2,013 research outputs found

    Alternating ‘flip’ solutions in ferrofluidic Taylor-Couette flow

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    Peer ReviewedPostprint (author's final draft

    Invariant solutions organizing pipe flow turbulence

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    Peer ReviewedPostprint (published version

    Parameter estimation for semilinear SPDEs from local measurements

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    This work contributes to the limited literature on estimating the diffusivity or drift coefficient of nonlinear SPDEs driven by additive noise. Assuming that the solution is measured locally in space and over a finite time interval, we show that the augmented maximum likelihood estimator introduced in Altmeyer, Reiss (2020) retains its asymptotic properties when used for semilinear SPDEs that satisfy some abstract, and verifiable, conditions. The proofs of asymptotic results are based on splitting the solution in linear and nonlinear parts and fine regularity properties in LpL^p-spaces. The obtained general results are applied to particular classes of equations, including stochastic reaction-diffusion equations. The stochastic Burgers equation, as an example with first order nonlinearity, is an interesting borderline case of the general results, and is treated by a Wiener chaos expansion. We conclude with numerical examples that validate the theoretical results.Comment: corrected versio

    Transition to turbulence in Taylor-Couette ferrofluidic flow

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    Y.D. was supported by Basic Science Research Program of the Ministry of Education, Science and Technology under Grant No. NRF-2013R1A1A2010067. Y.C.L. was supported by AFOSR under Grant No. FA9550-12-1-0095.Peer reviewedPublisher PD
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