# Ingo RehbergUniversity of Bayreuth · Institute of Physics

Ingo Rehberg

Prof. Dr.

Magnetic Dipole Clusters - Resurrection of Catastrophe Machines.
Talk presented March 30, 2023 at DPG-Meeting, Dresden.

## About

228

Publications

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Introduction

current work:
- MAGNETIC CLUSTERS: The equilibrium states of a "filled hexagon" ( https://doi.org/10.48550/arXiv.2203.13670 ) can be animated with presentation software (https://zenodo.org/record/6380540 ).
- GRAPHICAL MAGNETOGRANULOMETRY: In connection with [Phys. Rev. B 100, 134425 , 2019] and [JMMM 508, 166868, 2020] I try to publish the software in a user-friendly form.
- COGGING FREE MAGNETIC GEARS: understanding the puzzles outlined at 10.5281/zenodo.7037353

## Publications

Publications (228)

The dipole-dipole interaction is a substantial part of the force that holds matter together. Because the electric and magnetic dipole-dipole interactions are mathematically equivalent, this fundamental interaction can be experimentally examined with magnetic spheres. The software package "examine dipole clusters" allows an interactive examination o...

The ground states of cuboidal dipole clusters and their interaction are animated with the Python program named dipole_cube_animation_1.2.

DPG-Frühjahrstagung der Sektion Kondensierte Materie (SKM)
, 26. März bis 31. März 2023, Technische Universität Dresden

Hysteretic transitions between stable configurations of a hexagonal magnetic dipole cluster [1] are set in a broader context by revealing the nature of the corresponding instabilities [2]. Following the animation of this bifurcation scenario [3], we present an experimental setup where the height of the centre dipole serves as the bifurcation parame...

Six slides for the presentation, without the movies, as a pdf-file.

The ground state of a cuboidal dipole cluster is animated with the Python program named dipole_cube_animation_1.1.

In Version 1.2.2 (February 2023), features are added to simulate the experiment where the height of the central dipole is adjusted by hand, while the 6 dipoles forming the ring are restricted to rotations in the plane, which is experimentally realized by means of nonmagnetic ball bearings. A movie from the experiment can be displayed within the ani...

Magnetosomes are magnetic nanoparticles biosynthesized by magnetotactic bacteria. Due to a genetically strictly controlled biomineralization process, the ensuing magnetosomes have been envisioned as agents for biomedical and clinical applications. In the present work, different stability parameters of magnetosomes isolated from Magnetospirillum gry...

Experiments exploring the coupling of two rotating spherical magnets reveal a cogging-free coupling for two specific angles between the input and output rotation axes. The striking difference between these two phase-locked modes of operation is the reversed sense of rotation of the driven magnet. For other angles, the cogging leads to a more comple...

Python software for the animation of the magnetic field of fundamental geometries with a software example to fit such fields to measured data.

In the paper “Smith et al. (2022)” 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...

The influence of friction on the stability of vertical magnetic chains is stressed.

The animation of hysteretic transitions of a hexagonal magnetic dipole cluster. Details of the physics are described in https://doi.org/10.48550/arXiv.2203.13670 and the references cited therein. The Python code for "animate_dipole_cluster.py", Version 1.2.1, is available here: 10.5281/zenodo.6380539. , or from the author Ingo.Rehberg@uni-bayreuth....

An animated gif illustrating a hysteretic transition in a magnetic dipole cluster. The control parameter is an external magnetic field.

This animated gif shows one aspect of the interactive demonstration of the hysteretic transition in a hexagonal dipole cluster. The code is available at https://doi.org/10.5281/zenodo.6531680

The animation of hysteretic transitions of a hexagonal magnetic dipole cluster. Details of the physics are described in https://doi.org/10.48550/arXiv.2203.13670 and the references cited therein. The Python code for "animate_dipole_cluster.py", Version 1.2, is available here: https://zenodo.org/record/6380540, or from the author. Version 1.2 adds t...

A cubic dipole cluster has a degenerate ground state with a continuum of solutions, which can be experimentally realized with spherical magnets [1]. With this animation, one can step through the one-parameter family of ground state solutions, and watch the ensuing field in a number of projections.
Because these cubic clusters behave as dotriacont...

"animate_dipole_cluster_1.1.py": Python code for the animation of hysteretic transitions of a magnetic dipole cluster. Available at: https://zenodo.org/record/6380540 . The physics is described in https://doi.org/10.48550/arXiv.2203.13670 and the references cited therein.

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...

The pyhon source code for an interactive animation of the dynamics of the magnetic gear with two cogging free operation modes.

