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Nikola Popović Dirk Praetorius Anja Schlömerkemper 《Continuum Mechanics and Thermodynamics》2007,19(1-2):67-80
The mathematical and physical analysis of magnetoelastic phenomena is a topic of ongoing research. Different formulae have
been proposed to describe the magnetic forces in macroscopic systems. We discuss several of these formulae in the context
of rigid magnetized bodies. In case the bodies are in contact, we consider formulae both in the framework of macroscopic electrodynamics
and via a multiscale approach, i.e., in a discrete setting of magnetic dipole moments. We give mathematically rigorous proofs
for domains of polygonal shape (as well as for more general geometries) in two and three space dimensions. In an accompanying
second article, we investigate the formulae in a number of numerical experiments, where we focus on the dependence of the
magnetic force on the distance between the bodies and on the case when the two bodies are in contact. The aim of the analysis
as well as of the numerical simulation is to contribute to the ongoing debate about which formula describes the magnetic force
between macroscopic bodies best and to stimulate corresponding real-life experiments.
相似文献
2.
M. Genkin E. Lindroth 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2009,51(2):205-212
Solar magnetic structures are often observed in the form of flux tubes composed of a number of smaller elements called fibres
or threads, although theoretically such concentrations should not appear but should be flattened by magnetic diffusivity into
a uniform, low intensity field. In this paper we describe a mechanism which may be responsible for the fibrillation and also
for the very large diffusivity which dissipates magnetic flux tubes in hours instead of years. Firstly, the electric current
associated with magnetic field gradients usually increases the local electron temperature and reduces the resistivity, so
that the current becomes concentrated into sheets or streamers. Secondly, the magnetic field gradients continue to increase
until the current magnitude reaches its limit, which is determined by the electron-ion streaming instability. Then with appropriate
temperature and number densities, the Larmor radius of the ions overlaps the near discontinuity in Bz and generates a sharply peaked fluid motion at the edge that is close to the thermal speed. Finally, the resulting vorticity
generates an axial magnetic field opposing Bz in the term , and if this is sufficient to change the sign of this term, the very unstable backward heat equation results. This instability
repeatedly switches on and off and maintains the magnetic structure in the fibrillated form. Such structures are eventually
eliminated by magnetic diffusivity in the usual way, but because of the fluctuations in Bz, this occurs at a vastly increased rate. We show that this phenomenon increases the magnetic diffusivity, D, by a factor
~ 108 in agreement with some observations of plasma loops and supergranules. 相似文献
3.
In this paper a detailed mathematical model for an electromagnetic energy harvesting architecture based on a semi-analytical approach is introduced. This model estimates the generated energy of the architecture by computing the static and dynamic magnetic and electric fields that describe its dynamics. A comparison of the static fields with the results of a Finite Element Analysis simulation in COMSOL Multiphysics shows good agreement. The model also features increased accuracy and numerical stability. In the model the semi-analytical solutions for the electromagnetic damping force exerted by the induced current coil and the induced electromotive force on the coil provide additional insight into the interactions of electromagnetic induction and damping. Additionally, the energy estimation could be used as a figure of merit in an maximization process to identify the optimal dimensions of the energy harvester. 相似文献
4.
Nikola Popović Dirk Praetorius Anja Schlömerkemper 《Continuum Mechanics and Thermodynamics》2007,19(1-2):81-109
The analysis of magnetoelastic phenomena is a field of active research. Formulae for the magnetic force in macroscopic systems
have been under discussion for some time. In Popović et al. (Continum. Mech. Thermodyn. 2007), we rigorously justify several
of the available formulae in the context of rigid bodies in two and three space dimensions. In the present, second part of
our study, we investigate these formulae in a series of numerical experiments in which the magnetic force is computed in dependence
on the geometries of the bodies as well as on the distance between them. In case the two bodies are in contact, i.e., in the
limit as their distance tends to zero, we focus especially on a formula obtained in a discrete-to-continuum approximation.
The aim of our study is to help clarify the question which force formula is the correct one in the sense that it describes
nature most accurately and to suggest adequate real-life experiments for a comparison with the provided numerical data.
相似文献
5.
F. Delfino R. Procopio M. Rossi 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(1):31-38
The evaluation of the total force of magnetic origin acting upon a body in a stationary magnetic field is often carried out
using the so-called magnetic energy (or co-energy) method, which is based on the derivation of the magnetic energy (or co-energy) with respect to a virtual rigid displacement
of the considered body. The application of this method is usually justified by resorting to the energy conservation principle,
written in terms both of electrical and of mechanical quantities. In this paper we shall re-examine the whole matter in the
context of classical thermodynamics, in order to obtain a more comprehensive and general proof of the validity of the energy
(or co-energy) approach and to point out its limitations. Two typical configurations will be discussed; in the first one,
the field sources are represented by conducting bodies carrying free currents, whereas in the second one a permanent magnet
creates the driving field. All magnetic materials are assumed to be non-hysteretic and permanent magnets are represented by
means of the well-known linear model in the second quadrant of the (B,H) plane.
