Renormalized Mori–Zwanzig-reduced models for systems without scale separation
暂无分享,去创建一个
[1] C. Doering,et al. Applied analysis of the Navier-Stokes equations: Index , 1995 .
[2] A. Fisher,et al. The Theory of Critical Phenomena: An Introduction to the Renormalization Group , 1992 .
[3] Panos Stinis,et al. Numerical Computation of Solutions of the Critical Nonlinear Schrödinger Equation after the Singularity , 2010, Multiscale Model. Simul..
[4] Abhilash J. Chandy,et al. The t-Model as a Large Eddy Simulation Model for the Navier-Stokes Equations , 2009, Multiscale Model. Simul..
[5] Charles R. Doering,et al. Applied analysis of the Navier-Stokes equations: Index , 1995 .
[6] R. Zwanzig. Nonlinear generalized Langevin equations , 1973 .
[7] E. Hairer,et al. Solving Ordinary Differential Equations II , 2010 .
[8] Eric Darve,et al. Computing generalized Langevin equations and generalized Fokker–Planck equations , 2009, Proceedings of the National Academy of Sciences.
[9] Alexandre J. Chorin,et al. Problem reduction, renormalization, and memory , 2005 .
[10] C. Sulem,et al. The nonlinear Schrödinger equation : self-focusing and wave collapse , 2004 .
[11] Richard Bellman,et al. Perturbation techniques in mathematics, engineering & physics , 1973 .
[12] H. Mori. Transport, Collective Motion, and Brownian Motion , 1965 .
[13] David Bernstein,et al. Optimal Prediction of Burgers's Equation , 2007, Multiscale Model. Simul..
[14] P. Lax. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves , 1987 .
[15] E. Vanden-Eijnden,et al. Analysis of multiscale methods for stochastic differential equations , 2005 .
[16] Andrew J. Majda,et al. A mathematical framework for stochastic climate models , 2001 .
[17] Thierry Dubois,et al. Dynamic multilevel methods and the numerical simulation of turbulence , 1999 .
[18] E. Hairer,et al. Solving Ordinary Differential Equations I , 1987 .
[19] Alexandre J. Chorin,et al. Random choice solution of hyperbolic systems , 1976 .
[20] Panagiotis Stinis,et al. Higher Order Mori-Zwanzig Models for the Euler Equations , 2006, Multiscale Model. Simul..
[21] C. W. Gear,et al. Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis , 2003 .
[22] A. Stuart,et al. Extracting macroscopic dynamics: model problems and algorithms , 2004 .
[23] Alexandre J. Chorin,et al. Optimal prediction with memory , 2002 .
[24] Panagiotis Stinis,et al. Optimal prediction and the rate of decay for solutions of the Euler equations in two and three dimensions , 2007, Proceedings of the National Academy of Sciences.
[25] N. Goldenfeld. Lectures On Phase Transitions And The Renormalization Group , 1972 .
[26] Panagiotis Stinis,et al. Renormalized reduced models for singular PDEs , 2011, 1106.1677.
[27] A J Chorin,et al. Optimal prediction and the Mori-Zwanzig representation of irreversible processes. , 2000, Proceedings of the National Academy of Sciences of the United States of America.
[28] Howard Georgi,et al. Effective Field Theory , 1993 .
[29] G. Karniadakis,et al. Construction of dissipative particle dynamics models for complex fluids via the Mori-Zwanzig formulation. , 2014, Soft matter.
[30] Bertrand Delamotte,et al. A Hint of renormalization , 2002, hep-th/0212049.