73,440 research outputs found
An Intrinsic Approach to Forces in Magnetoelectric Media
This paper offers a conceptually straightforward method for the calculation
of stresses in polarisable media based on the notion of a drive form and its
property of being closed in spacetimes with symmetry. After an outline of the
notation required to exploit the powerful exterior calculus of differential
forms, a discussion of the relation between Killing isometries and conservation
laws for smooth and distributional drive forms is given. Instantaneous forces
on isolated spacetime domains and regions with interfaces are defined, based on
manifestly covariant equations of motion. The remaining sections apply these
notions to media that sustain electromagnetic stresses, with emphasis on
homogeneous magnetoelectric material. An explicit calculation of the average
pressure exerted by a monochromatic wave normally incident on a homogeneous,
magnetoelectric slab in vacuo is presented and the concluding section
summarizes how this pressure depends on the parameters in the magnetoelectric
tensors for the medium.Comment: 25 pages, 3 figures, to appear in Il Nuovo Cimento B, proceedings of
GCM8, Catania (Oct 2008) - References added, minor corrections mad
Nonlinear force-free modeling of the solar coronal magnetic field
The coronal magnetic field is an important quantity because the magnetic
field dominates the structure of the solar corona. Unfortunately direct
measurements of coronal magnetic fields are usually not available. The
photospheric magnetic field is measured routinely with vector magnetographs.
These photospheric measurements are extrapolated into the solar corona. The
extrapolated coronal magnetic field depends on assumptions regarding the
coronal plasma, e.g. force-freeness. Force-free means that all non-magnetic
forces like pressure gradients and gravity are neglected. This approach is well
justified in the solar corona due to the low plasma beta. One has to take care,
however, about ambiguities, noise and non-magnetic forces in the photosphere,
where the magnetic field vector is measured. Here we review different numerical
methods for a nonlinear force-free coronal magnetic field extrapolation:
Grad-Rubin codes, upward integration method, MHD-relaxation, optimization and
the boundary element approach. We briefly discuss the main features of the
different methods and concentrate mainly on recently developed new codes.Comment: 33 pages, 3 figures, Review articl
A Solution Set-Based Entropy Principle for Constitutive Modeling in Mechanics
Entropy principles based on thermodynamic consistency requirements are widely
used for constitutive modeling in continuum mechanics, providing physical
constraints on a priori unknown constitutive functions. The well-known
M\"uller-Liu procedure is based on Liu's lemma for linear systems. While the
M\"uller-Liu algorithm works well for basic models with simple constitutive
dependencies, it cannot take into account nonlinear relationships that exist
between higher derivatives of the fields in the cases of more complex
constitutive dependencies.
The current contribution presents a general solution set-based procedure,
which, for a model system of differential equations, respects the geometry of
the solution manifold, and yields a set of constraint equations on the unknown
constitutive functions, which are necessary and sufficient conditions for the
entropy production to stay nonnegative for any solution. Similarly to the
M\"uller-Liu procedure, the solution set approach is algorithmic, its output
being a set of constraint equations and a residual entropy inequality. The
solution set method is applicable to virtually any physical model, allows for
arbitrary initially postulated forms of the constitutive dependencies, and does
not use artificial constructs like Lagrange multipliers. A Maple implementation
makes the solution set method computationally straightforward and useful for
the constitutive modeling of complex systems.
Several computational examples are considered, in particular, models of gas,
anisotropic fluid, and granular flow dynamics. The resulting constitutive
function forms are analyzed, and comparisons are provided. It is shown how the
solution set entropy principle can yield classification problems, leading to
several complementary sets of admissible constitutive functions; such problems
have not previously appeared in the constitutive modeling literature
Dust-driven Dynamos in Accretion Disks
Magnetically driven astrophysical jets are related to accretion and involve
toroidal magnetic field pressure inflating poloidal magnetic field flux
surfaces. Examination of particle motion in combined gravitational and magnetic
fields shows that these astrophysical jet toroidal and poloidal magnetic fields
can be powered by the gravitational energy liberated by accreting dust grains
that have become positively charged by emitting photo-electrons. Because a dust
grain experiences magnetic forces after becoming charged, but not before,
charging can cause irreversible trapping of the grain so dust accretion is a
consequence of charging. Furthermore, charging causes canonical angular
momentum to replace mechanical angular momentum as the relevant constant of the
motion. The resulting effective potential has three distinct classes of
accreting particles distinguished by canonical angular momentum, namely (i)
"cyclotron-orbit", (ii) "Speiser-orbit", and (iii) "zero canonical angular
momentum" particles. Electrons and ions are of class (i) but depending on mass
and initial orbit inclination, dust grains can be of any class. Light-weight
dust grains develop class (i) orbits such that the grains are confined to
nested poloidal flux surfaces, whereas grains with a critical weight such that
they experience comparable gravitational and magnetic forces can develop class
(ii) or class (iii) orbits, respectively producing poloidal and toroidal field
dynamos.Comment: 70 pages, 16 figure
Modeling Magnetic Field Structure of a Solar Active Region Corona using Nonlinear Force-Free Fields in Spherical Geometry
We test a nonlinear force-free field (NLFFF) optimization code in spherical
geometry using an analytical solution from Low and Lou. Several tests are run,
ranging from idealized cases where exact vector field data are provided on all
boundaries, to cases where noisy vector data are provided on only the lower
boundary (approximating the solar problem). Analytical tests also show that the
NLFFF code in the spherical geometry performs better than that in the Cartesian
one when the field of view of the bottom boundary is large, say, . Additionally, We apply the NLFFF model to an active region
observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar
Dynamics Observatory (SDO) both before and after an M8.7 flare. For each
observation time, we initialize the models using potential field source surface
(PFSS) extrapolations based on either a synoptic chart or a flux-dispersal
model, and compare the resulting NLFFF models. The results show that NLFFF
extrapolations using the flux-dispersal model as the boundary condition have
slightly lower, therefore better, force-free and divergence-free metrics, and
contain larger free magnetic energy. By comparing the extrapolated magnetic
field lines with the extreme ultraviolet (EUV) observations by the Atmospheric
Imaging Assembly (AIA) on board SDO, we find that the NLFFF performs better
than the PFSS not only for the core field of the flare productive region, but
also for large EUV loops higher than 50 Mm.Comment: 34 pages, 8 figures, accepted for publication in Ap
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