A conformal variational approach for helices in nature

DOI10.1063/1.3236683zbMath1283.53003OpenAlexW2155754234MaRDI QIDQ3583668

Angel Ferrández, Manuel Barros

Publication date: 17 August 2010

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/db2c8b979996abb336e85486ea03707d9c8e849c

zbMATH Keywords

variational techniquesquantisationhelical structures in nature

Mathematics Subject Classification ID

Biochemistry, molecular biology (92C40) Curves in Euclidean and related spaces (53A04) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Variational principles of physics (49S05)

Related Items (13)

General helices with timelike slope axis in Minkowski 3-space ⋮ On polynomial general helices in \(n\)-dimensional Euclidean space \(\mathbb {R}^{n}\) ⋮ Equilibrium configurations of the noncircular cross-section elastic rod model with the elliptic KB method ⋮ Spacelike helices in Minkowski 4-space \(E_{1}^{4}\) ⋮ Gravitational magnetic curves on 3D Riemannian manifolds ⋮ On the energy density of helical proteins ⋮ A variational characterization and geometric integration for Bertrand curves ⋮ General helices with spacelike slope axis in Minkowski 3-space ⋮ New results for general helix in Euclidean 3-space ⋮ Magnetic fields in 2D and 3D sphere ⋮ Magnetic curves corresponding to Killing magnetic fields in ${\mathbb {E}}^3$E3 ⋮ General helices with lightlike slope axis ⋮ Helicoidal surfaces with constant anisotropic mean curvature

Uses Software

• CandS

Cites Work

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• Functionals linear in curvature and statistics of helical proteins
• Helices for mathematical modelling of proteins, nucleic acids and polymers
• Hopf tori in \(S^ 3\)
• The Hopf fibration --- seven times in physics
• Models of relativistic particle with curvature and torsion revisited
• How Helical Can a Closed, Twisted Space Curve be?
• Energy density functions for protein structures
• General helices and a theorem of Lancret
• Knot Types, Homotopies and Stability of Closed Elastic Rods
• Lagrangian Aspects of the Kirchhoff Elastic Rod
• Self-Linking and the Gauss Integral in Higher Dimensions

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