69 results found
© 2018 SIAM. Published by SIAM under the terms. This paper explores the concept of near-cloaking in the context of time-dependent heat propagation. We show that after the lapse of a certain threshold time, the boundary measurements for the homogeneous heat equation are close to the cloaked heat problem in a certain Sobolev space norm irrespective of the density-conductivity pair in the cloaked region. A regularized transformation media theory is employed to arrive at our results. Our proof relies on the study of the long time behavior of solutions to the parabolic problems with high contrast in density and conductivity coefficients. It further relies on the study of boundary measurement estimates in the presence of small defects in the context of steady conduction problems. We then present some numerical examples to illustrate our theoretical results.
Gomes SN, Pavliotis GA, 2018, Mean Field Limits for Interacting Diffusions in a Two-Scale Potential, JOURNAL OF NONLINEAR SCIENCE, Vol: 28, Pages: 905-941, ISSN: 0938-8974
Abdulle A, Pavliotis GA, Vaes U, 2017, Spectral Methods for Multiscale Stochastic Differential Equations, SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, Vol: 5, Pages: 720-761, ISSN: 2166-2525
Craster R, Guenneau S, Hutridurga H, et al., 2017, Regularized transformation optics for transient heat transfer, 2017 11th International Congress on Engineered Material Platforms for Novel Wave Phenomena (METAMATERIALS), Publisher: IEEE, Pages: 127-129
Duncan AB, Nusken N, Pavliotis GA, 2017, Using Perturbed Underdamped Langevin Dynamics to Efficiently Sample from Probability Distributions, JOURNAL OF STATISTICAL PHYSICS, Vol: 169, Pages: 1098-1131, ISSN: 0022-4715
Gomes SN, Kalliadasis S, Papageorgiou DT, et al., 2017, Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation, PHYSICA D-NONLINEAR PHENOMENA, Vol: 348, Pages: 33-43, ISSN: 0167-2789
Gomes SN, Papageorgiou DT, Pavliotis GA, 2017, Stabilizing non-trivial solutions of the generalized Kuramoto-Sivashinsky equation using feedback and optimal control, IMA JOURNAL OF APPLIED MATHEMATICS, Vol: 82, Pages: 158-194, ISSN: 0272-4960
Tomlin RJ, Papageorgiou DT, Pavliotis GA, 2017, Three-dimensional wave evolution on electrified falling films, JOURNAL OF FLUID MECHANICS, Vol: 822, Pages: 54-79, ISSN: 0022-1120
Bonnaillie-Noel V, Carrillo JA, Goudon T, et al., 2016, Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations, IMA JOURNAL OF NUMERICAL ANALYSIS, Vol: 36, Pages: 1536-1569, ISSN: 0272-4979
Duncan AB, Kalliadasis S, Pavliotis GA, et al., 2016, Noise-induced transitions in rugged energy landscapes, PHYSICAL REVIEW E, Vol: 94, ISSN: 2470-0045
Duncan AB, Lelievre T, Pavliotis GA, 2016, Variance Reduction Using Nonreversible Langevin Samplers, JOURNAL OF STATISTICAL PHYSICS, Vol: 163, Pages: 457-491, ISSN: 0022-4715
Thompson AB, Gomes SN, Pavliotis GA, et al., 2016, Stabilising falling liquid film flows using feedback control, PHYSICS OF FLUIDS, Vol: 28, ISSN: 1070-6631
Duncan AB, Elliott CM, Pavliotis GA, et al., 2015, A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces, JOURNAL OF NONLINEAR SCIENCE, Vol: 25, Pages: 389-449, ISSN: 0938-8974
Gomes SN, Pradas M, Kalliadasis S, et al., 2015, Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems, PHYSICAL REVIEW E, Vol: 92, ISSN: 2470-0045
Joubaud R, Pavliotis GA, Stoltz G, 2015, Langevin Dynamics with Space-Time Periodic Nonequilibrium Forcing, JOURNAL OF STATISTICAL PHYSICS, Vol: 158, Pages: 1-36, ISSN: 0022-4715
