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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this article we develop geometric versions of the classical Langevinequation on regular submanifolds in euclidean space in an easy, natural way andcombine them with a bunch of applications. The equations are formulated asStratonovich stochastic differential equations on manifolds. The first versionof the geometric Langevin equation has already been detected before byLeli\`evre, Rousset and Stoltz with a different derivation. We propose anadditional extension of the models, the geometric Langevin equations withvelocity of constant absolute value. The latters are seemingly new and providea galaxy of new, beautiful and powerful mathematical models. Up to the authorsbest knowledge there are not many mathematical papers available dealing withgeometric Langevin processes. We connect the first version of the geometricLangevin equation via proving that its generator coincides with the generalizedLangevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. All ourstudies are strongly motivated by industrial applications in modeling the fiberlay-down dynamics in the production process of nonwovens. We light up thegeometry occuring in these models and show up the connection with the sphericalvelocity version of the geometric Langevin process. Moreover, as a main point,we construct new smooth industrial relevant three-dimensional fiber lay-downmodels involving the spherical Langevin process. Finally, relations to a classof self-propelled interacting particle systems with roosting force arepresented and further applications of the geometric Langevin equations aregiven.

Geometric Langevin equations on submanifolds and applications to the stochastic melt-spinning process of nonwovens and biology