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Variable depth KdV equations and generalizations to more nonlinear regimes
Full text linkWe study here the water waves problem for uneven bottoms in a highly nonlinear regime where
the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known
that, for such regimes, a generalization of the KdV equation (somehow linked to
the Camassa-Holm equation) can be derived and justified [Constantin and Lannes,
Arch. Ration. Mech. Anal. 192 (2009) 165–186] when the bottom is
flat. We generalize here this result
with a new class of equations taking into account variable bottom topographies. Of course,
many variable depth KdV equations existing in the literature are recovered as particular cases.
Various regimes for the topography regimes are investigated and we prove consistency
of these models, as well as a full justification
for some of them. We also study the problem of wave breaking for our new
variable depth and highly nonlinear generalizations of the KdV equations
Derivation and analysis of a new 2D Green–Naghdi system
No full textWe derive here a variant of the Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard Green-Naghdi equations. Its mathematical interest is that it allows a control of the rotational part of the (vertically averaged) horizontal velocity, which is not the case for the usual Green-Naghdi equations. Using this property, we show that the solution of these new equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition. Finally, we prove that the new Green-Naghdi equations conserve the almost irrotationality of the vertically averaged horizontal component of the velocity
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Coupled and scalar asymptotic models for internal waves over variable topography
No full textThe Green–Naghdi type model in the Camassa–Holm regime derived in [Comm. Pure Appl. Anal. 14(6) (2015) 2203–2230], describe the propagation of medium amplitude internal waves over medium amplitude topography variations. It is fully justified in the sense that it is well-posed, consistent with the full Euler system and converges to the latter with corresponding initial data. In this paper, we generalize this result by constructing a fully justified coupled asymptotic model in a more complex physical case of variable topography. More precisely, we are interested in specific bottoms wavelength of characteristic order λb=λ/α where λ is a characteristic horizontal length (wave-length of the interface). We assume a slowly varying topography with large amplitude (βα=O(μ), where β characterizes the shape of the bottom). In addition, our system permits the full justification of any lower order, well-posed and consistent model. We apply the procedure to scalar models driven by simple unidirectional equations in the Camassa–Holm and long wave regimes and under some restrictions on the topography variations. We also show that wave breaking of solutions to such equations occurs in the Camassa–Holm regime with slow topography variations and for a specific set of parameters.Publishe
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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