Eigenvalues and eigenfunctions for general graetz problems

Eigenvalues and Eigenfunctions

The article describes the eigenvalue and eigenfunction problems. Basic properties, some applications and examples in system analysis are provided.

Conjugated Graetz Problems-i General Formalism and a Class of Solid-fluid Problems

Conjugated Graetz problems arise where two (or more) phases, with at least one phase in fully developed flow, exchange energy or mass across an intervening surface. In these problems the temperature or concentration fields are coupled through the conjugating conditions which express the continuity of fluxes and the rate of transfer. A general formalism is presented first for the analysis of the...

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

Eigenvalues and Eigenfunctions of the Laplacian

The problem of determining the eigenvalues and eigenvectors for linear operators acting on finite dimensional vector spaces is a problem known to every student of linear algebra. This problem has a wide range of applications and is one of the main tools for dealing with such linear operators. Some of the results concerning these eigenvalues and eigenvectors can be extended to infinite dimension...

Eigenvalues and eigenfunctions of a clover plate

We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories. The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows that it has b...