Computational Studies of Space Curve Dynamics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00379333" target="_blank" >RIV/68407700:21340/24:00379333 - isvavai.cz</a>

Výsledek na webu

<a href="https://km.fjfi.cvut.cz/ddny/historie/24-sbornik.pdf" target="_blank" >https://km.fjfi.cvut.cz/ddny/historie/24-sbornik.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Computational Studies of Space Curve Dynamics

Popis výsledku v původním jazyce

This paper presents a computational investigation into the dynamics of space curves, utilizing parametric method and flowing finite volume techniques. The parametric approach is employed to solve the equations governing the curves, tX = αT + βN + γB + F, X(0) = X0, where T is the unit tangent vector, N the normal vector, and B is the binormal vector in the Frenet frame. The scalar velocities α, β, γ are smooth functions of the position vector X element R3, the curvature κ, and of the torsion τ . The term F is a known external force vector acting on Γt in arbitrary direction (see [1]). The evolution equation is then solved using the method of lines. To mitigate instability issues inherent in the computation process, both natural redistribution and uniform redistribution techniques are implemented. Furthermore, the study introduces a special force term to examine its effect on curve dynamics. By integrating this term into the computational framework, we explore its impact on the behaviour and shape evolution of space curves. Through these computational methodologies and techniques, this research contributes to a deeper understanding of space curve dynamics, offering insights into their behaviour under various conditions and the influence of external forces.

Název v anglickém jazyce

Computational Studies of Space Curve Dynamics

Popis výsledku anglicky

This paper presents a computational investigation into the dynamics of space curves, utilizing parametric method and flowing finite volume techniques. The parametric approach is employed to solve the equations governing the curves, tX = αT + βN + γB + F, X(0) = X0, where T is the unit tangent vector, N the normal vector, and B is the binormal vector in the Frenet frame. The scalar velocities α, β, γ are smooth functions of the position vector X element R3, the curvature κ, and of the torsion τ . The term F is a known external force vector acting on Γt in arbitrary direction (see [1]). The evolution equation is then solved using the method of lines. To mitigate instability issues inherent in the computation process, both natural redistribution and uniform redistribution techniques are implemented. Furthermore, the study introduces a special force term to examine its effect on curve dynamics. By integrating this term into the computational framework, we explore its impact on the behaviour and shape evolution of space curves. Through these computational methodologies and techniques, this research contributes to a deeper understanding of space curve dynamics, offering insights into their behaviour under various conditions and the influence of external forces.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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