Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

We investigate here the ability of a Green-Naghdi model to reproduce strongly nonlinear and dispersive wave propagation. We test in particular the behavior of the new hybrid finite-volume and finite-difference splitting approach recently developed by the authors and collaborators on the challenging benchmark of waves propagating over a submerged bar. Such a configuration requires a model with very good dispersive properties, because of the high-order harmonics generated by topography-induced nonlinear interactions. We thus depart from the aforementioned work and choose to use a new Green-Naghdi system with improved frequency dispersion characteristics. The absence of dry areas also allows us to improve the treatment of the hyperbolic part of the equations. This leads to very satisfying results for the demanding benchmarks under consideration

Large time wellposdness to the 3-D Capillary-Gravity Waves in the long wave regime

In the regime of weakly transverse long waves, given long-wave initial data, we prove that the nondimensionalized water wave system in an infinite strip under influence of gravity and surface tension on the upper free interface has a unique solution on [0,{T}/\eps] for some \eps independent of constant $T.$ We shall prove in the subsequent paper \cite{MZZ2} that on the same time interval, these solutions can be accurately approximated by sums of solutions of two decoupled Kadomtsev-Petviashvili (KP) equations.Comment: Split the original paper(The long wave approximation to the 3-D capillary-gravity waves) into two parts, this is the first on

Derivation of the Zakharov equations

This paper continues the study of the validity of the Zakharov model describing Langmuir turbulence. We give an existence theorem for a class of singular quasilinear equations. This theorem is valid for well-prepared initial data. We apply this result to the Euler-Maxwell equations describing laser-plasma interactions, to obtain, in a high-frequency limit, an asymptotic estimate that describes solutions of the Euler-Maxwell equations in terms of WKB approximate solutions which leading terms are solutions of the Zakharov equations. Because of transparency properties of the Euler-Maxwell equations, this study is led in a supercritical (highly nonlinear) regime. In such a regime, resonances between plasma waves, electromagnetric waves and acoustic waves could create instabilities in small time. The key of this work is the control of these resonances. The proof involves the techniques of geometric optics of Joly, M\'etivier and Rauch, recent results of Lannes on norms of pseudodifferential operators, and a semiclassical, paradifferential calculus

Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon

This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a disturbance moving at constant speed on top of two layers of fluids of different densities. Starting from the full Euler equations, we present several nonlinear asymptotic models, in the long wave regime. These models are rigorously justified by consistency or convergence results. A careful theoretical and numerical analysis is then provided, in order to predict the behavior of the flow and in which situations the dead-water effect appears.Comment: To appear in Nonlinearit

A multiple-beam CLEAN for imaging intra-day variable radio sources

The CLEAN algorithm, widely used in radio interferometry for the deconvolution of radio images, performs well only if the raw radio image (dirty image) is, to good approximation, a simple convolution between the instrumental point-spread function (dirty beam) and the true distribution of emission across the sky. An important case in which this approximation breaks down is during frequency synthesis if the observing bandwidth is wide enough for variations in the spectrum of the sky to become significant. The convolution assumption also breaks down, in any situation but snapshot observations, if sources in the field vary significantly in flux density over the duration of the observation. Such time-variation can even be instrumental in nature, for example due to jitter or rotation of the primary beam pattern on the sky during an observation. An algorithm already exists for dealing with the spectral variation encountered in wide-band frequency synthesis interferometry. This algorithm is an extension of CLEAN in which, at each iteration, a set of N `dirty beams' are fitted and subtracted in parallel, instead of just a single dirty beam as in standard CLEAN. In the wide-band algorithm the beams are obtained by expanding a nominal source spectrum in a Taylor series, each term of the series generating one of the beams. In the present paper this algorithm is extended to images which contain sources which vary over both frequency and time. Different expansion schemes (or bases) on the time and frequency axes are compared, and issues such as Gibbs ringing and non-orthogonality are discussed. It is shown that practical considerations make it often desirable to orthogonalize the set of beams before commencing the cleaning. This is easily accomplished via a Gram-Schmidt technique.Comment: 9 pages, 7 figures. Accepted for publication in A&

Novos marcadores para fins de mapeamento e localização de QTLs a partir de PCR-RFLP de genes de genoma café brasileiro.