Received 25 July 2001 and Received in final form 5 November 2001 相似文献
6.
Séraphin M.Mefire 《计算数学(英文版)》2005,23(2):131-152
A numerical method combining the approaches of C.I. Goldstein and L.-A. Ying is used for the simulation in three-dimensional magnetostatics related to an exterior problem in magnetic induction. Recently introduced, this method is based on the use of a graded mesh obtained by gluing homothetic layers in the exterior domain and has been performed in the case of edge element discretizations. In this work, the theoretical and practical aspects of the method are inspected in the case of face element and volume element discretizations,for computing a magnetic induction. Error estimates, implementations, and numerical results are provided. 相似文献
7.
Yu.L. Sokolov V.P. Yakovlev V.G. Pal'chikov Yu.A. Pchelin 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,18(1):27-36
The properties of two-dimensional magnetic traps for laser-cooled atoms are analysed using complex functions. The two components
of the magnetic field from a series of parallel, infinitely long, current-carrying wires are represented by a single complex
number. The regions of the field where paramagnetic atoms can be trapped occur where the magnetic field is zero. The locations
of the zeroes of the field are obtained as the solution to a polynomial and the multiplicity m of the solution determines both the 2(m + 1)-pole nature of the trap and the field gradient through the centre. The zeroes of the field can be merged or split by
varying the locations of the currents, their strengths or by applying a uniform magnetic field. The theory is applied to magnetic
traps created from long thin wires or permanent magnets on a substrate. The properties of a number of magnetic trap configurations
used for atom guides are discussed.
Received 28 February 2001 and Received in final form 6 July 2001 相似文献
8.
A. Peñaranda C.E. Auguet L. Ramırez-Piscina 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,25(2):155-165
The simulation of the transition sequence of superheated Type I superconducting granules (SSG) in disordered suspensions when
an external magnetic field is slowly increased from zero has been studied. Simulation takes into account diamagnetic interactions
and the presence of surface defects. Results have been obtained for the transition sequence and surface fields distribution
covering a wide range of densities. These results are compared with previous analytical perturbative theory, which provides
qualitative information on transitions and surface magnetic fields during transitions, but with a range of validity apparently
limited to extremely dilute samples. Simulations taking into account the complete diamagnetic interactions between spheres
appear to be a promising tool in interpreting SSG experiments, in applications such as particle detectors, and in some fundamental
calculations of Solid State Physics.
Received 6 April 2001 and Received in final form 15 October 2001 相似文献
9.
Qiong-Gui Lin 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,54(1):27-36
The interaction between a general magnetic source and a
long type-II superconducting cylinder in the Meissner or mixed state
is studied within the London theory. We first study the Meissner
state and solve the Maxwell–London equations when the source is a
magnetic monopole located at an arbitrary position. Then the field
and supercurrent for a more complicated magnetic charge distribution
can be obtained by superposition. A magnetic point dipole with
arbitrary direction is studied in detail. It turns out that the
levitation force on the dipole contains in general an angular as well
as a radial component. By integration we obtain the field and
supercurrent when the source is a two-dimensional monopole (a
magnetically charged long thread along the axial direction), from
which the results for a two-dimensional point dipole easily follow.
In the latter case the levitation force points in the radial
direction regardless of the orientation of the dipole. The case for a
current carrying long straight wire parallel to the cylindrical axis
is solved separately. The limit of ideal Meissner state is discussed
in most cases. The case of mixed state is discussed briefly. It turns
out that vortex lines along the axial direction and vortex rings
concentric with the cylinder have no effect outside the cylinder and
the levitation forces remain the same as in the case of the Meissner
state. 相似文献
10.
In the present work we consider a circular elastic disk (conductor) of variable thickness under the influence of a steady coaxial current and bearing a coaxial viscoelastic coating (insulator). In both conductor and insulator there exist a heat source generation. As a first step, the solution of purely elastic conductor and insulator is obtained. Then the problem of model with viscoelastic coating is solved using the correspondence principle and Ilyushin’s approximation method. A numerical example is given and the results are discussed in order to investigate the influences of time, temperature, and rotation on the stresses and displacements. 相似文献
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