Lattice energy-momentum tensor with Symanzik improved actions

We define the energy-momentum tensor on lattice for the $\lambda \phi^4$ and for the nonlinear $\sigma$-model Symanzik tree-improved actions, using Ward identities or an explicit matching procedure. The resulting operators give the correct one loop scale anomaly, and in the case of the sigma model they can have applications in Monte Carlo simulations.Comment: Self extracting archive fil

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

The Monumental UNESCO Site of Panamá Viejo: Investigation of the Masonry Mortars

The presented study illustrates the characterisation of several artificial materials (bedding, joint mortars, and plasters) belonging to the masonries of the UNESCO site of Panamá Viejo, located in Panama City (Panama). This monumental site represents the first Spanish settlement on the Pacific Coast, founded 500 years ago, in 1519. Through mineralogical and petrographic analyses of the collected samples, as stereomicroscope and polarized light microscopy (PLM) observations of bulk and thin sections, respectively, environmental scanning electron microscopy and micro-chemical investigations (ESEM-EDX) and X-Ray Powder diffraction (XRPD) analysis, it was possible to identify the composition of the materials utilized for the production of mortars and plasters, in addition to the determination of their state of conservation. Therefore, this work represents a substantial step for the preservation of the Panamá Viejo site, in order to support the selection of the most suitable restoration products, such as consolidants, protectives, etc., but also for choosing the most compatible materials for possible replacements/integrations in the masonries

A new electrode design method in piezoelectric vibration energy harvesters to maximize output power

A resonant vibration energy harvester typically comprises of a clamped anchor and a vibrating shuttle with a proof mass. Piezoelectric materials are embedded in locations of high strain in order to transduce mechanical deformation into electrical charge. Conventional design for piezoelectric vibration energy harvesters (PVEH) usually utilizes piezoelectric materials and metal electrode layers covering the entire surface area of the cantilever with no consideration provided to examine the trade-off involved with respect to maximize output power. This paper reports on the theory and experimental verification underpinning optimization of the active electrode area in order to maximize output power. The calculations show that, in order to maximize the output power of a PVEH, the electrode should cover the piezoelectric layer from the peak strain area to a position, where the strain is a half of the average strain in all the previously covered area. With the proposed electrode design, the output power can be improved by 145% and 126% for a cantilever and a clamped-clamped beam, respectively. MEMS piezoelectric harvesters are fabricated to experimentally validate the theory.EPSRC (Grant EP/L010917/1

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

Modelling Li+ Ion Battery Electrode Properties

We formulated two detailed models for an electrolytic cell with particulate electrodes based on a lithium atom concentration dependent Butler-Volmer condition at the interface between electrode particles and the electrolyte. The first was based on a dilute-ion assumption for the electrolyte, while the second assumed that Li ions are present in excess. For the first, we used the method of multiple scales to homogenize this model over the microstructure, formed by the small lithium particles in the electrodes. For the second, we gave rigorous bounds for the effective electrochemical conductivity for a linearized case. We expect similar results and bounds for the "full nonlinear problem" because variational results are generally not adversely affected by a sinh term. Finally we used the asymptotic methods, based on parameters estimated from the literature, to attain a greatly simplified one-dimensional version of the original homogenized model. This simplified model accounts for the fact that diffusion of lithium atoms within individual electrode particles is relatively much faster than that of lithium ions across the whole cell so that lithium ion diffusion is what limits the performance of the battery. However, since most of the potential drop occurs across the Debye layers surrounding each electrode particle, lithium ion diffusion only significantly affects cell performance if there is more or less complete depletion of lithium ions in some region of the electrolyte which causes a break in the current flowing across the cell. This causes catastrophic failure. Providing such failure does not occur the potential drop across the cell is determined by the concentration of lithium atoms in the electrode particles. Within each electrode lithium atom concentration is, to leading order, a function of time only and not of position within the electrode. The depletion of electrode lithium atom concentration is directly proportional to the current being drawn off the cell. This leads one to expect that the potential of the cell gradually drops as current is drawn of it. We would like to emphasize that all the homogenization methods employed in this work give a systematic approach for investigating the effect that changes in the microstructure have on the behaviour of the battery. However, due to lack of time, we have not used this method to investigate particular particle geometries

Wide Localized Solitons in Systems with Time and Space-Modulated Nonlinearities

In this work we apply point canonical transformations to solve some classes of nonautonomous nonlinear Schr\"{o}dinger equation namely, those which possess specific cubic and quintic - time and space dependent - nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wavefunction and recover a time and space independent nonlinear equation which can be solved explicitly. The method applied here allow us to find wide localized (in space) soliton solutions to the nonautonomous nonlinear Schr\"{o}dinger equation, which were not presented before. We also generalize the external potential which traps the system and the nonlinearities terms.Comment: 19 pages, 5 figure