Pair Excitations and Vertex Corrections in Fermi Fluids

Based on an equations--of--motion approach for time--dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known ``correlated'' random--phase approximation (CRPA), our approach has the following properties: i) The CRPA is reproduced when pair fluctuations are neglected. ii) The first two energy--weighted sumrules are fulfilled implying a correct static structure. iii) No ad--hoc assumptions for the effective mass are needed to reproduce the experimental dispersion of the roton in 3He. iv) The density response function displays a novel form, arising from vertex corrections in the proper polarisation. Our theory is presented here with special emphasis on this latter point. We have also extended the approach to the single particle self-energy and included pair fluctuations in the same way. The theory provides a diagrammatic superset of the familiar GW approximation. It aims at a consistent calculation of single particle excitations with an accuracy that has previously only been achieved for impurities in Bose liquids.Comment: to be published in: JLTP (2007) Proc. Int. Symp. QFS2006, 1-6 Aug. 2006, Kyoto, Japa

A HIERARCHY OF GAUGED GRASSMANIAN MODELS IN 4p4p DIMENSIONS WITH SELF-DUAL INSTANTONS

We present a hierarchy of gauged Grassmanian models in $4p$ dimensions, where the gauge field takes its values in the $2^{2p- 1}\times 2^{2p-1}$ chiral representation of SO(4p). The actions of all these models are absolutely minimised by a hierarchy of self-duality equations, all of which reduce to a single pair of coupled ordinary differential equations when subjected to $4p$ dimensional spherical symmetry.Comment: latex file, 13 page

Special section on advances in reachability analysis and decision procedures: contributions to abstraction-based system verification

Reachability analysis asks whether a system can evolve from legitimate initial states to unsafe states. It is thus a fundamental tool in the validation of computational systems - be they software, hardware, or a combination thereof. We recall a standard approach for reachability analysis, which captures the system in a transition system, forms another transition system as an over-approximation, and performs an incremental fixed-point computation on that over-approximation to determine whether unsafe states can be reached. We show this method to be sound for proving the absence of errors, and discuss its limitations for proving the presence of errors, as well as some means of addressing this limitation. We then sketch how program annotations for data integrity constraints and interface specifications - as in Bertrand Meyers paradigm of Design by Contract - can facilitate the validation of modular programs, e.g., by obtaining more precise verification conditions for software verification supported by automated theorem proving. Then we recap how the decision problem of satisfiability for formulae of logics with theories - e.g., bit-vector arithmetic - can be used to construct an over-approximating transition system for a program. Programs with data types comprised of bit-vectors of finite width require bespoke decision procedures for satisfiability. Finite-width data types challenge the reduction of that decision problem to one that off-the-shelf tools can solve effectively, e.g., SAT solvers for propositional logic. In that context, we recall the Tseitin encoding which converts formulae from that logic into conjunctive normal form - the standard format for most SAT solvers - with only linear blow-up in the size of the formula, but linear increase in the number of variables. Finally, we discuss the contributions that the three papers in this special section make in the areas that we sketched above. © Springer-Verlag 2009

Integral equation method for the electromagnetic wave propagation in stratified anisotropic dielectric-magnetic materials

