SLIDES: Delta Overview

Presenter: Leo Winternitz, The Nature Conservancy, California Water Program, Sacramento, CA 17 slide

SLIDES: Delta Overview

Presenter: Leo Winternitz, The Nature Conservancy, California Water Program, Sacramento, CA 17 slide

Weak Transversality and Partially Invariant Solutions

New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of the symmetry group of the system in situations when the standard Lie method of symmetry reduction is not applicable.Comment: 23 pages, preprint CRM-284

Secondary production levels of the asiatic clam Corbicula fluminea from the Sacramento-San Joaquin Delta

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Lie algebra symmetry analysis of the Helfrich and Willmore surface shape equations

We compute the Lie symmetry algebra of the equation of Helfrich surfaces and we show that it is the algebra of conformal vector fields of R2. We also show that in the particular case of the Willmore surfaces we have to add the homothety vector field of R3 to the aforementioned algebra. We prove that a Helfrich surface that is invariant w.r.t. a conformal symmetry is a helicoid and that all such surface solutions satisfy one and the same system of ordinary differential equations obtained by symmetry reduction. We also show that for the Willmore surface shape equation the symmetry reduction leads to two systems of ODEs. Then we construct explicit solutions in the case of revolution surfaces. The results obtained can be extended to the study of PDE problems in 2 spatial dimensions admitting conformal Lie symmetries