arXiv subjects

Ingo Rehberg

Publications and source records attributed to Ingo Rehberg.

At least 19 recordsLinked to original sources

arXiv2026

Openable Force-Balanced Halbach Magnets: From Fibonacci Sphere Simulations to Icosahedral Realizations

A long-standing goal in magnet design is to completely surround a volume of highly homogeneous magnetic field with permanent magnets while maintaining practical access to that volume. In this work, we present a theoretical and experimental investigation of mechanically accessible spherical magnets in Halbach configuration that can be opened with minimal or vanishing force. Focusing on dipolar Halbach spheres composed of discrete magnetic subunits, we derive conditions for force-free opening along specific cutting planes. These conditions define a continuous set of geometries for which tensile magnetic forces cancel, leaving only shear components, enabling mechanically effortless opening. The theoretical predictions are validated experimentally using icosahedral approximations of the Halbach sphere, for which both opening forces and magnetic field properties are measured. The results demonstrate that excellent field homogeneity can be preserved while reducing opening forces by orders of magnitude. Although discussed in detail for the dipolar case, the theoretical framework is general and applicable to higher-order multipole Halbach systems. Finally, the concepts are extended to spherocylindrical Halbach configurations, highlighting their potential for large-volume, highly homogeneous, and mechanically accessible permanent-magnet systems for magnetic resonance

physics.ins-det↗

arXiv2025

Discretized Halbach spheres: Icosahedral symmetry for optimal field homogeneity

Halbach spheres provide a theoretically elegant means of generating highly homogeneous magnetic fields, but practical implementation is hindered by challenging fabrication and restricted interior access. This study examines discrete spherical Halbach configurations assembled from permanent magnets placed at the vertices of Platonic and Archimedean solids. Analytical calculations, numerical field simulations, and experimental measurements indicate that polyhedra with icosahedral symmetry achieve the most favorable balance among field strength, homogeneity, and interior accessibility. They produce exceptionally flat fourth-order central saddle points, resulting in a usable homogeneous field volume up to a factor of 260 larger than that of traditional Halbach disk or cylindrical arrays. Several magnet assemblies composed of cubical NdFeB magnets are fabricated and their three dimensional field distributions characterized, demonstrating homogeneous regions of up to several cubic centimeters with deviations below 1%. The findings establish discrete icosahedrally symmetric magnet arrays as practical, scalable building blocks for compact, highly homogeneous magnetic field sources suited to mobile magnetic resonance, and magnetophoretic applications.

physics.ins-det↗

arXiv2025

Analytic approach to creating homogeneous fields with finite-size magnets

Homogeneous magnetic fields can be generated through the strategic arrangement of permanent magnets. The Halbach array serves as a prominent example of an effective design following this principle. However, it is a two-dimensional approach because it is optimal when placing infinitely long magnets -- line dipoles -- on a circle. If shorter, more realistic magnets are to be used, the optimal arrangement of magnetic moments diverges from the classical Halbach geometry. This paper presents optimal solutions for three-dimensional arrangements calculated for point dipoles, including optimized orientations for single rings and stacks of two rings. They are superior to the original Halbach arrangement and a modification described in the literature, both in terms of the strength and the homogeneity of the magnetic field. Analytic formulae are provided for both cases and tested by experimental realizations.

cond-mat.mtrl-sci↗

arXiv2022

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

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.

cond-mat.mtrl-sci↗

arXiv2020

Dynamics of a magnetic gear with two cogging-free operation modes

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 driven magnet. For other angles the experiments reveal a more complex dynamical behavior, which is divided in three different classes. This is done by analysing the deviation from a periodic motion of the driven magnet, and by measuring the total harmonic distortion of this rotation. The experimental results can be understood by a mathematical model based on pure dipole-dipole interaction, with the addition of adequate friction terms.

physics.app-ph↗

arXiv2020

Graphical Magnetogranulometry of EMG909

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 arithmetic and the harmonic mean of the magnetic moment distribution function, and a guess for the geometric mean and the relative standard deviation. It has the advantage that it does not require a prejudiced guess of the distribution function of the poly-disperse suspension of magnetic particles.

cond-mat.soft↗

arXiv2019

Measuring magnetic moments of polydisperse ferrofluids utilizing 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 mathematical model: It does not rely on assuming a particular distribution function of the particles.

cond-mat.soft↗

arXiv2018

Dotriacontapoles -- almost self-assembled

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 cuboidal cluster. A method to build such dotriacontapoles is provided.

cond-mat.soft↗

arXiv2018

Self-assembly of magnetic iron oxide nanoparticles into cuboidal superstructures

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.

cond-mat.soft↗

arXiv2018

Exploring cogging free magnetic gears

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 these couplings is based on fundamental dipole-dipole interactions with analytically accessible solutions. Technical applications of this kind of coupling are foreseeable particularly for small machines, an advantage which also comes handy for classroom demonstrations of this feature of the fundamental concept of dipole-dipole coupling.

