67 results found
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
Craster R, Guenneau S, Hutridurga H, et al., 2017, Regularized transformation optics for transient heat transfer, Pages: 127-129
© 2017 IEEE. We report on certain cloaking strategies for transient heat transfer. Regularized Kohn's transform is employed to design cylindrical cloaks and to prove a near-cloak result. Our main result says that, after the lapse of a certain threshold time, the temperature field outside the cylindrical cloak is close to that of the uniformly conducting medium irrespective of the conductivity enclosed in the cloaked region.
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
Gomes SN, Pavliotis GA, 2017, Mean Field Limits for Interacting Diffusions in a Two-Scale Potential, Journal of Nonlinear Science, Pages: 1-37, ISSN: 0938-8974
© 2017 The Author(s) In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean–Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.
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
Schmuck M, Pradas M, Pavliotis GA, et al., 2013, Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media, NONLINEARITY, Vol: 26, Pages: 3259-3277, ISSN: 0951-7715
Abdulle A, Pavliotis GA, 2012, Numerical methods for stochastic partial differential equations with multiple scales, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 231, Pages: 2482-2497, ISSN: 0021-9991
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.