A PHP Error was encountered

Severity: Warning

Message: file_get_contents(https://...@pubfacts.com&api_key=b8daa3ad693db53b1410957c26c9a51b4908&a=1): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests

Filename: helpers/my_audit_helper.php

Line Number: 176

Backtrace:

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 176
Function: file_get_contents

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 250
Function: simplexml_load_file_from_url

File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3122
Function: getPubMedXML

File: /var/www/html/application/controllers/Detail.php
Line: 575
Function: pubMedSearch_Global

File: /var/www/html/application/controllers/Detail.php
Line: 489
Function: pubMedGetRelatedKeyword

File: /var/www/html/index.php
Line: 316
Function: require_once

Enhancing the description of multi-time-scale geophysical phenomena: Incorporating finite time Scale separation and feedback, illustrated with the case of a 1D variable of interest. | LitMetric

Stochastic approaches play a vital role in weather, climate, and, more in general, geophysics systems, addressing processes and scales beyond the resolution of deterministic models. Similar to equilibrium/non-equilibrium thermodynamics, intricate fast and local dynamics may not always be the primary focus. Practical applications often prioritize observables capturing phenomena at dominant temporal and spatial scales. Developing models for these "large-scale" observables, resulting from averaging fast and local contributions, can be simplified into Low Order Models (LOMs) with reduced degrees of freedom described by ordinary differential equations. Unresolved degrees of freedom are introduced as stochastic components, exhibiting either Markovian or non-Markovian characteristics. The challenge lies in deriving dependable stochastic differential equations representing the statistics of real large-scale, slow features in the climate/ocean system. While paralleling material physics, it is crucial to recognize that direct transfer of tools and outcomes is hindered by the non-Hamiltonian nature of climate/geophysical LOMs and the impracticality of a Markovian treatment of noise due to wide-ranging time scales. A critical examination of the conventional statistical mechanics approach, customized for such LOMs, becomes essential. To this end, we propose utilizing an approach based on the operator cumulant method, which has been recently revisited and generalized, along with the linear response method in a non-Hamiltonian setting. Formal results are then derived, and applications to some typical classes of examples are presented to clarify this approach.

Download full-text PDF

Source
http://dx.doi.org/10.1063/5.0192089DOI Listing

Publication Analysis

Top Keywords

fast local
8
degrees freedom
8
differential equations
8
enhancing description
4
description multi-time-scale
4
multi-time-scale geophysical
4
geophysical phenomena
4
phenomena incorporating
4
incorporating finite
4
finite time
4

Similar Publications

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!