Hydrodynamics of probabilistic ballistic annihilation

We consider a dilute gas of hard spheres in dimension $d \geq 2$ that upon collision either annihilate with probability $p$ or undergo an elastic scattering with probability $1-p$. For such a system neither mass, momentum, nor kinetic energy are conserved quantities. We establish the hydrodynamic equations from the Boltzmann equation description. Within the Chapman-Enskog scheme, we determine the transport coefficients up to Navier-Stokes order, and give the closed set of equations for the hydrodynamic fields chosen for the above coarse grained description (density, momentum and kinetic temperature). Linear stability analysis is performed, and the conditions of stability for the local fields are discussed.Comment: 19 pages, 3 eps figures include

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Avaliação do estado nutricional de atletas de ginástica olímpica do Rio de Janeiro e São Paulo Nutritional status evaluation of olympic gymnastics athletes from Rio de Janeiro and São Paulo, Brazil

Com o objetivo de avaliar o estado nutricional de atletas de ginástica olímpica, do sexo feminino, foram estudadas 46 ginastas, de 11 a 14 anos, pertencentes a clubes e academias das cidades do Rio de Janeiro e São Paulo. O estudo antropométrico envolveu medidas de massa corporal, estatura, dobras cutâneas e perímetros. Observou-se diferença significativa para as dobras cutâneas tricipital, suprailíaca, da coxa e da panturrilha e para o percentual de gordura (p<0,05). Para o estudo dietético foram utilizados recordatório de 24 horas e registro alimentar de três dias. As ginastas apresentaram baixo consumo energético. A percentagem de carboidratos, 50% a 58%, e a ingestão protéica de 1,5 a 1,7 g/kg de peso mostraram-se baixa e adequada, respectivamente, frente ao proposto para atletas. O conteúdo de vitaminas foi satisfatório, com exceção do ácido fólico para as adolescentes cariocas. Os minerais julgados inadequados foram cálcio, magnésio, ferro e zinco. O estado nutricional de ferro não apresentou alterações.<br>The purpose of this study was to evaluate the nutritional status of 46 female olympic gymnastics athletes, aged 11 to 14 years old, attending private gymnastics clubs of the cities of Rio de Janeiro and São Paulo. The anthropometric assessment involved measurements of height, body mass, skinfold thickness and circumferences. Significant difference was observed for the triceps, suprailiac, mid thigh and medial calf skinfolds and for the percentage of body fat (p<0.05). For the assessment of dietary intake a 24-hour recall and a 3-day self-register were used. The energy consumption and the percentage of carbohydrates (50% to 58%) in the diet were low and the protein ingestion (1.5 to 1.7 g/kg of body weight) was appropriate, according to values proposed for athletes. Vitamin intake was satisfactory, except for folic acid of gymnasts from Rio de Janeiro. From the minerals assessed, the intake of calcium, magnesium, zinc and iron was inadequate. No clinical signs of iron deficiency were observed