Dramatic Shape Sensitivity of Directional Emission Patterns from Similarly Deformed Cylindrical Polymer Lasers

Recent experiments on similarly shaped polymer micro-cavity lasers show a dramatic difference in the far-field emission patterns. We show for different deformations of the ellipse, quadrupole and hexadecapole that the large differences in the far-field emission patterns is explained by the differing ray dynamics corresponding to each shape. Analyzing the differences in the appropriate phase space for ray motion, it is shown that the differing geometries of the unstable manifolds of periodic orbits are the decisive factors in determining the far-field pattern. Surprisingly, we find that strongly chaotic ray dynamics is compatible with highly directional emission in the far-field.Comment: 14 pages, 16 figures (eps), RevTeX 4, submitted to JOSA

Dynamical Stability and Quantum Chaos of Ions in a Linear Trap

The realization of a paradigm chaotic system, namely the harmonically driven oscillator, in the quantum domain using cold trapped ions driven by lasers is theoretically investigated. The simplest characteristics of regular and chaotic dynamics are calculated. The possibilities of experimental realization are discussed.Comment: 24 pages, 17 figures, submitted to Phys. Rev

Hysteresis in Adiabatic Dynamical Systems: an Introduction

We give a nontechnical description of the behaviour of dynamical systems governed by two distinct time scales. We discuss in particular memory effects, such as bifurcation delay and hysteresis, and comment the scaling behaviour of hysteresis cycles. These properties are illustrated on a few simple examples.Comment: 28 pages, 10 ps figures, AMS-LaTeX. This is the introduction of my Ph.D. dissertation, available at http://dpwww.epfl.ch/instituts/ipt/berglund/these.htm

Transport of inertial particles by Lagrangian coherent structures : application to predator-prey interaction in jellyfish feeding

We use a dynamical systems approach to identify coherent structures from often chaotic motions of inertial particles in open flows. We show that particle Lagrangian coherent structures (pLCS) act as boundaries between regions in which particles have different kinematics. They provide direct geometric information about the motion of ensembles of inertial particles, which is helpful to understand their transport. As an application, we apply the methodology to a planktonic predator–prey system in which moon jellyfish Aurelia aurita uses its body motion to generate a flow that transports small plankton such as copepods to its vicinity for feeding. With the flow field generated by the jellyfish measured experimentally and the dynamics of plankton described by a modified Maxey–Riley equation, we use the pLCS to identify a capture region in which prey can be captured by the jellyfish. The properties of the pLCS and the capture region enable analysis of the effect of several physiological and mechanical parameters on the predator–prey interaction, such as prey size, escape force, predator perception, etc. The methods developed here are equally applicable to multiphase and granular flows, and can be generalized to any other particle equation of motion, e.g. equations governing the motion of reacting particles or charged particles

Tunable transport with broken space-time symmetries

Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space-time symmetries of the corresponding equations of motion. A systematic analysis of these symmetries uncovers the conditions necessary for obtaining directed transport. In this work we give a unified introduction into the symmetry analysis and demonstrate its action on the motion in one-dimensional periodic, both in time and space, potentials. We further generalize the analysis to quasi-periodic drivings, higher space dimensions, and quantum dynamics. Recent experimental results on the transport of cold and ultracold atomic ensembles in ac-driven optical potentials are reviewed as illustrations of theoretical considerations.Comment: Phys. Rep., in pres