Ginzburg-Landau theory for the time-dependent phase field in a two-dimensional d-wave superconductor

We derive a finite temperature time-dependent effective theory for the phase $\theta$ of the pairing field, which is appropriate for a 2D conducting electron system with non-retarded d-wave attraction. As for s-wave pairing the effective action contains terms with Landau damping, but their structure appears to be different from the s-wave case due to the fact that the Landau damping is determined by the quasiparticle group velocity $v_g$, which for the d-wave pairing does not have the same direction as the non-interacting Fermi velocity $v_F$. We show that for the d-wave pairing the Landau terms have a linear low temperature dependence and in contrast to the s-wave case are important for all finite temperatures.Comment: 4 pages, LaTeX; paper presented at New^3SC-3, Honolulu, Hawaii, USA, 2001. To be published in Physica

Multi-parameter generalization of nonextensive statistical mechanics

We show that the stochastic interpretation of Tsallis' thermostatistics given recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a multi-parameter generalization. The resulting class of distributions is able to fit experimental results which cannot be reproduced within the Boltzmann's or Tsallis' formalism.Comment: ReVTex 4.0, 4 eps figure

Fatty Acid Methyl Esters as Biosolvents of Epoxy Resins: A Physicochemical Study

The C8 to C18 fatty acid methyl esters (FAME) have been compared as solvents for two epoxy resin pre-polymers, bisphenol A diglycidyl ether (DGEBA) and triglycidyl paminophenol ether (TGPA). It was found that the solubilization limits vary according to the ester and that methyl caprylate is the best solvent of both resins. To explain these solubility performances, physical and chemical properties of FAME were studied, such as the Hansen parameters, viscosity, binary diffusion coefficient and vaporization enthalpy. Determination of the physicochemical parameters of FAME was carried out by laboratory experimentations and by calculation from bibliographic data. The Hansen parameters of FAME and epoxy resins pre-polymers were theoretically and experimentally determined. The FAME chain length showed a long dependence on the binary diffusion parameters and kinematic viscosity, which are mass and momentum transport properties. Moreover, the vaporization enthalpy of these compounds was directly correlated with the solubilization limits

Comparisons of Supergranule Characteristics During the Solar Minima of Cycles 22/23 and 23/24

Supergranulation is a component of solar convection that manifests itself on the photosphere as a cellular network of around 35 Mm across, with a turnover lifetime of 1-2 days. It is strongly linked to the structure of the magnetic field. The horizontal, divergent flows within supergranule cells carry local field lines to the cell boundaries, while the rotational properties of supergranule upflows may contribute to the restoration of the poloidal field as part of the dynamo mechanism that controls the solar cycle. The solar minimum at the transition from cycle 23 to 24 was notable for its low level of activity and its extended length. It is of interest to study whether the convective phenomena that influences the solar magnetic field during this time differed in character to periods of previous minima. This study investigates three characteristics (velocity components, sizes and lifetimes) of solar supergranulation. Comparisons of these characteristics are made between the minima of cycles 22/23 and 23/24 using MDI Doppler data from 1996 and 2008, respectively. It is found that whereas the lifetimes are equal during both epochs (around 18 h), the sizes are larger in 1996 (35.9 +/- 0.3 Mm) than in 2008 (35.0 +/- 0.3 Mm), while the dominant horizontal velocity flows are weaker (139 +/- 1 m/s in 1996; 141 +/- 1 m/s in 2008). Although numerical differences are seen, they are not conclusive proof of the most recent minimum being inherently unusual.Comment: 22 pages, 5 figures. Solar Physics, in pres

Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A \textbf{322}, (2003), 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.Comment: 18 page

Effective action approach and Carlson-Goldman mode in d-wave superconductors

We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional clean d-wave superconductors using the effective ``phase only'' action formalism. In conventional s-wave superconductors, it is known that the CG mode is observed as a peak in the structure factor of the pair susceptibility $S(\Omega, \mathbf{K})$ only just below the transition temperature T_c and only in dirty systems. On the other hand, our analytical results support the statement by Y.Ohashi and S.Takada, Phys.Rev.B {\bf 62}, 5971 (2000) that in d-wave superconductors the CG mode can exist in clean systems down to the much lower temperatures, $T \approx 0.1 T_c$. We also consider the manifestations of the CG mode in the density-density and current-current correlators and discuss the gauge independence of the obtained results.Comment: 23 pages, RevTeX4, 12 EPS figures; final version to appear in PR

Measurement of the Omega_c Lifetime

We present the measurement of the lifetime of the Omega_c we have performed using three independent data samples from two different decay modes. Using a Sigma- beam of 340 GeV/c we have obtained clean signals for the Omega_c decaying into Xi- K- pi+ pi+ and Omega- pi+ pi- pi+, avoiding topological cuts normally used in charm analysis. The short but measurable lifetime of the Omega_c is demonstrated by a clear enhancement of the signals at short but finite decay lengths. Using a continuous maximum likelihood method we determined the lifetime to be tau(Omega_c) = 55 +13-11(stat) +18-23(syst) fs. This makes the Omega_c the shortest living weakly decaying particle observed so far. The short value of the lifetime confirms the predicted pattern of the charmed baryon lifetimes and demonstrates that the strong interaction plays a vital role in the lifetimes of charmed hadrons.Comment: 15 pages, including 7 figures; gzipped, uuencoded postscrip

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Neutrino Propagation in a Strongly Magnetized Medium

We derive general expressions at the one-loop level for the coefficients of the covariant structure of the neutrino self-energy in the presence of a constant magnetic field. The neutrino energy spectrum and index of refraction are obtained for neutral and charged media in the strong-field limit ($M_{W}\gg \sqrt{B}\gg m_{e},T,\mu ,| \mathbf{p}|$) using the lowest Landau level approximation. The results found within the lowest Landau level approximation are numerically validated, summing in all Landau levels, for strong $B\gg T^{2}$ and weakly-strong $B \gtrsim T^{2}$ fields. The neutrino energy in leading order of the Fermi coupling constant is expressed as the sum of three terms: a kinetic-energy term, a term of interaction between the magnetic field and an induced neutrino magnetic moment, and a rest-energy term. The leading radiative correction to the kinetic-energy term depends linearly on the magnetic field strength and is independent of the chemical potential. The other two terms are only present in a charged medium. For strong and weakly-strong fields, it is found that the field-dependent correction to the neutrino energy in a neutral medium is much larger than the thermal one. Possible applications to cosmology and astrophysics are considered.Comment: 23 pages, 4 figures. Corrected misprints in reference

Magnetic Field Amplification in Galaxy Clusters and its Simulation

We review the present theoretical and numerical understanding of magnetic field amplification in cosmic large-scale structure, on length scales of galaxy clusters and beyond. Structure formation drives compression and turbulence, which amplify tiny magnetic seed fields to the microGauss values that are observed in the intracluster medium. This process is intimately connected to the properties of turbulence and the microphysics of the intra-cluster medium. Additional roles are played by merger induced shocks that sweep through the intra-cluster medium and motions induced by sloshing cool cores. The accurate simulation of magnetic field amplification in clusters still poses a serious challenge for simulations of cosmological structure formation. We review the current literature on cosmological simulations that include magnetic fields and outline theoretical as well as numerical challenges.Comment: 60 pages, 19 Figure