Browsing by Author "Betelu, Santiago"

Now showing 1 - 4 of 4
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    Capillarity driven spreading of power-law fluids
    (2001-04) Betelu, Santiago; Fontelos, M.A.
    We investigate the spreading of thin liquid films of power-law rheology. We construct an explicit travelling wave solution and source-type similarity solutions. We show that when the nonlinearity exponent $\lambda$ for the rheology is larger than one, the governing dimensionless equation $h_t+(h^{\lambda+2}|h_{xxx}|^{\lambda-1}h_{xxx})_x=0$ admits solutions with compact support and moving fronts. We also show that the solutions have bounded energy dissipation rate.
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    Focusing of an elongated hole in porous medium flow
    (2001-06) Angenent, Sigurd; Aronson, D.G.; Betelu, Santiago; Lowengrub, J.S.
    In the focusing problem we study solutions to the porous medium equation $u_t=\Delta u^m$ whose initial distributions are positive in the exterior of a compact two-dimensional region and zero inside. We assume that the initial interface is elongated and possesses reflectional symmetry with respect to both the x- and y- axes. We implement a numerical scheme that adapts the numerical grid around the interface so as to maintain a high resolution as the interface shrinks to a point. We find that as t tends to the focusing time T, the interface becomes oval-like with the lengths of the major and minor axes $O(\sqrt{T-t})$ and $O(T-t)$ respectively. Thus, the aspect ratio is $O(1/\sqrt{T-t})$. By scaling and formal asymptotic arguments, we derive an approximate solution which is valid for all m. This approximation indicates that the numerically observed power behavior for the major and minor axes is universal for all m>1.
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    A method for denoising textured surfaces
    (2001-04) Betelu, Santiago; Tannenbaum, Allen; Sapiro, Guillermo
    In this note, we present a simple method to denoise triangulated and implicit surfaces in a manner which preserves the 3D shape texture. The technique is based upon the synthesis of partial differential equations (PDE's), implicit surfaces, and Wiener filtering. The basic idea is to apply a computationally efficient local Wiener filter to an implicit representation of the surface. Such a representation can be directly given as the algorithm input or explicitly obtained via partial differential equation based implicitation techniques applied to the triangulated data. The proposed method has a computational complexity O(N log N).
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    Noise-resistant affine skeletons of planar curves
    (1999-12) Betelu, Santiago; Sapiro, Guillermo; Tannenbaum, Allen; Giblin, Peter J.