6,568 research outputs found
Functional summary statistics for point processes on the sphere with an application to determinantal point processes
We study point processes on , the -dimensional unit sphere
, considering both the isotropic and the anisotropic case, and
focusing mostly on the spherical case . The first part studies reduced
Palm distributions and functional summary statistics, including nearest
neighbour functions, empty space functions, and Ripley's and inhomogeneous
-functions. The second part partly discusses the appealing properties of
determinantal point process (DPP) models on the sphere and partly considers the
application of functional summary statistics to DPPs. In fact DPPs exhibit
repulsiveness, but we also use them together with certain dependent thinnings
when constructing point process models on the sphere with aggregation on the
large scale and regularity on the small scale. We conclude with a discussion on
future work on statistics for spatial point processes on the sphere
Global and local synthetic descriptions of the piano soundboard
Up to around 1.1 kHz, the soundboard of the piano behaves like a homogeneous
plate whereas upper in frequency, it can be described as a set of waveguides
defined by the ribs. In consequence: a) The acoustical coincidence phenomenon
is deeply modified in comparison with that occurring in homogeneous plates
since the dispersion curve of a waveguide can present none, one, or two
coincidence frequencies. This may result in a nonuniformity of the soundboard
radiation in the treble range, corresponding to the so-called killer octave,
where a good sustain is difficult to obtain. b) The mobility (mechanical
admittance) in the direction normal to the soundboard can be synthesised with
only a small number of parameters. It compares well with published measurements
(Giordano, JASA, 1998), in particular the step-like falloff of the local
impedance due to the localisation of the waves between ribs. c) The synthesised
mobility has the same features as those which can be derived independantly,
according to Skudrzyk (JASA, 1980) and Langley (JSV, 1994). This approach
avoids the detailed description of the soundboard, based on a very large number
of parameters. It can be used to predict global changes of the driving point
mobility, and possibly of the sound radiation in the treble range, resulting
from structural modifications
Vibroacoustics of the piano soundboard: Reduced models, mobility synthesis, and acoustical radiation regime
In string musical instruments, the sound is radiated by the soundboard,
subject to the strings excitation. This vibration of this rather complex
structure is described here with models which need only a small number of
parameters. Predictions of the models are compared with results of experiments
that have been presented in Ege et al. [Vibroacoustics of the piano soundboard:
(Non)linearity and modal properties in the low- and mid- frequency ranges,
Journal of Sound and Vibration 332 (5) (2013) 1288-1305]. The apparent modal
density of the soundboard of an upright piano in playing condition, as seen
from various points of the structure, exhibits two well-separated regimes,
below and above a frequency flim that is determined by the wood characteristics
and by the distance between ribs. Above flim, most modes appear to be
localised, presumably due to the irregularity of the spacing and height of the
ribs. The low-frequency regime is predicted by a model which consists of
coupled sub-structures: the two ribbed areas split by the main bridge and, in
most cases, one or two so-called cut-off corners. In order to assess the
dynamical properties of each of the subplates (considered here as homogeneous
plates), we propose a derivation of the (low-frequency) modal density of an
orthotropic homogeneous plate which accounts for the boundary conditions on an
arbitrary geometry. Above flim, the soundboard, as seen from a given excitation
point, is modelled as a set of three structural wave-guides, namely the three
inter-rib spacings surrounding the excitation point. Based on these low- and
high-frequency models, computations of the point-mobility and of the apparent
modal densities seen at several excitation points match published measurements.
The dispersion curve of the wave-guide model displays an acoustical radiation
scheme which differs significantly from that of a thin homogeneous plate. It
appears that piano dimensioning is such that the subsonic regime of acoustical
radiation extends over a much wider frequency range than it would be for a
homogeneous plate with the same low-frequency vibration. One problem in piano
manufacturing is examined in relationship with the possible radiation schemes
induced by the models.Comment: Research highlights: - Synthetic modelling of a piano soundboard
overa broad-frequency-range (several kHz). - Quantitative agreement between
predicted and measured apparent local modal density. -Modal density of a
plate with non-special orthotropy and arbitrary contour. -Similar
characteristic impedance between comparable pianos, over several kHz.
-Extension of the subsonic regime of acoustical radiation over a wide
frequency range. Journal of Sound and Vibration (2013)
http://dx.doi.org/10.1016/j.jsv.2013.03.01
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