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

Concentração de macronutrientes em função da idade, doses de fósforo aplicadas e partes de soja (Glycine max (L.) Merrill)

O presente trabalho foi desenvolvido visando atingir o seguinte objetivo: determinação das concentrações dos macronutrientes, nas partes da planta, em função de níveis de adubação fosfatada. Para verificar os parâmetros propostos foi instalado um fatorial 3³ com três repetições em solo da serie Guamium, no município de Piracicaba, SP. Usou-se o cultivar IAC-2 de habito de crescimento indeterminado. Aplicou-se no sulco na ocasião da semeadura as seguintes quantidades de fertilizantes: 0, 20 e 40 kg de N por ha; 0, 60 e 120 kg de P2O5por ha; 0, 30 e 60 kg de K2O por ha. Foram igualmente incorporados 2,7 t de calcário dolomitico por ha. Foram colhidas amostras de plantas em intervalos de 21 dias, a partir da emergência, até a queda parcial das folhas aos 105 dias de idade. Conclusões: concentrações maiores de nitrogênio, fósforo, potássio e enxofre foram encontradas nas folhas superiores; e as maiores concentrações de cálcio e magnêsio localizaram-se nas folhas inferiores. As variações nas concentrações de fósforo e magnêsio com a idade das plantas, foram afetadas pelas doses de fósforo.This study was conducted with the objective of determining the concentration of macronutrients in the plant as function of fertilization with nitrogen, phosphorus and potassium. A 3³ factorial experiment with three replications was performed. The experimental area was located at Piracicaba (ESALQ), the soil belonging to the Guamium series. IAC-2, an indeterminate soybean cultivar, was used. N, P and K were applied in the rows at the levels of 0, 20 and 40 kg/ha (N), 0, 60 and 120 kg/ha (P(2)0(5)), and 0, 30 and 60 kg/ha (K(2)0), Plant samples were taken at 21-day intervals at emergence and continuing until partial fall of the leaves (105 days after emergence). The several plant parts were analysed for macronutrients (.N, P, K, Ca, Mg and S). The following conclusions were reached: during the period of greatest efficiency of the crop, the level of 40 kg/ha of nitrogen increased the nitrogen concentration in the upper leaves. The level of 120 kg/ha of P2O5 increased the concentration of phosphorus and potassium in the upper leaves. The highest concentration of calcium and magnesium were found in the lower leaves, while the highest concentrations of sulphur were found in the upper leaves, independent of the levels of N, P and K applied to the soil