A simple framework to justify linear response theory (2009)
Hairer, Martin, Majda, Andrew J
The use of linear response theory for forced dissipative stochastic dynamical systems through the fluctuation dissipation theorem is an attractive way to study climate change systematically among...
Andrew J. Majda, Xiaoming Wang
New linear response formulas for unperturbed chaotic (stochastic) complex dynamical systems with time periodic coefficients are developed here. Such time periodic systems arise naturally in climate...
Frierson, Dargan M. W., Majda, Andrew J., Pauluis, Olivier M.
A simplified set of equations is derived systematically below for the interaction of large scale flow fields and precipitation in the tropical atmosphere. These equations, the Tropical Climate Model,...
Sandia National Laboratories Session Organizers and Invited Speakers (2004)
Broomsfield Colorado, Donald Estep, Gary Johnson, Donald Estep, Todd Arbogast, Pavel B. Bochev, ...
The report of the Second DOE Workshop on Multiscale Mathematics is a collaborative effort by the report editors, session organizers, and invited speakers. The report also includes technical
Abramov, Rafail V., Majda, Andrew J.
Discrete numerical approximations with additional conserved quantities are developed here both for barotropic geophysical flows generalizing the 2D incompressible fluid equations and suitable...
Rafail V. Abramov, Andrew J. Majda
Discrete numerical approximations with additional conserved quantities are developed here both for barotropic geophysical flows generalizing the 2D incompressible fluid equations and suitable...
Mathematical Analysis of Strong Fluid Mechanical Effects in Reacting and Nonreacting Gases. (1998)
This report covers the period October 1, 1985 through September 30, 1988, the three year period of this grant. The research performed under this grant includes mathematical analysis of strong fluid...
The following topics have been studied during this three year period: Transition to instability for unstable one-dimensional detonations. Development of the first asymptotic model to incorporate the...
Mathematical Analysis of Strong Fluid Mechanical Effects in Reactive & Nonreactive Flows. (1998)
The research performed under this grant includes mathematical analysis of strong fluid mechanical effects at high Mach number in reactive flow. (AN)
The research program being funded here emphasizes problems in turbulence and turbulent diffusion which are inherently statistical and involve many spatio-temporal scales. One goal of the research is...
Remarkable statistical behavior for truncated Burgers–Hopf dynamics
Majda, Andrew J., Timofeyev, Ilya
A simplified one-dimensional model system is introduced and studied here that exhibits intrinsic chaos with many degrees of freedom as well as increased predictability and slower decay of...
Spectral bifurcations in dispersive wave turbulence
Cai, David, Majda, Andrew J., McLaughlin, David W., Tabak, Esteban G.
Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct...
Models for stochastic climate prediction
Majda, Andrew J., Timofeyev, Ilya, Vanden Eijnden, Eric
There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate...
An equilibrium statistical model for the spreading phase of open-ocean convection
DiBattista, Mark T., Majda, Andrew J.
A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading...
A numerical strategy for efficient modeling of the equatorial wave guide
Majda, Andrew J., Khouider, Boualem
Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms...
Stochastic and mesoscopic models for tropical convection
Majda, Andrew J., Khouider, Boualem
A new way to parametrize certain aspects of tropical convection through stochastic and mesoscopic models is developed here. The technical idea is to adapt tools from statistical physics and materials...
Quantifying predictability in a model with statistical features of the atmosphere
Kleeman, Richard, Majda, Andrew J., Timofeyev, Ilya
The Galerkin truncated inviscid Burgers equation has recently been shown by the authors to be a simple model with many degrees of freedom, with many statistical properties similar to those occurring...
Coarse-grained stochastic models for tropical convection and climate
Khouider, Boualem, Majda, Andrew J., Katsoulakis, Markos A.
Prototype coarse-grained stochastic parametrizations for the interaction with unresolved features of tropical convection are developed here. These coarse-grained stochastic parametrizations involve...
Coarse-grained stochastic processes for microscopic lattice systems
Katsoulakis, Markos A., Majda, Andrew J., Vlachos, Dionisios G.
Diverse scientific disciplines ranging from materials science to catalysis to biomolecular dynamics to climate modeling involve nonlinear interactions across a large range of physically significant...
Criteria for regular spacing of reacting Mach stems
Nonlinear geometric optics is developed to construct translating self-similar high-frequency nonlinear wave patterns as perturbed solutions behind reacting shock waves. The geometric conditions...
A multiscale model for tropical intraseasonal oscillations
Majda, Andrew J., Biello, Joseph A.
The tropical intraseasonal 40- to 50-day oscillation (TIO) is the dominant component of variability in the tropical atmosphere with remarkable planetary-scale circulation generated as envelopes of...
Statistically relevant conserved quantities for truncated quasigeostrophic flow
Abramov, Rafail V., Majda, Andrew J.
Systematic applications of ideas from equilibrium statistical mechanics lead to promising strategies for assessing the unresolved scales of motion in many problems in science and engineering. A...
Stable time filtering of strongly unstable spatially extended systems
Grote, Marcus J., Majda, Andrew J.
Many contemporary problems in science involve making predictions based on partial observation of extremely complicated spatially extended systems with many degrees of freedom and with physical...
Distinct metastable atmospheric regimes despite nearly Gaussian statistics: A paradigm model
Majda, Andrew J., Franzke, Christian L., Fischer, Alexander, Crommelin, Daniel T.
