Lefschetz Center for Dynamical Systems Seminar
Abstract: I will present a numerical model of optical parametric oscillators that takes into account multi-mode operation of the OPO and the leading order effect of thermal deposition of optical field energy in the quadratic medium. Even though the model captures transient behaviour of the OPO on the order of the nonlinear mixing scale (nanoseconds), a novel and self-consistent advancement method is used to run simulations for durations commensurate with the thermal diffusion scale (milliseconds) and to steady-state (seconds). Using the model, I demonstrate self-induced thermal lensing of the optical fields and temperature-biased competition between two signal/idler pairs.
Brown University Center for Statistical Sciences Seminar
Reception following seminar at 167 Angell Street, 2nd floor conference room. |
Abstract: In unequal-probability-of-inclusion sample designs, correlations between the probability of inclusion and the sampled data can induce bias. Weights equal to the inverse of the probability of selection are often used to counteract this bias. Highly disproportional sample designs have large weights, which can introduce unnecessary variability in statistics such as the population mean estimate. Weight trimming or stratum collapsing models reduce large weights to fixed cut point values to reduce variance, but these approaches are usually ad-hoc with little systematic attention to the effect on MSE of the resulting estimates. An alternative approach (Holt and Smith 1979, Lazzaroni and Little 1998) uses hierarchical models to induce shrinkage across weight strata when obtaining posterior estimates of the population mean. An extension of this approach utilizes a non-parametric random-effects model that is robust against mean structure misspecification (Elliott and Little 2000). Robustness-efficiency tradeoffs of the nonparametric RE model against parametric RE models will be examined, as well as the performance of these models under differing sample designs. Extensions of this approach to linear and generalized linear regression parameters will also be considered.
Brown Analysis Seminar
Scientific Computing Seminar
Abstract: Atomic force microscopes employ cylindrical or stacked piezoceramic actuators to obtain angstrom level resolution. However, even at the low drive levels used to achieve these tolerances, the actuators exhibit hysteresis and certain constitutive nonlinearities. These effects must be accurately quantified and controlled to maintain the resolution, robustness and speed of both current instruments and future generations of devices based on this technology.
In this talk, a variety of techniques for modeling hysteresis in piezoceramic materials will be discussed, and inverse compensation techniques for linear and nonlinear control design in the microscopes will be presented. Finally reduced-order models based on proper orthogonal decompositions (POD) will be employed to provide controllers which can be implemented in real time.
PDE Seminar
<--- 2001 Index