245 research outputs found
Frame Indifferent Formulation of Maxwell's Elastic Fluid and the Rational Continuum Mechanics of the Electromagnetic Field
We show that the linearized equations of the incompressible elastic medium
admit a `Maxwell form' in which the shear component of the stress vector plays
the role of the electric field, and the vorticity plays the role of the
magnetic field. Conversely, the set of dynamic Maxwell equations are strict
mathematical corollaries from the governing equations of the incompressible
elastic medium. This suggests that the nature of `electromagnetic field' may
actually be related to an elastic continuous medium. The analogy is complete if
the medium is assumed to behave as fluid in shear motions, while it may still
behave as elastic solid under compressional motions. Then the governing
equations of the elastic fluid are re-derived in the Eulerian frame by
replacing the partial time derivatives by the properly invariant (frame
indifferent) time rates. The `Maxwell from' of the frame indifferent
formulation gives the frame indifferent system that is to replace the Maxwell
system. This new system comprises terms already present in the classical
Maxwell equations, alongside terms that are the progenitors of the
Biot--Savart, Oersted--Ampere's, and Lorentz--force laws. Thus a frame
indifferent (truly covariant) formulation of electromagnetism is achieved from
a single postulate that the electromagnetic field is a kind of elastic (partly
liquid partly solid) continuum.Comment: accepte
Helicity-Rotation-Gravity Coupling for Gravitational Waves
The consequences of spin-rotation-gravity coupling are worked out for linear
gravitational waves. The coupling of helicity of the wave with the rotation of
a gravitational-wave antenna is investigated and the resulting modifications in
the Doppler effect and aberration are pointed out for incident high-frequency
gravitational radiation. Extending these results to the case of a
gravitomagnetic field via the gravitational Larmor theorem, the rotation of
linear polarization of gravitational radiation propagating in the field of a
rotating mass is studied. It is shown that in this case the linear polarization
state rotates by twice the Skrotskii angle as a consequence of the spin-2
character of linear gravitational waves.Comment: 11 pages, no figures, accepted for publication in Phys. Rev. D; v2: a
few minor typos correcte
Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group
We consider non-relativistic electrons, each of the same charge to mass
ratio, moving in an external magnetic field with an interaction potential
depending only on the mutual separations, possibly confined by a harmonic
trapping potential. We show that the system admits a "relativity group" which
is a one-parameter family of deformations of the standard Galilei group to the
Newton-Hooke group which is a Wigner-Inonu contraction of the de Sitter group.
This allows a group-theoretic interpretation of Kohn's theorem and related
results. Larmor's Theorem is used to show that the one-parameter family of
deformations are all isomorphic. We study the "Eisenhart" or "lightlike" lift
of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart
lift is the Brdicka-Eardley-Nappi-Witten pp-wave solution of Einstein-Maxwell
theory, which may also be regarded as a bi-invariant metric on the
Cangemi-Jackiw group.Comment: Typos corrected, references adde
Diffraction of light by a planar aperture in a metallic screen
We present a complete derivation of the formula of Smythe [Phys.Rev.72, 1066
(1947)] giving the electromagnetic field diffracted by an aperture created in a
perfectly conducting plane surface. The reasoning, valid for any excitating
field and any hole shape, makes use only of the free scalar Green function for
the Helmoltz equation without any reference to a Green dyadic formalism. We
compare our proof with the one previously given by Jackson and connect our
reasoning to the general Huygens Fresnel theorem.Comment: J. Math. Phys. 47, 072901 (2006
Variational data assimilation for the initial-value dynamo problem
The secular variation of the geomagnetic field as observed at the Earth's surface results from the complex magnetohydrodynamics taking place in the fluid core of the Earth. One way to analyze this system is to use the data in concert with an underlying dynamical model of the system through the technique of variational data assimilation, in much the same way as is employed in meteorology and oceanography. The aim is to discover an optimal initial condition that leads to a trajectory of the system in agreement with observations. Taking the Earth's core to be an electrically conducting fluid sphere in which convection takes place, we develop the continuous adjoint forms of the magnetohydrodynamic equations that govern the dynamical system together with the corresponding numerical algorithms appropriate for a fully spectral method. These adjoint equations enable a computationally fast iterative improvement of the initial condition that determines the system evolution. The initial condition depends on the three dimensional form of quantities such as the magnetic field in the entire sphere. For the magnetic field, conservation of the divergence-free condition for the adjoint magnetic field requires the introduction of an adjoint pressure term satisfying a zero boundary condition. We thus find that solving the forward and adjoint dynamo system requires different numerical algorithms. In this paper, an efficient algorithm for numerically solving this problem is developed and tested for two illustrative problems in a whole sphere: one is a kinematic problem with prescribed velocity field, and the second is associated with the Hall-effect dynamo, exhibiting considerable nonlinearity. The algorithm exhibits reliable numerical accuracy and stability. Using both the analytical and the numerical techniques of this paper, the adjoint dynamo system can be solved directly with the same order of computational complexity as that required to solve the forward problem. These numerical techniques form a foundation for ultimate application to observations of the geomagnetic field over the time scale of centuries
Large-scale magnetic topologies of late M dwarfs
We present here the final results of the first spectropolarimetric survey of
a small sample of active M dwarfs, aimed at providing observational constraints
on dynamo action on both sides of the full-convection threshold (spectral type
M4). Our two previous studies (Donati et al. 2008b; Morin et al. 2008b) were
focused on early and mid M dwarfs. The present paper examines 11 fully
convective late M dwarfs (spectral types M5-M8). Tomographic imaging techniques
were applied to time-series of circularly polarised profiles of 6 stars, in
order to infer their large-scale magnetic topologies. For 3 other stars we
could not produce such magnetic maps, because of low variability of the Stokes
V signatures, but were able to derive some properties of the magnetic fields.
We find 2 distinct categories of magnetic topologies: on the one hand strong
axisymmetric dipolar fields (similar to mid M dwarfs), and on the other hand
weak fields generally featuring a significant non-axisymmetric component, and
sometimes a significant toroidal one. Comparison with unsigned magnetic fluxes
demonstrates that the second category of magnetic fields shows less
organization (less energy in the large scales), similarly to partly convective
early M dwarfs. Stars in both categories have similar stellar parameters, our
data do not evidence a separation between these 2 categories in the
mass-rotation plane. We also report marginal detection of a large-scale
magnetic field on the M8 star VB 10 featuring a significant toroidal
axisymmetric component, whereas no field is detectable on VB 8 (M7).Comment: 26 pages, 16 figures, 9 tables, 11 tables in appendix. Accepted for
publication in MNRA
Turbulent transport in hydromagnetic flows
The predictive power of mean-field theory is emphasized by comparing theory
with simulations under controlled conditions. The recently developed test-field
method is used to extract turbulent transport coefficients both in kinematic as
well as nonlinear and quasi-kinematic cases. A striking example of the
quasi-kinematic method is provided by magnetic buoyancy-driven flows that
produce an alpha effect and turbulent diffusion.Comment: 17 pages, 6 figures, topical issue of Physica Scripta on turbulent
mixing and beyon
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