Motion and Transport in Curve Dynamics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00379342" target="_blank" >RIV/68407700:21340/24:00379342 - isvavai.cz</a>

Výsledek na webu

<a href="https://ms-meet-2024.blogs.auckland.ac.nz/" target="_blank" >https://ms-meet-2024.blogs.auckland.ac.nz/</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Motion and Transport in Curve Dynamics

Popis výsledku v původním jazyce

We investigate the motion of closed non-intersecting curves with velocity given by curvature and force. This motion is considered in plane, along surfaces, or in space. It is treated by the parametric method with the velocity decomposed into the normal and tangent directions, in space also into the bi-normal direction. We admit scalar quantities to be transported along the curves by diffusion and influenced by mutual interaction with the curve. This forms a system of degenerate parabolic equations for which the local existence and uniqueness of solution can be obtained. A numerical discretization can be constructed using the method of flowing finite volumes. Long-term stability is supported by a redistribution scheme providing uniformity of discretization nodes of the curve. We demonstrate behavior of the solution on computational studies related to the dislocation dynamics in the crystalline structure of materials, dynamics of vortex rings in space, and electric signal spreading in excitable media. We also indicate future challenges related to the forced curvature motion of space curves.

Název v anglickém jazyce

Motion and Transport in Curve Dynamics

Popis výsledku anglicky

We investigate the motion of closed non-intersecting curves with velocity given by curvature and force. This motion is considered in plane, along surfaces, or in space. It is treated by the parametric method with the velocity decomposed into the normal and tangent directions, in space also into the bi-normal direction. We admit scalar quantities to be transported along the curves by diffusion and influenced by mutual interaction with the curve. This forms a system of degenerate parabolic equations for which the local existence and uniqueness of solution can be obtained. A numerical discretization can be constructed using the method of flowing finite volumes. Long-term stability is supported by a redistribution scheme providing uniformity of discretization nodes of the curve. We demonstrate behavior of the solution on computational studies related to the dislocation dynamics in the crystalline structure of materials, dynamics of vortex rings in space, and electric signal spreading in excitable media. We also indicate future challenges related to the forced curvature motion of space curves.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů