An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems

In the context of analyzing a new model for nonlinear diffusion in polymers, an unusual condition appears at the moving interface between the glassy and rubbery phases of the polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our equations, has received very little attention in the mathematical literature. Due to the unusual form of the moving-boundary condition, further study is needed as to the existence and uniqueness of solutions satisfying such a condition. The moving boundary condition which results is not solvable by similarity solutions, but can be solved by integral equation techniques. A solution process is outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic of a dissolving polymer

Lamb wave near field enhancements for surface breaking defects in plates

Near field surface wave ultrasonic enhancements have previously been used to detect surface breaking defects in thick samples using Rayleigh waves. Here, we present analogous surface wave enhancements for Lamb waves propagating in plates. By tracking frequency intensities in selected regions of time-frequency representations, we observe frequency enhancement in the near field, due to constructive interference of the incident wave mode with those reflected and mode converted at the defect. This is explained using two test models; a square based notch and an opening crack, which are used to predict the contribution to the out-of-plane displacement from the reflected and mode converted waves. This method has the potential to provide a reliable method for the near field identification and characterisation of surface breaking defects in plates

Mechanism for the failure of the Edwards hypothesis in the SK spin glass

The dynamics of the SK model at T=0 starting from random spin configurations is considered. The metastable states reached by such dynamics are atypical of such states as a whole, in that the probability density of site energies, $p(\lambda)$, is small at $\lambda=0$. Since virtually all metastable states have a much larger $p(0)$, this behavior demonstrates a qualitative failure of the Edwards hypothesis. We look for its origins by modelling the changes in the site energies during the dynamics as a Markov process. We show how the small $p(0)$ arises from features of the Markov process that have a clear physical basis in the spin-glass, and hence explain the failure of the Edwards hypothesis.Comment: 5 pages, new title, modified text, additional reference

Environmental justice, capabilities, and the theorization of well-being

Environmental justice (EJ) scholarship is increasingly framing justice in terms of capabilities. This paper argues that capabilities are fundamentally about well-being and as such there is a need to more explicitly theorize well-being. We explore how capabilities have come to be influential in EJ and how well-being has been approached so far in EJ specifically and human geography more broadly. We then introduce a body of literature from social psychology which has grappled theoretically with questions about well-being, using the insights we gain from it to reflect on some possible trajectories and challenges for EJ as it engages with well-being

Expert systems for real-time monitoring and fault diagnosis

Methods for building real-time onboard expert systems were investigated, and the use of expert systems technology was demonstrated in improving the performance of current real-time onboard monitoring and fault diagnosis applications. The potential applications of the proposed research include an expert system environment allowing the integration of expert systems into conventional time-critical application solutions, a grammar for describing the discrete event behavior of monitoring and fault diagnosis systems, and their applications to new real-time hardware fault diagnosis and monitoring systems for aircraft

Statistical Mechanics of Vibration-Induced Compaction of Powders

We propose a theory which describes the density relaxation of loosely packed, cohesionless granular material under mechanical tapping. Using the compactivity concept we develope a formalism of statistical mechanics which allows us to calculate the density of a powder as a function of time and compactivity. A simple fluctuation-dissipation relation which relates compactivity to the amplitude and frequency of a tapping is proposed. Experimental data of E.R.Nowak et al. [{\it Powder Technology} 94, 79 (1997) ] show how density of initially deposited in a fluffy state powder evolves under carefully controlled tapping towards a random close packing (RCP) density. Ramping the vibration amplitude repeatedly up and back down again reveals the existence of reversible and irreversible branches in the response. In the framework of our approach the reversible branch (along which the RCP density is obtained) corresponds to the steady state solution of the Fokker-Planck equation whereas the irreversible one is represented by a superposition of "excited states" eigenfunctions. These two regimes of response are analyzed theoretically and a qualitative explanation of the hysteresis curve is offered.Comment: 11 pages, 2 figures, Latex. Revised tex

Spiral vortices traveling between two rotating defects in the Taylor-Couette system

Numerical calculations of vortex flows in Taylor-Couette systems with counter rotating cylinders are presented. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method. Annular gaps of radius ratio $\eta=0.5$ and of several heights are simulated. They are closed by nonrotating lids that produce localized Ekman vortices in their vicinity and that prevent axial phase propagation of spiral vortices. Existence and spatio temporal properties of rotating defects, of modulated Ekman vortices, and of the spiral vortex structures in the bulk are elucidated in quantitative detail.Comment: 9 pages, 9 figure

Elastic Energy, Fluctuations and Temperature for Granular Materials

We probe, using a model system, elastic and kinetic energies for sheared granular materials. For large enough $P/E_y$ (pressure/Young's modulus) and $P/\rho v^2$ ($P/$kinetic energy density) elastic dominates kinetic energy, and energy fluctuations become primarily elastic in nature. This regime has likely been reached in recent experiments. We consider a generalization of the granular temperature, $T_g$, with both kinetic and elastic terms and that changes smoothly from one regime to the other. This $T_g$ is roughly consistent with a temperature adapted from equilibrium statistical mechanics.Comment: 4 pages, 4 figure

The nature of the long time decay at a second order transition point

We show that at a second order phase transition, of \phi^4 like system, a necessary condition for streched exponential decay of the time structure factor is obeyed. Using the ideas presented in this proof a crude estimate of the decay of the structure factor is obtained and shown to yield stretched exponential decay under very reasonable conditions.Comment: 7 page