A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure

We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control

Surface Code Threshold in the Presence of Correlated Errors

We study the fidelity of the surface code in the presence of correlated errors induced by the coupling of physical qubits to a bosonic environment. By mapping the time evolution of the system after one quantum error correction cycle onto a statistical spin model, we show that the existence of an error threshold is related to the appearance of an order-disorder phase transition in the statistical model in the thermodynamic limit. This allows us to relate the error threshold to bath parameters and to the spatial range of the correlated errors.Comment: 5 pages, 2 figure

Nonextensive Thermostatistics and the H-Theorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the ``molecular chaos hypothesis". For $q>0$, the $q$-transport equation satisfies an $H$-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' $q$-nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo

Solvable model for spatiotemporal chaos

We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a nontrivial spatial behavior. We also introduce and calculate a generalized spatiotemporal correlation function

Some thoughts on theoretical physics

Some thoughts are presented on the inter-relation between beauty and truth in science in general and theoretical physics in particular. Some conjectural procedures that can be used to create new ideas, concepts and results are illustrated in both Boltzmann-Gibbs and nonextensive statistical mechanics. The sociological components of scientific progress and its unavoidable and benefic controversies are, mainly through existing literary texts, briefly addressed as well.Comment: Short essay based on the plenary talk given at the International Workshop on Trends and Perspectives in Extensive and Non-Extensive Statistical Mechanics, held in November 19-21, 2003, in Angra dos Reis, Brazil. To appear in a Physica A special volume (2004) edited by E.M.F. Curado, H.J. Herrmann and M. Barbosa. 23 pages, including 3 figures. The new version has 25 pages and the same figures. The texts by Saramago and by Bersanelli are now translated into English. A few typos and minor improvements are included as wel

Automatic Unbounded Verification of Alloy Specifications with Prover9

Alloy is an increasingly popular lightweight specification language based on relational logic. Alloy models can be automatically verified within a bounded scope using off-the-shelf SAT solvers. Since false assertions can usually be disproved using small counter-examples, this approach suffices for most applications. Unfortunately, it can sometimes lead to a false sense of security, and in critical applications a more traditional unbounded proof may be required. The automatic theorem prover Prover9 has been shown to be particularly effective for proving theorems of relation algebras [7], a quantifier-free (or point-free) axiomatization of a fragment of relational logic. In this paper we propose a translation from Alloy specifications to fork algebras (an extension of relation algebras with the same expressive power as relational logic) which enables their unbounded verification in Prover9. This translation covers not only logic assertions, but also the structural aspects (namely type declarations), and was successfully implemented and applied to several examples