Imperial College London

ProfessorGrigoriosPavliotis

Faculty of Natural SciencesDepartment of Mathematics

Professor of Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8564g.pavliotis Website

 
 
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Location

 

621Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

57 results found

Abdulle A, Pavliotis GA, Vaes U, Specral methods for multiscale stochastic differential equations, SIAM/ASA Journal on Uncertainty Quantification, ISSN: 2166-2525

This paper presents a new method for the solution of multiscale stochastic differential equations atthe diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscalemethod (HMM) or the equation-free method, which rely on Monte Carlo simulations, in this paperwe introduce a new numerical methodology that is based on a spectral method. In particular, we usean expansion in Hermite functions to approximate the solution of an appropriate Poisson equation,which is used in order to calculate the coefficients of the homogenized equation. Spectral convergenceis proved under suitable assumptions. Numerical experiments corroborate the theory and illustratethe performance of the method. A comparison with the HMM and an application to singularlyperturbed stochastic PDEs are also presented.

JOURNAL ARTICLE

Tomlin RJ, Papageorgiou DT, Pavliotis GA, Three-dimensional wave evolution on electrified falling films, Journal of Fluid Mechanics, Vol: 822, Pages: 54-79, ISSN: 1469-7645

We consider the full three-dimensional dynamics of a thin falling liquid film on a flat plate inclined at some non-zero angle to the horizontal. In addition to gravitational effects, the flow is driven by an electric field which is normal to the substrate far from the flow. This extends the work of Tseluiko & Papageorgiou (J. Fluid Mech., vol. 556, 2006b, pp. 361–386) by including transverse dynamics. We study both the cases of overlying and hanging films, where the liquid lies above or below the substrate, respectively. Starting with the Navier–Stokes equations coupled with electrostatics, a fully nonlinear two-dimensional Benney equation for the interfacial dynamics is derived, valid for waves that are long compared to the film thickness. The weakly nonlinear evolution is governed by a Kuramoto–Sivashinsky equation with a non-local term due to the electric field effect. The electric field term is linearly destabilising and produces growth rates proportional to $|\unicode[STIX]{x1D743}|^{3}$ , where $\unicode[STIX]{x1D743}$ is the wavenumber vector of the perturbations. It is found that transverse gravitational instabilities are always present for hanging films, and this leads to unboundedness of nonlinear solutions even in the absence of electric fields – this is due to the anisotropy of the nonlinearity. For overlying films and a restriction on the strength of the electric field, the equation is well-posed in the sense that it possesses bounded solutions. This two-dimensional equation is studied numerically for the case of periodic boundary conditions in order to assess the effects of inertia, electric field strength and the size of the periodic domain. Rich dynamical behaviours are observed and reported. For subcritical Reynolds number flows, a sufficiently strong electric field can promote non-trivial dynamics for some choices of domain size, leading to fully two-dimensional evolutions of the interface. We also observe two-dimensiona

JOURNAL ARTICLE

Gomes SN, Kalliadasis S, Papageorgiou DT, Pavliotis GA, Pradas Met al., 2017, Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation, PHYSICA D-NONLINEAR PHENOMENA, Vol: 348, Pages: 33-43, ISSN: 0167-2789

JOURNAL ARTICLE

Bonnaillie-Noel V, Carrillo JA, Goudon T, Pavliotis GAet 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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Thompson AB, Gomes SN, Pavliotis GA, Papageorgiou DTet al., 2016, Stabilising falling liquid film flows using feedback control, PHYSICS OF FLUIDS, Vol: 28, ISSN: 1070-6631

JOURNAL ARTICLE

Duncan AB, Elliott CM, Pavliotis GA, Stuart AMet al., 2015, A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces, JOURNAL OF NONLINEAR SCIENCE, Vol: 25, Pages: 389-449, ISSN: 0938-8974

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Schmuck M, Pradas M, Pavliotis GA, Kalliadasis Set 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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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.

BOOK

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Lelièvre 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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Schmuck M, Pradas M, Kalliadasis S, Pavliotis GAet al., 2013, New Stochastic Mode Reduction Strategy for Dissipative Systems, PHYSICAL REVIEW LETTERS, Vol: 110, ISSN: 0031-9007

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Goddard BD, Nold A, Savva N, Pavliotis GA, Kalliadasis Set al., 2012, General Dynamical Density Functional Theory for Classical Fluids, PHYSICAL REVIEW LETTERS, Vol: 109, ISSN: 0031-9007

JOURNAL ARTICLE

Goddard BD, Pavliotis GA, Kalliadasis S, 2012, THE OVERDAMPED LIMIT OF DYNAMIC DENSITY FUNCTIONAL THEORY: RIGOROUS RESULTS, MULTISCALE MODELING & SIMULATION, Vol: 10, Pages: 633-663, ISSN: 1540-3459

JOURNAL ARTICLE

Nolen J, Pavliotis GA, Stuart AM, 2012, Multiscale Modelling and Inverse Problems, Multiscale Modelling and Inverse Problems (wNumerical Analysis of Multiscale Problems

CONFERENCE PAPER

Ottobre M, Pavliotis GA, Pravda-Starov K, 2012, Exponential return to equilibrium for hypoelliptic quadratic systems, JOURNAL OF FUNCTIONAL ANALYSIS, Vol: 262, Pages: 4000-4039, ISSN: 0022-1236

JOURNAL ARTICLE

Pavliotis GA, Pokern Y, Stuart AM, 2012, Parameter estimation for multiscale diffusions: an overview, Statistical methods for stochastic differential equations, Boca Raton, FL, Publisher: CRC Press, Pages: 429-472

BOOK CHAPTER

Pradas M, Pavliotis GA, Kalliadasis S, Papageorgiou DT, Tseluiko Det al., 2012, Additive noise effects in active nonlinear spatially extended systems, EUROPEAN JOURNAL OF APPLIED MATHEMATICS, Vol: 23, Pages: 563-591, ISSN: 0956-7925

JOURNAL ARTICLE

Schmuck M, Pradas M, Pavliotis GA, Kalliadasis Set al., 2012, Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 468, Pages: 3705-3724, ISSN: 1364-5021

JOURNAL ARTICLE

Ottobre M, Pavliotis GA, 2011, Asymptotic analysis for the generalized Langevin equation, NONLINEARITY, Vol: 24, Pages: 1629-1653, ISSN: 0951-7715

JOURNAL ARTICLE

Pradas M, Tseluiko D, Kalliadasis S, Papageorgiou DT, Pavliotis GAet al., 2011, Noise Induced State Transitions, Intermittency, and Universality in the Noisy Kuramoto-Sivashinksy Equation, PHYSICAL REVIEW LETTERS, Vol: 106, ISSN: 0031-9007

JOURNAL ARTICLE

Savva N, Pavliotis GA, Kalliadasis S, 2011, Contact lines over random topographical substrates. Part 1. Statics, JOURNAL OF FLUID MECHANICS, Vol: 672, Pages: 358-383, ISSN: 0022-1120

JOURNAL ARTICLE

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