Conservation, Convergence, and Computation for Evolving Heterogeneous Elastic Wires

Dall’Acqua, Anna; Jankowiak, Gaspard; Langer, Leonie; Rupp, Fabian

Conservation, Convergence, and Computation for Evolving Heterogeneous Elastic Wires

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2024

Autor:innen

Dall’Acqua, Anna

Jankowiak, Gaspard

Langer, Leonie

Rupp, Fabian

DOI (zitierfähiger Link)

https://doi.org/10.1137/23m159086x

Angaben zur Forschungsförderung

Austrian Science Fund (FWF): P 32788-N
Deutsche Forschungsgemeinschaft (DFG): 404870139

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics (SIAM). 2024, 56(4), S. 4494-4529. ISSN 0036-1410. eISSN 1095-7154. Verfügbar unter: doi: 10.1137/23m159086x

Zusammenfassung

The elastic energy of a bending-resistant interface depends on both its geometry and its material composition. We consider such a heterogeneous interface in the plane, modeled by a curve equipped with an additional density function. The resulting energy captures the complex interplay between curvature and density effects, resembling the Canham–Helfrich functional. We describe the curve by its inclination angle, so that the equilibrium equations reduce to an elliptic system of second order. After a brief variational discussion, we investigate the associated nonlocal L²-gradient flow evolution, a coupled quasilinear parabolic problem. We analyze the (non)preservation of quantities such as convexity, positivity, and symmetry, as well as the asymptotic behavior of the system. The results are illustrated by numerical experiments.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

heterogeneous material, elastic flow, maximum principle, convexity, symmetry, asymptotic behavior, Euler-Bernoulli elastic energy

Zitieren

ISO 690

DALL’ACQUA, Anna, Gaspard JANKOWIAK, Leonie LANGER, Fabian RUPP, 2024. Conservation, Convergence, and Computation for Evolving Heterogeneous Elastic Wires. In: SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics (SIAM). 2024, 56(4), S. 4494-4529. ISSN 0036-1410. eISSN 1095-7154. Verfügbar unter: doi: 10.1137/23m159086x

BibTex

@article{DallAcqua2024-08-31Conse-71198,
  year={2024},
  doi={10.1137/23m159086x},
  title={Conservation, Convergence, and Computation for Evolving Heterogeneous Elastic Wires},
  number={4},
  volume={56},
  issn={0036-1410},
  journal={SIAM Journal on Mathematical Analysis},
  pages={4494--4529},
  author={Dall’Acqua, Anna and Jankowiak, Gaspard and Langer, Leonie and Rupp, Fabian}
}

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Ja