D.A. Johnston

Use of microneedle array devices for continuous glucose monitoring: a review.

Microneedle array devices provide the opportunity to overcome the barrier characteristics of the outermost skin layer, the stratum corneum. This novel technology can be used as a therapeutic tool for transdermal drug delivery, including insulin, or as a diagnostic tool providing access to dermal biofluids, with subsequent analysis of its contents. Over the last decade, the use of microneedle array technology has been the focus of extensive research in the field of transdermal drug delivery. More recently, the diagnostic applications of microneedle technology have been developed. This review summarizes the existing evidence for the use of microneedle array technology as biosensors for continuous monitoring of the glucose content of interstitial fluid, focusing also on mechanics of insertion, microchannel characteristics, and safety profile.

Crumpling in dynamically triangulated random surfaces with extrinsic curvature

Abstract We present the results of a numerical simulation of dynamically triangulated random surfaces of fixed topology with extrinsic curvature. We use two different discretizations of the extrinsic curvature and observe the differing nature of the crumpling transitions and smooth phases. The effect of the extrinsic curvature on both the extrinsic and intrinsic geometry of the model is examined in three and four dimensions. We also discuss the similarities between our simulation and those of surfaces of fixed triangulation and consider the connection between models with extrinsic curvature and superstrings.

Multiple Potts models coupled to two-dimensional quantum gravity

Abstract We perform Monte Carlo simulations using the Wolff cluster algorithm of multiple q =2, 3, 4 state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the c >1 region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for c >1. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for c >1.

Information geometry and phase transitions

The introduction of a metric onto the space of parameters in models in statistical mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrisation, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a number of solvable statistical–mechanical models.

Phase diagram of the mean field model of simplicial gravity

Abstract We discuss the phase diagram of the balls in boxes model, with a varying number of boxes. The model can be regarded as a mean-field model of simplicial gravity. We analyse in detail the case of weights of the form p(q) = q−β, which correspond to the measure term introduced in the simplicial quantum gravity simulations. The system has two phases: elongated (fluid) and crumpled. For β ϵ (2, ∞) the transition between these two phases is first-order, while for β ϵ (1, 2) it is continuous. The transition becomes softer when β approaches unity and eventually disappears at β = 1. We then generalise the discussion to an arbitrary set of weights. Finally, we show that if one introduces an additional kinematic bound on the average density of balls per box then a new condensed phase appears in the phase diagram. It bears some similarity to the crinkled phase of simplicial gravity discussed recently in models of gravity interacting with matter fields.

A NUMERICAL TEST OF KPZ SCALING: POTTS MODELS COUPLED TO TWO-DIMENSIONAL QUANTUM GRAVITY

We perform Monte-Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3, 4 where no exact solution is available. Using Binder’s cumulant we find that the q=10 Potts model displays a first order phase transition on a dynamical graph, as it does on a fixed lattice. We also examine the internal geometry of the graphs generated in the simulation, finding a linear relationship between ring length probabilities and the central charge of the Potts model.

Sedentary Ghost Poles in Higher Derivative Gravity

Abstract Following Antoniadis and Tomboulis [1] we consider the gauge behaviour of the massive spin-2 ghost pole that appears in the propagator of higher derivative gravity theories. In contradistinction to [1] we observe that the pair of complex conjugate poles that appear in the resummed propagator are gauge independent. They are sedentary, that is, under a change in the gauge parameter they do not move. We derive this result using the ubiquitous Nielsen identities [11].

Phase transition strength through densities of general distributions of zeroes

A recently developed technique for the determination of the density of partition function zeroes using data coming from finite-size systems is extended to deal with cases where the zeroes are not restricted to a curve in the complex plane and/or come in degenerate sets. The efficacy of the approach is demonstrated by application to a number of models for which these features are manifest and the zeroes are readily calculable.

Scaling Relations for Logarithmic Corrections

Multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical-mechanical systems. Here, a Lee-Yang zero approach is used to systematically analyze the exponents of such logarithms and to propose scaling relations between them. These proposed relations are then confronted with a variety of results from the literature.

Information geometry of the spherical model.

Motivated by the observation that geometrizing statistical mechanics offers an interesting alternative to more standard approaches, we calculate the scaling behavior of the curvature R of the information geometry metric for the spherical model. We find that R approximately epsilon(-2), where epsilon=beta(c)-beta is the distance from criticality. The discrepancy from the naively expected scaling R approximately epsilon(-3) is explained and compared with that for the Ising model on planar random graphs, which shares the same critical exponents.