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Published February 23, 2023 | Version 1.2.2
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Python code for the animation of a magnetic catastrophe machine, V1.2.2

Authors/Creators

  • 1. University of Bayreuth

Description

An interactive Python program demonstrating the relaxation of the cluster described in the paper "Andrew D.P. Smith, Peter T. Haugen, Boyd F. Edwards: Hysteretic transition between states of a filled hexagonal magnetic dipole cluster, Journal of Magnetism and Magnetic Materials 549 (2022): 168991", and a related comment https://doi.org/10.48550/arXiv.2203.13670 . There a hysteretic transition between two stable arrangements of a cluster of seven dipoles is presented. The relative strength of the center dipole in a hexagonal arrangement serves as the bifurcation parameter. This experiment is great for classroom demonstrations, because it shows with its spontaneous symmetry breaking, the bi-stability, and the two different bifurcations leading to discontinuous jumps almost all of the elementary features of static nonlinear systems.

Notes

In Version 1.2.2, a movie of a real machine made from seven magnets is provided, which can be presented within the Python animation. Additional features are added to the interactive part of the software to simulate that the dipoles forming the hexagon in the experiment are restricted to the x-y-plane due to the ball bearings.

Files

Readme_for_Animate_Dipole_Cluster_1_2_2.pdf

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Additional details

Related works

Is cited by
arXiv:2203.13670v2 (arXiv)
Presentation: 10.5281/zenodo.7767346 (DOI)
Is supplement to
10.5281/zenodo.6484442 (DOI)

References

  • A. D. Smith, P. T. Haugen, B. F. Edwards, Hysteretic transition between states of a filled hexagonal magnetic dipole cluster, Journal of Magnetism and Magnetic Materials 549 (2022) 168991.
  • T. Friedrich, I. Rehberg, R. Richter, Comment on "self-assembly of magnetic balls: From chains to tubes", Phys. Rev. E 91 (2015) 057201
  • Simeon Völkel, Stefan Hartung, Ingo Rehberg, Comment on "Hysteretic transition between states of a filled hexagonal magnetic dipole cluster", arXiv:2203.13670
  • Simeon Völkel, Stefan Hartung, Ingo Rehberg, Comment on "Hysteretic transition between states of a filled hexagonal magnetic dipole cluster", Journal of Magnetism and Magnetic Materials, Volume 559, 2022, 169520, ISSN 0304-8853, https://doi.org/10.1016/j.jmmm.2022.169520. (https://www.sciencedirect.com/science/article/pii/S0304885322004437)