81 results found
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
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
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.
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
Schmuck M, Pavliotis GA, Kalliadasis S, 2013, Effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media, Pages: 1005-1010, ISSN: 2213-8684
© Springer International Publishing Switzerland 2013. Using thermodynamic and variational principles we study a basic phase field model for the mixture of two incompressible fluids in strongly perforated domains. We rigorously derive an effective macroscopic phase field equation under the assumption of periodic flow and a sufficiently large Péclet number 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., Proc. R. Soc. A, 468:3705–3724, 2012). As for the classical convection-diffusion problem, we obtain systematically diffusion-dispersion relations (including Taylor-Aris-dispersion). 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.
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
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
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
Nolen J, Pavliotis GA, Stuart AM, 2012, Multiscale modelling and inverse problems, Pages: 1-34, ISSN: 1439-7358
© Springer-Verlag Berlin Heidelberg 2012. The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and forcing can be estimated on the basis of observed data. The resulting inverse problems are usually ill-posed and some form of regularization is required. These notes discuss parameter estimation in situations where the unknown parameters vary across multiple scales. We illustrate the main ideas using a simple model for groundwater flow. We will highlight various approaches to regularization for inverse problems, including Tikhonov and Bayesian methods.We illustrate three ideas that arise when considering inverse problems in the multiscale context. The first idea is that the choice of space or set in which to seek the solution to the inverse problem is intimately related to whether a homogenized or full multiscale solution is required. This is a choice of regularization. The second idea is that, if a homogenized solution to the inverse problem is what is desired, then this can be recovered from carefully designed observations of the full multiscale system. The third idea is that the theory of homogenization can be used to improve the estimation of homogenized coefficients from multiscale data.
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
Pavliotis GA, Pokern Y, Stuart AM, 2012, Parameter estimation for multiscale diffusions: An overview, Pages: 429-472
© 2012 by Taylor & Francis Group, LLC. There are many applications where it is desirable to fit reduced stochastic descriptions (e.g. SDEs) to data. These include molecular dynamics (Schlick (2000), Frenkel and Smit (2002)), atmosphere/ocean science (Majda and Kramer (1999)), cellular biology (Alberts et al. (2002)) and econometrics (Dacorogna, Gençay, Müller, Olsen, and Pictet (2001)). The data arising in these problems often has a multiscale character and may not be compatible with the desired diffusion at small scales (see Givon, Kupferman, and Stuart (2004), Majda, Timofeyev, and Vanden-Eijnden (1999), Kepler and Elston (2001), Zhang, Mykland, and Aït-Sahalia (2005) and Olhede, Sykulski, and Pavliotis (2009)). The question then arises as to how to optimally employ such data to find a useful diffusion approximation.
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
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 1. Statics, JOURNAL OF FLUID MECHANICS, Vol: 672, Pages: 358-383, ISSN: 0022-1120
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
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
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
We consider models for the valuation of derivative securities that depend on foreign exchange rates. We derive partial differential equations for option prices in an arbitrage-free market with stochastic volatility. By use of standard techniques, and under the assumption of fast mean reversion for the volatility, these equations can be solved asymptotically. The analysis goes further to consider specific examples for a number of options, and to a considerable degree of complexity. © 2010 World Scientific Publishing Company.
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
Cotter CJ, Pavliotis GA, 2009, ESTIMATING EDDY DIFFUSIVITIES FROM NOISY LAGRANGIAN OBSERVATIONS, COMMUNICATIONS IN MATHEMATICAL SCIENCES, Vol: 7, Pages: 805-838, ISSN: 1539-6746
Papavasiliou A, Pavliotis GA, Stuart AM, 2009, Maximum likelihood drift estimation for multiscale diffusions, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, Vol: 119, Pages: 3173-3210, ISSN: 0304-4149
Pavliotis GA, Stuart AM, Zygalakis KC, 2009, Calculating effective diffusivities in the limit of vanishing molecular diffusion, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 228, Pages: 1030-1055, ISSN: 0021-9991
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