Reduction of Vaisman structures in complex and quaternionic geometry

We consider locally conformal Kähler geometry as an equivariant (homothetic) Kähler geometry: a locally conformal Kähler manifold is, up to equivalence, a pair $(K,\Gamma )$, where $K$ is a Kähler manifold and $\Gamma$ is a discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invariant of a locally conformal Kähler manifold $(K,\Gamma )$ as the rank of a natural quotient of $\Gamma$, and prove its invariance under reduction. This equivariant point of view leads to a proof that locally conformal Kähler reduction of compact Vaisman manifolds produces Vaisman manifolds and is equivalent to a Sasakian reduction. Moreover, we define locally conformal hyperKähler reduction as an equivariant version of hyperKähler reduction and in the compact case we show its equivalence with 3-Sasakian reduction. Finally, we show that locally conformal hyperKähler reduction induces hyperKähler with torsion (HKT) reduction of the associated HKT structure and the two reductions are compatible, even though not every HKT reduction comes from a locally conformal hyperKähler reduction.     

Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.     

Temperature dependence of the time-resolved emissions of CsI:Tl

Abstract

Time-resolved emissions of Csl:T1 are investigated. The system is laser-excited in the A-band at 308 nm and the emissions are observed in the range 370–650 nm, from 30 K to 300 K. Their analysis by means of a deconvolution permits the valuation of decay-times down to 1 ns. At every temperature many bands are observed and some of them show slow and fast components. The decay-times of the fast components are in the range 1–10 ns while the slow ones are even longer than 1 μs. In many cases intermediate decay-times of the order of 100 ns exist. The competition among the bands interests the application of this system as active material for tunable solid-state laser.     

Chaos control by using Motor Maps

In this paper a new method for chaos control is proposed, consisting of an unsupervised neural network, namely a Motor Map. In particular a feedback entrainment scheme is adopted: a chaotic system with a given parameter set generates the reference trajectory for another chaotic system with different parameters to be controlled: the Motor Map is required to provide the appropriate time-varying gain value for the feedback signal. The state of the controlled system is considered as input to the Motor Map. Particular efforts have been paid to the feasibility of the implementation. Indeed, the simulations performed have been oriented to design a Motor Map suitable for an hardware realization, thus some restrictive hypotheses, such as for example a low number of neurons, have been assumed. A huge number of simulations has been carried out by considering as system to be controlled a Double Scroll Chua Attractor as well as other chaotic attractors. Several reference trajectories have also been considered: a limit cycle generated by a Chua's circuit with different parameters values, a double scroll Chua attractor, a chaotic attractor of the family of the Chua's circuit attractors. In all the simulations instead of controlling the whole state space, only two state variables have been fed back. Good results in terms of settling time (namely, the period in which the map learns the control task) and steady state errors have been obtained with a few neurons. The Motor Map based adaptive controller offers high performances, specially in the case when the reference trajectory is switched into another one. In this case, a specialization of the neurons constituting the Motor Map is observed: while a group of neurons learns the appropriate control law for a reference trajectory, another group specializes itself to control the system when the other trajectory is used as a reference. A discrete components electronic realization of the Motor Map is presented and experimental results confirming the simulation results are shown. (c) 2002 American Institute of Physics.     

Novel active noise-reducing headset using earshell vibration control

Active noise-reducing (ANR) headsets are available commercially in applications varying from aviation communication to consumer audio. Current ANR systems use passive attenuation at high frequencies and loudspeaker-based active noise control at low frequencies to achieve broadband noise reduction. This paper presents a novel ANR headset in which the external noise transmitted to the user's ear via earshell vibration is reduced by controlling the vibration of the earshell using force actuators acting against an inertial mass or the earshell headband. Model-based theoretical analysis using velocity feedback control showed that current piezoelectric actuators provide sufficient force but require lower stiffness for improved low-frequency performance. Control simulations based on experimental data from a laboratory headset showed that good performance can potentially be achieved in practice by a robust feedback controller, while a single-frequency real-time control experiment verified that noise reduction can be achieved using earshell vibration control.     

From X- to O-shaped spatiotemporal spectra of light filaments in water

We show that the angle-wavelength spectra of light filaments excited by ultrashort pulses experience a transition from X- to O-like structures when their carrier wavelengths are switched from normal to anomalous dispersion. Calculations confirm that the O-shaped conical emission follows the elliptic geometry of the nonlinear Schr?dinger equation with anomalous dispersion.