Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Optical properties of multilayered porous silicon

International audienceWe present a short review of some optical devices based on multilayered porous silicon, which can be easily obtained by varying the formation current during the etching process. These include Bragg reflectors and Fabry–Pérot microcavities, which can be adjusted from the visible to the near infrared. The interface roughness, tragic in the case of multilayers, is studied. It can be drastically reduced when changing the electrolyte viscosity. The high reflectivities obtained in this way are measured by Cavity Ring–Down Spectroscopy. Problems occurring when realising thin layers and an efficient way to adjust precisely the optical thicknesses of the thin layers constituting the multilayered structure are also presented. Finally we present a method of calculation of the emission which takes absorption into account and is able to explain the angular dependence of the luminescence

Initial Data for General Relativity with Toroidal Conformal Symmetry

A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a $U(1)\times U(1)$ group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, the solutions are given in terms of a countable family of uncoupled ODEs on the orbit space.Comment: REVTEX, 9 pages, ESI Preprint 12

3D simulations of supernova remnants evolution including non-linear particle acceleration

If a sizeable fraction of the energy of supernova remnant shocks is channeled into energetic particles (commonly identified with Galactic cosmic rays), then the morphological evolution of the remnants must be distinctly modified. Evidence of such modifications has been recently obtained with the Chandra and XMM-Newton X-ray satellites. To investigate these effects, we coupled a semi-analytical kinetic model of shock acceleration with a 3D hydrodynamic code (by means of an effective adiabatic index). This enables us to study the time-dependent compression of the region between the forward and reverse shocks due to the back reaction of accelerated particles, concomitantly with the development of the Rayleigh-Taylor hydrodynamic instability at the contact discontinuity. Density profiles depend critically on the injection level η of particles: for η ≲ 10-4 modifications are weak and progressive, for η ˜ 10-3 modifications are strong and immediate. Nevertheless, the extension of the Rayleigh-Taylor unstable region does not depend on the injection rate. A first comparison of our simulations with observations of Tycho's remnant strengthens the case for efficient acceleration of protons at the forward shock

How agency models inspire large scale participatory planning and its evaluation

International audienceWe describe how three models, for sustainable change, human agency in collective resource management, and socio-environmental systems, have been used to design a protocol and the tools for a large scale (1500 participants, 35 villages) multi-level participatory process held in Africa for Integrated Natural Resource Management, through the European Project Afromaison. The process especially combines a common action model to support proposals by stakeholders, an integration matrix to build coherent plans, a role playing game design process, and a method to combine planning and playing to engage into the plans. It has also inspired the design of the attached monitoring and evaluation process. We describe the process in two countries, Ethiopia and Uganda, present the theoretical bases of the evaluation framework using the ENCORE paradigm and the implemented methodology transferred to local evaluators. We introduce some results and propose comments on potential learning back to the modelling community

Ferromagnetic (Ga,Mn)N epilayers versus antiferromagnetic GaMn3_3N clusters

Mn-doped wurtzite GaN epilayers have been grown by nitrogen plasma-assisted molecular beam epitaxy. Correlated SIMS, structural and magnetic measurements show that the incorporation of Mn strongly depends on the conditions of the growth. Hysteresis loops which persist at high temperature do not appear to be correlated to the presence of Mn. Samples with up to 2% Mn are purely substitutional Ga$_{1-x}$Mn$_x$N epilayers, and exhibit paramagnetic properties. At higher Mn contents, precipitates are formed which are identified as GaMn$_3$N clusters by x-ray diffraction and absorption: this induces a decrease of the paramagnetic magnetisation. Samples co-doped with enough Mg exhibit a new feature: a ferromagnetic component is observed up to $T_c\sim175$ K, which cannot be related to superparamagnetism of unresolved magnetic precipitates.Comment: Revised versio

Did Ebola emerge in West Africa by a policy-driven phase change in agroecology? Ebola's social context

SCOPUS: no.jinfo:eu-repo/semantics/publishe