A controversial topic in the recent climate modeling literature is the fashion in which metastable low-frequency regimes in the atmosphere occur despite nearly Gaussian statistics for these planetary...
Remarkable statistical behavior for truncated Burgers–Hopf dynamics
Majda, Andrew J., Timofeyev, Ilya
A simplified one-dimensional model system is introduced and studied here that exhibits intrinsic chaos with many degrees of freedom as well as increased predictability and slower decay of...
Spectral bifurcations in dispersive wave turbulence
Cai, David, Majda, Andrew J., McLaughlin, David W., Tabak, Esteban G.
Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct...
Models for stochastic climate prediction
Majda, Andrew J., Timofeyev, Ilya, Vanden Eijnden, Eric
There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate...
An equilibrium statistical model for the spreading phase of open-ocean convection
DiBattista, Mark T., Majda, Andrew J.
A “most probable state” equilibrium statistical theory for random distributions of hetons in a closed basin is developed here in the context of two-layer quasigeostrophic models for the spreading...
A numerical strategy for efficient modeling of the equatorial wave guide
Majda, Andrew J., Khouider, Boualem
Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms...
Stochastic and mesoscopic models for tropical convection
Majda, Andrew J., Khouider, Boualem
A new way to parametrize certain aspects of tropical convection through stochastic and mesoscopic models is developed here. The technical idea is to adapt tools from statistical physics and materials...
Quantifying predictability in a model with statistical features of the atmosphere
Kleeman, Richard, Majda, Andrew J., Timofeyev, Ilya
The Galerkin truncated inviscid Burgers equation has recently been shown by the authors to be a simple model with many degrees of freedom, with many statistical properties similar to those occurring...
Coarse-grained stochastic models for tropical convection and climate
Khouider, Boualem, Majda, Andrew J., Katsoulakis, Markos A.
Prototype coarse-grained stochastic parametrizations for the interaction with unresolved features of tropical convection are developed here. These coarse-grained stochastic parametrizations involve...
Coarse-grained stochastic processes for microscopic lattice systems
Katsoulakis, Markos A., Majda, Andrew J., Vlachos, Dionisios G.
Diverse scientific disciplines ranging from materials science to catalysis to biomolecular dynamics to climate modeling involve nonlinear interactions across a large range of physically significant...
Criteria for regular spacing of reacting Mach stems
Nonlinear geometric optics is developed to construct translating self-similar high-frequency nonlinear wave patterns as perturbed solutions behind reacting shock waves. The geometric conditions...
A multiscale model for tropical intraseasonal oscillations
Majda, Andrew J., Biello, Joseph A.
The tropical intraseasonal 40- to 50-day oscillation (TIO) is the dominant component of variability in the tropical atmosphere with remarkable planetary-scale circulation generated as envelopes of...
Statistically relevant conserved quantities for truncated quasigeostrophic flow
Abramov, Rafail V., Majda, Andrew J.
Systematic applications of ideas from equilibrium statistical mechanics lead to promising strategies for assessing the unresolved scales of motion in many problems in science and engineering. A...
Stable time filtering of strongly unstable spatially extended systems
Grote, Marcus J., Majda, Andrew J.
Many contemporary problems in science involve making predictions based on partial observation of extremely complicated spatially extended systems with many degrees of freedom and with physical...
Distinct metastable atmospheric regimes despite nearly Gaussian statistics: A paradigm model
Majda, Andrew J., Franzke, Christian L., Fischer, Alexander, Crommelin, Daniel T.
A controversial topic in the recent climate modeling literature is the fashion in which metastable low-frequency regimes in the atmosphere occur despite nearly Gaussian statistics for these planetary...
Majda, Andrew J., Grote, Marcus J.
Many contemporary problems in science involve making predictions based on partial observation of extremely complicated spatially extended systems with many degrees of freedom and physical...
Information flow between subspaces of complex dynamical systems
Majda, Andrew J., Harlim, John
The quantification of information flow between subspaces in ensemble predictions for complex dynamical systems is an important practical topic, for example, in weather prediction and climate change...
Majda, Andrew J., Stechmann, Samuel N., Khouider, Boualem
The Madden–Julian Oscillation (MJO) is the dominant component of tropical intraseasonal variability, and a theory explaining its structure and successful numerical simulation remains a major...
Stochastic models for convective momentum transport
Majda, Andrew J., Stechmann, Samuel N.
The improved parameterization of unresolved features of tropical convection is a central challenge in current computer models for long-range ensemble forecasting of weather and short-term climate...
Normal forms for reduced stochastic climate models
Majda, Andrew J., Franzke, Christian, Crommelin, Daan
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high-dimensional climate models is an important topic for atmospheric low-frequency...
Mathematical test models for superparametrization in anisotropic turbulence
Majda, Andrew J., Grote, Marcus J.
The complexity of anisotropic turbulent processes over a wide range of spatiotemporal scales in engineering turbulence and climate atmosphere ocean science requires novel computational strategies...
The skeleton of tropical intraseasonal oscillations
Majda, Andrew J., Stechmann, Samuel N.
The Madden–Julian oscillation (MJO) is the dominant mode of variability in the tropical atmosphere on intraseasonal timescales and planetary spatial scales. Despite the primary importance of the...