Imperial College London

Professor Grigorios A. Pavliotis

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

 

736aHuxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

78 results found

DurĂ¡n-Olivencia MA, Gvalani RS, Kalliadasis S, Pavliotis GAet al., 2019, Instability, rupture and fluctuations in thin liquid films: Theory and computations, Journal of Statistical Physics, Vol: 174, Pages: 579-604, ISSN: 0022-4715

Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction, as opposed to the perfectly uncorrelated limit studied by Grün et al. (J Stat Phys 122(6):1261–1291, 2006). We also present a numerical scheme based on a spectral collocation method, which is then utilised to simulate the stochastic thin-film equation. This scheme seems to be very convenient for numerical studies of the stochastic thin-film equation, since it makes it easier to select the frequency modes of the noise (following the spirit of the long-wave approximation). With our numerical scheme we explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we study the effect of the noise intensity on the rupture time, using a large number of sample paths as compared to previous studies.

JOURNAL ARTICLE

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.

JOURNAL ARTICLE

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.

WORKING PAPER

Tomlin R, Gomes SN, Pavliotis G, Papageorgiou Det al., Optimal control of thin liquid films and transverse mode effects, SIAM Journal on Applied Dynamical Systems, ISSN: 1536-0040

We consider the control of a three-dimensional thin liquid film on a flat substrate, inclined at anon-zero angle to the horizontal. Controls are applied via same-fluid blowing and suction throughthe substrate surface. We consider both overlying and hanging films, where the liquid lies above orbelow the substrate, respectively. We study the weakly nonlinear evolution of the system, which isgoverned by a forced Kuramoto–Sivashinsky equation in two space dimensions. The uncontrolledproblem exhibits three ranges of dynamics depending on the incline of the substrate: stable flat filmsolution, bounded chaotic dynamics, or unbounded exponential growth of unstable transverse modes.We proceed with the assumption that we may actuate at every point on the substrate. The mainfocus is the optimal control problem, which we first study in the special case that the forcing mayonly vary in the spanwise direction. The structure of the Kuramoto–Sivashinsky equation allows theexplicit construction of optimal controls in this case using the classical theory of linear quadraticregulators. Such controls are employed to prevent the exponential growth of transverse waves inthe case of a hanging film, revealing complex dynamics for the streamwise and mixed modes. Wethen consider the optimal control problem in full generality, and prove the existence of an optimalcontrol. For numerical simulations, we employ an iterative gradient descent algorithm. In the finalsection, we consider the effects of transverse mode forcing on the chaotic dynamics present in thestreamwise and mixed modes for the case of a vertical film flow. Coupling through nonlinearityallows us to reduce the average energy in solutions without directly forcing the linearly unstable dominant modes.

JOURNAL ARTICLE

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

JOURNAL ARTICLE

Ellam L, Girolami M, Pavliotis GA, Wilson Aet al., 2018, Stochastic modelling of urban structure, PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 474, ISSN: 1364-5021

JOURNAL ARTICLE

Craster RV, Guenneau SRL, Hutridurga HR, Pavliotis GAet al., 2018, CLOAKING VIA MAPPING FOR THE HEAT EQUATION, MULTISCALE MODELING & SIMULATION, Vol: 16, Pages: 1146-1174, ISSN: 1540-3459

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

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

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

JOURNAL ARTICLE

Craster R, Guenneau S, Hutridurga H, Pavliotis Get 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

CONFERENCE PAPER

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

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, Kalliadasis S, Pavliotis GA, Pradas Met al., 2016, Noise-induced transitions in rugged energy landscapes, PHYSICAL REVIEW E, Vol: 94, ISSN: 2470-0045

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

Krumscheid S, Pradas M, Pavliotis GA, Kalliadasis Set al., 2015, Data-driven coarse graining in action: Modeling and prediction of complex systems, PHYSICAL REVIEW E, Vol: 92, ISSN: 2470-0045

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

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

Gomes SN, Pradas M, Kalliadasis S, Papageorgiou DT, Pavliotis GAet al., 2015, Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems, PHYSICAL REVIEW E, Vol: 92, ISSN: 2470-0045

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

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

Hartmann C, Latorre JC, Zhang W, Pavliotis GAet 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.

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

Rubin KJ, Pruessner G, Pavliotis GA, 2014, Mapping multiplicative to additive noise, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 47, ISSN: 1751-8113

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

Schmuck M, Pradas M, Pavliotis GA, Kalliadasis Set 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

JOURNAL ARTICLE

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