rear Them. Paul Villiard. New York: Funk and Wagnalls, 1969. xiv, 242 pp. $10.00.

Excerpt: W.J.B. Crotch\u27s A Silkmoth Rearer\u27s Handbook (1956) and Wild Silk Moths of the United States by Michael Collins and Robert Weast (1961) have been standard rearers\u27 manuals for some time, but both are limited to one group of large moths, and there has been a decided need for a low-priced guide covering rearing procedures for a much wider range of Lepidoptera. For a number of reasons, Villiard\u27s book falls short of this goal

Coupled elastic membranes model for quantum heat transport in semiconductor nanowires

Presented here is a nanowire model, consisting of coupled elastic membranes with the purpose of investigating thermal transport in quasi-one-dimensional quantum systems. The vibrations of each elastic membrane are quantized and the flow of the vibrational energy between adjacent membranes is allowed. The ends of the nanowire are attached to thermal baths held at different temperatures. We derived quantum master equation for energy flow across the nanowire and obtained thermal currents and other key observables. We study the effects of a disordered boundary on the thermal current by randomizing the membrane radii. We evaluate the model as a nanowire analogue as well as study the effects of a disordered boundary on thermal conductivity. The calculations show that the membrane lattice model demonstrates diameter phonon confinement and a severe reduction in thermal conductivity due to surface roughness which is characteristic of semiconductor nanowires. The surface roughness also produces a length dependence of the thermal conductivity of the form $\kappa=\alpha L^{\beta}$, with $\beta$ dependent on disorder characteristics, in the otherwise ballistic regime. Finally, the parameters of the model are fitted to available experimental data for silicon nanowires and the results of the calculations are assessed against the experimental data.Comment: 12 Pages, 10 Figure

Unifying autocatalytic and zeroth order branching models for growing actin networks

The directed polymerization of actin networks is an essential element of many biological processes, including cell migration. Different theoretical models considering the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions. One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) or zeroth order in the number of existing filaments. Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament number. A smooth transition between the two cases is found at intermediate conditions. We also derive a threshold for the capping rate, above which autocatalytic growth is predicted at sufficiently low filament number. Below the threshold, zeroth order characteristics are predicted to dominate the dynamics of the network for all accessible filament numbers. Together, this allows cells to grow stable actin networks over a large range of different conditions.Comment: revtex, 5 pages, 4 figure