Homogenization of the linear Boltzmann equation in a domain with a periodic distribution of holes

Consider a linear Boltzmann equation posed on the Euclidian plane with a periodic system of circular holes and for particles moving at speed 1. Assuming that the holes are absorbing -- i.e. that particles falling in a hole remain trapped there forever, we discuss the homogenization limit of that equation in the case where the reciprocal number of holes per unit surface and the length of the circumference of each hole are asymptotically equivalent small quantities. We show that the mass loss rate due to particles falling into the holes is governed by a renewal equation that involves the distribution of free-path lengths for the periodic Lorentz gas. In particular, it is proved that the total mass of the particle system at time t decays exponentially fast as t tends to infinity. This is at variance with the collisionless case discussed in [Caglioti, E., Golse, F., Commun. Math. Phys. 236 (2003), pp. 199--221], where the total mass decays as Const./t as the time variable t tends to infinity.Comment: 29 pages, 1 figure, submitted; figure 1 corrected in new versio

Homogenization of transport problems and semigroups

10 pages, 1 figureInternational audienceIn some cases, the homogenization of evolution differential equations whose solution is given by the action of a semigroup on their initial data may lead to evolution problems with a completely different structure, usually integro-differential equations whose dynamics is not defined by a semigroup, but involves memory effects. A typical example is the homogenization --- or discretization --- of opacities in radiative transfer. In this paper, we propose a formulation of homogenized equations in terms of a semigroup acting on an enlarged phase space (i.e. on functions involving more variables than in the original problem.

The polyfactorial model of autism and the question of causality

After recalling the different pediatric, psychopathological and child psychiatric models of mental disorders in children and adolescents, the author presents in detail the so-called polyfactorial model, which includes primary, secondary, and mixed factors. This model is the epistemological heir of the Freudian concept of “complementary series.” The example of autism is then explored as a paradigm of the usefulness of this polyfactorial model. Finally, we reflect on the notion of causality, from Aristotelian causality to epigenetic causality, which could 1 day re-legitimize psychoanalysis and the impact of the relationship on genome expression

A DERIVATION OF THE VLASOV-NAVIER-STOKES MODEL FOR AEROSOL FLOWS FROM KINETIC THEORY

International audienceThis article proposes a derivation of the Vlasov-Navier-Stokes system for spray/aerosol flows. The distribution function of the dispersed phase is governed by a Vlasov-equation, while the velocity field of the propellant satisfies the Navier-Stokes equations for incompressible fluids. The dynamics of the dispersed phase and of the propellant are coupled through the drag force exerted by the propellant on the dispersed phase. We present a formal derivation of the model from a multiphase Boltzmann system for a binary gaseous mixture, involving the droplets/dust particles in the dispersed phase as one species, and the gas molecules as the other species. Under suitable assumptions on the collision kernels, we prove that the sequences of solutions to the multiphase Boltzmann system converge to distributional solutions to the Vlasov-Navier-Stokes equation in some appropriate distinguished scaling limit. Specifically, we assume (a) that the mass ratio of the gas molecules to the dust particles/droplets is small, (b) that the thermal speed of the dust particles/droplets is much smaller than that of the gas molecules and (c) that the mass density of the gas and of the dispersed phase are of the same order of magnitude

Do Brincar do Bebê ao Brincar da Criança: Um Estudo sobre o Processo de Subjetivação da Criança Autista

Could the primitive play of the baby reveal early traces of a probable autistic organization underway with the young child? To what extent the investment of the baby with regard to the objects of the external world and the environment could be associated with his fi rst experiences with the maternal object? Such questions are addressed in this article, which mainobjective is to address the subjectivation process of autistic children, on basis of the relation between the early play of the baby and the symbolic play of the young child. Through a longitudinal study of infants showing risk of autism, it has been found that it is possible to detect at an early age peculiarities in the way they invest and interact with the objects of their environment.O brincar primitivo do bebê poderia nos revelar traços precoces de uma provável organização autística em curso na criança pequena? Em que medida o investimento do bebê face aos objetos do mundo externo e do ambiente poderia ser associado a suas primeiras experiências com o objeto materno? Tais questões são levantadas neste artigo, cujo principal objetivo é abordar o processo de subjetivação da criança autista a partir da correlação entre o brincar primitivo do bebê e o brincar simbólico da criança. Através de um estudo longitudinal de bebês com risco de autismo, constatou-se que, desde uma idade precoce, é possível detectar particularidades na maneira como eles investem e interagem com os objetos do ambiente

Separation Practices in Children and Adolescents Admitted for Suicidal Behavior: A National Survey of French Psychiatrists

ObjectivesTo assess practices of French psychiatrists regarding their management of children and adolescents with suicidal behaviors, focusing on the use of a separation protocol in which the youths are separated from their relatives.MethodsIn 2017, we conducted an online cross-sectional survey of French psychiatrists caring for children and adolescents. Participants were asked to describe their practice of a separation protocol in children and adolescents admitted for suicidal behavior. Our main analysis followed a descriptive approach. We also explored whether participant characteristics were associated with the use of a separation protocol.ResultsThe response rate was 218/2403 (9,1%); 57.9 % of respondents worked in a University hospital, and 60% of respondents reported routinely hospitalizing children. A separation protocol was set up by 91.1% of survey participants (systematically 39.6%, on a case-by-case basis 51.5%). The mean age from which a separation protocol was indicated was above 11 years; 64% of participants reported a separation period of ≤ 48 h. The most common (87%) criterion cited for establishing a separation period was family relationship difficulties. The most common (80.9%) reason to justify the use of a separation protocol was to allow a better clinical assessment. Exploratory analyses did not identify any participant characteristics associated with the use of a separation protocol (p > 0.2 for all).ConclusionThe use of a separation protocol in children and adolescents admitted for suicidal behavior is a widespread practice in France, despite the deprivation of liberty it implies. This raises the question of the relevance and usefulness of such a practice

La place des psychothérapies dans la prise en charge des enfants autistes

Après avoir rappelé les bases du modèle polyfactoriel en tant qu’hypothèse plausible dans le champ de l’autisme infantile, la prise en charge multidimensionnelle de cette pathologie en découle comme une conséquence obligée. La place de psychothérapies demeure alors importante, non pas au regard de la cause, ou des causes, de l’autisme, mais comme accompagnement de la souffrance psychique liée d’une part au fait d’être autiste et d’autre part au processus de dégagement lui- même. La formation du psychothérapeute-psychanalyste lui permet de verbaliser les affects de l’enfant, de mettre des mots sur la figuration de ses angoisses archaïques, et de concourir à l’édification de son Moi corporel, ce qui soutient l’enfant dans son processus d’accès à l’intersubjectivité

La pulsion d’attachement, un concept stimulant dans le débat entre théorie des pulsions et théorie de la relation d’objet

Après avoir montré comment le concept de pulsion d’attachement, proposé par D. Anzieu, peut s’avérer fécond pour dépasser un certain nombre de polémiques qui ont eu lieu autour de la théorie de l’attachement, l’auteur fait ensuite l’hypothèse que ce concept, apparemment hérétique, permet peut-être de jeter un pont entre la théorie des pulsions et la théorie des relations d’objet