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- P Aerts, R Van Damme, L Van Elsacker, V Duchêne
- American journal of physical anthropology
- 2000

Spatio-temporal gait characteristics (step and stride length, stride frequency, duty factor) were determined for the hind-limb cycles of nine bonobos (Pan paniscus) walking quadrupedally and bipedally at a range of speeds. The data were recalculated to dimensionless quantities according to the principle of dynamic similarity. Lower leg length was used as… (More)

- Vincent Duchêne
- SIAM J. Math. Analysis
- 2010

In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume the thickness of the upper and lower fluids to be of comparable size, and small compared to the characteristic… (More)

We study the relevance of various scalar equations, such as inviscid Burgers’, Korteweg-de Vries (KdV), extended KdV, and higher order equations (of Camassa-Holm type), as asymptotic models for the propagation of internal waves in a two-fluid system. These scalar evolution equations may be justified with two approaches. The first method consists in… (More)

We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order to offer a unified and comprehensive exposition. Anterior models such as the shallow water and Boussinesq systems, as… (More)

- Vincent Duchêne
- J. Nonlinear Science
- 2014

The rigid-lid approximation is a commonly used simplification in the study of densitystratified fluids in oceanography. Roughly speaking, one assumes that the displacements of the surface are negligible compared with interface displacements. In this paper, we offer a rigorous justification of this approximation in the case of two shallow layers of… (More)

Boundedness of wave operators for Schrödinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.

We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one-dimensional waves, and consider the case of a flat bottom. Following the method presented in [6] for the one-layer case, we introduce a new family of symmetric hyperbolic models, that are equivalent… (More)

- Vincent Duchêne, Michael I. Weinstein
- Multiscale Modeling & Simulation
- 2011

We study one-dimensional scattering for a decaying potential with rapid periodic oscillations and strong localized singularities. In particular, we consider the Schrödinger equation Hǫ ψ ≡ ` −∂ x + V0(x) + q (x, x/ǫ) ́ ψ = kψ for k ∈ R and ǫ ≪ 1. Here, q(·, y + 1) = q(·, y), has mean zero and |V0(x) + q(x, ·)| → 0 as |x| → ∞. The distorted plane waves of Hǫ… (More)

- Vincent Duchêne, Samer Israwi, Raafat Talhouk
- SIAM J. Math. Analysis
- 2015

This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present a new Green-Naghdi type model in the Camassa-Holm (or medium amplitude) regime. This model is fully justified, in the… (More)

We investigate scattering, localization and dispersive time-decay properties for the onedimensional Schrödinger equation with a rapidly oscillating and spatially localized potential, q = q(x, x/ ), where q(x, y) is periodic and mean zero with respect to y. Such potentials model a microstructured medium. Homogenization theory fails to capture the correct… (More)