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Full-Text Articles in Physical Sciences and Mathematics
Beam Collapse As An Explanation Foranomalous Ocular Damage, James A. Powell, J. V. Moloney, A. C. Newell, R. A. Albanese
Beam Collapse As An Explanation Foranomalous Ocular Damage, James A. Powell, J. V. Moloney, A. C. Newell, R. A. Albanese
James A. Powell
The basic mathematical phenomena relevant to ocular damage caused by ultrashort laser pulses are discussed with the use of mathematical results and numerical modeling. The primary effects of nonlinear self-focusing and beam collapse are examined in the ocular safety context. Finite-time material response and group-velocity dispersion are discussed as possible mitigating factors. An argument is presented that indicates that the initial stages of beam collapse are essentially two-dimensional. Experiments are suggested that might help distinguish the most important contributing factors in the damage regime. The numerical methodology is detailed in an appendix.
Competition Between Generic And Nongeneric Fronts Inenvelope Equations, James A. Powell, A. C. Newell, C. K. R. T. Jones
Competition Between Generic And Nongeneric Fronts Inenvelope Equations, James A. Powell, A. C. Newell, C. K. R. T. Jones
James A. Powell
Arguments are presented for understanding the selection of the speed and the nature of the fronts that join stable and unstable states on the supercritical side of first-order phase transitions. It is suggested that from compact support, nonpositive-definite initial conditions, observable front behavior occurs only when the asymptotic spatial structure of a trajectory in the Galilean ordinary differential equation (ODE) corresponds to the most unstable temporal mode in the governing partial differential equation (PDE). This selection criterion distinguishes between a "nonlinear" front, which has its origin in the first-order nature of the bifurcation, and a "linear" front. The nonlinear front …