Solution of generalized fractional reaction-diffusion equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.Comment: LaTeX, 18 pages, corrected typo

Fractional reaction-diffusion equations

In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for reaction-diffusion systems with L\'evy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.Comment: LaTeX, 17 pages, corrected typo

Comparison of structural transformations and superconductivity in compressed Sulfur and Selenium

Density-functional calculations are presented for high-pressure structural phases of S and Se. The structural phase diagrams, phonon spectra, electron-phonon coupling, and superconducting properties of the isovalent elements are compared. We find that with increasing pressure, Se adopts a sequence of ever more closely packed structures (beta-Po, bcc, fcc), while S favors more open structures (beta-Po, simple cubic, bcc). These differences are shown to be attributable to differences in the S and Se core states. All the compressed phases of S and Se considered are calculated to have weak to moderate electron-phonon coupling strengths consistent with superconducting transition temperatures in the range of 1 to 20 K. Our results compare well with experimental data on the beta-Po --> bcc transition pressure in Se and on the superconducting transition temperature in beta-Po S. Further experiments are suggested to search for the other structural phases predicted at higher pressures and to test theoretical results on the electron-phonon interaction and superconducting properties

Free flux flow resistivity in strongly overdoped high-T_c cuprate; purely viscous motion of the vortices in semiclassical d-wave superconductor

We report the free flux flow (FFF) resistivity associated with a purely viscous motion of the vortices in moderately clean d-wave superconductor Bi:2201 in the strongly overdoped regime (T_c=16K) for a wide range of the magnetic field in the vortex state. The FFF resistivity is obtained by measuring the microwave surface impedance at different microwave frequencies. It is found that the FFF resistivity is remarkably different from that of conventional s-wave superconductors. At low fields (H<0.2H_c2) the FFF resistivity increases linearly with H with a coefficient which is far larger than that found in conventional s-wave superconductors. At higher fields, the FFF resistivity increases in proportion to \sqrt H up to H_c2. Based on these results, the energy dissipation mechanism associated with the viscous vortex motion in "semiclassical" d-wave superconductors with gap nodes is discussed. Two possible scenarios are put forth for these field dependence; the enhancement of the quasiparticle relaxation rate and the reduction of the number of the quasiparticles participating the energy dissipation in d-wave vortex state.Comment: 9 pages 7 figures, to appear in Phys. Rev.

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

Galaxy and mass assembly: Luminosity and stellar mass functions in GAMA groups

How do galaxy properties (such as stellar mass, luminosity, star formation rate, and morphology) and their evolution depend on the mass of their host dark matter halo? Using the Galaxy and Mass Assembly group catalogue, we address this question by exploring the dependence on host halo mass of the luminosity function (LF) and stellar mass function (SMF) for grouped galaxies subdivided by colour, morphology, and central/satellite. We find that spheroidal galaxies in particular dominate the bright and massive ends of the LF and SMF, respectively. More massive haloes host more massive and more luminous central galaxies. The satellites LF and SMF, respectively, show a systematic brightening of characteristic magnitude, and increase in characteristic mass, with increasing halo mass. In contrast to some previous results, the faint-end and low-mass slopes show little systematic dependence on halo mass. Semi-analytic models and simulations show similar or enhanced dependence of central mass and luminosity on halo mass. Faint and low-mass simulated satellite galaxies are remarkably independent of halo mass, but the most massive satellites are more common in more massive groups. In the first investigation of low-redshift LF and SMF evolution in group environments, we find that the red/blue ratio of galaxies in groups has increased since redshift z ~ 0.3 relative to the field population. This observation strongly suggests that quenching of star formation in galaxies as they are accreted into galaxy groups is a significant and ongoing process

Magnetic Field Generation in Stars

Enormous progress has been made on observing stellar magnetism in stars from the main sequence through to compact objects. Recent data have thrown into sharper relief the vexed question of the origin of stellar magnetic fields, which remains one of the main unanswered questions in astrophysics. In this chapter we review recent work in this area of research. In particular, we look at the fossil field hypothesis which links magnetism in compact stars to magnetism in main sequence and pre-main sequence stars and we consider why its feasibility has now been questioned particularly in the context of highly magnetic white dwarfs. We also review the fossil versus dynamo debate in the context of neutron stars and the roles played by key physical processes such as buoyancy, helicity, and superfluid turbulence,in the generation and stability of neutron star fields. Independent information on the internal magnetic field of neutron stars will come from future gravitational wave detections. Thus we maybe at the dawn of a new era of exciting discoveries in compact star magnetism driven by the opening of a new, non-electromagnetic observational window. We also review recent advances in the theory and computation of magnetohydrodynamic turbulence as it applies to stellar magnetism and dynamo theory. These advances offer insight into the action of stellar dynamos as well as processes whichcontrol the diffusive magnetic flux transport in stars.Comment: 41 pages, 7 figures. Invited review chapter on on magnetic field generation in stars to appear in Space Science Reviews, Springe

Luminous Red Novae: Stellar Mergers or Giant Eruptions?

We present extensive datasets for a class of intermediate-luminosity optical transients known as luminous red novae. They show double-peaked light curves, with an initial rapid luminosity rise to a blue peak (at -13 to -15 mag), which is followed by a longer-duration red peak that sometimes is attenuated, resembling a plateau. The progenitors of three of them (NGC 4490-2011OT1, M 101-2015OT1, and SNhunt248), likely relatively massive blue to yellow stars, were also observed in a pre-eruptive stage when their luminosity was slowly increasing. Early spectra obtained during the first peak show a blue continuum with superposed prominent narrow Balmer lines, with P Cygni profiles. Lines of Fe II are also clearly observed, mostly in emission. During the second peak, the spectral continuum becomes much redder, H alpha is barely detected, and a forest of narrow metal lines is observed in absorption. Very late-time spectra (similar to 6 months after blue peak) show an extremely red spectral continuum, peaking in the infrared (IR) domain. H alpha is detected in pure emission at such late phases, along with broad absorption bands due to molecular overtones (such as TiO, VO). We discuss a few alternative scenarios for luminous red novae. Although major instabilities of single massive stars cannot be definitely ruled out, we favour a common envelope ejection in a close binary system, with possibly a final coalescence of the two stars. The similarity between luminous red novae and the outburst observed a few months before the explosion of the Type IIn SN 2011ht is also discussed