On spectral minimal partitions II, the case of the rectangle

In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-\frac a2,\frac a2[\times ] -\frac b2,\frac b2[$, with $0< a\leq b$. It has been observed in \cite{HHOT} that when $0<\frac ab < \sqrt{\frac 38}$ the minimal 3-partition is obtained by the three nodal domains of the third eigenfunction corresponding to the three rectangles $]-\frac a2,\frac a2[\times ] -\frac b2,-\frac b6[$, $]-\frac a2,\frac a2[\times ] -\frac b6,\frac b6[$ and $]-\frac a2,\frac a2[\times ] \frac b6, \frac b2[$. We will describe a possible mechanism of transition for increasing $\frac ab$ between these nodal minimal 3-partitions and non nodal minimal 3-partitions at the value $\sqrt{\frac 38}$ and discuss the existence of symmetric candidates for giving minimal 3-partitions when $\sqrt{\frac 38}<\frac ab \leq 1$. Numerical analysis leads very naturally to nice questions of isospectrality which are solved by introducing Aharonov-Bohm Hamiltonians or by going on the double covering of the punctured rectangle

Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations

In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients that are given as averages of solutions to appropriate Poisson equations. We present a new numerical method for computing these coefficients that is based on the calculation of the eigenvalues and eigenfunctions of a Schr\"odinger operator. These theoretical results are supported by numerical simulations showcasing the efficiency of the method

Superconductivity in domains with corners

We study the two-dimensional Ginzburg-Landau functional in a domain with corners for exterior magnetic field strengths near the critical field where the transition from the superconducting to the normal state occurs. We discuss and clarify the definition of this field and obtain a complete asymptotic expansion for it in the large $\kappa$ regime. Furthermore, we discuss nucleation of superconductivity at the boundary

Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells I

We describe the asymptotic of the steady states of the out-of equilibrium Schrödinger-Poisson system, in the regime of quantum wells in a semiclassical island. After establishing uniform estimates on the nonlinearity, we show that the nonlinear steady states lie asymptotically in a finite-dimensional subspace of functions and that the involved spectral quantities are reduced to a finite number of so-called asymptotic resonant energies. The asymptotic finite dimensional nonlinear system is written in a general setting with only a partial information on its coefficients. After this first part, a complete derivation of the asymptotic nonlinear system will be done for some specific cases in a forthcoming article. UNE VERSION MODIFIEE DE CE TEXTE EST PARUE DANS LES ANNALES DE L'INSTITUT H. POINCARE, ANALYSE NON LINEAIRE

Un-doped and aluminum doped Zn1-xMgxO thin films deposited by infrared assisted spray-CVD for solar cells application

Date du colloque&nbsp;: 10/2012</p

Process intensification for the direct synthesis of adipic acid in a micro packed bed reactor

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A view through novel process windows

This mini-review discusses some of the recent work on novel process windows by the Micro Flow Chemistry and Process Technology group at the Eindhoven University of Technology, and their associates. Novel process windows consist of unconventional approaches to boost chemical production, often requiring harsh reaction conditions at short to very short time-scales. These approaches are divided into six routes: the use of high temperatures, high pressures, and high concentrations (or solvent-free), new chemical transformations, explosive conditions, and process simplification and integration. Microstructured reactors, due to their inherent safety, short time-scales, and the high degree of process control, are the means that make such extreme chemistry possible

A Summary of Main Experimental Results Concerning the Secondary Electron Emission of Copper

The secondary electron emission of surfaces exposed to the impact of energetic electrons contributes significantly to the electron cloud build-up. For the prediction of the consequences of this effect the measurements of the secondary electron yield carried out at CERN are an important source of information. New experimental results concerning the total secondary electron yield for very low primary electron energy (between 5 eV and 50 eV) will be also given in the case of as received copper. Furthermore the energy distribution of the re-emitted electrons is drastically influenced by the primary electron energy. The ratio of the number of reflected electrons to the total number of re-emitted electrons has been measured and its variation with the primary electron energy will be shown. As a consequence of these new experimental data, a numerical approximation to express the secondary electron yield as a function of the primary electron energy will be given for the low incident electron energy region (E < 50 eV). It has been shown that the decrease of the secondary electron yield due to the electron bombardment could reduce sufficiently the consequences electron cloud effect. To understand further the origin of this decrease, the results of experiments showing the variation of the electron induced desorption yield with the incident electron dose will be compared to the concomitant reduction of the secondary electron yield