stochastic diffusion
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2022 ◽  
Vol 166 ◽  
pp. 108448
David Vališ ◽  
Jakub Gajewski ◽  
Marie Forbelská ◽  
Zdeněk Vintr ◽  
Józef Jonak

2022 ◽  
Vol 15 (1) ◽  
pp. 63-71
Ahmed Nafidi ◽  
Oussama Rida ◽  
Meriem Bahij ◽  
Boujemaa Achchab

2021 ◽  
Vol 7 (4) ◽  
pp. 87-102
Manohar Potli ◽  
Chandrasekhar Reddy Atla

Reliability assessment of electrical distribution systems is an important criterion to determine system performance in terms of interruptions. Probabilistic assessment methods are usually used in reliability analysis to deal with uncertainties. These techniques require a longer execution time in order to account for uncertainty. Multi-Level Monte Carlo (MLMC) is an advanced Monte Carlo Simulation (MCS) approach to improve accuracy and reduce the execution time. This paper provides a systematic approach to model the static and dynamic uncertainties of Time to Failure (TTF) and Time to Repair (TTR) of power distribution components using a Stochastic Diffusion Process. Further, the Stochastic Diffusion Process is integrated into MLMC to estimate the impacts of uncertainties on reliability indices. The Euler Maruyama path discretization applied to evaluate the solution of the Stochastic Diffusion Process. The proposed Stochastic Diffusion Process-based MLMC method is integrated into a systematic failure identification technique to evaluate the distribution system reliability. The proposed method is validated with analytical and Sequential MCS methods for IEEE Roy Billinton Test Systems. Finally, the numerical results show the accuracy and fast convergence rates to handle uncertainties compared to Sequential MCS method.

2021 ◽  
Vol 5 (3) ◽  
pp. 315-333
Sheng-Tsaing Tseng ◽  
Chien-Yu Peng

2021 ◽  
Vol 2021 (5) ◽  
Jewel K. Ghosh ◽  
R. Loganayagam ◽  
Siddharth G. Prabhu ◽  
Mukund Rangamani ◽  
Akhil Sivakumar ◽  

Abstract Planar black holes in AdS have long-lived quasinormal modes which capture the physics of charge and momentum diffusion in the dual field theory. How should we characterize the effective dynamics of a probe system coupled to the conserved currents of the dual field theory? Specifically, how would such a probe record the long-lived memory of the black hole and its Hawking fluctuations? We address this question by exhibiting a universal gauge invariant framework which captures the physics of stochastic diffusion in holography: a designer scalar with a gravitational coupling governed by a single parameter, the Markovianity index. We argue that the physics of gauge and gravitational perturbations of a planar Schwarzschild-AdS black hole can be efficiently captured by such designer scalars. We demonstrate that this framework allows one to decouple, at the quadratic order, the long-lived quasinormal and Hawking modes from the short-lived ones. It furthermore provides a template for analyzing fluctuating open quantum field theories with memory. In particular, we use this set-up to analyze the diffusive Hawking photons and gravitons about a planar Schwarzschild-AdS black hole and derive the quadratic effective action that governs fluctuating hydrodynamics of the dual CFT. Along the way we also derive results relevant for probes of hyperscaling violating backgrounds at finite temperature.

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