Inter-dependence of the volume and stress ensembles and equipartition in statistical mechanics of granular systems

We discuss the statistical mechanics of granular matter and derive several significant results. First, we show that, contrary to common belief, the volume and stress ensembles are inter-dependent, necessitating the use of both. We use the combined ensemble to calculate explicitly expectation values of structural and stress-related quantities for two-dimensional systems. We thence demonstrate that structural properties may depend on the angoricity tensor and that stress-based quantities may depend on the compactivity. This calls into question previous statistical mechanical analyses of static granular systems and related derivations of expectation values. Second, we establish the existence of an intriguing equipartition principle - the total volume is shared equally amongst both structural and stress-related degrees of freedom. Third, we derive an expression for the compactivity that makes it possible to quantify it from macroscopic measurements.Comment: 5 pages, including 2 figures, To appear in Phys. Rev. Let

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

Mosses of Mt. Trus Madi, Sabah, Malaysia

A species list of mosses collected in Mt. Trus Madi, Sabah, between 10 September and 10 October 1996 is presented. A total of 153 taxa were collected, of which 11 are new to Borneo and five new to Sabah

Multiple wavemode scanning for near and far-side defect characterisation

The combination of ultrasonic inspections using different wavemodes can give more information than is available with single mode inspection. In this work, the response of shear and Rayleigh waves to surface-breaking defects propagating on the near-side and far-side of a sample is investigated. The directivity of shear waves generated by a racetrack coil electromagnetic acoustic transducer (EMAT) is identified and used to set an ideal separation for a pair of transmit-receive EMATs. Defects are indicated by a reduction in the transmitted Rayleigh wave amplitude, and by blocking of the shear wave. Used together, these can identify features in the bulk wave behaviour which are due to near-face surface-breaking defects, and give a full picture of both surfaces. By using a combination of the two wavemodes, the angle of propagation and length of any near-side defects can additionally be identified. A scanning method for samples is proposed

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

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

Geometric partition functions of cellular systems: Explicit calculation of the entropy in two and three dimensions

A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling the identification of a phase space and making it possible to take account of geometrical correlations systematically. Case studies are presented for which explicit calculations of the mean vertex density and porosity fluctuations are given as functions of compactivity. The formalism applies equally well to two- and three-dimensional granular assemblies.Comment: 14 pages, 4 figures, to appear in The European Physical Journal E - Soft Matte

Signal enhancement of the in-plane and out-of-plane Rayleigh wave components

Several groups have reported an enhancement of the ultrasonic Rayleigh wave when scanning close to a surface-breaking defect in a metal sample. This enhancement may be explained as an interference effect where the waves passing directly between source and receiver interfere with those waves reflected back from the defect. We present finite element models of the predicted enhancement when approaching a defect, along with experiments performed using electromagnetic acoustic transducers sensitive to either in-plane or out-of-plane motion. A larger enhancement of the in-plane motion than the out-of-plane motion is observed and can be explained by considering ultrasonic reflections and mode conversion at the defect

The decline of traditional banking: implications for financial stability and regulatory policy

In recent years, the traditional business of banks--making long-term loans and funding them by issuing short--dated deposits-has declined. This development has raised concerns that more banks will fail or be forced to assume greater risk to remain profitable. This article first examines the economic forces responsible for banks' reduced role in financial intermediation. The authors then consider whether banks may be jeopardizing the stability of the financial system by extending riskier loans or engaging in derivatives dealing and other "nontraditional" financial activities that bring higher returns but could carry greater risk. The authors conclude that because most nontraditional activities expose banks to risks and moral hazard problems similar to those associated with banks' traditional activities, the new activities can be regulated as effectively as the old.Banks and banking ; Financial services industry ; Bank supervision

The Decline of Traditional Banking: Implications for Financial Stabilityand Regulatory Policy

This paper outlines the fundamental economic forces that have led to the decline in traditional banking, that is the process of making loans and funding them by issuing short-dated deposits. The declining competitiveness of traditional banking may threaten financial stability by increasing bank failures and by increasing the incentives for banks to take on more risk, either by making more risky loans or by engaging in 'nontraditional' financial activities that promise higher returns but greater risk. This paper argues that most nontraditional activities, such as banks acting as derivatives dealers, expose banks to risks and moral hazard problems that are similar to those associated with banks' traditional activities, and that these activities can be regulated as effectively as can traditional activities. One regulatory approach to maintain financial stability and strengthen the banking system is to adopt a system of structured bank capital requirements with early corrective action by regulators. An important element in this approach is that market- value accounting principles would be applied to banks and there would be increased public disclosure by banks of the risks associated with their trading activities. With this regulatory structure in place, banks could be permitted greater freedom to expand into nontraditional activities.