Higher integrability of the gradient and dimension of the singular set for minimisers of the Mumford–Shah functional

The paper is concerned with the higher regularity properties of the minimizers of the Mumford–Shah functional. It is shown that, near to singular points where the scaled Dirichlet integral tends to 0, the discontinuity set is close to an Almgren area minimizing set. As a byproduct, the set of singular points of this type has Hausdorff dimension at most N-2, N being the dimension of the ambient space. Assuming higher integrability of the gradient this leads to an optimal estimate of the Hausdorff dimension of the full singular set. Received: 5 July 2001 / Accepted: 29 November 2001 / Published online: 23 May 2002     

Optimal control for Multi-Conjugate Adaptive Optics

Classic adaptive optics (AO) is now a proven technique that provides a closed loop real time correction of the turbulence. It is generally based on simple and efficient control algorithms. The next AO generation (Multi-Conjugate AO (MCAO) in its various forms and Extreme AO (XAO)) will require more sophisticated control approaches, especially in the case of wide field AO. We present here the concepts behind optimal control. The advantages compared to more standard approaches are stressed. A first experimental validation is presented. To cite this article: C. Petit et al., C. R. Physique 6 (2005).     

Material voids in elastic solids with anisotropic surface energies

This work discusses the role of highly anisotropic interfacial energy for problems involving a material void in a linearly elastic solid. Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of the void may be deduced from smoothness and convexity properties of the interfacial energy.     

Entire Solutions to Equivariant Elliptic Systems with Variational Structure

We consider the system Δu ? W _u (u) = 0, where \({u : \mathbb{R}^n \to \mathbb{R}^n}\) , for a class of potentials \({W : \mathbb{R}^n \to \mathbb{R}}\) that possess several global minima and are invariant under a general finite reflection group G. We establish existence of nontrivial G-equivariant entire solutions connecting the global minima of W along certain directions at infinity.     

Hexafluorobenzene: a powerful solvent for a noncovalent stereoselective organocatalytic Michael addition reaction

A dramatic enhancement of the diastereo- and enantioselectivity in the nitro-Michael addition reaction organocatalysed by a commercially available α,α-L-diaryl prolinol was disclosed when performing the reaction in unconventional hexafluorobenzene as a medium. DFT calculations were performed to clarify the origin of stereoselectivity and the role of C(6)F(6).     

The Use of Real-World Computer Models for Computer-Aided Design of Tracking Control Schemes for Induction Motors

The design of tracking controllers for induction motors is usually developed by neglecting the presence of power-supply devices, such as inverters, and measurement apparatuses, e.g., encoders. However, these components represent unmodeled dynamics that are present during the real operating conditions of the induction motor. Since the development of a numerical simulation study represents a low-cost, safe, and fast test to validate the design of tracking control schemes, the need arises to build a computer model of the overall system (i.e., motor, power supply, measurement devices, and tracking controller) as realistic as possible. In this context, the paper describes a computer model for simulation of an induction motor under a tracking control scheme including many real-world effects; namely, encoder's quantization, current sensors' noise, stator current dynamics, presence of a current-controlled voltage-source inverter within a stator current regulator loop, flux observer dynamics, saturation of the control signal, and discrete-time implementation of the control algorithm. The developed computer model is finally used in a case study and the simulation results obtained for an induction motor driving a single-link robotic arm under an H8 tracking control scheme are reported.     

Measurement of separate cosmic-ray electron and positron spectra with the fermi large area telescope

We measured separate cosmic-ray electron and positron spectra with the Fermi Large Area Telescope. Because the instrument does not have an onboard magnet, we distinguish the two species by exploiting Earth's shadow, which is offset in opposite directions for opposite charges due to Earth's magnetic field. We estimate and subtract the cosmic-ray proton background using two different methods that produce consistent results. We report the electron-only spectrum, the positron-only spectrum, and the positron fraction between 20 and 200?GeV. We confirm that the fraction rises with energy in the 20-100?GeV range. The three new spectral points between 100 and 200?GeV are consistent with a fraction that is continuing to rise with energy.     

(4-Vinylpyridine-Styrene) Copolymer as Host Polymer for Chromophoric Complexes with Potential Second Order Nonlinear Optical Properties

A series of new metal containing polymers for second order nonlinear optics have been prepared by grafting Cu (II) and Pd (II) chromophoric complexes on a preformed (4-vinylpyridine-styrene) copolymeric backbone. The metallated polymers have been chemically and physically characterized. They show high glass transition temperatures, high thermal stability and good solubility. Their properties have been compared with analogous metallated poly(4-vinylpyridine) samples: variations in the polymeric backbone, as well as in ligands, metal, and metallation ratio, allow to tune their properties.