1,427 research outputs found
Craig's XY distribution and the statistics of Lagrangian power in two-dimensional turbulence
We examine the probability distribution function (PDF) of the energy injection rate (power) in numerical simulations of stationary two-dimensional (2D) turbulence in the Lagrangian frame. The simulation is designed to mimic an electromagnetically driven fluid layer, a well-documented system for generating 2D turbulence in the laboratory. In our simulations, the forcing and velocity fields are close to Gaussian. On the other hand, the measured PDF of injected power is very sharply peaked at zero, suggestive of a singularity there, with tails which are exponential but asymmetric. Large positive fluctuations are more probable than large negative fluctuations. It is this asymmetry of the tails which leads to a net positive mean value for the energy input despite the most probable value being zero. The main features of the power distribution are well described by Craig's XY distribution for the PDF of the product of two correlated normal variables. We show that the power distribution should exhibit a logarithmic singularity at zero and decay exponentially for large absolute values of the power. We calculate the asymptotic behavior and express the asymmetry of the tails in terms of the correlation coefficient of the force and velocity. We compare the measured PDFs with the theoretical calculations and briefly discuss how the power PDF might change with other forcing mechanisms
Force Chain Evolution in a Two-Dimensional Granular Packing Compacted by Vertical Tappings
We experimentally study the statistics of force-chain evolution in a
vertically-tapped two-dimensional granular packing by using photoelastic disks.
In this experiment, the tapped granular packing is gradually compacted. During
the compaction, the isotropy of grain configurations is quantified by measuring
the deviator anisotropy derived from fabric tensor, and then the evolution of
force-chain structure is quantified by measuring the interparticle forces and
force-chain orientational order parameter. As packing fraction increases, the
interparticle force increases and finally saturates to an asymptotic value.
Moreover, the grain configurations and force-chain structures become
isotropically random as the tapping-induced compaction proceeds. In contrast,
the total length of force chains remains unchanged. From the correlations of
those parameters, we find two relations: (i) a positive correlation between the
isotropy of grain configurations and the disordering of force-chain
orientations, and (ii) a negative correlation between the increasing of
interparticle forces and the disordering of force-chain orientations. These
relations are universally held regardless of the mode of particle motions
with/without convection
Nonparametric Stochastic Volatility
Using recent advances in the nonparametric estimation of continuous-time processes under mild statistical assumptions as well as recent developments on nonparametric volatility estimation by virtue of market microstructure noise-contaminated high-frequency asset price data, we provide (i) a theory of spot variance estimation and (ii) functional methods for stochastic volatility modelling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, jumps in returns and volatility with possibly state-dependent jump intensities, as well as nonlinear risk-return trade-offs. Our identification approach and asymptotic results apply under weak recurrence assumptions and, hence, accommodate the persistence properties of variance in finite samples. Functional estimation of a generalized (i.e., nonlinear) version of the square-root stochastic variance model with jumps in both volatility and returns for the S&P500 index suggests the need for richer variance dynamics than in existing work. We find a linear specification for the variance's diffusive variance to be misspecified (and inferior to a more flexible CEV specification) even when allowing for jumps in the variance dynamics.Spot variance, stochastic volatility, jumps in returns, jumps in volatility, leverage effects, risk-return trade-offs, kernel methods, recurrence, market microstructure noise.
Grid-scale Fluctuations and Forecast Error in Wind Power
The fluctuations in wind power entering an electrical grid (Irish grid) were
analyzed and found to exhibit correlated fluctuations with a self-similar
structure, a signature of large-scale correlations in atmospheric turbulence.
The statistical structure of temporal correlations for fluctuations in
generated and forecast time series was used to quantify two types of forecast
error: a timescale error () that quantifies the deviations between
the high frequency components of the forecast and the generated time series,
and a scaling error () that quantifies the degree to which the
models fail to predict temporal correlations in the fluctuations of the
generated power. With no knowledge of the forecast models, we
suggest a simple memory kernel that reduces both the timescale error
() and the scaling error ()
On angled bounce-off impact of a drop impinging on a flowing soap film
Small drops impinging angularly on thin flowing soap films frequently
demonstrate the rare emergence of bulk elastic effects working in-tandem with
the more common-place hydrodynamic interactions. Three collision regimes are
observable: (a) drop piercing through the film, (b) it coalescing with the
flow, and (c) it bouncing off the film surface. During impact, the drop deforms
along with a bulk elastic deformation of the film. For impacts that are
close-to-tangential, the bounce-off regime predominates. We outline a reduced
order analytical framework assuming a deformable drop and a deformable
three-dimensional film, and the idealization invokes a phase-based parametric
study. Angular inclination of the film and the ratio of post and pre impact
drop sizes entail the phase parameters. We also perform experiments with
vertically descending droplets impacting against an inclined soap film, flowing
under constant pressure head. Model predicted phase domain for bounce-off
compares well to our experimental findings. Additionally, the experiments
exhibit momentum transfer to the film in the form of shed vortex dipole, along
with propagation of free surface waves. On consulting prior published work, we
note that for locomotion of water-walking insects using an impulsive action,
the momentum distribution to the shed vortices and waves are both significant,
taking up respectively 2/3-rd and 1/3-rd of the imparted streamwise momentum.
In view of the potentially similar impulse actions, this theory is applied to
the bounce-off examples in our experiments, and the resultant shed vortex
dipole momenta are compared to the momenta computed from particle imaging
velocimetry data. The magnitudes reveal identical order ( Ns),
suggesting that the bounce-off regime can be tapped as a simple analogue for
interfacial bio-locomotion relying on impulse reactions
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