{"title":"Computing the quasipotential for highly\ndissipative and chaotic SDEs an application to stochastic Lorenz’63","authors":"M. Cameron, Shuo Yang","doi":"10.2140/camcos.2019.14.207","DOIUrl":null,"url":null,"abstract":"The study of noise-driven transitions occurring rarely on the time-scale of systems modeled by SDEs is of crucial importance for understanding such phenomena as genetic switches in living organisms and magnetization switches of the Earth. For a gradient SDE, the predictions for transition times and paths between its metastable states are done using the potential function. For a nongradient SDE, one needs to decompose its forcing into a gradient of the so-called quasipotential and a rotational component, which cannot be done analytically in general. \nWe propose a methodology for computing the quasipotential for highly dissipative and chaotic systems built on the example of Lorenz'63 with an added stochastic term. It is based on the ordered line integral method, a Dijkstra-like quasipotential solver, and combines 3D computations in whole regions, a dimensional reduction technique, and 2D computations on radial meshes on manifolds or their unions. Our collection of source codes is available on M. Cameron's web page and on GitHub.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2018-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/camcos.2019.14.207","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 5
Abstract
The study of noise-driven transitions occurring rarely on the time-scale of systems modeled by SDEs is of crucial importance for understanding such phenomena as genetic switches in living organisms and magnetization switches of the Earth. For a gradient SDE, the predictions for transition times and paths between its metastable states are done using the potential function. For a nongradient SDE, one needs to decompose its forcing into a gradient of the so-called quasipotential and a rotational component, which cannot be done analytically in general.
We propose a methodology for computing the quasipotential for highly dissipative and chaotic systems built on the example of Lorenz'63 with an added stochastic term. It is based on the ordered line integral method, a Dijkstra-like quasipotential solver, and combines 3D computations in whole regions, a dimensional reduction technique, and 2D computations on radial meshes on manifolds or their unions. Our collection of source codes is available on M. Cameron's web page and on GitHub.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.