Relationship between photospheric currents and coronal magnetic helicity for force-free bipolar fields

Aims. The origin and evolution of the magnetic helicity in the solar corona are not well understood. For instance, the magnetic helicity of an active region is often about 1042 Mx2 (1026 Wb2), but the observed processes whereby it is thought to be injected into the corona do not yet provide an accurate estimate of the resulting magnetic helicity budget or time evolution. The variation in magnetic helicity is important for understanding the physics of flares, coronal mass ejections, and their associated magnetic clouds. To shed light on this topic, we investigate here the changes in magnetic helicity due to electric currents in the corona for a single twisted flux tube that may model characteristic coronal structures such as active region filaments, sigmoids, or coronal loops. Methods. For a bipolar photospheric magnetic field and several distributions of current, we extrapolated the coronal field as a nonlinear force-free field. We then computed the relative magnetic helicity, as well as the self and mutual helicities. Results. Starting from a magnetic configuration with a moderate amount of current, the amount of magnetic helicity can increase by 2 orders of magnitude when the maximum current strength is increased by a factor of 2. The high sensitivity of magnetic helicity to the current density can partially explain discrepancies between measured values on the photosphere, in the corona, and in magnetic clouds. Our conclusion is that the magnetic helicity strongly depends on both the strength of the current density and also on its distribution. Conclusions. Only improved measurements of current density at the photospheric level will advance our knowledge of the magnetic helicity content in the solar atmosphere

Comparison of Geometric Optimization Methods with Multiobjective Genetic Algorithms for Solving Integrated Optimal Design Problems

In this paper, system design methodologies for optimizing heterogenous power devices in electrical engineering are investigated. The concept of Integrated Optimal Design (IOD) is presented and a simplified but typical example is given. It consists in finding Pareto-optimal configurations for the motor drive of an electric vehicle. For that purpose, a geometric optimization method (i.e the Hooke and Jeeves minimization procedure) associated with an objective weighting sum and a Multiobjective Genetic Algorithm (i.e. the NSGA-II) are compared. Several performance issues are discussed such as the accuracy in the determination of Pareto-optimal configurations and the capability to well spread these solutions in the objective space

System optimization by multiobjective genetic algorithms and analysis of the coupling between variables, constraints and objectives

This paper presents a methodology based on Multiobjective Genetic Algorithms (MOGA’s) for the design of electrical engineering systems. MOGA’s allow to optimize multiple heterogeneous criteria in complex systems, but also simplify couplings and sensitivity analysis by determining the evolution of design variables along the Pareto-optimal front. A rather simplified case study dealing with the optimal dimensioning of an inverter – permanent magnet motor – reducer – load association is carried out to demonstrate the interest of the approach

Nonlinear force-free models for the solar corona I. Two active regions with very different structure

With the development of new instrumentation providing measurements of solar photospheric vector magnetic fields, we need to develop our understanding of the effects of current density on coronal magnetic field configurations. The object is to understand the diverse and complex nature of coronal magnetic fields in active regions using a nonlinear force-free model. From the observed photospheric magnetic field we derive the photospheric current density for two active regions: one is a decaying active region with strong currents (AR8151), and the other is a newly emerged active region with weak currents (AR8210). We compare the three-dimensional structure of the magnetic fields for both active region when they are assumed to be either potential or nonlinear force-free. The latter is computed using a Grad-Rubin vector-potential-like numerical scheme. A quantitative comparison is performed in terms of the geometry, the connectivity of field lines, the magnetic energy and the magnetic helicity content. For the old decaying active region the connectivity and geometry of the nonlinear force-free model include strong twist and strong shear and are very different from the potential model. The twisted flux bundles store magnetic energy and magnetic helicity high in the corona (about 50 Mm). The newly emerged active region has a complex topology and the departure from a potential field is small, but the excess magnetic energy is stored in the low corona and is enough to trigger powerful flares.Comment: 11 pages, 11 figure

Recombination and Self-Adaptation in Multi-objective Genetic Algorithms

This paper investigates the influence of recombination and self-adaptation in real-encoded Multi-Objective Genetic Algorithms (MOGAs). NSGA-II and SPEA2 are used as example to characterize the efficiency of MOGAs in relation to various recombination operators. The blend crossover, the simulated binary crossover and the breeder genetic crossover are compared for both MOGAs on multi-objective problems of the literature. Finally, a self-adaptive recombination scheme is proposed to improve the robustness of MOGAs

Comparison of Direct Multiobjective Optimization Methods for the Design of Electric Vehicles

"System design oriented methodologies" are discussed in this paper through the comparison of multiobjective optimization methods applied to heterogeneous devices in electrical engineering. Avoiding criteria function derivatives, direct optimization algorithms are used. In particular, deterministic geometric methods such as the Hooke & Jeeves heuristic approach are compared with stochastic evolutionary algorithms (Pareto genetic algorithms). Different issues relative to convergence rapidity and robustness on mixed (continuous/discrete), constrained and multiobjective problems are discussed. A typical electrical engineering heterogeneous and multidisciplinary system is considered as a case study: the motor drive of an electric vehicle. Some results emphasize the capacity of each approach to facilitate system analysis and particularly to display couplings between optimization parameters, constraints, objectives and the driving mission

Flows at the Edge of an Active Region: Observation and Interpretation

Upflows observed at the edges of active regions have been proposed as the source of the slow solar wind. In the particular case of Active Region (AR) 10942, where such an upflow has been already observed, we want to evaluate the part of this upflow that actually remains confined in the magnetic loops that connect AR10942 to AR10943. Both active regions were visible simultaneously on the solar disk and were observed by STEREO/SECCHI EUVI. Using Hinode/EIS spectra, we determine the Doppler shifts and densities in AR10943 and AR10942, in order to evaluate the mass flows. We also perform magnetic field extrapolations to assess the connectivity between AR10942 and AR10943. AR10943 displays a persistent downflow in Fe XII. Magnetic extrapolations including both ARs show that this downflow can be connected to the upflow in AR10942. We estimate that the mass flow received by AR10943 areas connected to AR10942 represents about 18% of the mass flow from AR10942. We conclude that the upflows observed on the edge of active regions represent either large-scale loops with mass flowing along them (accounting for about one-fifth of the total mass flow in this example) or open magnetic field structures where the slow solar wind originates.Comment: 20 pages, 9 figures, accepted for publication in Astrophys.

Sismotectonique de la ride de Horn (îles de Futuna et Alofi), un segment en compression dans la zone de fracture Nord-Fidjienne

Une importante crise sismique a eu lieu près des îles de Futuna et Alofi (Pacifique Sud-Ouest) en mars 1993. Le mécanisme focal du séisme principal (Ms = 6,5) ainsi que la distribution des répliques indiquent la présence d'une faille inverse sous la ride jusqu'à une profondeur de 20 km. La surrection des îles ainsi que l'épaississement crustal de la ride par écaillage de la croûte océanique sont dus à un régime compressif local, lié à une irrégularité de la frontière de la plaque Pacifique le long de la zone de fracture transformante sénestre Nord-Fidjienne. (Résumé d'auteur