Feedback control of unstable cellular solidification fronts

A. J. Pons, A. Karma, S. Akamatsu, M. Newey, A. Pomerance, H. Singer, and W. Losert
Phys. Rev. E 75, 021602 – Published 8 February 2007

Abstract

We present a feedback control scheme to stabilize unstable cellular patterns during the directional solidification of a binary alloy. The scheme is based on local heating of cell tips which protrude ahead of the mean position of all tips in the array. The feasibility of this scheme is demonstrated using phase-field simulations and, experimentally, using a real-time image processing algorithm, to track cell tips, coupled with a movable laser spot array device to heat the tips locally. We demonstrate, both numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable with uniform spacing through the feedback control which is maintained with minimal heating.

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  • Received 15 August 2006

DOI:https://doi.org/10.1103/PhysRevE.75.021602

©2007 American Physical Society

Authors & Affiliations

A. J. Pons1,*, A. Karma1, S. Akamatsu2,†, M. Newey2, A. Pomerance2, H. Singer2,‡, and W. Losert2

  • 1Physics Department and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA
  • 2Department of Physics, IPST and IREAP, University of Maryland, College Park, Maryland, USA

  • *Electronic address: a.pons-rivero@neu.edu
  • Permanent address: INSP, CNRS UMR 8875, Universités Paris VI and Paris VII, 140 rue de Lourmel, 75015 Paris, France.
  • Permanent address: Laboratorium für Festkörperphysik, ETH, CH-8093, Hönggerberg, Zürich, Switzerland.

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Issue

Vol. 75, Iss. 2 — February 2007

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