Ray model and ray-wave correspondence in coupled optical microdisks

We introduce a ray model for coupled optical microdisks, in which we select coupling-efficient rays among the splitting rays. We investigate the resulting phase-space structure and report island structures arising from the ray-coupling between the two microdisks. We find the microdisks's refractive index to influence the phase-space structure and calculate the stability and decay rates of the islands. Turning to ray-wave correspondence, we find many resonances to be directly related to the presence of these islands. We study the relation between the (ray-picture originating) island structures and the (wave-picture originating) spectral properties of resonances, especially the leakiness of the resonances which is represented as the imaginary part of the complex wave vector.Comment: 9 pages, 8 figure

A new equation of state for helium nanobubbles embedded in UO2 matrix calculated via molecular dynamics simulations

International audienceMolecular dynamics simulations have been carried out to determine the equation of state of helium inside nanobubbles embedded into UO2 matrix.The parameters of this equation of state are fitted with the Brearley and MacInnes hard-sphere model based on the formalism of Carnahan-Starling used in fuel performance codes.This new equation of state takes into account the interactions between the surrounding UO2 matrix and the helium atoms. Four nanobubble sizes of diameters 1, 2, 5, and 10 nm have been investigated over four temperatures 300, 500, 700, and 900 K and for initial helium concentration inside the bubble ranging from 0.33x10^5 to 3.9x10^5 mol.m^-3 (corresponding to helium-to-vacancy ratio of 0.3 to 3.3, respectively).We observe that helium atoms are inhomogeneously distributed inside the bubble.A boundary layer of 1 nm thickness appears at the bubble surface in which helium atoms are more concentrated and diffuse into the UO2 matrix. We also observe a saturation of the helium atoms that can be incorporated into the bubble.This concentration limit is equal to 1.6 helium atom per vacancy in UO2.It corresponds to an atomic volume of 7.8x10^-30 m^3, which is almost half of the value proposed with the original Brearley and MacInnes model (13x10^-30 m^3).For this threshold concentration and for bubble of diameter higher than 5~nm, micro-cracks and dislocations appear at the bubble surface.We calculated the critical pressures inside the bubble that yields to this onset of crack in UO2.These critical pressures are in good agreement with those calculated with the Griffith criterion for brittle fracture

Backward error analysis and the substitution law for Lie group integrators

Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees, and can be used to represent a large class of numerical methods. The theory of backward error analysis for differential equations has a particularly nice description when applied to methods represented by Butcher series. For the study of differential equations evolving on more general manifolds, a generalization of Butcher series has been introduced, called Lie--Butcher series. This paper presents the theory of backward error analysis for methods based on Lie--Butcher series.Comment: Minor corrections and additions. Final versio

Reducing the Effects of Unequal Number of Games on Rankings

Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In such settings, the standard derivations of the methods can produce nonsensical rankings. This paper introduces the idea of including a super-user into the rankings and considers the effect of this fictitious player on the ratings. We apply such techniques to rank batters and pitchers in Major League baseball, professional tennis players, and participants in a free online social game. The ideas introduced in this paper can further the scope that such methods are applied and the depth of insight they offer

Interactions between nutrition and gastrointestinal infections with parasitic nematodes in goats

Parasitic nematodes of the digestive tract remain one of the main constraints to goat production both in temperate and tropical countries. The usual mode of control of these gastrointestinal nematodes (GIN) based on the repeated use of anthelmintics is now strongly questioned because of the increasing development of resistance to these molecules. Among the alternative methods to anthelmintics currently available, the manipulation of host nutrition in order to improve the host resistance and/or resilience to parasitic infections seems to represent one of the most promising options to reduce the dependence on conventional chemotherapy and to favour the sustainable control of gastro intestinal nematode infections. This paper will review the available information on the interactions between nutrition and nematode parasitism in dairy or meat goats both in temperate and tropical conditions. It will refer to quantitative aspects of the diet (influence of the protein and/or energy parts) as well as to qualitative components (effects of plant secondary metabolites on worm biology) and will discuss the specificities of goats in regard of theses interactions

Asymptotic solvers for ordinary differential equations with multiple frequencies

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focusing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the oscillatory parameter and use its truncation as an exceedingly effective means to discretize the differential equation in question. Numerical examples illustrate the effectiveness of the method

A micropillar for cavity optomechanics

We present a new micromechanical resonator designed for cavity optomechanics. We have used a micropillar geometry to obtain a high-frequency mechanical resonance with a low effective mass and a very high quality factor. We have coated a 60-$\mu$m diameter low-loss dielectric mirror on top of the pillar and are planning to use this micromirror as part of a high-finesse Fabry-Perot cavity, to laser cool the resonator down to its quantum ground state and to monitor its quantum position fluctuations by quantum-limited optical interferometry

Higher-order averaging, formal series and numerical integration III: error bounds

In earlier papers, it has been shown how formal series like those used nowadays to investigate the properties of numerical integrators may be used to construct high-order averaged systems or formal first integrals of Hamiltonian problems. With the new approach the averaged system (or the formal first integral) may be written down immediately in terms of (i) suitable basis functions and (ii) scalar coefficients that are computed via simple recursions. Here we show how the coefficients/basis functions approach may be used advantageously to derive exponentially small error bounds for averaged systems and approximate first integrals.A. Murua and J.M. Sanz-Serna have been supported by projects MTM2010-18246-C03-03 and MTM2010-18246-C03-01 respectively from Ministerio de Ciencia e Innovación.Publicad