A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie

Local continuity laws on the phase space of Einstein equations with sources

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page

Multiscale statistical analysis of coronal solar activity

Multi-filter images from the solar corona are used to obtain temperature maps which are analyzed using techniques based on proper orthogonal decomposition (POD) in order to extract dynamical and structural information at various scales. Exploring active regions before and after a solar flare and comparing them with quiet regions we show that the multiscale behavior presents distinct statistical properties for each case that can be used to characterize the level of activity in a region. Information about the nature of heat transport is also be extracted from the analysis.Comment: 24 pages, 18 figure

Truncation effects in superdiffusive front propagation with L\'evy flights

A numerical and analytical study of the role of exponentially truncated L\'evy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov equation where the diffusion operator is replaced by a $\lambda$-truncated fractional derivative of order $\alpha$ where $1/\lambda$ is the characteristic truncation length scale. For $\lambda=0$ there is no truncation and fronts exhibit exponential acceleration and algebraic decaying tails. It is shown that for $\lambda \neq 0$ this phenomenology prevails in the intermediate asymptotic regime $(\chi t)^{1/\alpha} \ll x \ll 1/\lambda$ where $\chi$ is the diffusion constant. Outside the intermediate asymptotic regime, i.e. for $x > 1/\lambda$, the tail of the front exhibits the tempered decay $\phi \sim e^{-\lambda x}/x^{(1+\alpha)}$, the acceleration is transient, and the front velocity, $v_L$, approaches the terminal speed $v_* = (\gamma - \lambda^\alpha \chi)/\lambda$ as $t\to \infty$, where it is assumed that $\gamma > \lambda^\alpha \chi$ with $\gamma$ denoting the growth rate of the reaction kinetics. However, the convergence of this process is algebraic, $v_L \sim v_* - \alpha /(\lambda t)$, which is very slow compared to the exponential convergence observed in the diffusive (Gaussian) case. An over-truncated regime in which the characteristic truncation length scale is shorter than the length scale of the decay of the initial condition, $1/\nu$, is also identified. In this extreme regime, fronts exhibit exponential tails, $\phi \sim e^{-\nu x}$, and move at the constant velocity, $v=(\gamma - \lambda^\alpha \chi)/\nu$.Comment: Accepted for publication in Phys. Rev. E (Feb. 2009

Clustering transition in a system of particles self-consistently driven by a shear flow

We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists in that the effective velocity of every particle is given by the average of the external flow velocities felt by the particles located at a distance less than a typical radius, $R$. Numerical analysis reveals the existence of a transition to clustering depending on the parameters of the external flow and on $R$. A continuum description in terms of the number density of particles is derived, and a linear stability analysis of the density equation is performed in order to characterize the transitions observed in the model of interacting particles.Comment: 11 pages, 2 figures. To appear in PR

Execution time distributions in embedded safety-critical systems using extreme value theory

Several techniques have been proposed to upper-bound the worst-case execution time behaviour of programs in the domain of critical real-time embedded systems. These computing systems have strong requirements regarding the guarantees that the longest execution time a program can take is bounded. Some of those techniques use extreme value theory (EVT) as their main prediction method. In this paper, EVT is used to estimate a high quantile for different types of execution time distributions observed for a set of representative programs for the analysis of automotive applications. A major challenge appears when the dataset seems to be heavy tailed, because this contradicts the previous assumption of embedded safety-critical systems. A methodology based on the coefficient of variation is introduced for a threshold selection algorithm to determine the point above which the distribution can be considered generalised Pareto distribution. This methodology also provides an estimation of the extreme value index and high quantile estimates. We have applied these methods to execution time observations collected from the execution of 16 representative automotive benchmarks to predict an upper-bound to the maximum execution time of this program. Several comparisons with alternative approaches are discussed.The research leading to these results has received funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under the PROXIMA Project (grant agreement 611085). This study was also partially supported by the Spanish Ministry of Science and Innovation under grants MTM2012-31118 (2013-2015) and TIN2015-65316-P. Jaume Abella is partially supported by the Ministry of Economy and Competitiveness under Ramon y Cajal postdoctoral fellowship number RYC-2013- 14717.Peer ReviewedPostprint (author's final draft

Diffusive transport and self-consistent dynamics in coupled maps

The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps. Self-consistency, i.e. the back-influence of the transported quantity on the velocity field of the driving flow, despite of its critical importance, is usually overlooked in the description of realistic systems, for example in plasma physics. We propose a class of self-consistent models consisting of an ensemble of maps globally coupled through a mean field. Depending on the kind of coupling, two different general types of self-consistent maps are considered: maps coupled to the field only through the phase, and fully coupled maps, i.e. through the phase and the amplitude of the external field. The analogies and differences of the diffusion properties of these two kinds of maps are discussed in detail.Comment: 13 pages, 14 figure