PMID: 11308727Apr 20, 2001Paper

Renormalization group and perfect operators for stochastic differential equations

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Q HouA McKane

Abstract

We develop renormalization group (RG) methods for solving partial and stochastic differential equations on coarse meshes. RG transformations are used to calculate the precise effect of small-scale dynamics on the dynamics at the mesh size. The fixed point of these transformations yields a perfect operator: an exact representation of physical observables on the mesh scale with minimal lattice artifacts. We apply the formalism to simple nonlinear models of critical dynamics, and show how the method leads to an improvement in the computational performance of Monte Carlo methods.

References

Apr 29, 1998·Proceedings of the National Academy of Sciences of the United States of America·A J ChorinR Kupferman
Jan 15, 1990·Physical Review. a·A J McKaneA J Bray
Apr 15, 1990·Physical Review. a·B GrossmannM Grant
Nov 15, 1990·Physical Review. a·M Mondello, N Goldenfeld
Oct 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A Shinozaki, Y Oono
Feb 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M ZapotockyN Goldenfeld
Mar 1, 1993·Physical Review. B, Condensed Matter·M D LacasseM Grant
Mar 29, 2000·Proceedings of the National Academy of Sciences of the United States of America·A J ChorinR Kupferman

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Citations

Mar 5, 2004·Physical Review Letters·Navot Israeli, Nigel Goldenfeld
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Navot Israeli, Nigel Goldenfeld

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