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Full-Text Articles in Physical Sciences and Mathematics
Limiting Behavior Of Nondeterministic Fillings Of The Torus By Colored Squares, Pablo Rosell Gonzalez
Limiting Behavior Of Nondeterministic Fillings Of The Torus By Colored Squares, Pablo Rosell Gonzalez
Graduate Theses and Dissertations
In this work we study different dynamic processes for filling tori and n×∞ bands with edge-to-edge black and white squares at random. First we present a simulation for the Random Sequential Adsorption (RSA) with nearest-neighbor rejection on n×n tori. We are interested in the ratio of black to total tiles once the domain is saturated for large domains. Next we study the annealing process. Given a random excited tiling of an n×n torus, we show that as t→∞ the system reaches a stable state in which no tile is excited. This stable state can either be a tiling whose tiles …
A Restarted Homotopy Method For The Nonsymmetric Eigenvalue Problem, Brandon Hutchison
A Restarted Homotopy Method For The Nonsymmetric Eigenvalue Problem, Brandon Hutchison
Graduate Theses and Dissertations
The eigenvalues and eigenvectors of a Hessenberg matrix, H, are computed with a combination of homotopy increments and the Arnoldi method. Given a set, Ω, of approximate eigenvalues of H, there exists a unique vector f = f(H,Ω) in Rn where λ(H-e1ft)=Ω. A diagonalization of the homotopy H(t)=H−(1−t)e1ft at $t=0$ provides a prediction of the eigenvalues of H(t) at later times. These predictions define a new Ω that defines a new homotopy. The correction for each eigenvalue has an O(t2) error estimate, enabling variable step size and efficient convergence tests. Computations are done primarily in real arithmetic, and …