Stability and mode analysis of solar coronal loops using thermodynamic irreversible energy principles

We study the modes and stability of non - isothermal coronal loop models with different intensity values of the equilibrium magnetic field. We use an energy principle obtained via non - equilibrium thermodynamic arguments. The principle is expressed in terms of Hermitian operators and allow to consider together the coupled system of equations: the balance of energy equation and the equation of motion. We determine modes characterized as long - wavelength disturbances that are present in inhomogeneous media. This character of the system introduces additional difficulties for the stability analysis because the inhomogeneous nature of the medium determines the structure of the disturbance, which is no longer sinusoidal. Moreover, another complication is that we obtain a continuous spectrum of stable modes in addition to the discrete one. We obtain a unique unstable mode with a characteristic time that is comparable with the characteristic life-time observed for loops. The feasibility of wave-based and flow-based models is examined.Comment: 29 pages 10 figure

Estudio de modos de oscilación

El objeto de este trabajo es estudiar las oscilaciones y la estabilidad en la situación más general posible, es decir abarcando las oscilaciones radial y no radial en los casos adiabáticos y no adiabáticos. Para ello se han preparad códigos computacionales, que se aplican a los modelos más sencillos de pulsaciones estelares descriptos en la literatura, con el fin de ajustarlos para luego extender su aplicación a casos más complejos.Asociación Argentina de Astronomí

Thermal stability analysis of coronal loops

The coronal loops confine a low density (n=10¹⁰ cm⁻³) and hot plasma (T=10⁶ K), whose ends interact with the much denser and hotter photospheric fluid. The linear stability of the dynamical and thermal equilibria of the coronal plasma is analyzed. A formalism based on methods of irreversible thermodynamics was used, which systematically builds up (whenever it is possible) a variational principle for studying the stability. The stability conditions derived in this work are compared with results available in the literature, which were obtained by standard stability methods.Asociación Argentina de Astronomí

Quantum random walk on the line as a markovian process

We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic increase in the variance of the quantum walker's position with time is a direct consequence of the coherence of the quantum evolution. If the evolution is decoherent, as in the classical case, the variance is shown to increase linearly with time, as expected. Furthermore we show that this system has an evolution operator analogous to that of a resonant quantum kicked rotor. As this rotator may be described through a quantum computational algorithm, one may employ this algorithm to describe the time evolution of the quantum walker.Comment: few typos corrected, 13 pages, 2 figures, to appear in Physica

Markovian Behaviour and Constrained Maximization of the Entropy in Chaotic Quantum Systems

The separation of the Schr\"{o}dinger equation into a Markovian and an interference term provides a new insight in the quantum dynamics of classically chaotic systems. The competition between these two terms determines the localized or diffusive character of the dynamics. In the case of the Kicked Rotor, we show how the constrained maximization of the entropy implies exponential localization.Comment: 8 pages, 2 figure

Dynamical Localization in Quasi-Periodic Driven Systems

We investigate how the time dependence of the Hamiltonian determines the occurrence of Dynamical Localization (DL) in driven quantum systems with two incommensurate frequencies. If both frequencies are associated to impulsive terms, DL is permanently destroyed. In this case, we show that the evolution is similar to a decoherent case. On the other hand, if both frequencies are associated to smooth driving functions, DL persists although on a time scale longer than in the periodic case. When the driving function consists of a series of pulses of duration $\sigma$, we show that the localization time increases as $\sigma^{-2}$ as the impulsive limit, $\sigma\to 0$, is approached. In the intermediate case, in which only one of the frequencies is associated to an impulsive term in the Hamiltonian, a transition from a localized to a delocalized dynamics takes place at a certain critical value of the strength parameter. We provide an estimate for this critical value, based on analytical considerations. We show how, in all cases, the frequency spectrum of the dynamical response can be used to understand the global features of the motion. All results are numerically checked.Comment: 7 pages, 5 figures included. In this version is that Subsection III.B and Appendix A on the quasiperiodic Fermi Accelerator has been replaced by a reference to published wor

Numerical solution of the nonadiabatic model of pulsating stars through the application of a lagrangian formulation

The derivation of a thermodynamical Lagrangian for the non-adiabatical case using the techniques of the irreversible thermodynamic solves existing numerical problems. The usual method consists in obtaining the non-adiabatic solution by solving numerically the equation of motion, using as initial solution that of the adiabatic case. The variational principle associated with the thermodynamical Lagrangian permits to identify the non-adiabatic cases and to adjust the boundary conditions.Asociación Argentina de Astronomí

Stability analysis of quiescent prominences using thermodynamic irreversible energy principles

Using methods of non-equilibrium thermodynamics that extend and generalize the MHD energy principle of Bernstein et al. (1958, Proc. Roy. Soc. A, 244, 17) we develop a formalism in order to analyze the stability properties of prominence models considered as dissipative states i.e. states far form thermodynamic equilibrium. As an example, the criterion is applied to the Kippenhahn-Schlüter model (hereafter K-S) considering the addition of dissipative terms in the coupled system of equations: the balance of energy equation and the equation of motion. We show from this application, that periods corresponding to typical oscillations of the chromosphere and photosphere (3 and 5 min respectively), that were reported as observations of the prominence structure, can be explained as internal modes of the prominence itself. This is an alternative explanation to the one that supposes that the source of these perturbations are the cold foot chromospheric and photospheric basis

Hopf bifurcations in coronal loops. II. Nonlinear evolution of instabilities

In a previous paper, we have modeled the coupling between corona and chromosphere and derived a non-linear set of equations, where the global stability properties of the coronal plasma can be studied. The linear stability analysis indicates that the static equilibrium is stable unless the heating rate falls below a certain critical value. In the present paper, we study the nonlinear evolution of our equations both analytically and numerically. Applying a perturbative technique around the critical point, we find that a subcritical Hopf bifurcation takes place. The numerical integration of the equations agrees satisfactorily with the analytical results when they are compared close to the bifurcation. The nonthermal Doppler widths of EUV lines forming in the transition region can be explained by the existence of relatively low amplitude limit cycles.Fil:Gómez, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Sicardi Schifino, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Ferro Fontán, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina