Signature Characters for A_2 and B_2

The signatures of the inner product matrices on a Lie algebra's highest weight representation are encoded in the representation's signature character. We show that the signature characters of a finite-dimensional Lie algebra's highest weight representations obey simple difference equations that have a unique solution once appropriate boundary conditions are imposed. We use these results to derive the signature characters of all $A_2$ and $B_2$ highest weight representations. Our results extend, and explain, signature patterns analogous to those observed by Friedan, Qiu and Shenker in the Virasoro algebra's representation theory.Comment: 22 p

Laser Stripping for the PS2 Charge-Exchange Injection System

Laser stripping for an H- injection system into the proposed PS2 accelerator could provide an attractive alternative to the use of a conventional stripping foil. In this paper possible concepts for a 4 GeV laser stripping system are outlined and compared, using either laser or magnetic initial stripping steps and a resonant excitation of the intermediate H0 atom, followed by a final magnetic stripping. Issues of laser power, overall efficiency and emittance growth are discussed

Stability of nanoparticle laden aerosol liquid droplets

We develop a model for the thermodynamics and evaporation dynamics of aerosol droplets of a liquid such as water, surrounded by the gas. When the temperature and the chemical potential (or equivalently the humidity) are such that the vapour phase is the thermodynamic equilibrium state, then of course droplets of the pure liquid evaporate over a relatively short time. However, if the droplets also contain nanoparticles or any other non-volatile solute, then the droplets can become thermodynamically stable. We show that the equilibrium droplet size depends strongly on the amount and solubility of the nanoparticles within, i.e. on the nature of the particle interactions with the liquid, and of course also on the vapour temperature and chemical potential. We develop a simple thermodynamic model for such droplets and compare predictions with results from a lattice density functional theory that takes as input the same particle interaction properties, finding very good agreement. We also use dynamical density functional theory to study the evaporation/condensation dynamics of liquid from/to droplets as they equilibrate with the vapour, thereby demonstrating droplet stability

Towards In Situ Atomic Force Microscopy Imaging of Biofilm Growth on Stainless Steel

Atomic force microscopy (AFM) has been used to visualise the formation of bacterial biofilms on polished surfaces of 316 stainless steel. Imaging under ambient conditions revealed both the bacterial cells and the matrix of exopolymeric substances (EPS). These images exhibited good resolution with cell surface features as small as 30 nm distinguishable. In situ imaging was also carried out, and although the resolution was considerably reduced, images revealing the process of bacteria division have been obtained

Energetic Instability Unjams Sand and Suspension

Jamming is a phenomenon occurring in systems as diverse as traffic, colloidal suspensions and granular materials. A theory on the reversible elastic deformation of jammed states is presented. First, an explicit granular stress-strain relation is derived that captures many relevant features of sand, including especially the Coulomb yield surface and a third-order jamming transition. Then this approach is generalized, and employed to consider jammed magneto- and electro-rheological fluids, again producing results that compare well to experiments and simulations.Comment: 9 pages 2 fi

Dynamic response of phenolic resin and its carbon-nanotube composites to shock wave loading

We investigate with nonreactive molecular dynamics simulations the dynamic response of phenolic resin and its carbon-nanotube (CNT) composites to shock wave compression. For phenolic resin, our simulations yield shock states in agreement with experiments on similar polymers except the “phase change” observed in experiments, indicating that such phase change is chemical in nature. The elastic–plastic transition is characterized by shear stress relaxation and atomic-level slip, and phenolic resin shows strong strain hardening. Shock loading of the CNT-resin composites is applied parallel or perpendicular to the CNT axis, and the composites demonstrate anisotropy in wave propagation, yield and CNT deformation. The CNTs induce stress concentrations in the composites and may increase the yield strength. Our simulations suggest that the bulk shock response of the composites depends on the volume fraction, length ratio, impact cross-section, and geometry of the CNT components; the short CNTs in current simulations have insignificant effect on the bulk response of resin polymer

Book Reviews

The purpose of this book is, to quote from the preface, to present a clear, accurate, and impartial study of the law in the hope of offering assistance to those who are attempting to choose a career or who are about to enter upon the profession. This necessitates a review of the nature of the law, present day legal conditions, personal and educational requirements, the dangers and disadvantages incident to practice, the high professional demands made upon the lawyer, the varied fields of service open to him, his probable earnings and emoluments,--in a word, all that has a distinct and important bearing upon the law as a vocation

On the study of slow-fast dynamics, when the fast process has multiple invariant measures

Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in which the fast process is decoupled from the slow process and the case in which the two components are fully coupled. We work in the setting in which the slow process evolves according to an Ordinary Differential Equation (ODE) and the fast process is a continuous time Markov Process with finite state space and show that, in this setting, the limiting (averaged) dynamics can be described as a random ODE (that is, an ODE with random coefficients.) Keywords. Multiscale methods, Processes with multiple equilibria, Averaging, Collective Navigation, Interacting Piecewise Deterministic Markov Processes.Comment: 24 page