White noise limits for inertial particles in a random field

Multiscale Modeling and Simulation

Volumn 1, Issue 4, 2003, Pages 527-553

  Pavliotis, G A ^a   Stuart, A M ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Inertial particles; Ornstein Uhlenbeck process; Random velocity field; White noise

Indexed keywords

DIFFERENTIAL EQUATIONS; GAUSSIAN DISTRIBUTION; PARTICLES (PARTICULATE MATTER); STOCHASTIC SYSTEMS; VELOCITY;

FLUID VELOCITY FIELD; GAUSSIAN RANDOM FIELDS; INERTIAL PARTICLES; INFINITE DIMENSIONAL; INFINITE DIMENSIONS; ORNSTEIN-UHLENBECK PROCESS; RANDOM VELOCITY FIELDS; STOCHASTIC DIFFERENTIAL EQUATIONS;

WHITE NOISE;

EID: 85009513706     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/S1540345903421076     Document Type: Article

References (28)

1. P. O. A. Amsden and T. Butler, KIVA II: A Computer Program for Chemically Reactive Flows with Sprays, Los Alamos National Laboratory, Los Alamos, NM, 1989.
2. R. J. Adler, An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, IMS Lecture Notes Monogr. Ser. 12, Institute of Mathematical Statistics, Hayward, CA, 1990.
3. R. Dowell, Differentiable Approximation to Brownian Motion on Manifolds, Ph.D. Thesis, University of Warwick, Coventry, UK, 1980.
4. L. Evans, Partial Differential Equations, AMS, Providence, RI, 1998.
5. J. García-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems, Inst. Nonlinear Sci., Springer-Verlag, New York, 1999.
6. Y. Kabanov and S. Pergamenshchikov, Two-Scale Stochastic Systems: Asymptotic Analysis and Control, Appl. Math. 49, Springer-Verlag, Berlin, 2003.
7. I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed., Grad. Texts in Math. 113, Springer-Verlag, New York, 1991.
8. H. Kesten and G. Papanicolaou, A limit theorem for turbulent diffusion, Comm. Math. Phys., 65 (1979), pp. 97-128.
9. H. Kesten and G. C. Papanicolaou, A limit theorem for stochastic acceleration, Comm. Math. Phys., 78 (1980/81), pp. 19-63.
10. R. H. Kraichnan, Diffusion by a random velocity field, Phys. Fluids, 13 (1970), pp. 22-31.
11. P. Kramer, Two different rapid decorrelation in time limits for turbulent diffusion, J. Statist. Phys., 110 (2003), pp. 83-136.
12. P. R. Kramer and A. J. Majda, Stochastic mode reduction for particle-based simulation methods for complex microfluid systems, SIAM J. Appl. Math., to appear.
13. P. R. Kramer and A. J. Majda, Stochastic mode reduction for the immersed boundary method, SIAM J. Appl. Math., to appear.
14. T. Kurtz, A limit theorem for perturbed operator semigroups with applications to random evolutions, J. Funct. Anal., 12 (1973), pp. 55-67.
15. P. Lax, Functional Analysis, Wiley, New York, 2002.
16. A. Majda and P. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling and physical phenomena, Phys. Rep., 314 (1999), pp. 237-574.
17. A. Majda, I. Timofeyev, and E. V. Eijnden, A mathematical framework for stochastic climate models, Comm. Pure Appl. Math., 54 (2001), pp. 891-974.
18. X. Mao, Stochastic Differential Equations and Their Applications, Horwood Ser. Math. Appl., Horwood Publishing Limited, Chichester, 1997.
19. J. Mattingly and A. M. Stuart, Geometric ergodicity of some hypo-elliptic diffusions for particle motions, Markov Process. Related Fields, 8 (2002), pp. 199-214.
20. B. Oksendal, Stochastic Differential Equations, Springer-Verlag, Berlin, Heidelberg, New York, 1998.
21. H. G. Othmer, B. Lilly, and J. Dallon, Pattern formation in a cellular slime mold, in Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems (Minneapolis, MN, 1997), IMA Vol. Math. Appl. 119, Springer, New York, 2000, pp. 359-383.
22. G. C. Papanicolaou, Some probabilistic problems and methods in singular perturbations, Rocky Mountain J. Math., 6 (1976), pp. 653-674.
23. G. A. Pavliotis and A. M. Stuart, Itô versus Stratonovich White Noise Limits for Systems with Inertia and Colored Multiplicative Noise, Warwick Preprint Series 12/2003, 2003.
24. G. D. Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl. 44, Cambridge University Press, Cambridge, UK, 1992.
25. C. Qualls and H. Watanabe, Asymptotic properties of Gaussian random fields, Trans. Amer. Math. Soc., 177 (1973), pp. 155-171.
26. H. Sigurgeirsson and A. M. Stuart, Inertial particles in a random field, Stoch. Dyn., 2 (2002), pp. 295-310.
27. H. Sigurgeirsson and A. M. Stuart, A model for preferential concentration, Phys. Fluids, 14 (2002), pp. 4352-4361.
28. J. G. Verwer and B. P. Sommeijer, A numerical study of mixed parabolic-gradient systems, J. Comput. Appl. Math., 132 (2001), pp. 191-210.