A note on the motion of surfaces
, 1993 We study the motion of surfaces in an intrinsic formulation in which the surface is described by its metric and curvature tensors. The evolution equations for the six quantities contained in these tensors are reduced in number in two cases: (i) for ...
McLachlan, Robert I., Segur, Harvey
core +3 more sources
Characterizations of Special Curves [PDF]
, 2012 In this study, the new characterizations of special curves are investigated without using the curvatures of these special curves: general helices, slant helices, Bertrand curves, Mannheim curves.
Saracoglu, Semra, Yayli, Yusuf
core
Structured time-delay models for dynamical systems with connections to Frenet-Serret frame. [PDF]
Proc Math Phys Eng Sci, 2021 Hirsh SM +4 more
europepmc +1 more source
Heisenberg ferromagnetism as an evolution of a spherical indicatrix: localized solutions and elliptic dispersionless reduction [PDF]
, 2018 A geometrical formulation of Heisenberg ferromagnetism as an evolution of a curve on the unit sphere in terms of intrinsic variables is provided and investigated.
Demontis, Francesco +2 more
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A Ribbon Model for Nematic Polymer Networks. [PDF]
J Elast, 2023 Singh H, Virga EG.
europepmc +1 more source
A lower bound to the spectral threshold in curved tubes
, 2004 We consider the Laplacian in curved tubes of arbitrary cross-section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann ...
D. Krejčiřík +4 more
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Predicting the risk of rupture for vertebral aneurysm based on geometric features of blood vessels. [PDF]
R Soc Open Sci, 2021 Li S +5 more
europepmc +1 more source
On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3
, 1997 Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using
Carroll R +27 more
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Hopf Term, Loop Algebras and Three Dimensional Navier-Stokes Equation
, 1993 The dynamics of the 3 dimensional perfect fluid is equivalent to the motion of vortex filaments or "strings". We study the action principle and find that it is described by the Hopf term of the nonlinear sigma model.
Matsuo, Yutaka
core +2 more sources
New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures. [PDF]
Adv Mater, 2022 Makarov D +5 more
europepmc +1 more source