Hybrid resonance of Maxwell's equations in slab geometry

Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell's equations with smooth coefficients, where the dielectric tensor is a non diagonal hermitian matrix. The main part of this work is dedicated to the construction and analysis of a mathematical solution of the hybrid resonance with the limit absorption principle. We prove that the limit solution is singular: it is constituted of a Dirac mass at the origin plus a principle value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.Comment: This published version has been edited to improve the presentation of the result

Measuring Happiness: From Fluctuating Happiness to Authentic–Durable Happiness

On the basis of the theoretical distinction between self-centeredness and selflessness (Dambrun and Ricard, 2011), the main goal of this research was to develop two new scales assessing distinct dimensions of happiness. By trying to maximize pleasures and to avoid displeasures, we propose that a self-centered functioning induces a fluctuating happiness in which phases of pleasure and displeasure alternate repeatedly (i.e., Fluctuating Happiness). In contrast, a selfless psychological functioning postulates the existence of a state of durable plenitude that is less dependent upon circumstances but rather is related to a person’s inner resources and abilities to deal with whatever comes his way in life (i.e., Authentic–Durable Happiness). Using various samples (n = 735), we developed a 10-item Scale measuring Subjective Fluctuating Happiness (SFHS) and a 13-item scale assessing Subjective Authentic–Durable Happiness (SA–DHS). Results indicated high internal consistencies, satisfactory test–retest validities, and adequate convergent and discriminant validities with various constructs including a biological marker of stress (salivary cortisol). Consistent with our theoretical framework, while self-enhancement values were related only to fluctuating happiness, self-transcendence values were related only to authentic–durable happiness. Support for the distinction between contentment and inner-peace, two related markers of authentic happiness, also was found

Singular solutions for the plasma at the resonance

International audienceLittle is known on the mathematical theory of hybrid and cyclotron solutions of the Maxwell equations with the cold plasma dielectric tensor. Such equations arise in magnetic plasmas such the ones needed for the modeling the an electromagnetic wave in Tokamaks. The behavior of solutions can be extremely different to those in vacuum. This work intends to contribute to the local theory by means of original representation formulas based on special functions and a certain eikonal equation, and with a careful treatment of the singularity for the hybrid resonance

A numerical study of the solution of x-mode equations around the hybrid resonance

International audienceHybrid resonance is a physical phenomenon that appears for example in the heating of plasma, and as such is of scientific interest in the development of the ITER project. In this paper we focus some solutions with low regularity of Maxwell equations in plasmas under strong background magnetic field. Our purpose is two-fold. On one hand we investigate the finite element approximation of the one dimensional problem written in the frequency domain, and on the other hand we investigate two different finite difference approximations of the one dimensional time dependent problem. We will also compare the results of these different methods.La résonnance hybride est unphéno ene physique qui apparait par exemple lorsque l'on chauffe un plasma, et ainsi est d'intérêt scientifique dans le cadre du développement du projet ITER. Dans ce papier, nous nous concentrons sur certaines solutions faiblementr égulières de equations de Maxwell pour les plasmas sous l'influence de champ magnétiques forts. Notre but est ici double. D'un côté nou evaluons l'approximation numérique a l'aide des léments finis en une dimension en formulation fréquentielle, et de l'autre nous étudions l'approximation numérique à l'aide de deux méthodes de différences finies pour la formulation temporelle monodimensionelle. Nous comparons les résultats de ces différentes méthodes

A numerical study of the solution of X-Mode equations around the hybrid resonance*

The hybrid resonance is a physical phenomenon that appears for example in the heating of plasma, and as such is of scientific interest for the development of the ITER project. In this paper we focus on solutions of low regularity to Maxwell equations in magnetized plasmas. Our main purpose is three-fold. First, we aim at investigating the finite element approximation of the frequency-domain problem. Second, we would like to study the resonant solutions in the time domain, with the help of two different finite difference approximations. We finally compare the results with the ones obtained in the frequency domain, by numerical examination of the limiting absorption and limited amplitude principles

Liquid jet generation and break-up

International audienceThis work is motivated by the numerical simulation of the generation and break-up of droplets after the impact of a rigid body on a tank filled with a compressible fluid. This paper splits into two very different parts. The first part deals with the modeling and the numerical resolution of a spray of liquid droplets in a compressible medium like air. Phenomena taken into account are the breakup effects due to the velocity and pressure waves in the compressible ambient fluid. The second part is concerned with the transport of a rigid body in a compressible liquid, involving reciprocal effects between the two components. A new one-dimensional algorithm working on a fixed Eulerian mesh is proposed

Magnetic Equations with FreeFem++: the Grad-Shafranov Equation & the Current Hole

CEMRACS'10 research achievements: numerical modeling of fusion. Papers from the 15th Annual Summer Research Session (Centre d'étude Mathématique de Recherche Avancée en Calcul Scientifique) held in Marseille, July 19-August 27, 2010International audienceFreeFem++ is a software for the numerical solution of partial differential equations. It is based on finite element method. The FreeFem++ platform aims at facilitating teaching and basic research through prototyping. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic equations arising in Fusion Plasma in the context of the ITER project. First we consider the Grad-Shafranov equation, which is derived from the static ideal MHD equations assuming axisymetry. Some of the properties of the equation and its analytical solutions are discussed. Second we discretize a reduced resistive MHD model which admits solutions of the Grad-Shafranov equation as stationary solutions. Then the physical stability of these stationary solutions is investigated through numerical experiments and the numerical stability of the algorithm is discussed

Changes in social environment induce higher emotional disturbances than changes in physical environment in quail

International audienceIn intensive rearing, birds are exposed to frequent changes in both their social and physical environments, and this can have an impact on animal welfare under commercial conditions. The aim of the present study was to compare the emotional responses induced by social and non-social changes and to study the influence of the familiarity on these responses.Twenty-two female quail were first reared with a ball in 15–20-individual groups for 3 weeks from hatching. Then, each experimental subject was allocated either a familiar congener (CONG) or a familiar object (BALL). At 6 weeks of age the birds were fitted with a telemetric device to collect motor and cardiac activities. After that, each subject was exposed first to a separation from its cage-mate/familiar object, and secondly to the (re-)introduction of either the cage-mate/familiar object or of an unknown conspecific/another ball. Emotional responses were assessed through behavioural reactions and heart rate variability.Before being separated, both BALL and CONG quail showed stereotyped pacing that was more pronounced in BALL quail. BALL quail were not affected by the ball withdrawal, unlike CONG quail which reacted to the separation from their cage-mate by reducing activity and exploratory behaviour (P < 0.05). After the re-introduction, BALL quail remained closer to their ball and CONG quail spent more time with “stretched necks” than before the separation (P < 0.05). Surprisingly, CONG quail showed less stereotyped pacing when their partner was removed and recovered the initial level of stereotyped behaviour when their cage-mate was re-introduced (P < 0.01). Likewise, CONG quail also recovered the initial values of heart rate after the re-introduction of their cage-mate, indicating an increase in sympathetic activity compared to the isolation period. When the unfamiliar congener or ball was introduced in their cage, BALL quail pecked the unknown ball more than the familiar ball and had more contact with it (P < 0.05) and CONG quail had more contact with the unknown congener than with the cage-mate (P < 0.05).In conclusion, the quail appeared to experience a negative affective state before being separated, and there was no clear evidence of negative emotion in quail in response to the separation from either a social partner or an inanimate object. Nevertheless, the emotional responses of the quail in reaction to the (re-)introduction was influenced by the familiarity of the congener or the ball. Finally, changes in the quail's social environment induced more behavioural and cardiac modifications than changes in its non-social environment