Comment on "Hysteretic transition between states of a filled hexagonal magnetic dipole cluster"

Title data

Völkel, Simeon ; Hartung, Stefan ; Rehberg, Ingo:
Comment on "Hysteretic transition between states of a filled hexagonal magnetic dipole cluster".
Ithaca, NY : Cornell University , 2022
DOI: https://doi.org/10.48550/arXiv.2203.13670

Official URL:

Abstract in another language

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" 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. The authors clearly demonstrate the existence of two instabilities accompanied
by discontinuous jumps of the dipole arrangement, but leave the question about the nature of these
instabilities unanswered. This comment clarifies the nature of the two instabilities: the first one is
a symmetry-breaking sub-critical bifurcation with parabolic scaling of the magnetic potential energy
difference between the two branches, and the second one is a fold with its characteristic scaling in the
form of a semi-cubic parabola.

Further data

Item Type:	Preprint, postprint
Keywords:	Magnetostatics; Bifurcation; Hysteresis; Subcritical bifucation; Fold; Cusp catastrophe
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Former Professors > Chair Experimental Physics V - Univ.-Prof. Dr. Ingo Rehberg Profile Fields > Advanced Fields > Nonlinear Dynamics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Former Professors Profile Fields Profile Fields > Advanced Fields
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 530 Physics
Date Deposited:	30 Mar 2022 08:56
Last Modified:	26 Oct 2022 06:53
URI:	https://eref.uni-bayreuth.de/id/eprint/69063