Normal and anomalous diffusion of Brownian particles on disordered potentials

In this work we study the transition from normal to anomalous diffusion of Brownian particles on disordered potentials. The potential model consists of a series of "potential hills" (defined on unit cell of constant length) whose heights are chosen randomly from a given distribution. We calculate the exact expression for the diffusion coefficient in the case of uncorrelated potentials for arbitrary distributions. We particularly show that when the potential heights have a Gaussian distribution (with zero mean and a finite variance) the diffusion of the particles is always normal. In contrast when the distribution of the potential heights are exponentially distributed we show that the diffusion coefficient vanishes when system is placed below a critical temperature. We calculate analytically the diffusion exponent for the anomalous (subdiffusive) phase by using the so-called "random trap model". We test our predictions by means of Langevin simulations obtaining good agreement within the accuracy of our numerical calculations.Comment: 15 pages, 4 figure

The noise wars in helio- and asteroseismology

During this conference, latest results on helioseismology (both local and global) as well as in asteroseismology have been reviewed, the hottest questions discussed and the future prospects of our field fully debated. A conference so rich in the variety of topics addressed is impossible to be deeply reviewed in a paper. Therefore, I present here my particular view of the field as it is today, concentrating on the solar-like stars and global helioseismology. The link I found to do so is the constant battle in which we are all engaged against the sources of noise that difficult our studies. The noise in the data, the noise in the inversions, the precision and accuracy of our inferred models...Comment: Review of the ESF conference: The Modern Era of Helio and Asteroseismology to be published by AN. 6 pages, 6 figure

Resonant Response in Non-equilibrium Steady States

The time-dependent probability density function of a system evolving towards a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies \omega_n, with which the system reaches its stationary state, correspond to the imaginary part of such eigenvalues. If the system is further driven by a small and oscillating perturbation with a given frequency \omega, we formally prove that the linear response to the probability density function is enhanced when \omega = \omega_n. We prove that the occurrence of this phenomenon is characteristic of systems that reach a non-equilibrium stationary state. In particular we obtain an explicit formula for the frequency-dependent mobility in terms of the of the relaxation to the stationary state of the (unperturbed) probability current. We test all these predictions by means of numerical simulations considering an ensemble of non-interacting overdamped particles on a tilted periodic potential.Comment: 9 pages, 10 figures, submitted to Physical Review

Stellar pulsations of solar-like oscillators with CoRoT and Kepler

Today, asteroseismology is entering in its golden age thanks to the observations provided by the CoRoT and Kepler space missions. In particular, we will make significant progresses in the understanding of the structure and evolution of solar-like oscillating stars. These stars have acoustic modes stochastically excited by the near-surface convection. Thanks to the observations already provided by these two missions, we have detected several hundred of stars showing solar-like oscillations in the main sequence and several thousands in the red- giant branch. Here, I give an overview of the present status of the most important results obtained from both missions for stellar physics and the potential use of asteroseismology to characterize stars harboring planets.Comment: Proceedings of the IX Scientific Meeting of the Spanish Astronomical Society held on September 13--17, 2010, in Madrid, Spain.11 pages, 3 figure

Stellar dynamics of low mass stars from the surface to the interior measured by CoRoT and Kepler

Continuous high-precision photometry of stars, provided by space missions such as CoRoT, Kepler, and K2, represents a unique way to study stellar rotation and magnetism. The coupling of these studies of the surface dynamics with asteroseismology is changing our view to surface and internal dynamics. In this proceedings I will provide the latest developments in the understanding of surface and internal rotation and magnetic fields. I will also discuss the possible discovery of strong internal magnetic fields of dynamo origin in the convective cores of stars above 1.2-1.4 solar masses. I will finish by providing constraints on gyrochronology laws for low-mass stars and put the Sun into context of its magnetism when compared to other solar-analog stars.Comment: Proceedings of the 2016 Astrofluid conference. 13 Page

