Motion and Transport in Curve Dynamics

Result code in 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>
Result on the web
<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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Result language
angličtina
Original language name
Motion and Transport in Curve Dynamics
Original language description
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.
Czech name
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Czech description
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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