Shallow Linear Action Graphs and their Embeddings

Action calculi, which generalise process calculi such as Petri nets, π-calculusand ambient calculus, have been presented in terms of action graphs. We here offer linear action graphs as a primitive basis for action calculi. This paper presents the category of embeddings of undirected linear action graphs without nesting, using a novel form of graphical reasoning which simplifies some otherwise complex manipulations in regular algebra. The results are adapted in a few lines to directed graphs. This work is part of a long-term search for a uniform behavioural theory for process calculi. Received October 2000 / Accepted in revised form April 2001     

Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Structural acrylic adhesives for the sheet steel fabrication industries

Recent developments in rubber-toughened structural acrylic adhesives now offer sheet steel fabricators the opportunity to replace conventional metal fastening techniques such as spot welding with lower cost, durable, more versatile structural adhesive bonding. These developments, in particular much improved ability to bond oily/waxy surfaces common to the motor car industry and improved retention of fracture toughness after exposure to paint stoving temperatures, are discussed in this paper.     

Eliminating memory for fragmentation within partitionable SIMD/SPMDmachines

Efficient data layout is an important aspect of the compilation process. A model for the creation of perfect memory maps for large-scale parallel machines capable of user-controlled partitionable single-instruction-multiple data/single-program-multiple data (SIMD/SPMD) operation is developed. The term perfect implies that no memory fragmentation occurs and ensures that the memory map size is kept to a minimum. A major constraint on solving this problem is based on the single program nature of both the SIMD and SPMD modes of parallelism. It is assumed that all processors within the same submachine used identical addresses to access corresponding data items in each of their local memories. Necessary and sufficient conditions are derived for being able to create perfect memory maps, and results are applied to several partitionable interconnection networks     

Statistical tests of the IBM PC pseudorandom number generator

The widespread use of IBM personal computers in biomedical research and medical practice is evidenced by a variety of journal articles. Many of the application programs are written in the BASIC language, they model a stochastic process, and they depend on the Microsoft random number generator. Unfortunately, the Microsoft generator has exhibited a number of flaws including, for some seeds, a lack of uniformity of generated sequences of numbers, and serial correlation within such sequences. This paper provides evidence of these problems for several seeds, and provides suggestions for acceptable seeds which ensure that the generated sequences of numbers pass two fundamental statistical tests for randomness.     

Magnetic field dependence of shielding current density in Y-Ba-Cu-O rings at 77 K

A method for contactless measurement of the shielding critical current density and its dependence on the external magnetic field is described and analyzed. The obtained values are compared with those measured resistively on two different samples. It is shown that the shielding critical current densityJ _cs and the intergranular transport current densityJ _cr are identical if the measurement conditions are similar. A degradation ofJ _cs measured in the external field with AC ripple has been observed.