Developing and evaluating a hybrid wind instrument

A hybrid wind instrument generates self-sustained sounds via a real-time interaction between a computed excitation model (such as the physical model of human lips interacting with a mouthpiece) and a real acoustic resonator. Attempts to produce a hybrid instrument have so far fallen short, in terms of both the accuracy and the variation in the sound produced. The principal reason for the failings of previous hybrid instruments is the actuator which, controlled by the excitation model, introduces a fluctuating component into the air flow injected into the resonator. In the present paper, the possibility of using a loudspeaker to supply the calculated excitation signal is evaluated. A theoretical study has facilitated the modeling of the loudspeaker-resonator system and the design of a feedback and feedforward filter to successfully compensate for the presence of the loudspeaker. The resulting self-sustained sounds are evaluated by a mapping of their sound descriptors to the input parameters of the physical model of the embouchure, both for sustained and attack sounds. Results are compared with simulations. The largely coherent functioning confirms the usefulness of the device in both musical and research contexts

Decoherence of Friedmann-Robertson-Walker Geometries in the Presence of Massive Vector Fields with U(1) or SO(3) Global Symmetries

Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of {\em midi}superspace models in the presence of scalar fields and the inhomogeneous modes corresponding either to gravitational or scalar fields. In this work, we propose an alternative model to study the decoherence of homogeneous and isotropic geometries where the scalar field is replaced by a massive vector field with a global internal symmetry. We study here the cases with $U(1)$ and $SO(3)$ global internal symmetries. The presence of a mass term breaks the conformal invariance and allows for the longitudinal modes of the spin-1 field to be present in the Wheeler-DeWitt equation. In the case of the U(1) global internal symmetry, we have only one single ``classical'' degree of freedom while in the case of the SO(3) global symmetry, we are led to consider a simple two-dimensional minisuperspace model. These minisuperspaces are shown to be equivalent to a set of coupled harmonic oscillators where the kinetic term of the longitudinal modes has a coefficient proportional to the inverse of the scale factor. The conditions for a suitable decoherence process and correlations between coordinate and momenta are established. The validity of the semi-classical Einstein equations when massive vector fields (Abelian and non-Abelian) are present is also discussed.Comment: 26 pages, CERN-TH.7241/94 DAMTP R-94/2

Light with a self-torque: extreme-ultraviolet beams with time-varying orbital angular momentum

Twisted light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics and microparticle rotation. Here we introduce and experimentally validate a new class of light beams, whose unique property is associated with a temporal OAM variation along a pulse: the self-torque of light. Self-torque is a phenomenon that can arise from matter-field interactions in electrodynamics and general relativity, but to date, there has been no optical analog. In particular, the self-torque of light is an inherent property, which is distinguished from the mechanical torque exerted by OAM beams when interacting with physical systems. We demonstrate that self-torqued beams in the extreme-ultraviolet (EUV) naturally arise as a necessary consequence of angular momentum conservation in non-perturbative high-order harmonic generation when driven by time-delayed pulses with different OAM. In addition, the time-dependent OAM naturally induces an azimuthal frequency chirp, which provides a signature for monitoring the self-torque of high-harmonic EUV beams. Such self-torqued EUV beams can serve as unique tools for imaging magnetic and topological excitations, for launching selective excitation of quantum matter, and for manipulating molecules and nanostructures on unprecedented time and length scales.Comment: 24 pages, 4 figure

Associative memory storing an extensive number of patterns based on a network of oscillators with distributed natural frequencies in the presence of external white noise

We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory patterns are assumed to be given by uniformly distributed random numbers on $[0,2\pi)$ so that the patterns encode the phase differences of the oscillators. To derive the macroscopic order parameter equations for the network with an extensive number of stored patterns, we introduce the effective transfer function by assuming the fixed-point equation of the form of the TAP equation, which describes the time-averaged output as a function of the effective time-averaged local field. Properties of the networks associated with synchronization phenomena for a discrete symmetric natural frequency distribution with three frequency components are studied based on the order parameter equations, and are shown to be in good agreement with the results of numerical simulations. Two types of retrieval states are found to occur with respect to the degree of synchronization, when the size of the width of the natural frequency distribution is changed.Comment: published in Phys. Rev.

Localized Manifold Harmonics for Spectral Shape Analysis

The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases