82 results found
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
Olhede SC, Sykulski AM, Pavliotis GA, 2009, FREQUENCY DOMAIN ESTIMATION OF INTEGRATED VOLATILITY FOR ITO PROCESSES IN THE PRESENCE OF MARKET-MICROSTRUCTURE NOISE, MULTISCALE MODELING & SIMULATION, Vol: 8, Pages: 393-427, ISSN: 1540-3459
Thiffeault J-L, Pavliotis GA, 2008, Optimizing the source distribution in fluid mixing, PHYSICA D-NONLINEAR PHENOMENA, Vol: 237, Pages: 918-929, ISSN: 0167-2789
Pavliotis GA, Vogiannou A, 2008, Diffusive transport in periodic potentials: Underdamped dynamics, FLUCTUATION AND NOISE LETTERS, Vol: 8, Pages: L155-L173, ISSN: 0219-4775
Hairer M, Pavliotis GA, 2008, From ballistic to diffusive behavior in periodic potentials, Journal of Statistical Physics, Vol: 131, Pages: 175-202, ISSN: 1572-9613
The long-time/large-scale, small-friction asymptotic for the one dimensional Langevin equation with a periodic potential is studied in this paper. It is shown that the Freidlin-Wentzell and central limit theorem (homogenization) limits commute. We prove that, in the combined small friction, long-time/large-scale limit the particle position converges weakly to a Brownian motion with a singular diffusion coefficient which we compute explicitly. We show that the same result is valid for a whole one parameter family of space/time rescalings. The proofs of our main results are based on some novel estimates on the resolvent of a hypoelliptic operator.
Pavliotis GA, Stuart AM, 2007, Multiscale Methods Averaging and Homogenization, NEW YORK, Publisher: SPRINGER, ISBN: 978-0-387-73828-4
Pavliotis GA, Stuart AM, Zygalakis KC, 2007, Homogenization for inertial particles in a random flow, COMMUNICATIONS IN MATHEMATICAL SCIENCES, Vol: 5, Pages: 507-531, ISSN: 1539-6746
Bloemker D, Hairer M, Pavliotis GA, 2007, Multiscale analysis for stochastic partial differential equations with quadratic nonlinearities, NONLINEARITY, Vol: 20, Pages: 1721-1744, ISSN: 0951-7715
Gibbon JD, Pavliotis GA, 2007, Estimates for the two-dimensional Navier-Stokes equations in terms of the Reynolds number, JOURNAL OF MATHEMATICAL PHYSICS, Vol: 48, ISSN: 0022-2488
Pavliotis GA, Stuart AM, 2007, Parameter estimation for multiscale diffusions, JOURNAL OF STATISTICAL PHYSICS, Vol: 127, Pages: 741-781, ISSN: 0022-4715
Pavliotis G, Blomker D, Hairer M, 2007, Multiscale Analysis for SPDEs with Quadratic Nonlinearities, NONLINEARITY, Pages: 1721-1744
Pavliotis G, Blomker D, Hairer M, 2006, Multiscale analysis for SPDEs with quadratic nonlinearities, Publisher: arXiv
In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from bifurcation and the strength of the noise. We show that, due to the presence of two distinct timescales in our system, the noise (which acts only on the fast modes) gets transmitted to the slow modes and, as a result, the amplitude equation contains both additive and multiplicative noise.As an application we study the case of the one dimensional Burgers equation forced by additive noise in the orthogonal subspace to its dominant modes. The theory developed in the present article thus allows to explain theoretically some recent numerical observations from [Rob03].
Pavliotis GA, Stuart AM, Band L, 2006, Monte Carlo studies of effective diffusivities for inertial particles, Berlin, 6th international conference on Monte Carlo and Quasi-Monte Carlo methods in scientific computing, 7 - 10 June 2004, Juan les Pins, FRANCE, Publisher: Springer-Verlag Berlin, Pages: 431-441
Pavliotis GA, 2005, A multiscale approach to Brownian motors, PHYSICS LETTERS A, Vol: 344, Pages: 331-345, ISSN: 0375-9601
Blomker D, Hairer M, Pavliotis GA, 2005, Modulation equations: Stochastic bifurcation in large domains, COMMUNICATIONS IN MATHEMATICAL PHYSICS, Vol: 258, Pages: 479-512, ISSN: 0010-3616
We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations.
Pavliotis GA, Stuart AM, 2005, Periodic homogenization for inertial particles, PHYSICA D-NONLINEAR PHENOMENA, Vol: 204, Pages: 161-187, ISSN: 0167-2789
Pavliotis GA, Stuart AM, 2005, Analysis of white noise limits for stochastic systems with two fast relaxation times, MULTISCALE MODELING & SIMULATION, Vol: 4, Pages: 1-35, ISSN: 1540-3459
M Hairer, GA Pavliotis, 2004, Periodic homogenization for hypoelliptic diffusions, J. Stat. Phys 117 (1-2): 261-279 OCT 2004
KUPFERMAN R, PAVLIOTIS GA, STUART AM, 2004, Ito versus Stratonovich white-noise limits for systems with inertia and colored multiplicative noise, PHYS REV E, Vol: 70
Pavliotis GA, Stuart AM, 2003, White noise limits for inertial particles in a random field, MULTISCALE MODELING & SIMULATION, Vol: 1, Pages: 527-553
Pavliotis GA, Holmes MH, 2002, A perturbation-based numerical method for solving a three-dimensional axisymmetric indentation problem, JOURNAL OF ENGINEERING MATHEMATICS, Vol: 43, Pages: 1-17
Bozis G, Pavliotis G, 1999, Riemannian curvature and stability of monoparametric families of trajectories, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, Vol: 15, Pages: 141-153, ISSN: 0266-5611
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