Now showing items 1-6 of 6
Energy minimizers, gradient flow solutions, and computational investigations in the theory of biharmonic maps
We present the definitions, derive the relevant Euler-Lagrange equations, and establish various properties concerning biharmonic maps. We investigate several classes of examples exhibiting singular behavior. Existence of ...
A minimization of a curvature functional on fiber bundles
Let B be a smooth compact orientable surface without boundary and with $\chi(B) < 0.$ We examine two types of fiber bundles M over B with fiber F. The first is a principle fiber bundle with a two-torus fiber and the second ...
Can you hear the size of the vertices? An inverse spectral problem of Laplacians on weighted graphs
Let G be a simple graph with n vertices. We define a Laplacian $\Delta$ on G which depends on an assignment of a weight to each vertex of G. One of the eigenvalues of $\Delta$ will always be 0. We fix the remaining (n $-$ ...
A variational approach to the local uniqueness of minimal surfaces immersed in R(3)
In the past 20 years, many techniques have been developed for proving the existence of complete minimal surfaces immersed in space. Few methods are known for classifying such surfaces. In order to study the structure of ...
System identification for robust control
In the design of a robust control system, one needs a nominal model together with a quantitative bound on the uncertainty that results from under-modeling and disturbances. In this thesis we do not intentionally seek a ...
A priori error estimates of finite element models of systems of shallow water equations
In recent years, there has been much interest in the numerical solution of shallow water equations. The numerical procedure used to solve the shallow water equations must resolve the physics of the problem without introducing ...