Modeling repulsive forces on fibres via knot energies

Simon Blatt; Philipp Reiter

Molecular Based Mathematical Biology (2014)

  • Volume: 2, Issue: 1, page 29-50
  • ISSN: 2299-3266

Abstract

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Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five years that aim at modeling self-avoidance. The general idea is to produce “detangled” curves having particularly large distances between distant strands. In this survey we present several families of these so-called knot energies. It turns out that they are quite similar from an analytical viewpoint. We focus on proving self-avoidance and existence of minimizers in every knot class. For a suitable subfamily of these energies we show how to prove that these minimizers are even infinitely differentiable

How to cite

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Simon Blatt, and Philipp Reiter. "Modeling repulsive forces on fibres via knot energies." Molecular Based Mathematical Biology 2.1 (2014): 29-50. <http://eudml.org/doc/267043>.

@article{SimonBlatt2014,
abstract = {Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five years that aim at modeling self-avoidance. The general idea is to produce “detangled” curves having particularly large distances between distant strands. In this survey we present several families of these so-called knot energies. It turns out that they are quite similar from an analytical viewpoint. We focus on proving self-avoidance and existence of minimizers in every knot class. For a suitable subfamily of these energies we show how to prove that these minimizers are even infinitely differentiable},
author = {Simon Blatt, Philipp Reiter},
journal = {Molecular Based Mathematical Biology},
keywords = {repulsive forces; knot energies; molecular biology; stationary points},
language = {eng},
number = {1},
pages = {29-50},
title = {Modeling repulsive forces on fibres via knot energies},
url = {http://eudml.org/doc/267043},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Simon Blatt
AU - Philipp Reiter
TI - Modeling repulsive forces on fibres via knot energies
JO - Molecular Based Mathematical Biology
PY - 2014
VL - 2
IS - 1
SP - 29
EP - 50
AB - Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five years that aim at modeling self-avoidance. The general idea is to produce “detangled” curves having particularly large distances between distant strands. In this survey we present several families of these so-called knot energies. It turns out that they are quite similar from an analytical viewpoint. We focus on proving self-avoidance and existence of minimizers in every knot class. For a suitable subfamily of these energies we show how to prove that these minimizers are even infinitely differentiable
LA - eng
KW - repulsive forces; knot energies; molecular biology; stationary points
UR - http://eudml.org/doc/267043
ER -

References

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