The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.

Fluctuations of the Stokes and anti-Stokes surface-enhanced resonance Raman scattering intensities in an electrochemical environment

Stokes and anti-Stokes SERRS intensity fluctuations were observed from a roughened silver electrode immersed in diluted solutions of Brilliant Green (BG), a behaviour linked to single-molecule events. The distributions of the anti-Stokes to Stokes ratios were obtained and their shape showed a strong dependence on the applied potential.

Stokes and anti-Stokes luminescence of Er3+ doped Ga10Ge25S65 glass excited at 980 and 532 nm

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Avaliação de diferentes sistemas de cultivo in vitro para a micropropagação de Psychotria ipecacuanha (Brot.) Stokes

This work was carried out with Psychotria ipecacuanha, a Brazilian medicinal plant the roots of which contain emetine. The main objective was to develop a protocol for the micro-propagation of these species, by testing different culture techniques, the temporary immersion system, and the semi-solid and liquid media systems. In the semi-solid system, experiments were developed in flasks of two different sizes containing MS, B5, and WP media to which were added different growth regulators. Innoculum density was also evaluated. The liquid medium system consisted of MS medium supplemented with different growth regulators. For the temporary immersion system, the MS medium received an addition of 1.5mg/L BAP and 0.5mg/L GA3, and a reverse digital apparatus and vacuum pump were used. The liquid medium system with MS medium supplemented with 1.5mg/L BAP and 0.5mg/L GA3 presented the best results for shoot proliferation in a period of 30 days in culture (2.37 ± 0.32 shoots/explant). Cultures carried out for 90 days in the semi-solid system, using 8.5 × 5.5cm flasks and 3 explants per flask, developed 1.80 ± 0.20 shoots/explant, achieving 3.06 ± 0.51 cm of height adn presented superior survival ratio (96%). Explants cultured in temporary immersion system for 90 days showed 2.30 ± 1.10 shoots/explant achieving a growth of 2.08 ± 0.12 cm and 52% survival.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.

Influência da Fronteira em um Método Implícito para a Equação de Stokes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mapping the Energy Distribution of SERRS Hot Spots from Anti-Stokes to Stokes Intensity Ratios

The anomalies in the anti-Stokes to Stokes intensity ratios in single-molecule surface-enhanced resonance Raman scattering were investigated. Brilliant green and crystal violet dyes were the molecular probes, and the experiments were carried out on an electrochemically activated Ag surface. The results allowed new insights into the origin of these anomalies and led to a new method to confirm the single-molecule regime in surface-enhanced Raman scattering. Moreover, a methodology to estimate the distribution of resonance energies that contributed to the imbalance in the anti-Stokes to Stokes intensity ratios at the electromagnetic hot spots was proposed. This method allowed the local plasmonic resonance energies on the metallic surface to be spatially mapped.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

Su alcune applicazioni del teorema di Stokes

Nel lavoro si dimostrano il Teorema della Divergenza e il Teorema di Stokes e le sue generalizzazioni a una curva chiusa di ordine k e a una varietà M, n-dimensionale, orientata con bordo. Successivamente si espongono due applicazioni alla fisica: l'elettromagnetismo e la formula del rotore. Nel primo caso si mostra come applicando il Teorema alle leggi di Biot-Savarat e di Faraday si ottengono le equazioni di Maxwell; nel secondo invece si osserva come il rotore rappresenti la densità superficiale di circuitazione.

Equazione di Smoluchowski a coefficienti variabili e applicazioni

In questo lavoro viene presentato un modello matematico per l'aggregazione e la diffusione della beta-amiloide nel cervello umano affetto dalla malattia di Alzheimer, con la particolarità di considerare coefficienti di diffusione variabili e non costanti. Il modello è basato sull'equazione di Smoluchowski discreta per l'aggregazione, modificata in modo opportuno per considerare anche il fenomeno di diffusione.

Monte Carlo modeling of polarized light propagation: Stokes vs Jones - Part I

This bipartite comparative study aims at inspecting the similarities and differences between the Jones and Stokes–Mueller formalisms when modeling polarized light propagation with numerical simulations of the Monte Carlo type. In this first part, we review the theoretical concepts that concern light propagation and detection with both pure and partially/totally unpolarized states. The latter case involving fluctuations, or “depolarizing effects,” is of special interest here: Jones and Stokes–Mueller are equally apt to model such effects and are expected to yield identical results. In a second, ensuing paper, empirical evidence is provided by means of numerical experiments, using both formalisms.