Microcanonical temperature for a classical field: application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a UV cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behaviour of the specific heat.Comment: v1: 9 pages, 5 figures, revtex 4. v2: additional text in response to referee's comments, now 11 pages, to appear in Phys. Rev.

Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms

The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and phenomena. They have been derived in deterministic and, later, in stochastic frameworks. Other results first obtained for stochastic processes, and later considered in deterministic dynamics, describe the temporal evolution of fluctuations. The field has grown beyond expectation: research works and different perspectives are proposed at an ever faster pace. Indeed, understanding fluctuations is important for the emerging theory of nonequilibrium phenomena, as well as for applications, such as those of nanotechnological and biophysical interest. However, the links among the different approaches and the limitations of these approaches are not fully understood. We focus on these issues, providing: a) analysis of the theoretical models; b) discussion of the rigorous mathematical results; c) identification of the physical mechanisms underlying the validity of the theoretical predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007

Steady state fluctuation relation and time-reversibility for non-smooth chaotic maps

Steady state fluctuation relations for dynamical systems are commonly derived under the assumption of some form of time-reversibility and of chaos. There are, however, cases in which they are observed to hold even if the usual notion of time reversal invariance is violated, e.g. for local fluctuations of Navier-Stokes systems. Here we construct and study analytically a simple non-smooth map in which the standard steady state fluctuation relation is valid, although the model violates the Anosov property of chaotic dynamical systems. Particularly, the time reversal operation is performed by a discontinuous involution, and the invariant measure is also discontinuous along the unstable manifolds. This further indicates that the validity of fluctuation relations for dynamical systems does not rely on particularly elaborate conditions, usually violated by systems of interest in physics. Indeed, even an irreversible map is proved to verify the steady state fluctuation relation.Comment: 23 pages,8 figure

Space- and time-resolved investigation on diffusion kinetics of human skin following macromolecule delivery by microneedle arrays

Microscale medical devices are being developed for targeted skin delivery of vaccines and the extraction of biomarkers, with the potential to revolutionise healthcare in both developing and developed countries. The effective clinical development of these devices is dependent on understanding the macro-molecular diffusion properties of skin. We hypothesised that diffusion varied according to specific skin layers. Using three different molecular weights of rhodamine dextran (RD) (MW of 70, 500 and 2000 kDa) relevant to the vaccine and therapeutic scales, we deposited molecules to a range of depths (0–300 µm) in ex vivo human skin using the Nanopatch device. We observed significant dissipation of RD as diffusion with 70 and 500 kDa within the 30 min timeframe, which varied with MW and skin layer. Using multiphoton microscopy, image analysis and a Fick’s law analysis with 2D cartesian and axisymmetric cylindrical coordinates, we reported experimental trends of epidermal and dermal diffusivity values ranging from 1–8 µm2 s-1 to 1–20 µm2 s-1 respectively, with a significant decrease in the dermal-epidermal junction of 0.7–3 µm2 s-1. In breaching the stratum corneum (SC) and dermal-epidermal junction barriers, we have demonstrated practical application, delivery and targeting of macromolecules to both epidermal and dermal antigen presenting cells, providing a sound knowledge base for future development of skin-targeting clinical technologies in humans

Synergistic interplay of Gβγ and phosphatidylinositol 4,5-bisphosphate dictates Kv7.4 channel activity.

Kv7.4 channels are key determinants of arterial contractility and cochlear mechanosensation that, like all Kv7 channels, have an obligatory requirement for phosphatidylinositol 4,5-bisphosphate (PIP2). βγ G proteins (Gβγ) have been identified as novel positive regulators of Kv7.4. The present study ascertained whether Gβγ increased Kv7.4 open probability through an increased sensitivity to PIP2. In HEK cells stably expressing Kv7.4, PIP2 or Gβγ increased open probability in a concentration dependent manner. Depleting PIP2 prevented any Gβγ-mediated stimulation whilst an array of Gβγ inhibitors prohibited any PIP2-induced current enhancement. A combination of PIP2 and Gβγ at sub-efficacious concentrations increased channel open probability considerably. The stimulatory effects of three Kv7.2-7.5 channel activators were also lost by PIP2 depletion or Gβγ inhibitors. This study alters substantially our understanding of the fundamental processes that dictate Kv7.4 activity, revealing a more complex and subtle paradigm where the reliance on local phosphoinositide is dictated by interaction with Gβγ

Microneedles: A New Frontier in Nanomedicine Delivery

This review aims to concisely chart the development of two individual research fields, namely nanomedicines, with specific emphasis on nanoparticles (NP) and microparticles (MP), and microneedle (MN) technologies, which have, in the recent past, been exploited in combinatorial approaches for the efficient delivery of a variety of medicinal agents across the skin. This is an emerging and exciting area of pharmaceutical sciences research within the remit of transdermal drug delivery and as such will undoubtedly continue to grow with the emergence of new formulation and fabrication methodologies for particles and MN. Firstly, the fundamental aspects of skin architecture and structure are outlined, with particular reference to their influence on NP and MP penetration. Following on from this, a variety of different particles are described, as are the diverse range of MN modalities currently under development. The review concludes by highlighting some of the novel delivery systems which have been described in the literature exploiting these two approaches and directs the reader towards emerging uses for nanomedicines in combination with MN