scholarly journals Homoclinic snaking near the surface instability of a polarisable fluid

2015 ◽  
Vol 783 ◽  
pp. 283-305 ◽  
Author(s):  
David J. B. Lloyd ◽  
Christian Gollwitzer ◽  
Ingo Rehberg ◽  
Reinhard Richter
Keyword(s):  
Magnetic Field ◽  
Specific Area ◽  
Energy Functional ◽  
Numerical Continuation ◽  
Strength Parameter ◽  
Physical Systems ◽  
Rosensweig Instability ◽  
Homoclinic Snaking ◽  
Maxwell Points ◽  
Unstable Branch

We report on localised 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 neighbourhood of the unstable branch of the domain-covering hexagons of the Rosensweig instability upon which the patches equilibrate and stabilise. They are found to coexist 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 provide 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 localised hexagons in the Young–Laplace equation coupled to the Maxwell equations. We find that 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 two-dimensional localised patches of cellular patterns in many physical systems.

The energy and helicity of knotted magnetic flux tubes

1995 ◽  
Vol 451 (1943) ◽  
pp. 609-629 ◽  
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Minimum Energy ◽  
Circular Cross Section ◽  
Parametric Representation ◽  
Energy Functional ◽  
Helical Axis ◽  
Torus Knots ◽  
Flux Tubes ◽  
Kink Mode

Magnetic relaxation of a magnetic field embedded in a perfectly conducting incompressible fluid to minimum energy magnetostatic equilibrium states is considered. It is supposed that the magnetic field is confined to a single flux tube which may be knotted. A local non-orthogonal coordinate system, zero-framed with respect to the knot, is introduced, and the field is decomposed into toroidal and poloidal ingredients with respect to this system. The helicity of the field is then determined; this vanishes for a field that is either purely toroidal or purely poloidal. The magnetic energy functional is calculated under the simplifying assumptions that the tube is axially uniform and of circular cross-section. The case of a tube with helical axis is first considered, and new results concerning kink mode instability and associated bifurcations are obtained. The case of flux tubes in the form of torus knots is then considered and the ‘ground-state’ energy function ͞m ( h ) (where h is an internal twist parameter) is obtained; as expected, ͞m ( h ), which is a topological invariant of the knot, increases with increasing knot complexity. The function ͞m ( h ) provides an upper bound on the corresponding function m ( h ) that applies when the above constraints on tube structure are removed. The technique is applicable to any knot admitting a parametric representation, on condition that points of vanishing curvature are excluded.

Magnetized liquid 3He at finite temperature: A variational calculation approach

2016 ◽  
Vol 30 (22) ◽  
pp. 1650129 ◽  
Author(s):  
Gholam Hossein Bordbar ◽  
Mohammad Taghi Mohammadi Sabet
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Correlation Function ◽  
Finite Temperature ◽  
Spin Correlation ◽  
Energy Functional ◽  
Variational Calculation ◽  
A Value ◽  
Dependent Correlation ◽  
Good Agreement

Using the spin-dependent (SD) and spin-independent (SI) correlation functions, we have investigated the properties of liquid [Formula: see text] in the presence of magnetic field at finite temperature. Our calculations have been done using the variational method based on cluster expansion of the energy functional. Our results show that the low field magnetic susceptibility obeys Curie law at high temperatures. This behavior is in a good agreement with the experimental data as well as the molecular field theory results in which the spin dependency has been introduced in correlation function. Reduced susceptibility as a function of temperature as well as reduced temperature has been also investigated, and again we have seen that the spin-dependent correlation function leads to a good agreement with the experimental data. The Landau parameter, [Formula: see text], has been calculated, and for this parameter, a value about [Formula: see text] has been found in the case of spin–spin correlation. In the case of spin-independent correlation function, this value is about [Formula: see text]. Therefore, inclusion of spin dependency in the correlation function leads to a more compatible value of [Formula: see text] with experimental data. The magnetization and susceptibility of liquid [Formula: see text] have also been investigated as a function of magnetic field. Our results show a downward curvature in magnetization of system with spin-dependent correlation for all densities and relevant temperatures. A metamagnetic behavior has been observed as a maximum in susceptibility versus magnetic field, when the spin–spin correlation has been considered. This maximum occurs at [Formula: see text] for all densities and temperatures. This behavior has not been observed in the case of spin-independent correlation function.

