Python code for the animation of a magnetic catastrophe machine, V1.2.2
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
Files
Readme_for_Animate_Dipole_Cluster_1_2_2.pdf
Files
(66.8 MB)
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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)