# Modeling repulsive forces on fibres via knot energies

Molecular Based Mathematical Biology (2014)

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

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topSimon 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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