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.Comment: 14pages, 3figure

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

Determining a Flow Stress Model for High Temperature Deformation of Ti-6Al-4V

In some commercial titanium extrusion practices, twisting of the extrudate can occur, which can result in the need to crop the back and front end of the extruded material, thereby reducing yield and increasing material losses. Understanding more about the behaviour of material during the extrusion process, and investigating the cause of defects such as twisting by use of finite element (FE) modelling techniques could help to reduce these losses, improve the productivity of the extrusion process, and the overall quality of the material produced. One of the most important components of FE techniques for hot deformation is the type of flow stress model that is used in the simulations. In this investigation isothermal uniaxial compression testing was performed on cylindrical specimens of Ti-6Al-4V at temperatures ranging from 950 °C to 1200°C and strain rates of 0.1 s-1 to 50 s-1, to produce true stress against true strain and load against die travel curves which were subsequently used to develop a new specific flow stress model for use in hot deformation above the beta transus, which can ultimately be applied to the hot extrusion of Ti-6Al-4V. From analysis of this data it was concluded that flow softening and work hardening do not occur during deformation, and that low friction conditions exist between the material and the tooling. The activation energy for deformation was found to be 193178 J.mol-1, and the flow stress model was shown to give a good fit to the raw data at low strain rates, but this relationship broke down at higher strain rates. Finally the importance of generating a flow stress model specific to a particular operation, and set of experimental data, rather than relying on existing data available in the literature is demonstrated

A direct path to dependable software

What would it take to make software more dependable? Until now, most approaches have been indirect: some practices – processes, tools or techniques – are used that are believed to yield dependable software, and the argument for dependability rests on the extent to which the developers have adhered to them. This article argues instead that developers should produce direct evidence that the software satisfies its dependability claims. The potential advantages of this approach are greater credibility (since the argument is not contingent on the effectiveness of the practices) and reduced cost (since development resources can be focused where they have the most impact)

Dietary studies in birds: testing a non-invasive method using digital photography in seabirds

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Dietary studies give vital insights into foraging behaviour, with implications for understanding changing environmental conditions and the anthropogenic impacts on natural resources. Traditional diet sampling methods may be invasive or subject to biases, so developing non-invasive and unbiased methods applicable to a diversity of species is essential. We used digital photography to investigate the diet fed to chicks of a prey-carrying seabird and compared our approach (photo-sampling) to a traditional method (regurgitations) for the greater crested tern Thalasseus bergii. Over three breeding seasons, we identified >24 000 prey items of at least 48 different species, more than doubling the known diversity of prey taken by this population of terns. We present a method to estimate the length of the main prey species (anchovy Engraulis encrasicolus) from photographs, with an accuracy <1 mm and precision ~ 0·5 mm. Compared to regurgitations at two colonies, photo-sampling produced similar estimates of prey composition and size, at a faster species accumulation rate. The prey compositions collected by two researchers photo-sampling concurrently were also similar. Photo-sampling offers a non-invasive tool to accurately and efficiently investigate the diet composition and prey size of prey-carrying birds. It reduces biases associated with observer-based studies and is simple to use. This methodology provides a novel tool to aid conservation and management decision-making in the light of the growing need to assess environmental and anthropogenic change in natural ecosystems.Department of Science and Technology, South Afric

Liquid 4He: contributions to first principles theory of quantized vortices, thermohydrodynamic properties, and the lambda transition

Liquid 4He has been studied extensively for almost a century, but there are still a number of outstanding weak or missing links in our comprehension of it. This paper reviews some of the principal paths taken in previous research and then proceeds to fill gaps and create an integrated picture with more complete understanding through first principles treatment of a realistic model that starts with a microscopic, atomistic description of the liquid. Newly derived results for vortex cores and thermohydrodynamic properties for a two-fluid model are used to show that interacting quantized vortices may produce a lambda anomaly in specific heat near the superfluid transition where flow properties change. The nature of the order in the superfluid state is explained. Experimental support for new calculations is exhibited, and a unique specific heat experiment is proposed to test predictions of the theory. Relevance of the theory to modern research in cosmology, astrophysics, and Bose-Einstein condensates is discussed.Comment: 155 pages, 28 figure

Bound states between dark matter particles and emission of gravitational radiation

Bound states of two weakly interactive massive particles are studied. It is assumed that the WIMPonium is formed due to the gravitational interaction, since the weak interaction can sometimes be repulsive. The lifetimes of the spontaneous emission of gravitational radiation and of the WIMPs annihilation into a pair of gravitons are computed, and are shown to be many orders of magnitude larger than the age of the universe.Comment: Accepted for publication in GER