84 results found
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.
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
Using thermodynamic and variational principles we examine a basic phase field model for a mixture of two incompressible fluids in strongly perforated domains. With the help of the multiple scale method with drift and our recently introduced splitting strategy for Ginzburg-Landau/Cahn-Hilliard-type equations (Schmuck et al 2012 Proc. R. Soc. A 468 3705-24), we rigorously derive an effective macroscopic phase field formulation under the assumption of periodic flow and a sufficiently large Péclet number. As for classical convection-diffusion problems, we obtain systematically diffusion-dispersion relations (including Taylor-Aris-dispersion). Our results also provide a convenient computational framework to macroscopically track interfaces in porous media. In view of the well-known versatility of phase field models, our study proposes a promising model for many engineering and scientific applications such as multiphase flows in porous media, microfluidics, and fuel cells. © 2013 IOP Publishing Ltd & London Mathematical Society.
Papageorgiou DT, Pavliotis GA, Papaefthymiou ES, 2013, Nonlinear interfacial dynamics in stratified multilayer channel flows, Journal of Fluid Mechanics, Vol: 734, Pages: 114-143, ISSN: 0022-1120
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
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
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
Krumscheid S, Pavliotis GA, Kalliadasis S, 2013, SEMIPARAMETRIC DRIFT AND DIFFUSION ESTIMATION FOR MULTISCALE DIFFUSIONS, Multiscale Modeling & Simulation, Vol: 11, Pages: 442-473, ISSN: 1540-3467
Goddard BD, Nold A, Savva N, et al., 2013, Inertia and hydrodynamic interactions in dynamical density functional theory, Springer Proceedings in Complexity, Pages: 999-1004
© Springer International Publishing Switzerland 2013. We study the dynamics of a colloidal fluid in the full position-momentum phase space, including hydrodynamic interactions, which strongly influence the non-equilibrium properties of the system. For large systems, the number of degrees of freedom prohibits direct simulation and a reduced model is necessary. Under standard assumptions, we derive a dynamical density functional theory (DDFT), which is a generalisation of many existing DDFTs, and shows good agreement with stochastic simulations.
Schmuck M, Pavliotis GA, Kalliadasis S, 2013, Effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media, European Conference of Complex Systems 2012 (ECCS'12), Publisher: Springer Proceedings in Complexity 2013, Pages: 1005-1010
Schmuck M, Pradas M, Pavliotis GA, et 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
Pradas M, Pavliotis GA, Kalliadasis S, et al., 2012, Additive noise effects in active nonlinear spatially extended systems, EUROPEAN JOURNAL OF APPLIED MATHEMATICS, Vol: 23, Pages: 563-591, ISSN: 0956-7925
Goddard BD, Nold A, Savva N, et al., 2012, General dynamical density functional theory for classical fluids, PHYSICAL REVIEW LETTERS, Vol: 109, ISSN: 0031-9007
We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.
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
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
Consider the overdamped limit for a system of interacting particles in thepresence of hydrodynamic interactions. For two-body hydrodynamic interactionsand one- and two-body potentials, a Smoluchowski-type evolution equation isrigorously derived for the one-particle distribution function. This newequation includes a novel definition of the diffusion tensor. A comparison withexisting formulations of dynamic density functional theory is also made.
Abdulle A, Pavliotis GA, 2012, Numerical Methods for Stochastic Partial Differential Equations with Multiple Scales, Journal of Computational Physics, Vol: 231, Pages: 2482-2497
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
Pavliotis GA, Pokern Y, Stuart AM, 2012, Parameter estimation for multiscale diffusions: an overview, Vol: 124, Pages: 429-472
Nolen J, Pavliotis GA, Stuart AM, 2012, Multiscale Modelling and Inverse Problems, Multiscale Modelling and Inverse Problems (wNumerical Analysis of Multiscale Problems
Ottobre M, Pavliotis GA, 2011, Asymptotic analysis for the generalized Langevin equation, NONLINEARITY, Vol: 24, Pages: 1629-1653, ISSN: 0951-7715
Savva N, Pavliotis GA, Kalliadasis S, 2011, Contact lines over random topographical substrates. Part 2. Dynamics, JOURNAL OF FLUID MECHANICS, Vol: 672, Pages: 384-410, ISSN: 0022-1120
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
Pradas M, Tseluiko D, Kalliadasis S, et al., 2011, Noise Induced State Transitions, Intermittency, and Universality in the Noisy Kuramoto-Sivashinksy Equation, PHYSICAL REVIEW LETTERS, Vol: 106, ISSN: 0031-9007
Pavliotis GA, 2010, Asymptotic analysis of the Green-Kubo formula, IMA JOURNAL OF APPLIED MATHEMATICS, Vol: 75, Pages: 951-967, ISSN: 0272-4960
Savva N, Kalliadasis S, Pavliotis GA, 2010, Two-Dimensional Droplet Spreading over Random Topographical Substrates, PHYSICAL REVIEW LETTERS, Vol: 104, ISSN: 0031-9007
Blömker D, Hairer M, Pavliotis GA, 2010, Some remarks on stabilization by additive noise, Stochastic partial differential equations and applications, Publisher: Dept. Math., Seconda Univ. Napoli, Caserta, Pages: 37-50
Cuthbertson C, Pavliotis G, Rafailidis A, et al., 2010, Asymptotic analysis for foreign exchange derivatives with stochastic volatility, International Journal of Theoretical and Applied Finance, Vol: 13, Pages: 1131-1147, ISSN: 0219-0249
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