Predictive maintenance for the heated hold-up tank

We present a numerical method to compute an optimal maintenance date for the test case of the heated hold-up tank. The system consists of a tank containing a fluid whose level is controlled by three components: two inlet pumps and one outlet valve. A thermal power source heats up the fluid. The failure rates of the components depends on the temperature, the position of the three components monitors the liquid level in the tank and the liquid level determines the temperature. Therefore, this system can be modeled by a hybrid process where the discrete (components) and continuous (level, temperature) parts interact in a closed loop. We model the system by a piecewise deterministic Markov process, propose and implement a numerical method to compute the optimal maintenance date to repair the components before the total failure of the system.Comment: arXiv admin note: text overlap with arXiv:1101.174

Strategic Investment Timing Under Profit Complementarities

This paper analyses strategic investment games between two firms that compete for the adoption of a new more efficient technology whose returns are uncertain. We assume that once one of the two firms adopted the new technology, joint adoption is preferable for both firms, that is there are profit complementarities in the product market. There are, moreover, externalities derivig from the first firm's investment. By modelling the switch from a well established technology to a new one as a dynamic stochastic game, we fully characterize the equilibria of the game under both non-cooperative and cooperative firms' behaviour. We show that in the cooperative equilibrium firms will invest later under negative externalities and earlier under positive externalities. Thus we identify circumstances in which competiton can be suboptimal (too much waiting). Overall, compared to earlier models that only allow for a new market game, our model examines a richer set of strategic interactions of adoption decisions

Pre-asymptotic corrections to fractional diffusion equations

The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to the presence of obstacles which hinder particle migration. The asymptotic behavior of these systems is usually well described by fractional diffusion, which provides an elegant and unified framework for modeling anomalous transport. We show that pre-asymptotic corrections to fractional diffusion might become relevant, depending on the microscopic dynamics of the particles. To incorporate these effects, we derive a modified transport equation and validate its effectiveness by a Monte Carlo simulation.Comment: 6 pages, 3 figure

Monte Carlo evaluation of FADE approach to anomalous kinetics

In this paper we propose a comparison between the CTRW (Monte Carlo) and Fractional Derivative approaches to the modelling of anomalous diffusion phenomena in the presence of an advection field. Galilei variant and invariant schemes are revised.Comment: 13 pages, 6 figure

Some Insights in Superdiffusive Transport

In this paper we deal with high-order corrections for the Fractional Derivative approach to anomalous diffusion, in super-diffusive regime, which become relevand whenever one attempts to describe the behavior of particles close to normal diffusion.Comment: 14 pages, 7 figure

Monte Carlo Approach to Dynamic PSA: Neural Solution of Equations Describing Core Transients

The PSA analysis of a real plant represent a formidable com-putational task usually afforded either with an analytical approach based on the theory of the Markov chains or with a Monte Carlo simulation. In our opinion this latter methodology, thanks to its unique flexibility features, represents the only viable approach to the problem when time dependencies have impacts on the analy-sis: examples are time dependent transition rates (ageing), timing of the protection, control and safety systems, operator actions etc. Moreover the PSA analysis of a real plant demands taking into account the process variable dynamics when the evolution of the underlying physical process interacts with the system hardware configuration, e.g. when the process variables influence the failure rates or activate the protection systems. The inclusion of these dy-namic aspects dramatically burdens the analysis: a solution could be presently attempted only through short cuts to the solution of the deterministic equations governing the evolution of the process variables. In the present paper we consider the application of a multi-layered neural network for the solution of the mathematical mod-els related to the core behaviour of a PWR under varying thermal-hydraulic conditions. Since the neural network works very rapid-ly, this approach seems to be a good candidate for being included in a Monte Carlo dynamic PSA code which requires solving thou-sands of times the model equations relating to the different hard-ware plant configurations. Possible approximations thereby intro-duced could be tolerated if comparable with those following from the uncertainties of the stochastic parameters. The time reduction advantage is expected to increase when the future parallel com-puters become widely available

La formalizzazione matematica nelle teorie economiche: problemi e prospettive

All\u2019interno della comunit\ue0 degli economisti sembra essere oggi presente un crescente disagio e un diffuso malcontento relativamente alle capacit\ue0 della modellistica neoclassica di comprendere e spiegare i fenomeni economici. La relazione intende esaminare criticamente il contributo della formalizzazione matematica nelle teorie economiche, mettendo in evidenza sia punti di forza di un tale approccio sia le debolezze insite in un\u2019analisi che rischia spesso di privilegiare la bellezza dello strumento rispetto all\u2019oggetto di studio. Si considerano poi alcune delle moderne prospettive per l\u2019indagine economica offerte dalla modellistica basata sulla simulazione a computer che consente di tener conto della complessit\ue0 della realt\ue0 in misura maggiore di un approccio puramente analitico. Viene infine evidenziata l\u2019importanza di garantire la coesistenza di una pluralit\ue0 di scuole di pensiero in economia e si esaminano altres\uec le difficolt\ue0 per la valutazione della ricerca provocate dell\u2019esistenza di un paradigma dominante. Nelle conclusioni viene enfatizzata la necessit\ue0 di considerare l\u2019economia come una vera scienza sociale