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Publications [#281386] of Laurens E. Howle

Papers Published

  1. Wagner, BA; Bertozzi, AL; Howle, LE, Positive feedback control of Rayleigh-Bénard convection, Discrete and Continuous Dynamical Systems Series B, vol. 3 no. 4 (November, 2003), pp. 619-642, American Institute of Mathematical Sciences (AIMS), ISSN 1531-3492 [doi]
    (last updated on 2023/06/01)

    Abstract:
    We consider the problem of active feedback control of Rayleigh-Bénard convection via shadowgraphic measurement. Our theoretical studies show, that when the feedback control is positive, i.e. is tuned to advance the onset of convection, there is a critical threshold beyond which the system becomes linearly ill-posed so that short-scale disturbances are greatly amplified. Experimental observation suggests that finite size effects become important and we develop a theory to explain these contributions. As an efficient modelling tool for studying the dynamics of such a controlled pattern forming system, we use a Galerkin approximation to derive a dimension reduced model.