A finite difference method for Piecewise Deterministic Processes with memory

In this paper the numerical approximation of solutions of Liouville-Master Equations for time-dependent distribution functions of Piecewise Deterministic Processes with memory is considered. These equations are linear hyperbolic PDEs with non-constant coefficients, and boundary conditions that depend on integrals over the interior of the integration domain. We construct a finite difference method of the first order, by a combination of the upwind method, for PDEs, and by a direct quadrature, for the boundary condition. We analyse convergence of the numerical solution for distribution functions evolving towards an equilibrium. Numerical results for two problems, whose analytical solutions are known in closed form, illustrate the theoretical finding.Comment: 20 pages, 7 figure

A Fluctuation-Dissipation Process without Time Scale

We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically, with a good agreement between theory and numerical treatment. As a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution. The distribution tails are truncated, the distribution border is signalled by sharp peaks and, in the weak dissipation limit, the central distribution body becomes identical to a truncated Levy distribution.Comment: REVTeX 3.1, 7 pages, 2 EPS figures, uses epsfig.sty. Submitted to Phys. Rev.

Canonical and non-canonical equilibrium distribution

We address the problem of the dynamical foundation of non-canonical equilibrium. We consider, as a source of divergence from ordinary statistical mechanics, the breakdown of the condition of time scale separation between microscopic and macroscopic dynamics. We show that this breakdown has the effect of producing a significant deviation from the canonical prescription. We also show that, while the canonical equilibrium can be reached with no apparent dependence on dynamics, the specific form of non-canonical equilibrium is, in fact, determined by dynamics. We consider the special case where the thermal reservoir driving the system of interest to equilibrium is a generator of intermittent fluctuations. We assess the form of the non-canonical equilibrium reached by the system in this case. Using both theoretical and numerical arguments we demonstrate that Levy statistics are the best description of the dynamics and that the Levy distribution is the correct basin of attraction. We also show that the correct path to non-canonical equilibrium by means of strictly thermodynamic arguments has not yet been found, and that further research has to be done to establish a connection between dynamics and thermodynamics.Comment: 13 pages, 6 figure

Dynamic versus thermodynamic approach to non-canonical equilibrium

We study the dynamic and thermodynamic origin of non-canonical equilibria, and we discuss their connection with the generalized central limit theorem and the micro-canonical Boltzmann principle. We reach the conclusion that the zeroth law of thermodynamics and the Boltzmann principle are fulfilled thanks to an apparent fault turned into a benefit: the dynamic approach can only produce a truncated form of inverse power law equilibrium.Comment: submit to Physica

The Tsunami Assessment Modelling System by the Joint Research Centre

The Tsunami Assessment Modeling System was developed by the European Commission, Joint Research Centre, in order to serve Tsunami early warning systems such as the Global Disaster Alerts and Coordination System (GDACS) in the evaluation of possible consequences by a Tsunami of seismic nature. The Tsunami Assessment Modeling System is currently operational and is calculating in real time all the events occurring in the world, calculating the expected Tsunami wave height and identifying the locations where the wave height should be too high. The first part of the paper describes the structure of the system, the underlying analytical models and the informatics arrangement; the second part shows the activation of the system and the results of the calculated analyses. The final part shows future development of this modeling tool.JRC.G.2-Support to external securit

Analisi di processi discontinui in un impianto di produzione di cosmetici

In un'azienda Italiana di cosmetici si è studiata la possibilità di passare da uno schema produttivo tradizionale ad uno standardizzato in modo da ottenere processi ripetibili sia in durata che in qualità. Questo rende possibile una più precisa organizzazione della produzione e l'ottenimento di prodotti sempre uguali. In questo modo si evitano perdite economiche legate direttamente ed indirettamente alla non omogeneità dei prodotti ottenuti. Lo studio è stato volto soprattutto alla caratterizzazione dei processi discontinui in reattori agitati con camicia esterna, cercando di standardizzare le fasi di riscaldamento e raffreddamento, causa principale dell'irregolarità dei processi

Access to the Work Product of an Attorney Disqualified for Opposing a Former Client: First Wisconsin Mortgage Trust

The purposes of this Recent Development are to analyze the effect of the Seventh Circuit\u27s work product decision on disqualification standards and to develop a consistent framework for determining whether access to the work product of an attorney disqualified for opposing a former client should be allowed. This Recent Development urges that in order to provide the effective guidance necessary for both voluntary compliance and judicial enforcement, the Code must incorporate those judicial standards that most closely reflect its standards in this area. Thus the Recent Development proposes an Ethical Consideration regarding access to work product that reflects the ethical concerns underlying Canon