Experimental observation and animations of the dynamics of a magnetic gear build from two magnetic dipoles.

The coupling of two rotating spherical magnets is investigated experimentally. For two specific angles between the input and output rotation axes, a cogging-free coupling is observed, where the driven magnet is phase-locked to the driving one. The striking difference between these two modes of operation is the reversed sense of rotation of the driv...

The size of magnetic particles in suspension is extracted from magnetization curves.

The coupling of two rotating spherical magnets is investigated experimentally. For two specific angles between the input and output rotation axes, a cogging-free coupling is observed, where the driven magnet is phase-locked to the driving one. The striking difference between these two modes of operation is the reversed sense of rotation of the driv...

Poster on work by Lloyd, Gollwitzer, Rehberg, Richter published in Journal of Fluid Mechanics, vol. 783, pp. 283-305

The coupling of two rotating spherical magnets is investigated experimentally. For two specific angles between the input and output rotation axes, a cogging-free coupling is observed, where the driven magnet is phase-locked to the driving one. The striking difference between these two modes of operation is the reversed sense of rotation of the driv...

The magnetization curve of the commercially available ferrofluid EMG909 is measured. It can adequately be described by a superposition of four Langevin terms. The effective dipole strength of the magnetic particles in this fluid is subsequently obtained by a graphical rectification of the magnetization curve based on the inverse Langevin function....

The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle distribution. It has an advantage compared to the fitting of magnetization curves to some appropriate mathematic...

Experimental data and results from an interactive animation of the magnetic field of a cuboidal cluster of eight dipoles.

Particle Size Characterization from Rectified Magnetization Curves

The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of
the magnetization curves based on the inverse Langevin function. The method yields the arithmetic
and the harmonic mean of the particle distribution. It has an advantage compared to the fitting
of magnetization curves to some appropriate mathematic...

The magnetization curve of the ferrofluid EMG909 is measured. It can adequately be described by a superposition of four Langevin terms. The effective dipole strength of the magnetic particles in this fluid is subsequently obtained by a graphical rectification of the magnetization curve based on the inverse Langevin function. The method yields the a...

The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle distribution. It has an advantage compared to the fitting of magnetization curves to some appropriate mathematic...

Magnetogranulometry: obtain information about the distribution of magnetic moments in a ferrofluid
We propose a graphical rectification method:
• based on inverse Langevin function
• avoids fitting to a distribution function
• yields arithmetic mean, harmonic mean, and coefficient of variation of magnetic moment

The magentic induction is measured by a Hall probe within a two-dimensional plane.

The magnetic induction around a cuboidal cluster of dipoles in its contiuuos ground state can be explored interactively.

The magnetic field of a cuboidal cluster of eight magnetic spheres is measured. It decays with the inverse seventh power of the distance. This corresponds formally to a multipole named a dotriacontapole. This strong decay is explained on the basis of dipole-dipole interaction and the symmetry of the ensuing ground state of the cuboidal cluster. A m...

The magnetic field of a cuboidal cluster of eight magnetic spheres is measured: It decays with the inverse seventh power of the distance. This corresponds formally to a hitherto unheard-of multipole,
namely a dotriacontapole.
This strong decay is explained on the basis of dipole-dipole interaction and the symmetry of the ensuing ground state of t...

The magnetic field of a cuboidal cluster of eight magnetic spheres is measured. It decays with the inverse seventh power of the distance. This corresponds formally to a hitherto unheard-of multipole, namely a dotriacontapole. This strong decay is explained on the basis of dipole-dipole interaction and the symmetry of the ensuing ground state of the...

This chapter describes the synthesis and some characteristics of magnetic iron oxide nanoparticles, mainly nanocubes, and focus on their self-assembly into crystalline cuboids in dispersion. The influence of external magnetic fields, the concentration of particles, and the temperature on the assembly process is experimentally investigated.

This chapter describes the synthesis and some characteristics of magnetic iron oxide nanoparticles, mainly nanocubes, and focus on their self-assembly into crystalline cuboids in dispersion. The influence of external magnetic fields, the concentration of particles, and the temperature on the assembly process is experimentally investigated.

The spatial decay of the magnetic field of a cluster of 8 dipoles.

The coupling of two rotating spherical magnets is investigated experimentally, with particular emphasis on those motions where the driven magnet follows the driving one with a uniform angular speed, which is a feature of the so called cogging free couplings. The experiment makes use of standard equipment and digital image processing. The theory for...

