Enrique Thomann

Bio: Enrique Thomann is an academic researcher from Oregon State University. The author has contributed to research in topics: Uniqueness & Navier–Stokes equations. The author has an hindex of 17, co-authored 61 publications receiving 857 citations. Previous affiliations of Enrique Thomann include Courant Institute of Mathematical Sciences.

Influences of fire–vegetation feedbacks and post-fire recovery rates on forest landscape vulnerability to altered fire regimes

Abstract: 1Smithsonian Conservation Biology Institute, Front Royal, VA, USA; 2Department of Mathematics, Oregon State University, Corvallis, OR, USA; 3Department of Geography, University of Colorado at Boulder, Boulder, CO, USA; 4School of Environment, University of Auckland, Auckland, New Zealand; 5Department of Geography, Portland State University, Portland, OR, USA; 6Laboratorio Ecotono, INIBIOMA, CONICET-Universidad Nacional del Comahue, Bariloche, Río Negro, Argentina; 7Departamento de Ecología, Universidad Nacional del Comahue, Bariloche, Río Negro, Argentina and 8Center for Tropical Forest Science– Forest Global Earth Observatory, Smithsonian Tropical Research Institute, Panama

Occupation and local times for skew Brownian motion with applications to dispersion across an interface

Abstract: This research was partially supported by the grant GrantCMG EAR-0724865 from the National Science Foundation.

Multi‐dimensional shock fronts for second order wave equations

Abstract: On etudie l'existence au temps court et la stabilite structurelle des fronts de choc multidimensionnels pour des equations d'onde quasi lineaires scalaires d'ordre 2

Majorizing kernels and stochastic cascades with applications to incompressible Navier-Stokes equations

Abstract: A general method is developed to obtain conditions on initial data and forcing terms for the global existence of unique regular solutions to incompressible 3d Navier-Stokes equations. The basic idea generalizes a probabilistic approach introduced by LeJan and Sznitman (1997) to obtain weak solutions whose Fourier transform may be represented by an expected value of a stochastic cascade. A functional analytic framework is also developed which partially connects stochastic iterations and certain Picard iterates. Some local existence and uniqueness results are also obtained by contractive mapping conditions on the Picard iteration.

On the Navier-Stokes equations

Abstract: A criterion is given for the convergence of numerical solutions of the Navier-Stokes equations in two dimensions under steady conditions. The criterion applies to all cases, of steady viscous flow in two dimensions and shows that if the local ' mesh Reynolds number ', based on the size of the mesh used in the solution, exceeds a certain fixed value, the numerical solution will not converge.

Navier-stokes, fluid dynamics, and image and video inpainting

Abstract: Image inpainting involves filling in part of an image or video using information from the surrounding area. Applications include the restoration of damaged photographs and movies and the removal of selected objects. We introduce a class of automated methods for digital inpainting. The approach uses ideas from classical fluid dynamics to propagate isophote lines continuously from the exterior into the region to be inpainted. The main idea is to think of the image intensity as a 'stream function for a two-dimensional incompressible flow. The Laplacian of the image intensity plays the role of the vorticity of the fluid; it is transported into the region to be inpainted by a vector field defined by the stream function. The resulting algorithm is designed to continue isophotes while matching gradient vectors at the boundary of the inpainting region. The method is directly based on the Navier-Stokes equations for fluid dynamics, which has the immediate advantage of well-developed theoretical and numerical results. This is a new approach for introducing ideas from computational fluid dynamics into problems in computer vision and image analysis.

The quantum hydrodynamic model for semiconductor devices

Abstract: The classical hydrodynamic equations can be extended to include quantum effects by incorporating the first quantum corrections These quantum corrections are $O( {\hbar ^2 } )$ The full three-dimensional quantum hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner–Boltzmann equation The QHD conservation laws have the same form as the classical hydrodynamic equations, but the energy density and stress tensor have additional quantum terms These quantum terms allow particles to tunnel through potential barriers and to build up in potential wellsThe three-dimensional QHD transport equations are mathematically classified as having two Schrodinger modes, two hyperbolic modes, and one parabolic mode The one-dimensional steady-state QHD equations are discretized in conservation form using the second upwind methodSimulations of a resonant tunneling diode are presented that show charge buildup in the quantum well and negative differential resistance (NDR) in the current-v