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Python code for the animation of hysteretic transitions of a magnetic dipole cluster

Name: Python code for the animation of hysteretic transitions of a magnetic dipole cluster
Creator: Rehberg, Ingo
Keywords: dipole cluster, animation, Python, subcritical bifurcation, fold

integration_instructionsResearch softwarekeyboard_double_arrow_right Software 23 Mar 2022 English Publisher:Zenodo

Authors: Rehberg, Ingo;

doi: 10.5281/zenodo.6405333 , 10.5281/zenodo.6531680 , 10.5281/zenodo.6380540 , 10.5281/zenodo.6559574

Python code for the animation of hysteretic transitions of a magnetic dipole cluster

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Abstract

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.

{"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 V\u00f6lkel, Stefan Hartung, Ingo Rehberg, Comment on \"Hysteretic transition between states of a filled hexagonal magnetic dipole cluster\", arXiv:2203.13670"]}

In Version 1.2, an additional control paramter is available, namely the height of the central dipole.

Related Organizations

University of Bayreuth
Germany

Keywords

dipole cluster, animation, Python, subcritical bifurcation, fold

2 Research products, page of 1

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