English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

It is generally argued that the solution to a stochastic PDE withmultiplicative noise---such as $\dot{u}=\frac12 u"+u\xi$, where $\xi$ denotesspace-time white noise---routinely produces exceptionally-large peaks that are"macroscopically multifractal." See, for example, Gibbon and Doering (2005),Gibbon and Titi (2005), and Zimmermann et al (2000). A few years ago, we provedthat the spatial peaks of the solution to the mentioned stochastic PDE indeedform a random multifractal in the macroscopic sense of Barlow and Taylor (1989;1992). The main result of the present paper is a proof of a rigorousformulation of the assertion that the spatio-temporal peaks of the solutionform infinitely-many different multifractals on infinitely-many differentscales, which we sometimes refer to as "stretch factors." A simpler, thoughstill complex, such structure is shown to also exist for theconstant-coefficient version of the said stochastic PDE.

A macroscopic multifractal analysis of parabolic stochastic PDEs