Simulations of substructures in relativistic jets

We present a set of simulations of relativistic jets from accretion disk initial setup with a new code in Fortran 90 to get numerical solutions of a system of General Relativistic Magnetohydrodynamics (GRMHD) partial differential equations in a fixed Black Hole (BH) spacetime which is able to show substructures formations inside the jet as well as a lobe formation on the disk. For this, a central scheme of finite volume method without dimensional split and no Riemann solvers (a Nessyahu-Tadmor method) was implemented. Thus, we were able to obtain stable numerical solutions with spurious oscillations under control and no excessive numerical dissipation. We setup a magnetized accretion disk uncharged plasma surrounding a central Schwarzschild BH immersed in a magnetosphere which evolve to the ejection of matter in the form of jet with its substructures over a distance of almost twenty times the BH radius.Comment: 12 pages, 20 figure

Chiral condensate thermal evolution at finite baryon chemical potential within ChPT

We present a model independent study of the chiral condensate evolution in a hadronic gas, in terms of temperature and baryon chemical potential. The meson-meson interactions are described within Chiral Perturbation Theory and the pion-nucleon interaction by means of Heavy Baryon Chiral Perturbation Theory, both at one loop. Together with the virial expansion, this provides a model independent systematic expansion at low temperatures and chemical potentials, which includes the physical quark masses. This can serve as a guideline for further studies on the lattice. We also obtain estimates of the critical line of temperature and chemical potential where the chiral condensate melts, which systematically lie somewhat higher than recent lattice calculations but are consistent with several hadronic models.Comment: 3 Pages. Talk presented in the IVth International Conference on Quarks and Nuclear Physics. Madrid, Spain. 5th-10th June 200

Noise-induced rectification in out-of-equilibrium structures

We consider the motion of overdamped particles on random potentials subjected to a Gaussian white noise and a time-dependent periodic external forcing. The random potential is modeled as the potential resulting from the interaction of a point particle with a random polymer. The random polymer is made up, by means of some stochastic process, from a finite set of possible monomer types. The process is assumed to reach a non-equilibrium stationary state, which means that every realization of a random polymer can be considered as an out-of-equilibrium structure. We show that the net flux of particles on this random medium is non-vanishing when the potential profile on every monomer is symmetric. We prove that this ratchet-like phenomenon is a consequence of the irreversibility of the stochastic process generating the polymer. On the contrary, when the process generating the polymer is at equilibrium (thus fulfilling the detailed balance condition) the system is unable to rectify the motion. We calculate the net flux of the particles in the adiabatic limit for a simple model and we test our theoretical predictions by means of Langevin dynamics simulations. We also show that, out of the adiabatic limit, the system also exhibits current reversals as well as non-monotonic dependence of the diffusion coefficient as a function of forcing amplitude.Comment: 10 pages, 7 Figure

Variation in p-mode power over solar cycle 23 as seen from BiSON and GOLF observations

We analyzed BiSON and GOLF/SoHO data with a new technique, to investigate p-mode power variation over solar cycle 23. We found a decrease in the mean velocity power of about 20% for BiSON during the ascending phase, in agreement with previous findings. We also found that GOLF, during the red-wing configuration, seems to be working at a different height than the theoretically computed one.Comment: 4 pages, 2 figures, Conference proceeding GONG 2008 / SOHO XXI Meetin

Differential calculus and connections on a quantum plane at a cubic root of unity

We consider the algebra of N x N matrices as a reduced quantum plane on which a finite-dimensional quantum group H acts. This quantum group is a quotient of U_q(sl(2,C)), q being an N-th root of unity. Most of the time we shall take N=3; in that case \dim(H) = 27. We recall the properties of this action and introduce a differential calculus for this algebra: it is a quotient of the Wess-Zumino complex. The quantum group H also acts on the corresponding differential algebra and we study its decomposition in terms of the representation theory of H. We also investigate the properties of connections, in the sense of non commutative geometry, that are taken as 1-forms belonging to this differential algebra. By tensoring this differential calculus with usual forms over space-time, one can construct generalized connections with covariance properties with respect to the usual Lorentz group and with respect to a finite-dimensional quantum group.Comment: 53 pages, 1 small PS figure, Latex, diagrams.sty (included); few errors corrected, final version to appear in Rev. Math. Phy