Juan M. Restrepo

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An application of Pontryagin's Maximum Principle, data assimilation is used to blend possibly incomplete or nonuniformly distributed spatio-temporal observational data into geo-physical models. Used extensively in engineering control theory applications, data assimilation has relatively recently been introduced into meteorological forecasting,(More)
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)
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)
From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system--a saline jet descending through a salinity gradient--which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a(More)
We introduce a model for the dynamics of oil in suspension, appropriate for shallow waters, including the nearshore environment. This model is capable of oil mass conservation and does so by evolving the oil on the sea surface as well as the oil in the subsurface. The shallower portion of the continental shelf poses compounding unique modeling challenges.(More)
We describe experimental observations of fully developed, large-amplitude bars under the action of a shearing fluid. The experiments were performed in an annular tank filled with water and sheared above by a steady motor source. The same steady shearing flow can produce a variety of different erodible bed manifestations: advective or precessive bars, which(More)
We propose a variant of the Bred Vector (BV) algorithm, orginally introduced by Z. Toth and E. Kalnay (Bulletin of the American Mete-outputs to changes in initial conditions for weather forecasting. The new algorithm, which we call the Ensemble Bred Vector or EBV, is based on collective dynamics in an essential way. As such, it features distinctive(More)
For a self-adjoint linear operator with discrete spectrum or a Hermitian matrix the " extreme " eigenvalues define the boundaries of clusters in the spectrum of real eigenvalues. The outer extreme ones are the largest and the smallest eigenvalues. If there are extended intervals in the spectrum in which no eigenvalues are present, the eigenvalues bounding(More)
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