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The Shallow Water Equations In Lagrangian Coordinates, J. L. Mead
The Shallow Water Equations In Lagrangian Coordinates, J. L. Mead
Mathematics Faculty Publications and Presentations
Recent advances in the collection of Lagrangian data from the ocean and results about the well-posedness of the primitive equations have led to a renewed interest in solving flow equations in Lagrangian coordinates. We do not take the view that solving in Lagrangian coordinates equates to solving on a moving grid that can become twisted or distorted. Rather, the grid in Lagrangian coordinates represents the initial position of particles, and it does not change with time. However, using Lagrangian coordinates results in solving a highly nonlinear partial differential equation. The nonlinearity is mainly due to the Jacobian of the coordinate …
Quantum Deformations Of Fundamental Groups Of Oriented 3-Manifolds, Uwe Kaiser
Quantum Deformations Of Fundamental Groups Of Oriented 3-Manifolds, Uwe Kaiser
Mathematics Faculty Publications and Presentations
We compute two-term skein modules of framed oriented links in oriented 3-manifolds. They contain the self-writhe and total linking number invariants of framed oriented links in a universal way. The relations in a natural presentation of the skein module are interpreted as monodromies in the space of immersions of circles into the 3-manifold.