1,012 research outputs found
Accuracy of magnetic energy computations
For magnetically driven events, the magnetic energy of the system is the
prime energy reservoir that fuels the dynamical evolution. In the solar
context, the free energy is one of the main indicators used in space weather
forecasts to predict the eruptivity of active regions. A trustworthy estimation
of the magnetic energy is therefore needed in three-dimensional models of the
solar atmosphere, eg in coronal fields reconstructions or numerical
simulations. The expression of the energy of a system as the sum of its
potential energy and its free energy (Thomson's theorem) is strictly valid when
the magnetic field is exactly solenoidal. For numerical realizations on a
discrete grid, this property may be only approximately fulfilled. We show that
the imperfect solenoidality induces terms in the energy that can lead to
misinterpreting the amount of free energy present in a magnetic configuration.
We consider a decomposition of the energy in solenoidal and nonsolenoidal parts
which allows the unambiguous estimation of the nonsolenoidal contribution to
the energy. We apply this decomposition to six typical cases broadly used in
solar physics. We quantify to what extent the Thomson theorem is not satisfied
when approximately solenoidal fields are used. The quantified errors on energy
vary from negligible to significant errors, depending on the extent of the
nonsolenoidal component. We identify the main source of errors and analyze the
implications of adding a variable amount of divergence to various solenoidal
fields. Finally, we present pathological unphysical situations where the
estimated free energy would appear to be negative, as found in some previous
works, and we identify the source of this error to be the presence of a finite
divergence. We provide a method of quantifying the effect of a finite
divergence in numerical fields, together with detailed diagnostics of its
sources
Competition between crystalline electric field singlet and itinerant states of f electrons
A new kind of phase transition is proposed for lattice fermion systems with
simplified f^2 configurations at each site. The free energy of the model is
computed in the mean-field approximation for both the itinerant state with the
Kondo screening, and a localized state with the crystalline electric field
(CEF) singlet at each site. The presence of a first-order phase transition is
demonstrated in which the itinerant state changes into the localized state
toward lower temperatures. In the half-filled case, the insulating state at
high temperatures changes into a metallic state, in marked contrast with the
Mott transition in the Hubbard model. For comparison, corresponding states are
discussed for the two-impurity Kondo system with f^1 configuration at each
site.Comment: 10 pages LaTeX , 2 eps figures Accepted for publication in Z.Phys.
Phase separation in asymmetrical fermion superfluids
Motivated by recent developments on cold atom traps and high density QCD we
consider fermionic systems composed of two particle species with different
densities. We argue that a mixed phase composed of normal and superfluid
components is the energetically favored ground state. We suggest how this phase
separation can be used as a probe of fermion superfluidity in atomic traps.Comment: 9 pages, LaTeX2e, version to appear in Phys.Rev.Let
The Influence of Spatial Resolution on Nonlinear Force-Free Modeling
The nonlinear force-free field (NLFFF) model is often used to describe the
solar coronal magnetic field, however a series of earlier studies revealed
difficulties in the numerical solution of the model in application to
photospheric boundary data. We investigate the sensitivity of the modeling to
the spatial resolution of the boundary data, by applying multiple codes that
numerically solve the NLFFF model to a sequence of vector magnetogram data at
different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active
Region 10978 on 2007 December 13. We analyze the resulting energies and
relative magnetic helicities, employ a Helmholtz decomposition to characterize
divergence errors, and quantify changes made by the codes to the vector
magnetogram boundary data in order to be compatible with the force-free model.
This study shows that NLFFF modeling results depend quantitatively on the
spatial resolution of the input boundary data, and that using more highly
resolved boundary data yields more self-consistent results. The free energies
of the resulting solutions generally trend higher with increasing resolution,
while relative magnetic helicity values vary significantly between resolutions
for all methods. All methods require changing the horizontal components, and
for some methods also the vertical components, of the vector magnetogram
boundary field in excess of nominal uncertainties in the data. The solutions
produced by the various methods are significantly different at each resolution
level. We continue to recommend verifying agreement between the modeled field
lines and corresponding coronal loop images before any NLFFF model is used in a
scientific setting.Comment: Accepted to ApJ; comments/corrections to this article are welcome via
e-mail, even after publicatio
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