Weak Turbulence and Quasilinear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach

We derive weak turbulence and quasilinear models for relativistic charged particle dynamics in pitch-angle and energy space, due to interactions with electromagnetic waves propagating (anti-)parallel to a uniform background magnetic field. We use a Markovian approach that starts from the consideration of single particle motion in a prescribed electromagnetic field. This Markovian approach has a number of benefits, including: 1) the evident self-consistent relationship between a more general weak turbulence theory and the standard resonant diffusion quasilinear theory (as is commonly used in e.g. radiation belt and solar wind modeling); 2) the general nature of the Fokker-Planck equation that can be derived without any prior assumptions regarding its form; 3) the clear dependence of the form of the Fokker-Planck equation and the transport coefficients on given specific timescales. The quasilinear diffusion coefficients that we derive are not new in and of themselves, but this concise derivation and discussion of the weak turbulence and quasilinear theories using the Markovian framework is physically very instructive. The results presented herein form fundamental groundwork for future studies that consider phenomena for which some of the assumptions made in this manuscript may be relaxed.

Consistency Checking of the IEC 61508 PFH Formulas and New Formulas Proposal Based on the Markovian Approach

Safety Instrumented Systems (SISs) are of prime importance in protecting people, assets and environment from hazardous events. Therefore, it is important to be able to assess accurately their performance indicators. For this end, IEC 61508 standard has provided two reliability metrics: the average failure probability of a SIS lowly demanded (PFDavg) and the average failure frequency of a SIS highly or continuously demanded (PFH). The aim of this paper is to investigate the IEC 61508 PFH formulas and to propose new ones based on the Markovian approach. Indeed, the new edition of IEC 61508 provides PFH formulas reflecting the possibility of automatic shutdown of the monitored process upon detection of a dangerous failure in the SIS. However, the IEC 61508 attempt remains incomplete and provide non-conservative results, which is dangerous from a safety point of view.

Information Spreading on Memory Activity-Driven Temporal Networks

Information spreading dynamics on temporal networks have attracted significant attention in the field of network science. Extensive real-data analyses revealed that network memory widely exists in the temporal network. This paper proposes a mathematical model to describe the information spreading dynamics with the network memory effect. We develop a Markovian approach to describe the model. Using the Monte Carlo simulation method, we find that network memory may suppress and promote the information spreading dynamics, which depends on the degree heterogeneity and fraction of bigots. The network memory effect suppresses the information spreading for small information transmission probability. The opposite situation happens for large value of information transmission probability. Moreover, network memory effect may benefit the information spreading, which depends on the degree heterogeneity of the activity-driven network. Our results presented in this paper help us understand the spreading dynamics on temporal networks.

Semi-Markovian approach to optimizing the time of systematic preventive maintenance and the level of maintenance over a finite horizon

This work is concerned with the problem of optimizing maintenance policies in terms of economical rewards and availability. We consider a system with multiple states in terms of healthy mode (good state, degraded state and failure state) and maintenance action (running state, stopped for maintenance). The level of maintenance (perfect or not) is also taken into account. We propose semi-Markovian model highlighting the effects of dwell times and transitions on economical rewards. We determine an optimal policy conditionally upon the current state according to eight decision parameters related to time intervals between two preventive maintenances and the level of maintenance. We show through a sensitive analysis that decision parameters have nonlocal effects that imply a multiple objective function. Hence, we propose a compromise by optimizing the asymptotic average reward.