We experimentally investigate magnetic surface swimmers on water. These objects self-assemble from ferromagnetic microparticles and a nonmagnetic disk. They are floating on the liquid surface due to interface tension and move under the influence of a harmonically oscillating homogeneous magnetic field oriented vertically, which is distinguished by...

Using a highly viscous magnetic fluid, the dynamics in the aftermath of the Rosensweig instability can be slowed down by more than 2000 times. In this way we expand the regime where the growth rate is predicted to scale linearly with the bifurcation parameter by six orders of magnitude, while this regime is tiny for standard ferrofluids and cannot...

Physik Journal 15 (2016) Nr. 4 , 31. Magnetkugeln sind ein inspirierendes physikalisches Spielzeug. Mit ihnen kann man nicht nur chemische, physikalische und mathematische Fragestellungen illustrieren, sondern auch der Kreativität auf die Sprünge helfen. So ist es von der Frage nach dem magnetischen Grundzustand eines mühevoll zusammengesetzten Wür...

Significance
We discovered that small magnetic nanocubes spontaneously assemble into highly ordered chains, sheets, and cuboids in solution by applying a magnetic field. We elucidate how these assemblies are formed by working out the three-dimensional equilibrium arrangement of the dipoles. This classic physics problem turned out to be amazingly co...

We report on localized patches of cellular hexagons observed on the surface of a magnetic fluid in a vertical magnetic field. These patches are spontaneously generated by jumping into the neighborhood of the unstable branch of the domain covering hexagons of the Rosensweig instability upon which the patches equilibrate and stabilise. They are found...

Experiments on a thin layer of cohesive wet granular matter under vertical
agitation reveal kink separated domains that collide with the container at
different phases. Due to the strong cohesion arising from the formation of
liquid bridges between adjacent particles, the domains move collectively upon
agitation. Depending on the periodicity of this...

The paper states that magnetic balls preferably assemble in a tube geometry if the number of particles exceeds $N\ensuremath{\ge}14$. We find that for substantially higher particle counts, such as $N>1300$, a round cluster of densely packed magnetic balls with an fcc lattice can outmatch the described tube structure.

The orientational order of vertically agitated granular rod monolayers is
investigated experimentally and compared with equilibrium Monte Carlo
simulations and density functional theory. At sufficiently high density, short
rods form a tetratic state and long rods form a uniaxial nematic state. The
length-to-width ratio at which the order changes fr...

We report on localized patches of cellular hexagons observed on the surface of a magnetic fluid in a vertical magnetic field. These patches are spontaneously generated by jumping into the neighborhood of the unstable branch of the domain covering hexagons of the Rosensweig instability. They are found to co-exist in intervals around this branch. We...

The geometric arrangement of interacting (magnetic) dipoles is a question of
fundamental importance in physics, chemistry and engineering. Motivated by
recent progress concerning the self-assembly of magnetic structures, the
equilibrium orientation of 8 interacting dipoles in a cubic cluster is
investigated in detail. Instead of discrete equilibria...

We found two errors in the paper "Thermal convection in a thermosensitive colloidal suspension"(2010 New J. Phys. 12 053003), which were both originally our mistake. In table 1, two units are wrong. The solutal expansion β has no unit, while the unit of the Soret coefficient ST is 1/K. The respective lines in this table should correctly read: Solut...

Agitated wet granular matter can be considered as a nonequilibrium model system for phase transitions, where the macroscopic particles replace the molecules and the capillary bridges replace molecular bonds. It is demonstrated experimentally that a two-dimensional wet granular crystal driven far from thermal equilibrium melts from its free surface,...

The onset of transient Soret-driven convection is investigated experimentally in a colloidal suspension of thermosensitive nanoparticles by the shadowgraph technique and by particle tracking observations. From the shadowgraph images, the concentration profile is reconstructed, giving evidence of a convective motion inside the transient boundary lay...

A recently proposed stabilization mechanism for the Rayleigh–Taylor instability, using magnetic fluids and azimuthally rotating magnetic fields, is experimentally investigated in a cylindrical geometry and compared with the theoretical model. This approach allows the imperfection of the experimental setup to be exploited for measuring the critical...

The onset of buoyancy driven convection in a transient boundary layer at large Rayleigh numbers is discussed theoretically by using a minimal yet powerful method proposed by Howard. The method is applied to thermal and Soret-driven convection in bulk fluid layers, in Hele-Shaw geometries and in porous media with, respectively, isothermal as well as...

If a fluid streams over an extended area of sand, the grains will
self-organize by forming complex structures like ripples or dunes. Below
the surface, the inner structure of a dune is determined by the
individual fate of the particles. In general, agitated granular matter
is known to show de-mixing whenever particles differ in size or density,
and...

