Juan M. Restrepo

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Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation u t + u x + (u p) x ? u xxt = 0: For p > 5, the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of(More)
The aim of data assimilation is to infer the state of a system from a geophysi-cal model and possibly incomplete or nonuniformly distributed spatiotemporal observational data. Used extensively in engineering control theory applications, data assimilation has relatively recently been introduced into meteorological forecasting, natural-resource recovery(More)
Description: This workshop will assess the current state-of-the-art and identify needs and opportunities for future research at the intersection of large-scale inverse problems and uncertainty quantification. It will bring together and cross-fertilize the perspectives of researchers in the areas of inverse problems and data assimilation, statistics,(More)
Considered here is a model equation put forward by Benjamin that governs approximately the evolution of waves on the interface of a two-uid system in which surface tension eeects cannot be ignored. Our principal focus is the traveling-wave solutions called solitary waves, and three aspects will be investigated. A constructive proof of the existence of these(More)
Described here is a path integral, sampling-based approach for data assimilation, of sequential data and evolutionary models. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution,(More)
i ii Abstract A model is proposed for the formation and evolution of three-dimensional sedimen-tary structures such as longshore sand ridges on the continental shelf in water deeper than that of the shoaling region. Owing to the striking similarity between the bar spacing and the length scales in which interactions among the most energetic modes of shallow(More)
This paper presents and evaluates the numerical solution of a coupled system of equations that arises in a model for the formation and evolution of three-dimensional longshore sand ridges. The model is based on the interaction between surrcial or internal weakly nonlinear shallow-water waves, having weak spanwise spatial dependence, and the deformable(More)