Self-similar solutions to the mean curvature flow in R3\mathbb{R}^{3}

In this paper we make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces of revolution and ruled surfaces in $\mathbb{R}^{3}$. We prove that self-similar solutions of the MCF by non-cylindrival surfaces and conical surfaces in $\mathbb{R}^{3}$ are trivial. Moreover, we characterize the self-similar solutions of the MCF by surfaces of revolutions under a homothetic helicoidal motion in $\mathbb{R}^{3}$ in terms of the curvature of the generating curve. Finally, we characterize the self-similar solutions for the MCF by cylindrical surfaces under a homothetic helicoidal motion in $\mathbb{R}^3$. Explicit families of exact solutions for the MCF by cylindrical surfaces in $\mathbb{R}^{3}$ are also given

Scaling in the crossover from random to correlated growth

In systems where deposition rates are high compared to diffusion, desorption and other mechanisms that generate correlations, a crossover from random to correlated growth of surface roughness is expected at a characteristic time t_0. This crossover is analyzed in lattice models via scaling arguments, with support from simulation results presented here and in other authors works. We argue that the amplitudes of the saturation roughness and of the saturation time scale as {t_0}^{1/2} and t_0, respectively. For models with lateral aggregation, which typically are in the Kardar-Parisi-Zhang (KPZ) class, we show that t_0 ~ 1/p, where p is the probability of the correlated aggregation mechanism to take place. However, t_0 ~ 1/p^2 is obtained in solid-on-solid models with single particle deposition attempts. This group includes models in various universality classes, with numerical examples being provided in the Edwards-Wilkinson (EW), KPZ and Villain-Lai-Das Sarma (nonlinear molecular-beam epitaxy) classes. Most applications are for two-component models in which random deposition, with probability 1-p, competes with a correlated aggregation process with probability p. However, our approach can be extended to other systems with the same crossover, such as the generalized restricted solid-on-solid model with maximum height difference S, for large S. Moreover, the scaling approach applies to all dimensions. In the particular case of one-dimensional KPZ processes with this crossover, we show that t_0 ~ nu^{-1} and nu ~ lambda^{2/3}, where nu and lambda are the coefficients of the linear and nonlinear terms of the associated KPZ equations. The applicability of previous results on models in the EW and KPZ classes is discussed.Comment: 14 pages + 5 figures, minor changes, version accepted in Phys. Rev.

Teste e validação do plantio direto de feijão entre fileira de café.

A cafeicultura na região da Zona da Mata Mineira é explorada em pequenas propriedades, utilizando práticas de manejo inadequadas, com excessiva movimentação do solo e ausência de cobertura vegetal, em solos pobres e desgastados. O sistema de plantio direto caracteriza-se pela manutenção da cobertura vegetal e mínima interferência no solo, evitando a sua degradação. O objetivo deste trabalho foi testar e validar o plantio direto de feijão entre fileiras de café. Foram instaladas 2 unidades de teste e validação (UTVs), uma no Sítio Olho D?Água e outra no Sítio Respicho, com áreas de 2800 e 7720 m², respectivamente, em Senador Firmino ? MG, em locais anteriormente ocupados com capim Brachiária, usado como pastagem para bovinos. Dessecou-se o capim com herbicida e planto-se o feijão, no espaçamento de 0,50 x 0,20 m, entre as fileiras de café, distanciadas de 3 m. Para promover a transferência de tecnologia foram realizadas visitas técnicas e reuniões para demonstração de métodos e de resultados. As produções de grãos de feijão obtidas nas UTVs instaladas no Sitio Olho D?Água e Respicho, foram de 280 e 150 kg, equivalentes a renda bruta de R$933,00 e R$500,00, respectivamente. Realizaram-se 13 eventos de transferência de tecnologia, envolvendo cafeicultores, extensionistas e pesquisadores, totalizando 107 participações. Demonstrou-se que o sistema de plantio direto condiciona a infiltração da água no solo, evitando a erosão, e vários produtores manifestaram a intenção de utilizar o sistema

