Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1302.4132

A simple stochastic parameterization for reduced models of multiscale dynamics

Rafail V. Abramov
View original source ↗Read source document ↗Export metadata ↓

Abstract

Multiscale dynamics are frequently present in real-world processes, such as the atmosphere-ocean and climate science. Because of time scale separation between a small set of slowly evolving variables and much larger set of rapidly changing variables, direct numerical simulations of such systems are difficult to carry out due to many dynamical variables and the need for an extremely small time discretization step to resolve fast dynamics. One of the common remedies for that is to approximate a multiscale dynamical systems by a closed approximate model for slow variables alone, which reduces the total effective dimension of the phase space of dynamics, as well as allows for a longer time discretization step. Recently we developed a new method for constructing a deterministic reduced model of multiscale dynamics where coupling terms were parameterized via the Fluctuation-Dissipation theorem. In this work we further improve this previously developed method for deterministic reduced models of multiscale dynamics by introducing a new method for parameterizing slow-fast interactions through additive stochastic noise in a systematic fashion. For the two-scale Lorenz 96 system with linear coupling, we demonstrate that the new method is able to recover additional features of multiscale dynamics in a stochastically forced reduced model, which the previously developed deterministic method could not reproduce.

Explore related subjects

math.DSnlin.CD

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Rafail V. Abramov. 2013-02-17. A simple stochastic parameterization for reduced models of multiscale dynamics. https://doi.org/10.3390/fluids1010002

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Effective equidistribution of orbits under semisimple groups on congruence quotients

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group.This extends a previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we allow for periodic orbits of semisimple groups with nontrivial centralizer in the ambient group. Our proof uses crucially an effective closing lemma from work of the author with Lindenstrauss, Margulis,Mohammadi, and Shah.

math.DS↗
arXiv2026

Generalized entropy of measure-induced maps

A classical result by E. Glasner and B. Weiss states that the topological entropy of a map $f$ is zero if and only if the topological entropy of its measure-induced map $f_*$ is zero, where $f_*$ is defined as the push-forward of a measure. In this work, we use generalized entropy to distinguish the complexity of these maps and prove that the measure-induced map is much more complex than the original map. Moreover, we introduce the generalized mean dimension, an invariant that is useful for distinguishing dynamical systems with zero mean dimension, including those with the small-boundary property, and we show a relationship between this new invariant and generalized entropy.

math.DS↗
arXiv2026

The endpoint problem for $\varepsilon$-hypercyclicity

For a fixed $0<\varepsilon<1$, F. Bayart asked in 2024 whether there exists an operator $T$ such that, for every $0<δ<1$, $T$ is $δ$-hypercyclic if and only if $δ\in[\varepsilon,1)$. We answer this question affirmatively by constructing a weighted backward shift on $\ell_2(\mathbb N_0,\ell_2(\mathbb N_0))$ with this property.

math.DS↗