O mapeamento genético é uma das estratégias mais visadas para fins de melhoramento genético e ganha maior importância a partir do surgimento de marcadores do tipo SNPs ou INDELs, facilitado pelos projetos genomas, sobretudo de ESTs. Assim, análises in silico de busca de polimorfismo SNPs em seqüências relacionadas com qualidade de bebida e derivadas de C.arabica e C.canephora foram analisadas e o polimorfismo entre as duas espécies validado para seis genes (quatro proteases e dois de sacarose) a partir de estudos de laboratório utilizando a técnica PCR-RFLP. Para tanto, após confirmação do polimorfismo nas duas espécies parentais, foram genotipadas 90 plantas F2 derivadas da autofecundação de um híbrido interespecífico de Coffea arabica e C. canephora 4x. Após a obtenção dos amplificados, estes foram digeridos com diversas enzimas de restrição de quatro bases (Alu I, Dde I, Eco RI, Hae III, Mse I e Msp, Fnu DII, Taq I; Scr FI). Dos seis genes analisados, quatro deles apresentaram segregação do tipo 3:1 na população F2 (Cisteína 8, Cisteína 5, B-Fructosidase e Sacarose Fosfato Síntase), demonstrando a utilização dos mesmos para fins de mapeamento

The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations

In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters $\epsilon$ and $\delta$ measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.Comment: 24 pages, to appear in Discrete and Continuous Dynamical System

Construção de um mapa genético a partir de uma população F2 derivada do cruzamento entre Coffea arabica e C. canephora e Sua utilidade para qualidade de bebida.

Mapas genéticos com base em marcadores moleculares têm sido desenvolvidos em grande número de plantas como uma estratégia eficaz para seleção assistida pelo marcador. No presente estudo, marcadores AFLP e SSR foram utilizados para construção de um mapa genético em uma população F2 criada a partir da autofecundação do híbrido F1 do cruzamento entre Coffea arabica e Coffea canephora. Foram identificados 349 marcadores AFLP e 50 alelos SSR segregantes em 90 plantas F2. Para construção do mapa, apenas marcas em dose única e segregação 3:1 no F2 foram consideradas (248 marcadores AFLP e SSR 27 alelos, ou 68,9% dos marcadores polimórficos). Cento e sessenta e nove marcadores foram mapeados (155 AFLP e 14 SSR). Trinta e sete grupos ligação correspondentes a um total de 1011 cM foram obtidos, com uma distância média entre as marcas de 5,98 cm e 4,6 marcadores por grupo de ligação. Quarenta e seis marcadores associados a características agronômicas de interesse foram encontrados, dos quais, dezenove foram associados com teor de açúcar, oito de cafeína, oito para CGA, um para a cafeína e CGA e dez para a produção total por planta. A análise baseada em marcadores de dose única permitiu obter informação de QTL putativo associado à qualidade de bebida do café e produtividade. Marcadores adicionais serão incluídos a este trabalho para maior cobertura do genoma café

Second order averaging for the nonlinear Schroedinger equation with strongly anisotropic potential

International audienceWe consider the three dimensional Gross-Pitaevskii equation (GPE) describing a Bose-Einstein Condensate (BEC) which is highly confi ned in vertical z direction. The highly confi ned potential induces high oscillations in time. If the confi nement in the z direction is a harmonic trap (which is widely used in physical experiments), the very special structure of the spectrum of the confi nement operator will imply that the oscillations are periodic in time. Based on this observation, it can be proved that the GPE can be averaged out with an error of order of epsilon, which is the typical period of the oscillations. In this article, we construct a more accurate averaged model, which approximates the GPE up to errors of order epsilon squared. Then, expansions of this model over the eigenfunctions (modes) of the vertical Hamiltonian Hz are given in convenience of numerical application. Effi cient numerical methods are constructed for solving the GPE with cylindrical symmetry in 3D and the approximation model with radial symmetry in 2D, and numerical results are presented for various kinds of initial data

Modern optical astronomy: technology and impact of interferometry

The present `state of the art' and the path to future progress in high spatial resolution imaging interferometry is reviewed. The review begins with a treatment of the fundamentals of stellar optical interferometry, the origin, properties, optical effects of turbulence in the Earth's atmosphere, the passive methods that are applied on a single telescope to overcome atmospheric image degradation such as speckle interferometry, and various other techniques. These topics include differential speckle interferometry, speckle spectroscopy and polarimetry, phase diversity, wavefront shearing interferometry, phase-closure methods, dark speckle imaging, as well as the limitations imposed by the detectors on the performance of speckle imaging. A brief account is given of the technological innovation of adaptive-optics (AO) to compensate such atmospheric effects on the image in real time. A major advancement involves the transition from single-aperture to the dilute-aperture interferometry using multiple telescopes. Therefore, the review deals with recent developments involving ground-based, and space-based optical arrays. Emphasis is placed on the problems specific to delay-lines, beam recombination, polarization, dispersion, fringe-tracking, bootstrapping, coherencing and cophasing, and recovery of the visibility functions. The role of AO in enhancing visibilities is also discussed. The applications of interferometry, such as imaging, astrometry, and nulling are described. The mathematical intricacies of the various `post-detection' image-processing techniques are examined critically. The review concludes with a discussion of the astrophysical importance and the perspectives of interferometry.Comment: 65 pages LaTeX file including 23 figures. Reviews of Modern Physics, 2002, to appear in April issu