Numerical Study of a Particle Method for Gradient Flows

We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting scheme preserves the gradient flow structure at the particle level, and enables us to obtain a gradient descent formulation after time discretisation. We give several simulations to illustrate the validity of this method, as well as a detailed study of one-dimensional aggregation-diffusion equations.Comment: 27 pages, 21 figure

A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques

Self-gravitating Brownian systems and bacterial populations with two or more types of particles

We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both microcanonical and canonical ensembles. We show how the critical temperature (Jeans instability) and the critical energy (Antonov instability) depend on the relative mass of the particles and on the dimension of space. We then study the dynamical evolution of a multi-components gas of self-gravitating Brownian particles in the canonical ensemble. Self-similar solutions describing the collapse below the critical temperature are obtained analytically. We find particle segregation, with the scaling profile of the slowest collapsing particles decaying with a non universal exponent that we compute perturbatively in different limits. These results are compared with numerical simulations of the two-species Smoluchowski-Poisson system. Our model of self-attracting Brownian particles also describes the chemotactic aggregation of a multi-species system of bacteria in biology

A new variational approach to the stability of gravitational systems

We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system subject to its own gravity. A well-known conjecture in astrophysics is that the steady state solutions which are nonincreasing functions of their microscopic energy are nonlinearly stable by the flow. This was proved at the linear level by several authors based on the pioneering work by Antonov in 1961. Since then, standard variational techniques based on concentration compactness methods as introduced by P.-L. Lions in 1983 have led to the nonlinear stability of subclasses of stationary solutions of ground state type. In this paper, inspired by pioneering works from the physics litterature (Lynden-Bell 94, Wiechen-Ziegler-Schindler MNRAS 88, Aly MNRAS 89), we use the monotonicity of the Hamiltonian under generalized symmetric rearrangement transformations to prove that non increasing steady solutions are local minimizer of the Hamiltonian under equimeasurable constraints, and extract compactness from suitable minimizing sequences. This implies the nonlinear stability of nonincreasing anisotropic steady states under radially symmetric perturbations

The Einstein-Vlasov sytem/Kinetic theory

The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades where the main focus has been on nonrelativistic- and special relativistic physics, e.g. to model the dynamics of neutral gases, plasmas and Newtonian self-gravitating systems. In 1990 Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (e.g. fluid models). The first part of this paper gives an introduction to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental in order to get a good comprehension of kinetic theory in general relativity.Comment: 31 pages. This article has been submitted to Living Rev. Relativity (http://www.livingreviews.org

Parental risk perception of 0-3-year-old children exposure to household pesticides

El objetivo de este estudio fue conocer las prácticas y la percepción sobre los riesgos de los plaguicidas domésticos (PDs) en madres y padres de niños en etapas tempranas del desarrollo. Sujetos y Método: Investigación de diseño cualitativo mediante entrevistas a madres y padres en 18 domicilios con niños de 0 a 3 años afiliados al Seguro de Salud del Hospital Italiano de Buenos Aires en el año 2015. Se identificaron categorías analíticas, se conceptualizaron categorías analíticas interpretativas de mayor nivel de abstracción y finalmente se construyeron diagramas para representar y organizar los hallazgos. Resultados: Las entrevistas mostraron que las madres y padres: 1) Utilizaban habitualmente PDs, 2) Mostraron en general baja preocupación por los peligros para la salud de los PDs y productos químicos hogareños excepto un grupo pequeño más sensibilizado, 3) Les preocupaba más las picaduras de insectos en sus hijos que la exposición a PDs, 4) Confiaban en los servicios de fumigación y/o en el marco normativo que los regula, y 5) Manifestaron interés en que el pediatra les brindara información acerca de los productos químicos que se utilizan diariamente en el hogar. Otras categorías analíticas mostraron un ajuste constante entre toxicidad, patogenicidad, higiene y bienestar. Conclusiones: Dado que los niveles de exposición hogareña considerados inocuos para adultos pueden ser toxicológicamente relevantes para individuos en desarrollo, los entes de gobierno y salud deberían proveer a los padres de herramientas intelectuales para decodificar los mensajes del mercadeo de PDs, así como para conceptualizar la relación entre contacto con PDs y trastornos de salud infantil.The objective of this work was to know the practices and risk perception of household pesticides (HPs) of mothers and fathers of children in early developmental stages. Subjects and Method: Qualitative research carried out in 2015. We conducted interviews in 18 homes with mothers and fathers of children aged 0 to 3 years registered in the General Health Insurance Plan of the Hospital Italiano de Buenos Aires (Metropolitan Area of Buenos Aires). The analytical categories were identified, interpre-tive analytical categories of higher-level abstraction were conceptualized, and finally, diagrams were constructed to represent and organize the findings. Results: The interviews showed that mothers and fathers: 1) used HPs regularly, 2) showed low concern for the health hazards of HPs and other household chemicals, except for a small, more sensitized group of parents, 3) they were more concerned regarding mosquito bites than exposure of their children to HPs, 4) relied on fumigation services and the normative framework that regulates them, and 5) expressed interest and willingness to receive more information and orientation from the pediatrician about the safe use of chemical products at home. Other analytical categories showed a constant parental adjustment between toxicity, patho-genicity, hygiene, and well-being. Conclusions: Since home exposures levels to HPs considered safe for adults may be toxicologically relevant for young children, government and health agencies should provide parents with tools to decode HPs marketing and publicity messages, as well as to conceptua-lize the relationship between HPs use and childhood health disorders.Fil: Kandel Gambarte, Paula Cristina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; Argentina. Instituto Universitario Hospital Italiano de Buenos Aires. Rectorado.; ArgentinaFil: Rovedatti, María Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Biodiversidad y Biología Experimental; ArgentinaFil: Ferloni, Analía. Hospital Italiano. Instituto de Ciencias Básicas y Medicina Experimental; ArgentinaFil: Pereiro, Natalia. Hospital Italiano. Instituto de Ciencias Básicas y Medicina Experimental; ArgentinaFil: Cruz, Martín G.. Hospital Italiano. Instituto de Ciencias Básicas y Medicina Experimental; ArgentinaFil: Aragone, Soledad. Hospital Italiano. Instituto de Ciencias Básicas y Medicina Experimental; ArgentinaFil: Figar, Silvana B.. Instituto Universitario Hospital Italiano de Buenos Aires. Rectorado.; ArgentinaFil: Dawidowski, Adriana Ruth. Instituto Universitario Hospital Italiano de Buenos Aires. Rectorado.; ArgentinaFil: Wolansky, Marcelo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Química Biológica de la Facultad de Ciencias Exactas y Naturales; Argentin