Flexible paramagnetic membranes in fast precessing fields

Vázquez-Montejo, Pablo; de la Cruz, Mónica Olvera

doi:10.1103/physreve.98.032603

Title: Flexible paramagnetic membranes in fast precessing fields

Journal Article · Mon Sep 10 00:00:00 EDT 2018 · Physical Review. E

DOI:https://doi.org/10.1103/physreve.98.032603· OSTI ID:1541216

Vázquez-Montejo, Pablo ^[1]; de la Cruz, Mónica Olvera ^[2]

Northwestern Univ., Evanston, IL (United States). Dept. of Materials Science and Engineering; Univ. Autónoma de Yucatán, Mérida (Mexico). Faculty of Mathematics; Univ. Nacional Autonoma de Mexico (UNAM), Mexico City (Mexico). Inst. of Mathematics
Northwestern Univ., Evanston, IL (United States). Dept. of Materials Science and Engineering. Dept. of Physics and Astronomy

Elastic membranes composed of paramagnetic beads offer the possibility of assembling versatile actuators operated autonomously by external magnetic fields. Here we develop a theoretical framework to study shapes of such paramagnetic membranes under the influence of a fast precessing magnetic field. Their conformations are determined by the competition of the elastic and magnetic energies, arising as a result of their bending and the induced dipolar interactions between nearest-neighbors beads. In the harmonic approximation, the elastic energy is quadratic in the surface curvatures. To account for the magnetic energy we introduce a continuum limit energy, quadratic in the projections of the surface tangents onto the precession axis. We derive the Euler-Lagrange equation governing the equilibria of these membranes, as well as the corresponding stresses. We apply this framework to examine paramagnetic membranes with quasiplanar, cylindrical, and helicoidal geometries. In all cases we found that their shape, energy, and stresses can be modified by means of the parameters of the magnetic field, mainly by the angle of precession.

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Research Organization:: Energy Frontier Research Centers (EFRC) (United States). Center for Bio-Inspired Energy Science (CBES); Northwestern Univ., Evanston, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0000989

OSTI ID:: 1541216

Alternate ID(s):: OSTI ID: 1469266

Journal Information:: Physical Review. E, Vol. 98, Issue 3; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 3 works

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