8,881 research outputs found
Noncommutative generalization of SU(n)-principal fiber bundles: a review
This is an extended version of a communication made at the international
conference ``Noncommutative Geometry and Physics'' held at Orsay in april 2007.
In this proceeding, we make a review of some noncommutative constructions
connected to the ordinary fiber bundle theory. The noncommutative algebra is
the endomorphism algebra of a SU(n)-vector bundle, and its differential
calculus is based on its Lie algebra of derivations. It is shown that this
noncommutative geometry contains some of the most important constructions
introduced and used in the theory of connections on vector bundles, in
particular, what is needed to introduce gauge models in physics, and it also
contains naturally the essential aspects of the Higgs fields and its associated
mechanics of mass generation. It permits one also to extend some previous
constructions, as for instance symmetric reduction of (here noncommutative)
connections. From a mathematical point of view, these geometrico-algebraic
considerations highlight some new point on view, in particular we introduce a
new construction of the Chern characteristic classes
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
Gradient discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media with discontinuous pressures at the matrix fracture interfaces
We investigate the discretization of Darcy flow through fractured porous
media on general meshes. We consider a hybrid dimensional model, invoking a
complex network of planar fractures. The model accounts for matrix-fracture
interactions and fractures acting either as drains or as barriers, i.e. we have
to deal with pressure discontinuities at matrix-fracture interfaces. The
numerical analysis is performed in the general framework of gradient
discretizations which is extended to the model under consideration. Two
families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the
Hybrid Finite Volume scheme (HFV) are detailed and shown to satisfy the
gradient scheme framework, which yields, in particular, convergence. Numerical
tests confirm the theoretical results. Gradient Discretization; Darcy Flow,
Discrete Fracture Networks, Finite Volum
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Orientation and distribution of recent gullies in the southern hemisphere of Mars: observations from HRSC/MEX and MOC/MGS data
Abstract not available
The relativistic solar particle event of 2005 January 20: origin of delayed particle acceleration
The highest energies of solar energetic nucleons detected in space or through
gamma-ray emission in the solar atmosphere are in the GeV range. Where and how
the particles are accelerated is still controversial. We search for
observational information on the location and nature of the acceleration
region(s) by comparing the timing of relativistic protons detected on Earth and
radiative signatures in the solar atmosphere during the particularly
well-observed 2005 Jan. 20 event. This investigation focuses on the
post-impulsive flare phase, where a second peak was observed in the
relativistic proton time profile by neutron monitors. This time profile is
compared in detail with UV imaging and radio spectrography over a broad
frequency band from the low corona to interplanetary space. It is shown that
the late relativistic proton release to interplanetary space was accompanied by
a distinct new episode of energy release and electron acceleration in the
corona traced by the radio emission and by brightenings of UV kernels. These
signatures are interpreted in terms of magnetic restructuring in the corona
after the coronal mass ejection passage. We attribute the delayed relativistic
proton acceleration to magnetic reconnection and possibly to turbulence in
large-scale coronal loops. While Type II radio emission was observed in the
high corona, no evidence of a temporal relationship with the relativistic
proton acceleration was found
Belief Hierarchical Clustering
In the data mining field many clustering methods have been proposed, yet
standard versions do not take into account uncertain databases. This paper
deals with a new approach to cluster uncertain data by using a hierarchical
clustering defined within the belief function framework. The main objective of
the belief hierarchical clustering is to allow an object to belong to one or
several clusters. To each belonging, a degree of belief is associated, and
clusters are combined based on the pignistic properties. Experiments with real
uncertain data show that our proposed method can be considered as a propitious
tool
Mass predictions, partial difference equations and higher‐order isospin effects
The Garvey‐Kelson mass relation has been extended by introducing inhomogeneous source terms to improve problems with long‐range extrapolations. Such mass relations are third‐order partial difference equations with solutions representing mass equations. It was found that inhomogeneous source terms based on shell‐dependent Coulomb and symmetry energy terms are not sufficient to improve upon extrapolations. However, contributions from higher‐order perturbations in isospin (mostly cubic) have a significant effect. A many‐parameter mass equation was constructed as the solution of an inhomogeneous difference equation with properly adjusted shell‐dependent source terms. The standard deviation for reproducing the experimental mass values is σm=194 keV. Nuclear contributions were subjected to the constraint of charge symmetry, and Coulomb displacement energies are reproduced with σc=41 keV. Mass predictions for over 4000 nuclei with A≳16 and both N≥Z and N<Z (except N=Z=odd for A<40) are reported.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87305/2/62_1.pd
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