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

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