scholarly journals Electromagnetic Compatibility Analysis of Substation Environment using Finite Difference Method

2019 ◽  
Vol 8 (12S2) ◽  
pp. 521-527
Keyword(s):  
Magnetic Field ◽  
Finite Difference ◽  
Electromagnetic Compatibility ◽  
Specific Area ◽  
Grid System ◽  
Compatibility Analysis ◽  
Area Of Interest ◽  
Microelectronic Devices ◽  
Smart Grid System ◽  
The Magnetic Field

The implementation of the smart grid system transformed the old substation into a new automated substation. All equipment and component installed in the high voltage substation need to be electromagnetically compatible with each other. Thus, the magnetic field distributed in the environment must be predicted and quantified. Furthermore, with the use of more sensitive microelectronic devices in the system, it creates a need to reassess the substation environment compatibility for current and future circumstances. In this paper, the calculation method used to determine magnetic field distribution within a substation environment has been reviewed. A new routine which allows the user to focus at a specific area of the substation and calculate the field has been developed in-house using MATLAB. The new routine calculates the magnetic field using a finite difference approach and allows a much better field resolution to be achieved in a specific area of interest within the substation.

scholarly journals Magnetic motion of spherical frictional charged particles on the unit sphere

2019 ◽  
Vol 65 (5 Sept-Oct) ◽  
pp. 496 ◽  
Author(s):  
Talat Körpınar ◽  
Ridvan Cem Demirkol
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Potential Energy ◽  
Frictional Force ◽  
Poynting Vector ◽  
Positive Curvature ◽  
Charged Particles ◽  
Energy Functional ◽  
Ordinary Space ◽  
Potential Energy Functional

Mathematically, the sphere unit S² is described to be a 2-sphere in an ordinary space with a positive curvature. In this study, we aim to present the manipulation of a spherical charged particle in a continuous motion with a magnetic field on the sphere S² while it is exposed to a frictional force. In other words, we effot to derive the exact geometric characterization for the spherical charged particle under the influence of a frictional force field on the unit 2-sphere. This approach also helps to discover some physical and kinematical characterizations belonging to the particle such as the magnetic motion, the torque, the potential energy functional, and the Poynting vector.

Energy-Based Models for Free-Form Surface Shape Design

1989 ◽  
Author(s):  
G. Celniker ◽  
D. Gossard
Keyword(s):  
Equations Of Motion ◽  
Energy Functional ◽  
Surface Shape ◽  
Free Form ◽  
Small Scale ◽  
Shape Design ◽  
Local Shape ◽  
Physical Systems ◽  
Time Simulation ◽  
Parametric Description

Abstract A parametric description of an elastic surface is used as the basis for a free-form shape design package. The energy functional of shape deformation are used to develop the equations of motion for the surface. The user, interacting with the model during a time simulation of its motion, is capable of guiding the surface into desirable configurations. The dynamic nature of these models cause them to seek shapes with desirable properties which can free the user from having to control every aspect of the surface while achieving design goals. The strong analogy between these models and physical systems allows the user to control the shape in intuitive fashions. This approach gives the user considerable control of the global aspects of the shape while retaining control of small scale local shape.

Dynamic Interfacial Phenomena at Water-Magnetic Fluid System Subject to Alternating Magnetic Field

2016 ◽  
Vol 856 ◽  
pp. 15-20
Author(s):  
Masato Nakanishi ◽  
Seiichi Sudo ◽  
Hideya Nishiyama
Keyword(s):  
Magnetic Field ◽  
Permanent Magnet ◽  
Magnetic Fluid ◽  
High Speed ◽  
Video Camera ◽  
Alternating Magnetic Field ◽  
Fluid System ◽  
Camera System ◽  
High Speed Video Camera ◽  
Rosensweig Instability

Responses of a magnetic fluid interface adsorbed on a small permanent magnet in water container subjected to an alternating magnetic field were studied with a high-speed video camera system. The directions of the external alternating magnetic field were parallel and anti-parallel to that of the permanent magnet. It was found that the interface of water-magnetic fluid responds to the external alternating magnetic field in elongation and contraction with Rosensweig instability at the interface. Frequency characteristics of the interface response of water-magnetic fluid system subjected to alternating magnetic field were revealed over a wide frequency band experimentally.

