Eigenvalue Separation in Some Random Matrix Models

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the size of the matrices are fixed and c goes to infinity, and higher rank analogues of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions, and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogues an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained.Comment: 25 pages, 9 figures include

Electron beam chemistry produces high purity metals

Application of radiation chemistry for deposition of metals by irradiation of aqueous solutions with high energy electrons is presented. Design of reaction vessel for irradiation of solution is illustrated. Features of radiochemical technique and procedures followed are described

The application of semiconductors to quasi- optical isolators for use at submillimeter wavelengths

Semiconductor application to quasi-optical isolators - nonreciprocal reflection beam isolator and far infrared isolators using Faraday rotatio

Robust Emergent Activity in Dynamical Networks

We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we develop a macroscopic description of the system in terms of the statistical features of the subnetwork of active nodes. We find the asymptotic characteristics of this subnetwork to be remarkably robust: the size of the active set is independent of the total number of nodes in the network, and the average degree of the active nodes is independent of both the network size and its connectivity. These results suggest that very different networks evolve to active subnetworks with the same characteristic features. This has strong implications for dynamical networks observed in the natural world, notably the existence of a characteristic range of links per species across ecological systems.Comment: 4 pages, 5 figure

Evolutionary Stability of Ecological Hierarchy

A self-similar hierarchical solution that is both dynamically and evolutionarily stable is found to the multi dimensional Lotka-Volterra equation with a single chain of prey-predator relations. This gives a simple and natural explanation to the key features of hierarchical ecosystems, such as its ubiquity, pyramidal population distribution, and higher aggressiveness among higher trophic levels. pacs{87.23.Kg, 89.75.Da, 05.45.-a} keywords{Lotka-Volterra equation, Trophic pyramid, Self-similarity}Comment: 4 Pages RevTeX4, 1 Fig, 1 Table, shortened by publishers reques

Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations

A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the attractors. A mutation introduces some new aspects: the emergence of structurally stable attractors, and chaotic itinerant behavior. In addition, it is reported that a neutral attractor can exist in the mutataion rate -> +0 region.Comment: 4 pages, 9 figure

Use of radiation in preparative chemistry

A summary and updating of previous work on the use of radiation chemistry for the preparation of pure materials are presented. Work was chiefly concerned with the reduction of metal salts in solution to the free metal using 2 MeV electrons. Metals deposited from aqueous solution are copper, silver, zinc, cadmium, thallium, tin, lead, antimony, iron, nickel, cobalt, and palladium. Dry organic solvents were evaluated for the deposition of metals based on a study involving deposition of antimony from soltions of antimony (III) chloride. The use of organic liquids for the preparation of anhydrous metal halides is also presented. Reaction mechanisms for both organic liquids and aqueous system are discussed

Overcoming the barriers to implementing urban road user charging schemes

Urban road user charging offers the potential to achieve significant improvements in urban transport, but is notoriously difficult to implement. Cities need guidance on the range of factors to be considered in planning and implementing such schemes. This paper summarises the results of a 3 year programme which has collated evidence on the issues of most concern to cities. A state of the art report has provided evidence on 14 themes, ranging from objectives and design to implementation and evaluation. A set of 16 case studies has reviewed experience in design and implementation across Europe. The paper summarises their findings, provides references to more detailed information, presents the resulting policy recommendations to European, national and local government, and outlines the areas in which further research is needed