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

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

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&

An analytical study of PPP-RTK corrections: precision, correlation and user-impact

PPP-RTK extends the PPP concept by providing single-receiver users, next to orbits and clocks, also information about the satellite phase and code biases, thus enabling single-receiver ambiguity resolution. It is the goal of the present contribution to provide an analytical study of the quality of the PPP-RTK corrections as well as of their impact on the user ambiguity resolution performance. We consider the geometry-free and the geometry-based network derived corrections, as well as the impact of network ambiguity resolution on these corrections. Next to the insight that is provided by the analytical solutions, the closed form expressions of the variance matrices also demonstrate how the corrections depend on network parameters such as number of epochs, number of stations, number of satellites, and number of frequencies. As a result we are able to describe in a qualitative sense how the user ambiguity resolution performance is driven by the data from the different network scenarios

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

Review and principles of PPP-RTK methods

PPP-RTK is integer ambiguity resolution-enabled precise point positioning. In this contribution, we present the principles of PPP-RTK, together with a review of different mechanizations that have been proposed in the literature. By application of S-system theory, the estimable parameters of the different methods are identified and compared. Their interpretation is essential for gaining a proper insight into PPP-RTK in general, and into the role of the PPP-RTK corrections in particular. We show that PPP-RTK is a relative technique for which the ‘single-receiver user’ integer ambiguities are in fact double-differenced ambiguities. We determine the transformational links between the different methods and their PPP-RTK corrections, thereby showing how different PPP-RTK methods can be mixed between network and users. We also present and discuss four different estimators of the PPP-RTK corrections. It is shown how they apply to the different PPP-RTK models, as well as why some of the proposed estimation methods cannot be accepted as PPP-RTK proper. We determine analytical expressions for the variance matrices of the ambiguity-fixed and ambiguity-float PPP-RTK corrections. This gives important insight into their precision, as well as allows us to discuss which parts of the PPP-RTK correction variance matrix are essential for the user and which are not

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