The Crystalline Dynamics of Spiral-Shaped Curves

The Crystalline Dynamics of Spiral-Shaped Curves

We study the motion of spiral-shaped polygonal curves by crystalline curvature. We describe this dynamics by the corresponding infinitely dimensional system of ordinary differential equations and show that the considered model is uniquely solvable. Banach’s Contraction Mapping Theorem and the Bellma...

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Veröffentlicht in:Journal of statistical physics 2015-07, Vol.160 (2), p.409-416
Hauptverfasser: Dudzinski, Marcin, Gorka, Przemyslaw
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Zusammenfassung:We study the motion of spiral-shaped polygonal curves by crystalline curvature. We describe this dynamics by the corresponding infinitely dimensional system of ordinary differential equations and show that the considered model is uniquely solvable. Banach’s Contraction Mapping Theorem and the Bellman–Gronwall inequality are the main tools applied in our proof.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-015-1254-5