The 2-3-4 spike competition in the Rosensweig instability

2019 ◽  
Vol 870 ◽  
pp. 389-404 ◽  
Author(s):  
A. N. Spyropoulos ◽  
A. G. Papathanasiou ◽  
A. G. Boudouvis
Keyword(s):  
Magnetic Field ◽  
Eigenvalue Problems ◽  
Surface Deformation ◽  
Large Diameter ◽  
Three Dimensional ◽  
Small Diameter ◽  
Rosensweig Instability ◽  
The Stability ◽  
Selection Mechanisms ◽  
Parameter Continuation

The horizontal free surface of a magnetic liquid (ferrofluid) pool turns unstable when the strength of a vertically applied uniform magnetic field exceeds a threshold. The instability, known as normal field instability or Rosensweig’s instability, is accompanied by the formation of liquid spikes either few, in small diameter pools, or many, in large diameter pools; in the latter case, the spikes are arranged in hexagonal or square patterns. In small pools where only few spikes – 2, 3 or 4 in this work – can be accommodated, their appearance/disappearance/re-appearance observed in experiments, as applied field strength varies, is investigated by computer-aided bifurcation and linear stability analysis. The equations of three-dimensional capillary magneto-hydrostatics give rise to a three-dimensional free boundary problem which is discretized by the Galerkin/finite element method and solved for multi-spike surface deformation coupled with magnetic field distribution simultaneously with a compact numerical scheme based on Newton iteration. Standard eigenvalue problems are solved in the course of parameter continuation to reveal the multiplicity and the stability of the emerging deformations. The computational predictions reveal selection mechanisms among equilibrium states and explain the corresponding experimental observations and measurements.

scholarly journals THE ADJOINT PROBLEM IN THE PRESENCE OF A DEFORMED SURFACE: THE EXAMPLE OF THE ROSENSWEIG INSTABILITY ON MAGNETIC FLUIDS

2002 ◽  
Vol 16 (08) ◽  
pp. 1155-1170 ◽  
Author(s):  
ADRIAN LANGE
Keyword(s):  
Magnetic Field ◽  
A Priori ◽  
Adjoint Operator ◽  
Horizontal Layer ◽  
Adjoint Problem ◽  
Vertical Magnetic Field ◽  
Amplitude Equations ◽  
Rosensweig Instability ◽  
Pattern Forming ◽  
Almost All

The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.

Synthesis of Hybrid Fe3O4–Silica–M(Zn, Cu, Ni) Submicrospheres and its Application for Adsorption on Bovine Hemoglobin

2015 ◽  
Vol 1120-1121 ◽  
pp. 903-908
Author(s):  
Yue Tong ◽  
Min Zhang ◽  
Ya Ru Nie ◽  
Jun Jun Linghu ◽  
Jun Qing Yu ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Sol Gel ◽  
Specific Area ◽  
Metal Chloride ◽  
Core Shell ◽  
Bovine Hemoglobin ◽  
Magnetic Response ◽  
Ferrous Chloride ◽  
Magnetic Metal ◽  
Core Shell Structure

Magnetic metal silica submicrospheres were produced from silica coated on magnetic nanoparticles using well controlled hydrothermalled method and were characterized by TEM, XRD, FTIR, XPS. The well-designed mesoporous magnetic metal silciate had a large specific area, high magnetization. Firstly, SiO2-coated maghemite (Fe3O4@SiO2 composites) were synthesized by an sol-gel method, in which the iron ferrous chloride as well as TEOS acted as the precursor for maghemite and SiO2, respectively. The Fe3O4@SiO2 composites revealed a core-shell structure, Then, Fe3O4@SiO2/X3Si2O5(OH)4(X = Ni, Cu, Zn) was obtained by hydrothermalled with metal chloride. The resulting composites show not only a magnetic response to an externally applied magnetic field, but also can be a good adsorbent for bovine hemoglobin in the ambient temperature.

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