Dark Matter in the USSM

We discuss the neutralino dark matter within classes of extended supersymmetric models, referred to as the USSM, containing one additional SM singlet Higgs plus an extra Z', together with their superpartners the singlino and bino'.Comment: 4 pages, 3 figs. Talk given at LCWS08, Chicago, IL, USA, 11/16-20/200

LHC Signatures of the Constrained Exceptional Supersymmetric Standard Model

We discuss two striking Large Hadron Collider (LHC) signatures of the constrained version of the exceptional supersymmetric standard model (cE6SSM), based on a universal high energy soft scalar mass m_0, soft trilinear coupling A_0 and soft gaugino mass M_{1/2}. The first signature we discuss is that of light exotic colour triplet charge 1/3 fermions, which we refer to as D-fermions. We calculate the LHC production cross section of D-fermions, and discuss their decay patterns. Secondly we discuss the E6 type U(1)_N spin-1 Z' gauge boson and show how it may decay into exotic states, increasing its width and modifying the line shape of the dilepton final state. We illustrate these features using two representative cE6SSM benchmark points, including an "early LHC discovery" point, giving the Feynman rules and numerical values for the relevant couplings in order to facilitate further studies.Comment: 30 pages, 5 figures, corrections to figure caption

Ray methods for free boundary problems

We discuss the use of the WKB ansatz in a variety of parabolic problems involving a small parameter. We analyse the Stefan problem for small latent heat, the Black–Scholes problem for an American put option, and some nonlinear diffusion equations, in each case constructing an asymptotic solution by the use of ray methods

Stryker Osteonics: Prosthetic Knee Joint

We examine, within a simple bearing model of a knee joint that only consideres pure sliding, the effect of the presence of a small vertical hole in the load area on the fluid film properties. The calculations indicate that fluid is entrapped in such a hole, which, for constant load, causes a smaller minimal film separation of the two surfaces. This will lower the horizontal friction, but may also bring about surface contact in high load situations

Nonuniqueness in a minimal model for cell motility

Two–phase flow models have been used previously to model cell motility, however these have rapidly become very complicated, including many physical processes, and are opaque. Here we demonstrate that even the simplest one–dimensional, two–phase, poroviscous, reactive flow model displays a number of behaviours relevant to cell crawling. We present stability analyses that show that an asymmetric perturbation is required to cause a spatially uniform, stationary strip of cytoplasm to move, which is relevant to cell polarization. Our numerical simulations identify qualitatively distinct families of travelling–wave solution that co–exist at certain parameter values. Within each family, the crawling speed of the strip has a bell–shaped dependence on the adhesion strength. The model captures the experimentally observed behaviour that cells crawl quickest at intermediate adhesion strengths, when the substrate is neither too sticky nor too slippy