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Full-Text Articles in Dynamical Systems
Tridiagonal Matrices And Boundary Conditions, J. J. P. Veerman, David K. Hammond
Tridiagonal Matrices And Boundary Conditions, J. J. P. Veerman, David K. Hammond
Mathematics and Statistics Faculty Publications and Presentations
We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary condition.
Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J. J. P. Veerman, Jovan Petrovic
Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J. J. P. Veerman, Jovan Petrovic
Mathematics and Statistics Faculty Publications and Presentations
Coherent state transfer is an important requirement in the construction of quantum computer hardware. The state transfer can be realized by linear next-neighbour-coupled finite chains. Starting from the commensurability of chain eigenvalues as the general condition of periodic dynamics, we find chains that support full periodic state revivals. For short chains, exact solutions are found analytically by solving the inverse eigenvalue problem to obtain the coupling coefficients between chain elements. We apply the solutions to design optical waveguide arrays and perform numerical simulations of light propagation thorough realistic waveguide structures. Applications of the presented method to the realization of a …