GEOMETRIC LANGEVIN EQUATIONS ON SUBMANIFOLDS AND APPLICATIONS TO THE STOCHASTIC MELT-SPINNING PROCESS OF NONWOVENS AND BIOLOGY

DOI10.1142/S0219493713500019zbMath1277.82042arXiv1204.5695MaRDI QIDQ2862995

Patrik Stilgenbauer, Martin Grothaus

Publication date: 20 November 2013

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.5695

zbMATH Keywords

curvilinear Ornstein-Uhlenbeck processfiber lay-downgeometric Langevin processself-propelled interacting particle systemsStratonovich SDEs on manifolds

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (9)

Spectral asymptotics for kinetic Brownian motion on surfaces of constant curvature ⋮ Parametrix for a semiclassical subelliptic operator ⋮ Hypocoercive estimates on foliations and velocity spherical Brownian motion ⋮ Hypocoercivity of Langevin-type dynamics on abstract smooth manifolds ⋮ Stochastic stability of Pollicott-Ruelle resonances ⋮ Hypocoercivity for geometric Langevin equations motivated by fibre lay‐down models arising in industrial application ⋮ A hypocoercivity related ergodicity method for singularly distorted non-symmetric diffusions ⋮ Hypocoercivity for Kolmogorov backward evolution equations and applications ⋮ Essential m-dissipativity and hypocoercivity of Langevin dynamics with multiplicative noise

Cites Work

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• A 3D MODEL FOR FIBER LAY-DOWN IN NONWOVEN PRODUCTION PROCESSES
• Hydrodynamic Limit of a Fokker–Planck Equation Describing Fiber Lay-Down Processes
• Hierarchy of mathematical models for production processes of technical textiles
• Construction of the Brownian motion and the Ornstein-Uhlenbeck process in a Riemannian manifold on basis of the Gangolli-Mc.Kean injection scheme
• A Stochastic Model and Associated Fokker–Planck Equation for the Fiber Lay-Down Process in Nonwoven Production Processes

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