cond-mat.soft↗

arXiv2016

Retarding the growth of the {Rosensweig} instability unveils a new scaling regime

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 can not be resolved experimentally there. We measure the growth of the pattern by means of a two-dimensional imaging technique, and find that the slopes of the growth and decay rates are not the same - a qualitative discrepancy to the theoretical predictions. We solve this discrepancy by taking into account a viscosity which is assumed to be different for the growth and decay. This may be a consequence of the measured shear thinning of the ferrofluid.

nlin.PS↗

arXiv2015

Homoclinic snaking near the surface instability of a polarizable fluid

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 to co-exist in intervals of the applied magnetic field strength parameter around this branch. We formulate a general energy functional for the system and a corresponding Hamiltonian that provides a pattern selection principle allowing us to compute Maxwell points (where the energy of a single hexagon cell lies in the same Hamiltonian level set as the flat state) for general magnetic permeabilities. Using numerical continuation techniques we investigate the existence of localized hexagons in the Young-Laplace equation coupled to the Maxwell equations. We find cellular hexagons possess a Maxwell point providing an energetic explanation for the multitude of measured hexagon patches. Furthermore, it is found that planar hexagon fronts and hexagon patches undergo homoclinic snaking corroborating the experimentally detected intervals. Besides making a contribution to the specific area of ferrofluids, our work paves the ground for a deeper understanding of homoclinic snaking of 2D localized patches of cellular patterns in many physical systems.

nlin.PS↗

arXiv2015

Pattern formation in wet granular matter under vertical vibrations

Experiments on a thin layer of cohesive wet granular matter under vertical vibrations 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 vibrations. Depending on the periodicity of this collective motion, the kink fronts may propagate, couple with each other and form rotating spiral patterns in the case of period tripling, or stay as standing wave patterns in the case of period doubling. Moreover, both patterns may coexist with granular `gas bubbles' - phase separation into a liquidlike and a gaslike state. Stability diagrams for the instabilities measured with various granular layer mass $m$ and container height $H$ are presented. The onsets for both types of patterns and their dependency on $m$ and $H$ can be quantitatively captured with a model considering the granular layer as a single particle colliding completely inelastically with the container.

cond-mat.soft↗

arXiv2015

Ordering in granular rod monolayers driven far from thermodynamic equilibrium

The orientational order in vertically agitated granular rod monolayers is investigated experimentally and compared quantitatively with equilibrium Monte Carlo simulations and density functional theory. At sufficiently high number 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 from tetratic to uniaxial is around $7.3$ in both experiments and simulations. This agreement illustrates the universal aspects of the ordering of rod-shaped particles across equilibrium and nonequilibrium systems. Moreover, the assembly of granular rods into ordered states is found to be independent of the agitation frequency and strength, suggesting that the detailed nature of energy injection into such a nonequilibrium system does not play a crucial role.

cond-mat.soft↗

arXiv2014

Infinite Geometric Frustration in a Cubic Dipole Cluster

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 find a new type of ground state consisting of infinitely many orientations. This continuum of energetically degenerate states represents a yet unknown form of magnetic frustration. The corresponding dipole rotations in the flat potential valley of this Goldstone mode enable the construction of frictionless magnetic couplings. Using novel computer-assisted algebraic geometry methods, we moreover completely enumerate all equilibrium configurations. The seemingly simple cubic system allows for exactly 9536 unstable discrete equilibria falling into 183 distinct energy families.

cond-mat.soft↗

arXiv2013

Analogue of surface melting in a macroscopic non-equilibrium system

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, preceded by an amorphous state. The transition into the surface melting state, as revealed by the bond orientational order parameters, behaves like a first order phase transition, with a threshold being traceable to the rupture energy of a single capillary bridge. The observation of such a transition in the macroscopic nonequilibrium system triggers the question of the universality of surface melting.

cond-mat.soft↗

arXiv2013

Dynamics of rotating spirals in agitated wet granular matter

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 correspond to the kinks between regions with different colliding phases with the vibrating plate, have been found to be the dominating pattern. From both top view snapshots and laser profilometry methods, the rotation frequency of the spiral arms is characterized with image processing procedures. Both methods reveal that there exists a finite rotation frequency $ν_{\rm r}$ at a threshold vibration acceleration, above which $ν_{\rm r}$ increases linearly with the peak vibration acceleration with a slope strongly dependent on the vibration frequency.

cond-mat.soft↗

arXiv2013

Scaling of the normal coefficient of restitution for wet impacts

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 and impact velocities of a binary impact, is frequently used to characterize the amount of energy dissipation associated. We measure the COR by tracing a freely falling sphere bouncing on a wet surface with the liquid film thickness monitored optically. For fixed ratio between the film thickness and the particle size, the dependence of the COR on the impact velocity and various properties of the liquid film can be characterized with the Stokes number, defined as the ratio between the inertia of the particle and the viscosity of the liquid. Moreover, the COR for infinitely large impact velocities derived from the scaling can be analyzed by a model considering the energy dissipation from the inertia of the liquid film.

cond-mat.soft↗