Jensen, M;
Majee, AK;
Prohl, A;
Schellnegger, C;
(2019)
Dynamic Programming for Finite Ensembles of Nanomagnetic Particles.
Journal of Scientific Computing
, 80
pp. 351-375.
10.1007/s10915-019-00940-3.
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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=(S2)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.
| Type: | Article |
|---|---|
| Title: | Dynamic Programming for Finite Ensembles of Nanomagnetic Particles |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s10915-019-00940-3 |
| Publisher version: | https://doi.org/10.1007/s10915-019-00940-3 |
| Language: | English |
| Additional information: | This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | math.NA, math.NA, math.OC, 45K05, 46S50, 49L20, 49L25, 91A23, 93E20 |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10156976 |
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