Twistor Spaces for QKT Manifolds

We find that the target space of two-dimensional (4,0) supersymmetric sigma models with torsion coupled to (4,0) supergravity is a QKT manifold, that is, a quaternionic K\"ahler manifold with torsion. We give four examples of geodesically complete QKT manifolds one of which is a generalisation of the LeBrun geometry. We then construct the twistor space associated with a QKT manifold and show that under certain conditions it is a K\"ahler manifold with a complex contact structure. We also show that, for every 4k-dimensional QKT manifold, there is an associated 4(k+1)-dimensional hyper-K\"ahler one.Comment: 25 pages, phyzz

Quantitative risk analysis for road tunnels complying with EU regulations

Tunnels have improved the connection of regions within the European Commission (EC) and have been used lately as a catalyst for economic development of previously isolated regions. However, the increasing number of these important infrastructures is raising upfront an endogenous problem, which is the severity of accidents that may occur. These risks have much greater impact when heavy goods vehicles (HGVs) or dangerous goods (DGs) are involved in the accident. As a result, the EC launched the EC Directive 2004/54/EC. In order to achieve a minimum acceptable level of safety, the EC Directive 2004/54/EC suggests, apart from the measures imposed based on tunnel characteristics, the implementation of a risk analysis in cases such as the opening of the road tunnel to DGs. The most widely accepted method for such quantitative risk analysis (QRA) is the OECD/PIARC QRA Model. This research exploits the QRA Model to perform a QRA for five illustrative cases in order to explore the sufficiency of the minimum tunnel safety measures imposed by the Directive when transportation of HGVs and DGs is allowed through the tunnel. The research concludes that, at least for tunnels with marginal values of the EC Directive classes for length and traffic, the risk exposure (F/N curves) lays over the acceptable safety limits of ALARP (as low as reasonably practicable) models. Thus, the manager of the tunnel should take seriously into account the provision of the Directive for further risk analysis and consider more safety measures as well as take into account the risk associated with the alternative routes

The effects of organic farming on the soil physical environment

The aim of this research was to investigate the effects of organic farming practices on the development of soil physical properties, and in particular, soil structure in comparison with conventional agricultural management. The soil structure of organically and conventionally managed soils at one site was compared in a quantitative manner at different scales of observations using image analysis. Key soil physical and chemical properties were measured as well as the pore fractal geometry to characterise pore roughness. Organically managed soils had higher organic matter content and provided a more stable soil structure than conventionally managed soils. The higher porosity (%) at the macroscale in soil under conventional management was due to fewer larger pores while mesoand microscale porosity was found to be greater under organic management. Organically managed soils typically provided spatially well distributed pores of all sizes and of greater roughness compared to those under conventional management. These variations in the soil physical environment are likely to impact significantly on the performance of these soils for a number of key processes such as crop establishment and water availabilit

Towards an effective-action approach to fermion-loop corrections

We present a study of the effective action approach to incorporate higher-order effects in e^+e^- -> n fermions. In its minimal version, the effective action approach is found to exhibit problems with unitarity and high-energy behaviour. We identify the origin of these problems by investigating the zero-mode solutions of the Ward Identities. A numerical analysis of the importance of the zero-mode solutions is presented for four-fermion production processes.Comment: 43 pages, 1 figure. Accepted for publication in Nuclear Physics

Numerical analysis of the SIMP model for the topology optimization of minimizing compliance in linear elasticity

We study the finite element approximation of the solid isotropic material with penalization (SIMP) model for the topology optimization of the compliance of a linearly elastic structure. To ensure the existence of a minimizer to the infinite-dimensional problem, we consider two popular restriction methods: $W^{1,p}$-type regularization and density filtering. Previous results prove weak(-*) convergence in the solution space of the material distribution to an unspecified minimizer of the infinite-dimensional problem. In this work, we show that, for every isolated minimizer, there exists a sequence of finite element minimizers that strongly converges to the minimizer in the solution space. As a by-product, this ensures that there exists a sequence of unfiltered discretized material distributions that does not exhibit checkerboarding

Density profiles and collective excitations of a trapped two component Fermi vapour

We discuss the ground state and the small-amplitude excitations of a degenerate vapour of fermionic atoms placed in two hyperfine states inside a spherical harmonic trap. An equations-of-motion approach is set up to discuss the hydrodynamic dissipation processes from the interactions between the two components of the fluid beyond mean-field theory and to emphasize analogies with spin dynamics and spin diffusion in a homogeneous Fermi liquid. The conditions for the establishment of a collisional regime via scattering against cold-atom impurities are analyzed. The equilibrium density profiles are then calculated for a two-component vapour of 40K atoms: they are little modified by the interactions for presently relevant values of the system parameters, but spatial separation of the two components will spontaneously arise as the number of atoms in the trap is increased. The eigenmodes of collective oscillation in both the total particle number density and the concentration density are evaluated analytically in the special case of a symmetric two-component vapour in the collisional regime. The dispersion relation of the surface modes for the total particle density reduces in this case to that of a one-component Fermi vapour, whereas the frequencies of all other modes are shifted by the interactions.Comment: 14 pages, 4 figure

Curved branes from string dualities

We describe a simple method for generating new string solutions for which the brane worldvolume is a curved space. As a starting point we use solutions with NS-NS charges combined with 2-d CFT's representing different parts of space-time. We illustrate our method with many examples, some of which are associated with conformally invariant sigma models. Using U-duality, we also obtain supergravity solutions with RR charges which can be interpreted as D-branes with non-trivial worldvolume geometry. In particular, we discuss the case of a D5-brane wrapped on AdS_3 x S^3, a solution interpolating between AdS_3 x S^3 x R^5 and AdS_3 x S^3 x S^3 x R, and a D3-brane wrapped over S^3 x R or AdS_2 x S^2. Another class of solutions we discuss involves NS5-branes intersecting over a 3-space and NS5-branes intersecting over a line. These solutions are similar to D7-brane or cosmic string backgrounds.Comment: 21 pages, harvmac; misprint correcte