Architectural issues related to the optical implementation of an EGS network based on embedded control

Free-space optical implementations of switching networks have been proposed to circumvent many of the system-level problems that may be encountered in systems that require many high-density, high-bandwidth connections. The details of a new class of switching network (the EGS network), that is well-suited to free-space implementations, is described. The common control injection problem that plagues most free-space photonic networks, i.e. how can control information from an electronic source be injected into the network for applications that require relatively high network reconfiguration rates, is examined. A new technique for control injection, called embedded control, which permits network operation even with relatively high network reconfiguration rates is also proposed.     

N. Charton,A. Feldermann,A. Theis,M. H. Stenzel,T. P. Davis,C. Barner‐Kowollik,Initiator efficiency of 2,2′‐azobis(isobutyronitrile) in bulk dodecyl acrylate free‐radical polymerizations over a wide conversion and molecular weight range (2004) 42(20) 5170–5179

The original article to which this Erratum refers was published in J Polym Sci Part A: Polym Chem (2004) 42(20) 5170–5179. No abstract.     

Higher-order radiative perturbation theory

As a computationally effective tool, the first-order term of the radiative perturbation theory has been computed successfully, and has been applied in a number of areas. In this article, we develop the computational expressions for the higher-order terms of the perturbation expansion in a plane parallel atmosphere. These expressions are then implemented, and numerical results for some typical cases are presented. These results indicate that the computation is successful and that the higher-order terms are essential in cases where the first-order term alone cannot predict the perturbation with sufficient accuracy.     

Profinite groups of finite cohomological dimension

Let 1→N→G→G/N→1 be a short exact sequence of profinite groups, and let p be a prime number. We prove that if G is of finite cohomological p-dimension n:=cd_p(G)<∞ and if the order of $\text{H}{}^{\mathrm{k}}\text{(N,}\text{F}{}_{\mathrm{p}}\text{)}$ is finite for k:=cd_p(N), the virtual cohomological p-dimension of G/N equals n?k. To cite this article: T. Weigel, P. Zalesskii, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems

Multi-valued solutions are constructed for 2 × 2 first-order systems using a generalization of the hodograph transformation. The solution is found as a complex analytic function on a complex Riemann surface for which the branch points move as part of the solution. The branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds. We perform an analysis of stability of these singularities with respect to perturbations of the initial data. The generic singularity types are folds, cusps, and nondegenerate umbilic points with non-zero 3-jet. An isolated singularity is generically a square root branch point corresponding to a fold. Two types of collisions between singularities are generic: At a “tangential” collision between two singularities moving at the same characteristic speed, a cube root branch point is formed, corresponding to a cusp. A “non-tangential” collision, between two square root branch points moving at different characteristic speeds, remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point. These results are also valid for a diagonalizable n-th order system for which there are exactly two speeds. © 1993 John Wiley & Sons, Inc.     

On the Connectivity of Cobordisms and Half-Projective TQFT's

We consider a generalization of the axioms of a TQFT, the so-called half-projective TQFT's, where we inserted an anomaly, , in the composition law. Here μ₀ is a coboundary (in a group cohomological sense) on the cobordism categories with non-negative, integer values. The element of the ring over which the TQFT is defined does not have to be invertible. In particular, it may be zero. This modification makes it possible to extend quantum-invariants, which vanish on S ¹×S ², to non-trivial TQFT's. Note, that a TQFT in the ordinary sense of Atiyah with this property has to be trivial all together. We organize our discussions such that the notion of a half-projective TQFT is extracted as the only possible generalization under a few very natural assumptions. Based on separate work with Lyubashenko on connected TQFT's, we construct a large class of half-projective TQFT's with . Their invariants all vanish on S ¹×S ², and they coincide with the Hennings invariant for non-semisimple Hopf algebras and, more generally, with the Lyubashenko invariant for non-semisimple categories. We also develop a few topological tools that allow us to determine the cocycle μ₀ and find numbers, ϱ(M), such that the linear map associated to a cobordism, M, is of the form . They are concerned with connectivity properties of cobordisms, as for example maximal non-separating surfaces. We introduce in particular the notions of “interior” homotopy and homology groups, and of coordinate graphs, which are functions on cobordisms with values in the morphisms of a graph category. For applications we will prove that half-projective TQFT's with vanish on cobordisms with infinite interior homology, and we argue that the order of divergence of the TQFT on a cobordism, M, in the “classical limit” can be estimated by the rank of its maximal free interior group, which coincides with ϱ(M). Received: 20 October 1997 / Accepted: 18 March 1998     

Large-scale computer simulation of fully developed turbulent channel flow with heat transfer

Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.     

Fiber formation via solution spinning of the cellulose/ammonia/ammonium thiocyanate system

Fiber formation via the cellulose/ammonia/ammonium thiocyanate system by wet spinning has been investigated. This report presents a characterization of the structure and tensile properties of fibers spun under various coagulation conditions. Microscopic observations showed that the molecular size of coagulant was the dominant factor governing the crosssectional shape of the fibers. Density, birefringence, and crystallinity data indicated that a higher cellulose concentration and lower coagulation temperature favored development of a fiber with a denser and more oriented structure. Under optimum conditions, a welldefined fibrillar structure was obtained. Fiber tensile property measurements suggested the existence of a linear relationship between the fiber breaking tenacity and the product of the square of the Hermans' orientation factor and the infrared crystallinity index.     

Determination of the Tolman cone angle from crystallographic parameters and a statistical analysis using the crystallographic data base

Summary A new method of evaluating the Tolman cone angle from X-ray structural data available from the Cambridge Crystallographic Data Base has been developed and a statistical analysis of the cone angles of the phosphines PPh₃, PMe₂Ph, PMePh₂, PMe₃, PEt₃ and PCy₃ (Cy = cyclohexyl) in transition metal complexes has been completed.     

On the Immersion Relation and an Embedding Problem for Infinite Graphs

Recent results on the immersion relation for graphs are applied to show that there exist (uncountable) graphs A and G such that G contains n disjoint copies of A for each positive integer n, but the graph N₀A consisting of infinitely many disjoint copies of A does not embed in G, where by ‘embedding’ we mean ‘immersion in the weak sense’.