Space-time Reconstruction of Oceanic Sea States via Variational Stereo Methods

We present a remote sensing observational method for the measurement of the spatio-temporal dynamics of ocean waves. Variational techniques are used to recover a coherent space-time reconstruction of oceanic sea states given stereo video imagery. The stereoscopic reconstruction problem is expressed in a variational optimization framework. There, we design an energy functional whose minimizer is the desired temporal sequence of wave heights. The functional combines photometric observations as well as spatial and temporal regularizers. A nested iterative scheme is devised to numerically solve, via 3-D multigrid methods, the system of partial differential equations resulting from the optimality condition of the energy functional. The output of our method is the coherent, simultaneous estimation of the wave surface height and radiance at multiple snapshots. We demonstrate our algorithm on real data collected off-shore. Statistical and spectral analysis are performed. Comparison with respect to an existing sequential method is analyzed.

A Variational Stereo Method for the Three-Dimensional Reconstruction of Ocean Waves

We develop a novel remote sensing technique for the observation of waves on the ocean surface. Our method infers the 3-D waveform and radiance of oceanic sea states via a variational stereo imagery formulation. In this setting, the shape and radiance of the wave surface are given by minimizers of a composite energy functional that combines a photometric matching term along with regularization terms involving the smoothness of the unknowns. The desired ocean surface shape and radiance are the solution of a system of coupled partial differential equations derived from the optimality conditions of the energy functional. The proposed method is naturally extended to study the spatiotemporal dynamics of ocean waves and applied to three sets of stereo video data. Statistical and spectral analysis are carried out. Our results provide evidence that the observed omnidirectional wavenumber spectrum S(k) decays as k-2.5 is in agreement with Zakharov's theory (1999). Furthermore, the 3-D spectrum of the reconstructed wave surface is exploited to estimate wave dispersion and currents.

Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Error estimation and iterative improvement for the numerical solution of operator equations /

Bibliography: p. 85-87.

A multirate ordinary differential equation integrator /

Originally presented as the author's thesis, University of Illinois at Urbana-Champaign.

On Newton-iterative methods for the solution of systems of nonlinear equations /

Based on the author's thesis, Yale.

An economical algorithm for the solution of elliptic difference equations independent of user-supplied parameters,

Extra t.p., with thesis statement, inserted.

Evaluation of an integration technique for the solution of nonlinear equations.

Thesis (M.S.)--University of Illinois at Urbana-Champaign.

Rapid solution of finite element equations on locally refined grids by multi-level methods /

"UILU-ENG 80 1712."

Die partiellen Differential-Gleichungen der mathematischen Physid nach Riemann's Vorlesungen

Mode of access: Internet.

Ueber die integration der differential gleichung (t-a)(t-b)(t-c) d²y/dt² + (a+bt+ct²) dy/dt + (d+et)y=0 ...

Inaug.-dis.--Göttingen.

Über die Integration der allgemeinen Riccatischen Gleichung dy/dx + y² = x und der von ihr abhängigen Differential-Gleichungen.

Imprint label on cover: Leipzig, C. A. Koch.

Lehrbuch der differential-gleichungen... Mit einem anhange: Die resultate der im lehrbuche angeführten übungsaufgaben enthaltend,

Translation of: A treatise on differential equations.

Über die partielle Differential-Gleichung [Delta]v+k²v=0 und deren Auftreten in der mathematischen Physik.

Available on demand as hard copy or computer file from Cornell University Library.

Einleitung in die Theorie der linearen Differential-Gleichungen mit einer unabhängigen Variablen,

Available on demand as hard copy or computer file from Cornell University Library.