1,259 research outputs found
Energy conserving schemes for the simulation of musical instrument contact dynamics
Collisions are an innate part of the function of many musical instruments.
Due to the nonlinear nature of contact forces, special care has to be taken in
the construction of numerical schemes for simulation and sound synthesis.
Finite difference schemes and other time-stepping algorithms used for musical
instrument modelling purposes are normally arrived at by discretising a
Newtonian description of the system. However because impact forces are
non-analytic functions of the phase space variables, algorithm stability can
rarely be established this way. This paper presents a systematic approach to
deriving energy conserving schemes for frictionless impact modelling. The
proposed numerical formulations follow from discretising Hamilton's equations
of motion, generally leading to an implicit system of nonlinear equations that
can be solved with Newton's method. The approach is first outlined for point
mass collisions and then extended to distributed settings, such as vibrating
strings and beams colliding with rigid obstacles. Stability and other relevant
properties of the proposed approach are discussed and further demonstrated with
simulation examples. The methodology is exemplified through a case study on
tanpura string vibration, with the results confirming the main findings of
previous studies on the role of the bridge in sound generation with this type
of string instrument
When the words are not everything: the use of laughter, fillers, back-channel, silence, and overlapping speech in phone calls
This article presents an observational study on how some common conversational cues – laughter, fillers, back-channel, silence, and overlapping speech – are used during mobile phone conversations. The observations are performed over the SSPNet Mobile Corpus, a collection of 60 calls between pairs of unacquainted individuals (120 subjects for roughly 12 h of material in total). The results show that the temporal distribution of the social signals above is not uniform, but it rather reflects the social meaning they carry and convey. In particular, the results show significant use differences depending on factors such as gender, role (caller or receiver), topic, mode of interaction (agreement or disagreement), personality traits, and conflict handling style
Toward Realistic and Practical No-Hair Relations for Neutron Stars in the Non-Relativistic Limit
The gravitational properties of astrophysical objects depend sensitively on
their internal structure. In Newtonian theory, the gravitational potential of a
rotating star can be fully described by an infinite number of multipole moments
of its mass distribution. Recently, this infinite number of moments for
uniformly-rotating stars were shown semi-analytically to be expressible in
terms of just the first three: the mass, the spin, and the quadrupole moment of
the star. The relations between the various lower multipole moments were
additionally shown to depend weakly on the equation of state, when considering
neutron stars and assuming single polytropic equations of state. Here we extend
this result in two ways. First, we show that the universality also holds for
realistic equations of state, thus relaxing the need to use single polytropes.
Second, we derive purely analytical universal relations by perturbing the
equations of structure about an polytrope that reproduce semi-analytic
results to . We also find that the linear-order perturbation
vanishes in some cases, which provides further evidence and a deeper
understanding of the universality.Comment: 10 pages, 5 figures, published versio
Tidal heating and torquing of a Kerr black hole to next-to-leading order in the tidal coupling
We calculate the linear vacuum perturbations of a Kerr black hole surrounded
by a slowly-varying external spacetime to third order in the ratio of the
black-hole mass to the radius of curvature of the external spacetime. This
expansion applies to two relevant physical scenarios: (i) a small Kerr black
hole immersed in the gravitational field of a much larger external black hole,
and (ii) a Kerr black hole moving slowly around another external black hole of
comparable mass. This small-hole/slow-motion approximation allows us to
parametrize the perturbation through slowly-varying, time-dependent electric
and magnetic tidal tensors, which then enables us to separate the Teukolsky
equation and compute the Newman-Penrose scalar analytically to third order in
our expansion parameter. We obtain generic expressions for the mass and angular
momentum flux through the perturbed black hole horizon, as well as the rate of
change of the horizon surface area, in terms of certain invariants constructed
from the electric and magnetic tidal tensors. We conclude by applying these
results to the two scenarios described above.Comment: 15 pages, no figures, published versio
Phenomenological model for the gravitational-wave signal from precessing binary black holes with two-spin effects
The properties of compact binaries, such as masses and spins, are imprinted
in the gravitational-waves they emit and can be measured using parameterised
waveform models. Accurately and efficiently describing the complicated
precessional dynamics of the various angular momenta of the system in these
waveform models is the object of active investigation. One of the key models
extensively used in the analysis of LIGO and Virgo data is the
single-precessing-spin waveform model IMRPhenomPv2. In this article we present
a new model IMRPhenomPv3 which includes the effects of two independent spins in
the precession dynamics. Whereas IMRPhenomPv2 utilizes a single-spin
frequency-dependent post-Newtonian rotation to describe precession effects, the
improved model, IMRPhenomPv3, employs a double-spin rotation that is based on
recent developments in the description of precessional dynamics. Besides
double-spin precession, the improved model benefits from a more accurate
description of precessional effects. We validate our new model against a large
set of precessing numerical-relativity simulations. We find that IMRPhenomPv3
has better agreement with the inspiral portion of precessing binary-black-hole
simulations and is more robust across a larger region of the parameter space
than IMRPhenomPv2. As a first application we analyse, for the first time, the
gravitational-wave event GW151226 with a waveform model that describes two-spin
precession. Within statistical uncertainty our results are consistent with
published results. IMRPhenomPv3 will allow studies of the measurability of
individual spins of binary black holes using GWs and can be used as a
foundation upon which to build further improvements, such as modeling
precession through merger, extending to higher multipoles, and including tidal
effects.Comment: 15 pages, 5 figure
Gravitational Waveforms for Precessing, Quasicircular Compact Binaries with Multiple Scale Analysis: Small Spin Expansion
We obtain analytical gravitational waveforms in the frequency-domain for
precessing, quasi-circular compact binaries with small spins, applicable, for
example, to binary neutron star inspirals. We begin by calculating an analytic
solution to the precession equations, obtained by expanding in the
dimensionless spin parameters and using multiple-scale analysis to separate
timescales. We proceed by analytically computing the Fourier transform of
time-domain waveform through the stationary phase approximation. We show that
the latter is valid for systems with small spins. Finally, we show that these
waveforms have a high overlap with numerical waveforms obtained through direct
integration of the precession equations and discrete Fourier transformations.
The resulting, analytic waveform family is ideal for detection and parameter
estimation of gravitational waves emitted by inspiraling binary neutron stars
with ground-based detectors.Comment: 37 pages, 14 figures, final published versio
- …