Dynamic programming for finite ensembles of nanomagnetic particles

Jensen, Max, Majee, Ananta K, Prohl, Andreas and Schellnegger, Christian (2019) Dynamic programming for finite ensembles of nanomagnetic particles. Journal of Scientific Computing, 80 (1). pp. 351-375. ISSN 0885-7474

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Abstract

We use optimal control via a distributed exterior field to steer the dynamics of an ensemble of N interacting ferromagnetic particles which are immersed into a heat bath by minimizing a quadratic functional. Using the dynamic programming principle, we show the existence of a unique strong solution of the optimal control problem. By the Hopf–Cole transformation, the associated Hamilton–Jacobi–Bellman equation of the dynamic programming principle may be re-cast into a linear PDE on the manifold M=(S^2)^N, whose classical solution may be represented via Feynman–Kac formula. We use this probabilistic representation for Monte-Carlo simulations to illustrate optimal switching dynamics.

Item Type: Article
Keywords: Stochastic Landau–Lifschitz–Gilbert equation, Stratonovich noise, HJB equation, Dynamic programming principle, Hopf–Cole transformation, Discretization
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics > QA0274 Stochastic processes
Q Science > QA Mathematics > QA0297 Numerical analysis
Depositing User: Max Jensen
Date Deposited: 18 Mar 2019 14:56
Last Modified: 05 Jul 2019 14:45
URI: http://sro.sussex.ac.uk/id/eprint/82508

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