75 results found
Schmuck M, Pavliotis GA, Kalliadasis S, 2019, Recent advances in the evolution of interfaces: Thermodynamics, upscaling, and universality, Computational Materials Science, Vol: 156, Pages: 441-451, ISSN: 0927-0256
We consider the evolution of interfaces in binary mixtures permeating strongly heterogeneous systems such as porous media. To this end, we first review available thermodynamic formulations for binary mixtures based on general reversible-irreversible couplings and the associated mathematical attempts to formulate a non-equilibrium variational principle in which these non-equilibrium couplings can be identified as minimizers. Based on this, we investigate two microscopic binary mixture formulations fully resolving heterogeneous/perforated domains: (a) a flux-driven immiscible fluid formulation without fluid flow; (b) a momentum-driven formulation for quasi-static and incompressible velocity fields. In both cases we state two novel, reliably upscaled equations for binary mixtures/multiphase fluids in strongly heterogeneous systems by systematically taking thermodynamic features such as free energies into account as well as the system's heterogeneity defined on the microscale such as geometry and materials (e.g. wetting properties). In the context of (a), we unravel a universality with respect to the coarsening rate due to its independence of the system's heterogeneity, i.e. the well-known O(t1/3)-behaviour for homogeneous systems holds also for perforated domains. Finally, the versatility of phase field equations and their thermodynamic foundation relying on free energies, make the collected recent developments here highly promising for scientific, engineering and industrial applications for which we provide an example for lithium batteries.
Duncan A, Zygalakis K, Pavliotis G, 2018, Nonreversible Langevin Samplers: Splitting Schemes, Analysis and Implementation
For a given target density, there exist an infinite number of diffusion processes which are ergodic with respect to this density. As observed in a number of papers, samplers based on nonreversible diffusion processes can significantly outperform their reversible counterparts both in terms of asymptotic variance and rate of convergence to equilibrium. In this paper, we take advantage of this in order to construct efficient sampling algorithms based on the Lie-Trotter decomposition of a nonreversible diffusion process into reversible and nonreversible components. We show that samplers based on this scheme can significantly outperform standard MCMC methods, at the cost of introducing some controlled bias. In particular, we prove that numerical integrators constructed according to this decomposition are geometrically ergodic and characterise fully their asymptotic bias and variance, showing that the sampler inherits the good mixing properties of the underlying nonreversible diffusion. This is illustrated further with a number of numerical examples ranging from highly correlated low dimensional distributions, to logistic regression problems in high dimensions as well as inference for spatial models with many latent variables.
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
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
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
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
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
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
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
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
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
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
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
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
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
, 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.
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.
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
Rubin KJ, Pruessner G, Pavliotis GA, 2014, Mapping multiplicative to additive noise, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 47, ISSN: 1751-8113
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
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
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
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
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