Time-energy correlations in solar flare occurrence

The existence of time-energy correlations in flare occurrence is still an open and much debated problem. This study addresses the question whether statistically significant correlations are present between energies of successive flares as well as energies and waiting times. We analyze the GOES catalog with a statistical approach based on the comparison of the real catalog with a reshuffled one where energies are decorrelated. This analysis reduces the effect of background activity and is able to reveal the role of obscuration. We show the existence of non-trivial correlations between waiting times and energies, as well as between energies of subsequent flares. More precisely, we find that flares close in time tend to have the second event with large energy. Moreover, after large flares the flaring rate significantly increases, together with the probability of other large flares. Results suggest that correlations between energies and waiting times are a physical property and not an effect of obscuration. These findings could give important information on the mechanisms for energy storage and release in the solar corona

Scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics

In this paper we investigate the relation between the scaling properties of the linear response function $R(t,s)$, of the thermoremanent magnetization (TRM) and of the zero field cooled magnetization (ZFC) in the context of phase ordering kinetics. We explain why the retrival of the scaling properties of $R(t,s)$ from those of TRM and ZFC is not trivial. Preasymptotic contributions generate a long crossover in TRM, while ZFC is affected by a dangerous irrelevant variable. Lack of understanding of both these points has generated some confusion in the literature. The full picture relating the exponents of all the quantities involved is explicitely illustrated in the framework of the large $N$ model. Following this scheme, an assessment of the present status of numerical simulations for the Ising model can be made. We reach the conclusion that on the basis of the data available up to now, statements on the scaling properties of $R(t,s)$ can be made from ZFC but not from TRM. From ZFC data for the Ising model with $d=2,3,4$ we confirm the previously found linear dependence on dimensionality of the exponent $a$ entering $R(t,s) \sim s^{-(1+a)}f(t/s)$. We also find evidence that a recently derived form of the scaling function $f(x)$, using local scale invariance arguments [M.Henkel, M.Pleimling, C.Godr\`{e}che and J.M.Luck, Phys.Rev.Lett. {\bf 87}, 265701 (2001)], does not hold for the Ising model.Comment: 26 pages, 14 figure

Roughening of an interface in a system with surface or bulk disorder

We study numerically the roughening properties of an interface in a two-dimensional Ising model with either random bonds or random fields, which are representative of universality classes where disorder acts only on the interface or also away from it, in the bulk. The dynamical structure factor shows a rich crossover pattern from the form of a pure system at large wavevectors $k$, to a different behavior, typical of the kind of disorder, at smaller $k$'s. For the random field model a second crossover is observed from the typical behavior of a system where disorder is only effective on the surface, as the random bond model, to the truly large scale behavior, where bulk-disorder is important, that is observed at the smallest wavevectors.Comment: 13 pages, 8 figure

Dynamical scaling in branching models for seismicity

We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this scaling hypothesis. We present a numerical protocol able to generate a synthetic catalog with an arbitrary large number of events. The numerical data reproduce the hierarchical organization in time and magnitude of experimental inter-event time distribution.Comment: 3 figures to appear on Physical Review Letter

Fluctuation dissipation ratio in the one dimensional kinetic Ising model

The exact relation between the response function $R(t,t^{\prime})$ and the two time correlation function $C(t,t^{\prime})$ is derived analytically in the one dimensional kinetic Ising model subjected to a temperature quench. The fluctuation dissipation ratio $X(t,t^{\prime})$ is found to depend on time through $C(t,t^{\prime})$ in the time region where scaling $C(t,t^{\prime}) = f(t/t^{\prime})$ holds. The crossover from the nontrivial form $X(C(t,t^{\prime}))$ to $X(t,t^{\prime}) \equiv 1$ takes place as the waiting time $t_w$ is increased from below to above the equilibration time $t_{eq}$.Comment: 2 figure

Fluctuations of two-time quantities and non-linear response functions

We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and co-variance. In a first general part of the Article, we show the equivalence of the variance of the response function with the second-order susceptibility of a composite operator, and we derive an equilibrium fluctuation-dissipation theorem beyond-linear order relating it to the other variances. In a second part of the paper we apply the formalism to the study to non-disordered ferromagnets, in equilibrium or in the coarsening kinetics following a critical or sub-critical quench. We show numerically that the variances and the non-linear susceptibility obey scaling with respect to the coherence length $\xi$ in equilibrium, and with respect to the growing length $L(t)$ after a quench, similarly to what is known for the autocorrelation and the autoresponse functions.Comment: 21 pages, 5 figures. To appear on Jsta

Visual servoing of aerial manipulators

The final publication is available at link.springer.comThis chapter describes the classical techniques to control an aerial manipulator by means of visual information and presents an uncalibrated image-based visual servo method to drive the aerial vehicle. The proposed technique has the advantage that it contains mild assumptions about the principal point and skew values of the camera, and it does not require prior knowledge of the focal length, in contrast to traditional image-based approaches.Peer ReviewedPostprint (author's final draft

Nonequilibrium fluctuation-dissipation theorem and heat production

We use a relationship between response and correlation function in nonequilibrium systems to establish a connection between the heat production and the deviations from the equilibrium fluctuation-dissipation theorem. This scheme extends the Harada-Sasa formulation [Phys. Rev. Lett. 95, 130602 (2005)], obtained for Langevin equations in steady states, as it also holds for transient regimes and for discrete jump processes involving small entropic changes. Moreover, a general formulation includes two times and the new concepts of two-time work, kinetic energy, and of a two-time heat exchange that can be related to a nonequilibrium "effective temperature". Numerical simulations of a chain of anharmonic oscillators and of a model for a molecular motor driven by ATP hydrolysis illustrate these points.Comment: 5 pages, 3 figure