Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Extracting the rho meson wavefunction from HERA data

We extract the light-cone wavefunctions of the rho meson using the HERA data on diffractive rho photoproduction. We find good agreement with predictions for the distribution amplitude based on QCD sum rules and from the lattice. We also find that the data prefer a transverse wavefunction with enhanced end-point contributions.Comment: 13 pages, 7 figures, significant improvements over the original version with a new section on distribution amplitudes adde

Rise of the centrist: from binary to continuous opinion dynamics

We propose a model that extends the binary ``united we stand, divided we fall'' opinion dynamics of Sznajd-Weron to handle continuous and multi-state discrete opinions. Disagreement dynamics are often ignored in continuous extensions of the binary rules, so we make the most symmetric continuum extension of the binary model that can treat the consequences of agreement (debate) and disagreement (confrontation) within a population of agents. We use the continuum extension as an opportunity to develop rules for persistence of opinion (memory). Rules governing the propagation of centrist views are also examined. Monte Carlo simulations are carried out. We find that both memory effects and the type of centrist significantly modify the variance of average opinions in the large timescale limits of the models. Finally, we describe the limit of applicability for Sznajd-Weron's model of binary opinions as the continuum limit is approached. By comparing Monte Carlo results and long time-step limits, we find that the opinion dynamics of binary models are significantly different to those where agents are permitted more than 3 opinions

Hastings-Levitov aggregation in the small-particle limit

We establish some scaling limits for a model of planar aggregation. The model is described by the composition of a sequence of independent and identically distributed random conformal maps, each corresponding to the addition of one particle. We study the limit of small particle size and rapid aggregation. The process of growing clusters converges, in the sense of Caratheodory, to an inflating disc. A more refined analysis reveals, within the cluster, a tree structure of branching fingers, whose radial component increases deterministically with time. The arguments of any finite sample of fingers, tracked inwards, perform coalescing Brownian motions. The arguments of any finite sample of gaps between the fingers, tracked outwards, also perform coalescing Brownian motions. These properties are closely related to the evolution of harmonic measure on the boundary of the cluster, which is shown to converge to the Brownian web

Acoustic Emission from crumpling paper

From magnetic systems to the crust of the earth, many physical systems that exibit a multiplicty of metastable states emit pulses with a broad power law distribution in energy. Digital audio recordings reveal that paper being crumpled, a system that can be easily held in hand, is such a system. Crumpling paper both using the traditional hand method and a novel cylindrical geometry uncovered a power law distribution of pulse energies spanning at least two decades: (exponent 1.3 - 1.6) Crumpling initally flat sheets into a compact ball (strong crumpling), we found little or no evidence that the energy distribution varied systematically over time or the size of the sheet. When we applied repetitive small deformations (weak crumpling) to sheets which had been previously folded along a regular grid, we found no systematic dependence on the grid spacing. Our results suggest that the pulse energy depends only weakly on the size of the paper regions responsible for sound production.Comment: 12 pages of text, 9 figures, submitted to Phys. Rev. E, additional information availible at http://www.msc.cornell.edu/~houle/crumpling

The characteristics of cognitive neuroscience tests in a schizophrenia cognition clinical trial: Psychometric properties and correlations with standard measures.

In comparison to batteries of standard neuropsychological tests, cognitive neuroscience tests may offer a more specific assessment of discrete neurobiological processes that may be aberrant in schizophrenia. However, more information regarding psychometric properties and correlations with standard neuropsychological tests and functional measures is warranted to establish their validity as treatment outcome measures. The N-back and AX-Continuous Performance Task (AX-CPT) are two promising cognitive neuroscience tests designed to measure specific components of working memory and contextual processing respectively. In the current study, we report the psychometric properties of multiple outcome measures from these two tests as well as their correlations with standard neuropsychological measures and functional capacity measures. The results suggest that while the AX-CPT and N-back display favorable psychometric properties, they do not exhibit greater sensitivity or specificity with functional measures than standard neurocognitive tests

Elasticity near the vulcanization transition

Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A semi-microscopic statistical-mechanical theory is presented of the latter signature that accounts for both thermal fluctuations and quenched disorder. It is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change

Metamorphosis of plasma turbulence-shear flow dynamics through a transcritical bifurcation

The structural properties of an economical model for a confined plasma turbulence governor are investigated through bifurcation and stability analyses. A close relationship is demonstrated between the underlying bifurcation framework of the model and typical behavior associated with low- to high-confinement transitions such as shear flow stabilization of turbulence and oscillatory collective action. In particular, the analysis evinces two types of discontinuous transition that are qualitatively distinct. One involves classical hysteresis, governed by viscous dissipation. The other is intrinsically oscillatory and non-hysteretic, and thus provides a model for the so-called dithering transitions that are frequently observed. This metamorphosis, or transformation, of the system dynamics is an important late side-effect of symmetry-breaking, which manifests as an unusual non-symmetric transcritical bifurcation induced by a significant shear flow drive.Comment: 17 pages, revtex text, 9 figures comprised of 16 postscript files. Submitted to Phys. Rev.

Sol gel graphene/TiO2 nanoparticles for the photocatalytic-assisted sensing and abatement of NO2

Abstract Human exposure to volatile organic compounds and NO2 can lead to health problems, therefore strategies to mitigate against the risks are required. Abatement and sensing are approaches which could both neutralise and monitor these species thus providing a safer environment and warning occupants of harmful levels. This paper presents pure TiO2 and TiO2/graphene hybrids synthesized through a sol-gel route. Electron optical, helium ion microscopy, X-ray diffraction and spectroscopic methods have been applied to elucidate the physical and chemical behaviour. NO2 sensing properties of TiO2/graphene hybrids formed by the addition of graphene to the reaction vessel prior to initiating the sol gel reaction followed by annealing (GTiO2S), and an alternative manufacturing method involving the addition of graphene to TiO2 nanoparticles which had already been annealed (GTiO2M) were compared and evaluated. A conductometric sensor based on TiO2/graphene prepared using material GTiO2S showed a higher response to NO2 compared to sensors based on pure TiO2 and TiO2/graphene prepared with material GTiO2M. Under UV irradiation generated by a low power LED, the sensor showed a remarkably enhanced response to 1750 ppb NO2, about double the response in the dark, and a limit of detection of about 50 ppb of NO2 (Signal/Noise = 3). Photocatalytic tests to assess the degradation of NOx showed that TiO2/graphene hybrids using material GTiO2S were the most active amongst the whole series of TiO2-based materials. Our data highlights the unique characteristics of material GTiO2S TiO2/graphene and the suitability for multi-purpose applications in the field of environmental monitoring and remediation. The capability of the material for both sensing and abatement of NOx could be exploited to offer a safer environment through providing a warning of the presence of NOx whilst also reducing levels

Gender, foundation degrees and the knowledge economy

This article questions the concept of ‘education for employment’, which constructs a discourse of individual and societal benefit in a knowledge‐driven economy. Recent policy emphasis in the European Union promotes the expansion of higher education and short‐cycle vocational awards such as the intermediate two‐year Foundation Degree recently introduced into England and Wales. Studies of vocational education and training (VET) and the knowledge economy have focused largely on the governance of education and on the development and drift of policy. Many VET programmes have also been considered for their classed, raced and gendered take‐up and subsequent effect on employment. This article builds on both fields of study to engage with the finer cross‐analyses of gender, social class, poverty, race and citizenship. In its analysis of policy texts the article argues that in spite of a discourse of inclusivity, an expanded higher education system has generated new inequalities, deepening social stratification. Drawing on early analyses of national quantitative data sets, it identifies emerging gendered, classed and raced patterns and considers these in relation to occupationally and hierarchically stratified labour markets, both within and without the knowledge economy