Final state interaction in D+→K−π+π+D^+\to K^-\pi^+\pi^+ with KπK\pi I=1/2 and 3/2 channels

The final state interaction contribution to $D^+$ decays is computed for the $K^-\pi^+\pi^+$ channel within a light-front relativistic three-body model for the final state interaction. The rescattering process between the kaon and two pions in the decay channel is considered. The off-shell decay amplitude is a solution of a four-dimensional Bethe-Salpeter equation, which is decomposed in a Faddeev form. The projection onto the light-front of the coupled set of integral equations is performed via a quasi-potential approach. The S-wave $K\pi$ interaction is introduced in the resonant isospin $1/2$ and the non-resonant isospin $3/2$ channels. The numerical solution of the light-front tridimensional inhomogeneous integral equations for the Faddeev components of the decay amplitude is performed perturbatively. The loop-expansion converges fast, and the three-loop contribution can be neglected in respect to the two-loop results for the practical application. The dependence on the model parameters in respect to the input amplitude at the partonic level is exploited and the phase found in the experimental analysis, is fitted with an appropriate choice of the real weights of the isospin components of the partonic amplitude. The data suggests a small mixture of total isospin $5/2$ to the dominant $3/2$ one. The modulus of the unsymmetrized decay amplitude, which presents a deep valley and a following increase for $K\pi$ masses above $1.5$ GeV, is fairly reproduced. This suggests the assignment of the quantum numbers $0^+$ to the isospin 1/2 $K^*(1630)$ resonance

Phase transitions and crossovers in reaction-diffusion models with catalyst deactivation

The activity of catalytic materials is reduced during operation by several mechanisms, one of them being poisoning of catalytic sites by chemisorbed impurities or products. Here we study the effects of poisoning in two reaction-diffusion models in one-dimensional lattices with randomly distributed catalytic sites. Unimolecular and bimolecular single-species reactions are considered, without reactant input during the operation. The models show transitions between a phase with continuous decay of reactant concentration and a phase with asymptotic non-zero reactant concentration and complete poisoning of the catalyst. The transition boundary depends on the initial reactant and catalyst concentrations and on the poisoning probability. The critical system behaves as in the two-species annihilation reaction, with reactant concentration decaying as t^{-1/4} and the catalytic sites playing the role of the second species. In the unimolecular reaction, a significant crossover to the asymptotic scaling is observed even when one of those parameters is 10% far from criticality. Consequently, an effective power-law decay of concentration may persist up to long times and lead to an apparent change in the reaction kinetics. In the bimolecular single-species reaction, the critical scaling is followed by a two-dimensional rapid decay, thus two crossovers are found.Comment: 8 pages, 7 figure

An Environmental Friendly Procedure for Photometric Determination of Hypochlorite in Tap Water Employing a Miniaturized Multicommuted Flow Analysis Setup

A photometric procedure for the determination of ClO− in tap water employing a miniaturized multicommuted flow analysis setup and an LED-based photometer is described. The analytical procedure was implemented using leucocrystal violet (LCV; 4,4′,4′′-methylidynetris (N,N-dimethylaniline), C25H31N3) as a chromogenic reagent. Solenoid micropumps employed for solutions propelling were assembled together with the photometer in order to compose a compact unit of small dimensions. After control variables optimization, the system was applied for the determination of ClO− in samples of tap water, and aiming accuracy assessment samples were also analyzed using an independent method. Applying the paired t-test between results obtained using both methods, no significant difference at the 95% confidence level was observed. Other useful features include low reagent consumption, 2.4 μg of LCV per determination, a linear response ranging from 0.02 up to 2.0 mg L−1  ClO−, a relative standard deviation of 1.0% (n = 11) for samples containing 0.2 mg L−1  ClO−, a detection limit of 6.0 μg L−1  ClO−, a sampling throughput of 84 determinations per hour, and a waste generation of 432 μL per determination