A thorough understanding of the energy dissipation in the dynamics of wet
granular matter is essential for a continuum description of natural phenomena
such as debris flow, and the development of various industrial applications
such as the granulation process. The coefficient of restitution (COR), defined
as the ratio between the relative rebound a...

Pattern formation of a thin layer of vertically agitated wet granular matter
is investigated experimentally. Due to the strong cohesion arising from the
capillary bridges formed between adjacent particles, agitated wet granular
matter exhibits a different scenario compared with cohesionless dry particles.
Rotating spirals with three arms, which cor...

This paper reports on the influence of the structure of tailored ABA-triblock copolymers on physical gelation of the nematic liquid crystal 4'-n-pentyl-4-cyanobiphenyl (5CB), rheological properties, and the electro-optical response of the gels. The block copolymer gelators, comprised of two polystyrene A-blocks connected to a cyanobiphenyl-function...

The design of two custom sample holders with a spherical cavity for commercial vibrating sample magnetometer systems is described. For such cavities, the magnetization \documentclass[12pt]{minimal}\begin{document}$\vec{M}$\end{document}M⃗ and the internal magnetic field \documentclass[12pt]{minimal}\begin{document}$\vec{H_i}$\end{document}Hi⃗ of a...

The influence of a wetting liquid on the coefficient of restitution (COR) is
investigated experimentally by tracing freely falling particles bouncing on a
wet surface. The dependence of the COR on the impact velocity and various
properties of the particle and the wetting liquid is presented and discussed in
terms of dimensionless numbers that chara...

The transition from the solidlike to the liquidlike state of a monolayer
of wet glass beads under horizontally swirling motion is investigated
experimentally. Due to the cohesion arising from the formation of
capillary bridges, the wet particles initially form a crystal like
structure at moderate driving. As the driving frequency increases, this
st...

As the experience of playing football in the rain may tell, wetting
could influence the coefficient of restitution (COR) dramatically. This
is due to the extra energy dissipation from the wetting liquid, for
instance viscous damping. To unveil the underlying mechanisms accounting
for the influence, we study experimentally the COR by tracing free
fa...

Spatiotemporal patterns in nature, such as ripples or dunes, formed by a
fluid streaming over a sandy surface show complex behavior despite their simple
forms. Below the surface, the granular structure of the sand particles is
subject to self-organization processes, exhibiting such phenomena as reverse
grading when larger particles are found on top...

The viscoelastic properties of a binary mixture of a mesogenic side-chain block copolymer in a low molecular weight nematic liquid crystal are studied for mass concentrations ranging from the diluted regime up to a liquid crystalline gel state at about 3%. In the gel state, the system does not flow, exhibits a polydomain structure on a microscopic...

Pattern formation of a thin layer of vertically agitated wet granular matter is investigated experimentally. Rotating spirals with three arms, which correspond to the kinks between regions with different colliding phases, are the dominating pattern. This preferred number of arms corresponds to period tripling of the agitated granular layer, unlike...

We report on the response of a thin layer of ferrofluid to a spatially
modulated magnetic field. This field is generated by means of a constant
current in a special arrangement of aluminum wires. The full surface profile of
the liquid layer is recorded by means of the absorption of X-rays. The outcome
is analyzed particularly with regard to the mag...

By means of a local magnetic perturbation we generate localized states on the surface of a ferrofluid in the bistable regime of the Rosensweig instability. Establishing a magnetic ramp at the edge of the vessel enables us to record the growth of the localized spikes with a high speed camera. From the pictures we extract their growth rate. Under var...

Because of the energy dissipation through friction and inelastic collisions between particles, agitated granular matter is generally speaking in a state far from thermal equilibrium. It can be considered as being a complex state of matter, which combines properties of the fluid and of the solid state. In order to provide data for modeling this pecu...

We describe and demonstrate a method to reconstruct an amplitude equation
from the nonlinear relaxation dynamics in the succession of the Rosensweig
instability. A flat layer of a ferrofluid is cooled such that the liquid has a
relatively high viscosity. Consequently, the dynamics of the formation of the
Rosensweig pattern becomes very slow. By sud...

A contactless pumping mechanism is realized in a layer of ferrofluid via a spatiotemporally modulated magnetic field. The resulting pressure gradient leads to a liquid ramp, which is measured by means of x-rays. The transport mechanism works best if a resonance of the surface waves with the driving is achieved. The behavior can be understood by con...