The extended polar writhe: a tool for open curves mechanics

A measure of the writhing of a curve is introduced and is used to extend the Călugăreanu decomposition for closed curves, as well as the polar decomposition for curves bound between planes. The new writhe measure is also shown to be able to assess changes in linking due to belt-trick and knotting type deformations, and further its utility is illustrated on examples taken from elastic rod parameter-continuation studies. Finally C++ and mathematica codes are made available and shown to be faster than existing algorithms for the numerical computation of the writhe.

• Publication year

  2016

• Venue

  Journal of Physics A: Mathematical and Theoretical

• Publication date

  2016-05-27

• Fields of study

  Mathematics, Physics, Engineering

• Identifiers
  DOI 10.1088/1751-8113/49/21/215201
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• The evolution of writhe in kink-unstable flux ropes and erupting filaments

  2014cited by this paper
• What Controls DNA Looping?

  2014cited by this paper
• ON THE HELICITY OF OPEN MAGNETIC FIELDS

  2014cited by this paper
• NEWTONIAN AND NON-NEWTONIAN MAGNETIC-FIELD RELAXATIONS IN SOLAR-CORONAL MHD

  2013cited by this paper
• TWIST ACCUMULATION AND TOPOLOGY STRUCTURE OF A SOLAR MAGNETIC FLUX ROPE

  2013cited by this paper
• Contorting a heavy and naturally curved elastic rod

  2013cited by this paper
• Solution structure of a truncated anti‐MUC1 DNA aptamer determined by mesoscale modeling and NMR

  2012cited by this paper
• Probing the elasticity of DNA on short length scales by modeling supercoiling under tension.

  2012cited by this paper
• On the Shape of Force-Free Field Lines in the Solar Corona

  2012cited by this paper
• BUILDUP AND RELEASE OF MAGNETIC TWIST DURING THE X3.4 SOLAR FLARE OF 2006 DECEMBER 13

  2012cited by this paper
• TWIST, WRITHE, AND HELICITY IN THE INNER PENUMBRA OF A SUNSPOT

  2011cited by this paper
• Absolute magnetic helicity and the cylindrical magnetic field

  2011cited by this paper
• GAUSS' LINKING NUMBER REVISITED

  2011cited by this paper
• Hopf solitons and elastic rods

  2010cited by this paper
• The theory and applications of writhing

  2010cited by this paper
• The writhe of helical structures in the solar corona

  2010cited by this paper
• THE TOPOLOGICAL CHANGES OF SOLAR CORONAL MAGNETIC FIELDS. III. RECONNECTED FIELD TOPOLOGY PRODUCED BY CURRENT-SHEET DISSIPATION

  2010cited by this paper
• Measurement of the torque on a single stretched and twisted DNA using magnetic tweezers.

  2009cited by this paper
• Complete sets of cyclic mutually unbiased bases in even prime-power dimensions

  2009cited by this paper
• Writhe in the stretch-twist-fold dynamo

  2009cited by this paper
• Writhe formulas and antipodal points in plectonemic DNA configurations.

  2008cited by this paper
• Chirality of coiled coils: elasticity matters.

  2008cited by this paper
• On end rotation for open rods undergoing large deformations

  2007cited by this paper
• Writhing and coiling of closed filaments

  2006cited by this paper
• The writhe of open and closed curves

  2006influential reference
• On the writhing number of a non-closed curve

  2005influential reference
• Writhing geometry of open DNA

  2003influential reference
• Ten years of tension: single-molecule DNA

  2003cited by this paper
• Ten years of tension: single-molecule DNA mechanics

  2003cited by this paper
• The micromechanics of DNA

  2003cited by this paper
• Reductions and hodograph solutions of the dispersionless KP hierarchy

  2002cited by this paper
• Computing the Writhing Number of a Polygonal Knot

  2002influential reference
• DIFFERENTIAL TOPOLOGY

  2002cited by this paper
• Comment on ‘Cyclic rotations, contractibility and Gauss–Bonnet’

  2002cited by this paper
• Theory of Supercoiled Elastic Rings with Self-Contact and Its Application to DNA Plasmids

  2000cited by this paper
• Computation of writhe in modeling of supercoiled DNA.

  2000cited by this paper
• Elasticity and Geometry

  2000cited by this paper
• Elastic Rod Model of a DNA Loop in the Lac Operon

  1999cited by this paper
• The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in mononucleosomes.

  1998influential reference
• Knots as stable soliton solutions in a three-dimensional classical field theory.

  1998cited by this paper
• Elastic rod model of a supercoiled DNA molecule

  1998cited by this paper
• Cyclic rotations, contractibility, and Gauss-Bonnet

  1998cited by this paper
• Spontaneous Helix Hand Reversal and Tendril Perversion in Climbing Plants

  1998cited by this paper
• Dynamics of a Thin Twisted Flux Tube

  1997cited by this paper
• Torsional directed walks, entropic elasticity, and DNA twist stiffness.

  1997cited by this paper
• A Continuum Rod Model of Sequence-Dependent DNA Structure

  1996cited by this paper
• CONFORMATIONS OF LINEAR DNA

  1996cited by this paper
• FORMULAE FOR THE CALCULATION AND ESTIMATION OF WRITHE

  1995cited by this paper
• The writhe of a self-avoiding walk

  1994cited by this paper
• The Kirchhoff elastic rod, the nonlinear Schrödinger equation, and DNA supercoiling

  1994cited by this paper
• Nonlinear problems of elasticity

  1994cited by this paper
• Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads.

  1992cited by this paper
• Analysis of the formation and elimination of loops in twisted cable

  1990cited by this paper
• The ambiguous twist of Love

  1982cited by this paper
• Decomposition of the linking number of a closed ribbon: A problem from molecular biology.

  1978cited by this paper
• Elastic model of supercoiling.

  1977cited by this paper
• There is More than One Way to Frame a Curve

  1975cited by this paper
• Relaxation of toroidal plasma and generation of reverse magnetic fields

  1974cited by this paper
• Sur les classes d'isotopie des noeuds tridimensionnels et leurs invariants

  1961cited by this paper

• Mechanical instabilities and snapping phenomena in helical rods with perversion

  2025cites this paper
• Rising of Two Crossing Prominences and the Resulting Oscillations

  2024cites this paper
• Novel topological methods for identifying surprising protein tertiary structure relationships

  2023cites this paper
• Lexicon for classifying ear-canal shapes

  2023cites this paper
• Quantification of the Writhe Number of the Evolution of Solar Filament Axes

  2023cites this paper
• The Rotation of Magnetic Flux Ropes Formed during Solar Eruption

  2022cites this paper
• WASP: a software package for correctly characterizing the topological development of ribbon structures

  2020cites this paper
• Analytical expression of elastic rods at equilibrium under 3D strong anchoring boundary conditions

  2018cites this paper
• Bifurcations of buckled , clamped anisotropic rods and thin bands under lateral end translations

  2018cites this paper
• Stable elastic knots with no self-contact

  2018cites this paper
• Calcul de configurations de tiges élastiques pour la modélisation des acides nucléiques

  2018cites this paper
• Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations

  2017cites this paper
• Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. III. Twist Number Method

  2017cites this paper
• Critical phenomena in helical rods with perversion

  year unknowncites this paper