Physical Sciences and Mathematics Commons^™

Simulation Of Engineering Systems Described By High-Index Dae And Discontinuous Ode Using Single Step Methods, Marc Compere

Publications

This dissertation presents numerical methods for solving two classes of or-dinary diferential equations (ODE) based on single-step integration meth-ods. The first class of equations addressed describes the mechanical dynamics of constrained multibody systems. These equations are ordinary differential equations (ODE) subject to algebraic constraints. Accordinly they are called differential-algebraic equations (DAE).

Specific contributions made in this area include an explicit transforma-tion between the Hessenberg index-3 form for constrained mechanical systems to a canonical state-space form used in the nonlinear control communities. A hybrid solution method was developed that incorporates both sliding-mode control (SMC) from the controls literature and post-stabilization from …

Two Photon Absorption In Chromophore Doped Solid Matrices, S.C. Mancas, Michael Canva, Yves Levy, Kathleen A. Richardson, Giselle Roger

Publications

Over the past decades organic materials have shown an important potential for applications in the field of nonlinear optics. Two-photon absorbing materials can be optically addressed in three dimensions of space, which make them unique for many new applications, including 3D displays, optical memories, bio-sensors, etc. Fluorescent organic chromophores can be synthesized with structures especially optimized for this nonlinear optical property. Yet, for some applications, they have to be incorporated in solid state matrices. We especially investigate hybrid organic/inorganic doped matrices synthesized by solgel process. However , the linear transmission for such molecules is often significantly less than unity. Two-photon …