A mean-field model of superconducting vortices in three dimensions

A mean-field model for the motion of vortices in a type II superconductor is formulated, drawing on analogies with vortices in an inviscid fluid. The model admits discontinuous solutions, and the conditions on such an interface are derived. In a natural limiting case the model is shown to reduce to a novel, vectorial nonlinear diffusion equation. Finally, generalizations of the model to incorporate vortex pinning and fluctuation effects are described

A hierarchy of models for type-II superconductors

A hierarchy of models for type-II superconductors is presented. Through appropriate asymptotic limits we pass from the mesoscopic Ginzburg-Landau model to the London model with isolated superconducting vortices as line singularities, to vortex-density models, and finally to macroscopic critical-state models

Comment on "Model for Heat Conduction in Nanofluids"

A Comment on the Letter by D. Hemanth Kumar et al., Phys. Rev. Lett. 93, 144301 (2004)Comment: 2 page

Derivation of the bidomain equations for a beating heart with a general microstructure

A novel multiple scales method is formulated that can be applied to problems which have an almost\ud periodic microstructure not in Cartesian coordinates but in a general curvilinear coordinate system.\ud The method is applied to a model of the electrical activity of cardiac myocytes and used to derive a\ud version of the bidomain equations describing the macroscopic electrical activity of cardiac tissue. The\ud treatment systematically accounts for the non-uniform orientation of the cells within the tissue and for\ud deformations of the tissue occurring as a result of the heart beat

Stochastic modelling of reaction-diffusion processes:\ud algorithms for bimolecular reactions

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A+B → C, or A+A → C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site)

Exponentially slow transitions on a Markov chain: the frequency of Calcium Sparks

Calcium sparks in cardiac muscle cells occur when a cluster of Ca2+ channels open and release Ca2+ from an internal store. A simplified model of Ca2+ sparks has been developed to describe the dynamics of a cluster of channels, which is of the form of a continuous time Markov chain with nearest neighbour transitions and slowly varying jump functions. The chain displays metastability, whereby the probability distribution of the state of the system evolves exponentially slowly, with one of the metastable states occurring at the boundary. An asymptotic technique for analysing the Master equation (a differential-difference equation) associated with these Markov chains is developed using the WKB and projection methods. The method is used to re-derive a known result for a standard class of Markov chains displaying metastability, before being applied to the new class of Markov chains associated with the spark model. The mean first passage time between metastable states is calculated and an expression for the frequency of calcium sparks is derived. All asymptotic results are compared with Monte Carlo simulations

The ``Out-Longitudinal'' Cross Term and Other Model Independent Features of the Two-Particle HBT Correlation Function

Using two specific models and a model independent formalism, we show that an ``out-longitudinal'' cross term should be included in any gaussian fits to correlation data. In addition, we show that correlation radii (including the cross term) measure lengths of homogeneity within the source, not necessarily geometric sizes.Comment: 4 pages, uuencoded compressed postscrip