For both chaotic and randomly-forced systems, we show the problem can be naturally formulated within the framework of Koopman operators and the Mori-Zwanzig projection operator formalism. We give a heuristic derivation of a NARMAX (Nonlinear Auto-Regressive Moving Average with eXogenous input) model ...
We present here a collection of modelsfor the Euler equations which are based also on the Mori-Zwanzig formalism. Themodels arise from a Taylor expansion of a different operator, the orthogonaldynamics evolution operator, which appears in the memory integrand. The zero,first and second order ...
Chu, W., Li, X.: The Mori–Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics. Commun. Math. Sci. 17(2), 539–563 (2019) 9. Ciccotti, G., Ryckaert, J.-P.: On the derivation of the generalized Langevin equation for interacting Brownian...
P(t) is the Zwanzig-Mori projection operator; for any phase space function g, it is defined: Pg = g L + g δa L ∗ δa δa −1 L ∗ δa (2.5) For shortness, the time parameters have been omitted here. ∗ denotes an operation which consists of a product, a ...
Also, the comparison between different analytical models is not always straightforward, and an effort toward a unified formalism is highly desirable (Bafileetal., 2006)…The THz Dynamics of Liquids Probed by Inelastic X-Ray ScatteringAlessandro Cunsolo...
The Mori-Zwanzig projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. ...
Closure modeling based on the Mori-Zwanzig formalism has proven effective to improve the stability and accuracy of projection-based model order reduction. However, closure models are often expensive and infeasible for complex nonlinear systems. Towards efficient model reduction of general problems, this ...
Mori-Zwanzig projection formalism: from linear to nonlinear, arXiv:0904.2691 - Xing - 2009 () Citation Context ...ting to a subspace composed by the first m components of x and the corresponding velocity components. Generalization to collective coordinates is straightforward, and is given in ...
Mathematics A modified Zwanzig-Mori formalism UNIVERSITY OF MARYLANDCOLLEGE PARK Charles David Levermore HalbertJ. TRecent advances in science have led to a better understanding ofphysical phenomena across a vast range of time and length scales.This has given the research community access to ...
Molecular dynamicsNanoscale Energy TransportMori-Zwanzig formalismEnergy transport equations are derived directly from a many-particle system as a coarse-grained (CG) description. This effort is motivated by the observation that the conventional heat equation is unable to describe the heat conduction ...