Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page

Radio detection of the young binary HD 160934

Precise determination of dynamical masses of pre-main-sequence (PMS) stars is essential to calibrate stellar evolution models that are widely used to derive theoretical masses of young low-mass objects. Binary stars in young, nearby loose associations are particularly good candidates for this calibration since all members share a common age. Interestingly, some of these young binaries present a persistent and compact radio emission, which makes them excellent targets for astrometric VLBI studies. We aim to monitor the orbital motion of the binary system HD 160934, a member of the AB Doradus moving group. We observed HD 160934 with the Very Large Array and the European VLBI Network at 8.4 and 5 GHz, respectively. The orbital information derived from these observations was analyzed along with previously reported orbital measurements. We show that the two components of the binary, HD 160934 A and HD 160934 c, display compact radio emission at VLBI scales, providing precise information on the relative orbit. Revised orbital elements were estimated. Future VLBI monitoring of this pair should determine precise model-independent mass estimates for the A and c components, which will serve as calibration tests for PMS evolutionary models.Comment: 5 pages, 5 figures, accepted for publication in A&

Electromagnetic Forming of AZ31B Magnesium Alloy Sheet

In the first stage of this work, polycrystalline specimens of AZ31B magnesium alloy have been characterized by uniaxial tensile tests at quasi-static and dynamic strain rates at room temperature. The influence of the strain rate is outlined and experimental results were fitted to the parameters of Johnson-Cook constitutive material model. In the second stage of the present study, sheets of AZ31B magnesium alloy have been biaxially formed by electromagnetic forming using different coil and die configurations. Deformation values measured from electromagnetic formed parts are compared to the ones achieved with uniaxial tensile tests and also with the values obtained by conventional forming technologies. Finally, numerical simulations have been carried out using an alternative method for computing the electromagnetic fields in the EMF process simulation, a combination of Finite Element Method (FEM) for conductor parts and Boundary Element Method (BEM) for the surrounding air (or more generally insulators) that is being implemented into commercial code LS-DYNA®

Quality-Based Thermokinetic Optimization of Ready-to-Eat Whole Edible Crab (Cancer pagurus) Pasteurisation Treatments

Traditional processing practices used in the manufacture of ready-to-eat edible crab products include a double-heat treatment involving an initial cooking step followed by washing and packaging and finally, a second heat pasteurisation. The latter, pasteurisation step, results in the most severe impact on product quality. The main objective of this research was to optimise this pasteurisation step using quality index degradation kinetic approach. Preliminary work involved the characterisation of temperature rise in the crab cold-spot during pasteurisation. Equivalent treatments (F90°C 10°C = 10 min) were defined in order to assess the impact of pasteurisation temperature on different crab quality indexes in both crab meat types, white and brown. Colour degradation of crab white meat was defined as the critical quality parameter to be monitored during thermal pasteurisation. The effect of time and temperature on the kinetics of white meat colour change (¿E*) were characterised and fitted to an exponential equation. Following this, an industry focus group was used to define white meat colour change vs product quality and defined ‘good’ (¿E* = 7), ‘acceptable’ (7 < ¿E* < 9) and ‘unacceptable’ (¿E* = 9) quality. Finally, using the developed equations, optimal pasteurisation conditions were defined and validated. To produce ‘good’ quality crab, optimal temperatures ranged between 96 and 100 °C while temperatures between 104 and 108 °C produced ‘acceptable’ quality in crabs of 400 and 800 g, respectively. Overall, the results show that the equations obtained could be used in a decision support system (DSS) to define heat pasteurisation conditions to optimise the quality of ready-to-eat edible crab

High performance computing for a 3-D optical diffraction tomographic application in fluid velocimetry

Optical Diffraction Tomography has been recently introduced in fluid velocimetry to provide three dimensional information of seeding particle locations. In general, image reconstruction methods at visible wavelengths have to account for diffraction. Linear approximation has been used for three-dimensional image reconstruction, but a non-linear and iterative reconstruction method is required when multiple scattering is not negligible. Non-linear methods require the solution of the Helmholtz equation, computationally highly demanding due to the size of the problem. The present work shows the results of a non-linear method customized for spherical particle location using GPU computing and a made-to-measure storing format

Efficiency Improvement and Analysis of Changes in Microstructure Associated to a Uniform Pressure Actuator

During the 1st international Conference on HIGH SPEED FORMING held in Dortmund in 2004 a new forming coil giving significant advantages was presented in the framework of ongoing R&D programs at OSU (The Ohio State University). It established the improvement provided by the return path for currents induced in the workpiece. To quantify the mentioned improvement, Labein has performed classical cone forming experiments with both configurations and analyzed energetic efficiency using well known alloys, more precisely AA 6016 and 1050. Both deformation mechanisms and contour analysis of the specimens were studied. General purpose multi-turn coils provide pressure distributions not extended to the whole forming area, resulting in zones undergoing significant delay as die the deformation sequence is referred. As a result, varied deformation patterns can be found along the contour of a cone specimen formed in such way. Firstly, a macroscopic survey of the specimens shows that uniform pressure distributes deformation over the entire formed area during the deformation process. Secondly, the effect on efficiency provided by this new coil concept is focuses not only on the ability for distributing deformation, but on the energy required to create such deformation. Finally, to validate the whole simulation, the predicted strain level, shape, and internal energy of the workpiece are compared with the experimental specimens. A key point in the validation process is checking the internal energy. It is known that the ratio of stored energy to deformation energy ranges in the order of 30 %. The procedure for the experiments follows this methodology

Symmetry breaking from Scherk-Schwarz compactification

We analyze the classical stable configurations of an extra-dimensional gauge theory, in which the extra dimensions are compactified on a torus. Depending on the particular choice of gauge group and the number of extra dimensions, the classical vacua compatible with four-dimensional Poincar\'e invariance and zero instanton number may have zero energy. For SU(N) on a two-dimensional torus, we find and catalogue all possible degenerate zero-energy stable configurations in terms of continuous or discrete parameters, for the case of trivial or non-trivial 't Hooft non-abelian flux, respectively. We then describe the residual symmetries of each vacua.Comment: 24 pages, 1 figure, Section 4 modifie

Expansion around half-integer values, binomial sums and inverse binomial sums

I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a symbolic computer algebra system. The method is an extension of the technique of nested sums. The algorithms allow in addition the evaluation of binomial sums, inverse binomial sums and generalizations thereof.Comment: 21 page