Kalliadasis S, Krumscheid S, Pavliotis GA, 2015, A new framework for extracting coarse-grained models from time series with multiscale structure, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 296, Pages: 314-328, ISSN: 0021-9991
Krumscheid S, Pradas M, Pavliotis GA, et al., 2015, Data-driven coarse graining in action: Modeling and prediction of complex systems, PHYSICAL REVIEW E, Vol: 92, ISSN: 2470-0045
Ottobre M, Pavliotis GA, Pravda-Starov K, 2015, Some remarks on degenerate hypoelliptic Ornstein-Uhlenbeck operators, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, Vol: 429, Pages: 676-712, ISSN: 0022-247X
Schmuck M, Pradas M, Pavliotis GA, et al., 2015, A new mode reduction strategy for the generalized Kuramoto-Sivashinsky equation, IMA JOURNAL OF APPLIED MATHEMATICS, Vol: 80, Pages: 273-301, ISSN: 0272-4960
Hartmann C, Latorre JC, Zhang W, et al., 2014, Optimal control of multiscale systems using reduced-order models, Journal of Computational Dynamics, Vol: 1, Pages: 279-306
© American Institute of Mathematical Sciences. We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal control computed from the reduced-order model to control the original, high-dimensional system? The strategy "first reduce, then optimize"-rather than "first optimize, then reduce"-is motivated by the fact that solving optimal control problems for high-dimensional multiscale systems is numerically challenging and often computationally prohibitive. We state suffcient and necessary conditions, under which the "first reduce, then control" strategy can be employed and discuss when it should be avoided. We further give numerical examples that illustrate the "first reduce, then optmize" approach and discuss possible pitfalls.
Latorre JC, Kramer PR, Pavliotis GA, 2014, Numerical methods for computing effective transport properties of flashing Brownian motors, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 257, Pages: 57-82, ISSN: 0021-9991
Pavliotis GA, 2014, Stochastic Processes and Applications Diffusion Processes, the Fokker-Planck and Langevin Equations, Publisher: Springer, ISBN: 9781493913220
This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences.
Rubin KJ, Pruessner G, Pavliotis GA, 2014, Mapping multiplicative to additive noise, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 47, ISSN: 1751-8113
Schmuck M, Pavliotis GA, Kalliadasis S, 2014, Effective macroscopic interfacial transport equations in strongly heterogeneous environments for general homogeneous free energies, APPLIED MATHEMATICS LETTERS, Vol: 35, Pages: 12-17, ISSN: 0893-9659
Krumscheid S, Pavliotis GA, Kalliadasis S, 2013, SEMIPARAMETRIC DRIFT AND DIFFUSION ESTIMATION FOR MULTISCALE DIFFUSIONS, MULTISCALE MODELING & SIMULATION, Vol: 11, Pages: 442-473, ISSN: 1540-3459
Latorre JC, Pavliotis GA, Kramer PR, 2013, Corrections to Einstein's Relation for Brownian Motion in a Tilted Periodic Potential, JOURNAL OF STATISTICAL PHYSICS, Vol: 150, Pages: 776-803, ISSN: 0022-4715
Lelievre T, Nier F, Pavliotis GA, 2013, Optimal Non-reversible Linear Drift for the Convergence to Equilibrium of a Diffusion, JOURNAL OF STATISTICAL PHYSICS, Vol: 152, Pages: 237-274, ISSN: 0022-4715
Papaefthymiou ES, Papageorgiou DT, Pavliotis GA, 2013, Nonlinear interfacial dynamics in stratified multilayer channel flows, JOURNAL OF FLUID MECHANICS, Vol: 734, Pages: 114-143, ISSN: 0022-1120
Schmuck M, Pradas M, Kalliadasis S, et al., 2013, New Stochastic Mode Reduction Strategy for Dissipative Systems, PHYSICAL REVIEW LETTERS, Vol: 110, ISSN: 0031-9007
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