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Full-Text Articles in Physical Sciences and Mathematics
Steady State Solutions For A System Of Partial Differential Equations Arising From Crime Modeling, Bo Li
Steady State Solutions For A System Of Partial Differential Equations Arising From Crime Modeling, Bo Li
HMC Senior Theses
I consider a model for the control of criminality in cities. The model was developed during my REU at UCLA. The model is a system of partial differential equations that simulates the behavior of criminals and where they may accumulate, hot spots. I have proved a prior bounds for the partial differential equations in both one-dimensional and higher dimensional case, which proves the attractiveness and density of criminals in the given area will not be unlimitedly high. In addition, I have found some local bifurcation points in the model.
Spectral Properties Of Photonic Crystals: Bloch Waves And Band Gaps, Robert Paul Viator Jr
Spectral Properties Of Photonic Crystals: Bloch Waves And Band Gaps, Robert Paul Viator Jr
LSU Doctoral Dissertations
The author of this dissertation studies the spectral properties of high-contrast photonic crystals, i.e. periodic electromagnetic waveguides made of two materials (a connected phase and included phase) whose electromagnetic material properties are in large contrast. A spectral analysis of 2nd-order divergence-form partial differential operators (with a coupling constant k) is provided. A result of this analysis is a uniformly convergent power series representation of Bloch-wave eigenvalues in terms of the coupling constant k in the high-contrast limit k -> infinity. An explicit radius of convergence for this power series is obtained, and can be written explicitly in terms of the …