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Showing 1 to 7 of 7 for “"area preserving"”.
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Homoclinic Points in the Composition of Two Reflections
We examine a class of planar area preserving mappings and give a geometric condition that guarantees the existence of homoclinic points. To be more precise, let $f,g:R \to R$ be $C^1$ functions with domain all of $R$. Let $F:R^2 \to R^2$ denote a horizontal reflection in the curve $x=-f(y)$, and …
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From determinism to stochasticity
Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-06-03T17:40:28Z No. of bitstreams: 1 1986_mistriotis.pdf: 3975733 bytes, checksum: 43533a8fc01e8af27a7fcab38a485c7a (MD5)
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Parallel algorithms for direct blood flow simulations
… vesicles. Vesicles and red blood cells are both area preserving closed membranes that resist bending. Beyond red blood cells, vesicles can be used to investigate the behavior of cell membranes, intracellular organelles, and viral particles. Given the importance of vesicle flows, in this thesis we …
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Multi-Symplectic Integrators for Nonlinear Wave Equations
<p>Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown to be robust, efficient and accurate in long-term calculations. In this thesis, we show how symplectic integrators have a natural generalization to Hamiltonian PDEs by introducing the concept of …
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Geometric and electromagnetic response and anomalies in topological phases of matter
… of the quantum Hall fluid to time-dependent area-preserving deformations, which are a particular example of a geometric perturbation. In Chapter 2 we study classical two-dimensional fluids with Hall viscosity in their own right. In particular, we study the physics of a swimmer immersed in …
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The Lie Symmetries of a Few Classes of Harmonic Functions
In a differential geometry setting, we can analyze the solutions to systems of differential equations in such a way as to allow us to derive entire classes of solutions from any given solution. This process involves calculating the Lie symmetries of a system of equations and looking at the …
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Topological phases, non-equilibrium dynamics and parallels of black hole phenomena in condensed matter
… in Minkowksi spacetime and the algebra of area preserving transformations in the lowest Landau level of quantum hall effect, an applied saddle potential acts as an equivalent to the Rindler Hamiltonian giving rise to a parallel of Hawking-Unurh effect. In the lowest Landau level, the saddle …