Bunching-induced optical nonlinearity and instability in cold atoms [Invited].

We report a new nonlinear optical process that occurs in a cloud of cold atoms at low-light-levels when the incident optical fields simultaneously polarize, cool, and spatially-organize the atoms. We observe an extremely large effective fifth-order nonlinear susceptibility of χ(⁵) = 7.6 × 10⁻¹⁵ (m/V)⁴, which results in efficient Bragg scattering via six-wave mixing, slow group velocities (∼ c/10⁵), and enhanced atomic coherence times (> 100 μs). In addition, this process is particularly sensitive to the atomic temperatures, and provides a new tool for in-situ monitoring of the atomic momentum distribution in an optical lattice. For sufficiently large light-matter couplings, we observe an optical instability for intensities as low as ∼ 1 mW/cm² in which new, intense beams of light are generated and result in the formation of controllable transverse optical patterns.

Regularity of invariant densities for 1D systems with random switching

© 2015 IOP Publishing Ltd & London Mathematical Society.This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

Physical Insights, Steady Aerodynamic Effects, and a Design Tool for Low-Pressure Turbine Flutter

The successful, efficient, and safe turbine design requires a thorough understanding of the underlying physical phenomena. This research investigates the physical understanding and parameters highly correlated to flutter, an aeroelastic instability prevalent among low pressure turbine (LPT) blades in both aircraft engines and power turbines. The modern way of determining whether a certain cascade of LPT blades is susceptible to flutter is through time-expensive computational fluid dynamics (CFD) codes. These codes converge to solution satisfying the Eulerian conservation equations subject to the boundary conditions of a nodal domain consisting fluid and solid wall particles. Most detailed CFD codes are accompanied by cryptic turbulence models, meticulous grid constructions, and elegant boundary condition enforcements all with one goal in mind: determine the sign (and therefore stability) of the aerodynamic damping. The main question being asked by the aeroelastician, ``is it positive or negative?'' This type of thought-process eventually gives rise to a black-box effect, leaving physical understanding behind. Therefore, the first part of this research aims to understand and reveal the physics behind LPT flutter in addition to several related topics including acoustic resonance effects. A percentage of this initial numerical investigation is completed using an influence coefficient approach to study the variation the work-per-cycle contributions of neighboring cascade blades to a reference airfoil. The second part of this research introduces new discoveries regarding the relationship between steady aerodynamic loading and negative aerodynamic damping. Using validated CFD codes as computational wind tunnels, a multitude of low-pressure turbine flutter parameters, such as reduced frequency, mode shape, and interblade phase angle, will be scrutinized across various airfoil geometries and steady operating conditions to reach new design guidelines regarding the influence of steady aerodynamic loading and LPT flutter. Many pressing topics influencing LPT flutter including shocks, their nonlinearity, and three-dimensionality are also addressed along the way. The work is concluded by introducing a useful preliminary design tool that can estimate within seconds the entire aerodynamic damping versus nodal diameter curve for a given three-dimensional cascade.