47,724 research outputs found
A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation
The bubbles involved in sonochemistry and other applications of cavitation
oscillate inertially. A correct estimation of the wave attenuation in such
bubbly media requires a realistic estimation of the power dissipated by the
oscillation of each bubble, by thermal diffusion in the gas and viscous
friction in the liquid. Both quantities and calculated numerically for a single
inertial bubble driven at 20 kHz, and are found to be several orders of
magnitude larger than the linear prediction. Viscous dissipation is found to be
the predominant cause of energy loss for bubbles small enough. Then, the
classical nonlinear Caflish equations describing the propagation of acoustic
waves in a bubbly liquid are recast and simplified conveniently. The main
harmonic part of the sound field is found to fulfill a nonlinear Helmholtz
equation, where the imaginary part of the squared wave number is directly
correlated with the energy lost by a single bubble. For low acoustic driving,
linear theory is recovered, but for larger drivings, namely above the Blake
threshold, the attenuation coefficient is found to be more than 3 orders of
magnitude larger then the linear prediction. A huge attenuation of the wave is
thus expected in regions where inertial bubbles are present, which is confirmed
by numerical simulations of the nonlinear Helmholtz equation in a 1D standing
wave configuration. The expected strong attenuation is not only observed but
furthermore, the examination of the phase between the pressure field and its
gradient clearly demonstrates that a traveling wave appears in the medium
Biologically Inspired Dynamic Textures for Probing Motion Perception
Perception is often described as a predictive process based on an optimal
inference with respect to a generative model. We study here the principled
construction of a generative model specifically crafted to probe motion
perception. In that context, we first provide an axiomatic, biologically-driven
derivation of the model. This model synthesizes random dynamic textures which
are defined by stationary Gaussian distributions obtained by the random
aggregation of warped patterns. Importantly, we show that this model can
equivalently be described as a stochastic partial differential equation. Using
this characterization of motion in images, it allows us to recast motion-energy
models into a principled Bayesian inference framework. Finally, we apply these
textures in order to psychophysically probe speed perception in humans. In this
framework, while the likelihood is derived from the generative model, the prior
is estimated from the observed results and accounts for the perceptual bias in
a principled fashion.Comment: Twenty-ninth Annual Conference on Neural Information Processing
Systems (NIPS), Dec 2015, Montreal, Canad
Multiscale Turbulence Models Based on Convected Fluid Microstructure
The Euler-Poincar\'e approach to complex fluids is used to derive multiscale
equations for computationally modelling Euler flows as a basis for modelling
turbulence. The model is based on a \emph{kinematic sweeping ansatz} (KSA)
which assumes that the mean fluid flow serves as a Lagrangian frame of motion
for the fluctuation dynamics. Thus, we regard the motion of a fluid parcel on
the computationally resolvable length scales as a moving Lagrange coordinate
for the fluctuating (zero-mean) motion of fluid parcels at the unresolved
scales. Even in the simplest 2-scale version on which we concentrate here, the
contributions of the fluctuating motion under the KSA to the mean motion yields
a system of equations that extends known results and appears to be suitable for
modelling nonlinear backscatter (energy transfer from smaller to larger scales)
in turbulence using multiscale methods.Comment: 1st version, comments welcome! 23 pages, no figures. In honor of
Peter Constantin's 60th birthda
Stochastic representation of the Reynolds transport theorem: revisiting large-scale modeling
We explore the potential of a formulation of the Navier-Stokes equations
incorporating a random description of the small-scale velocity component. This
model, established from a version of the Reynolds transport theorem adapted to
a stochastic representation of the flow, gives rise to a large-scale
description of the flow dynamics in which emerges an anisotropic subgrid
tensor, reminiscent to the Reynolds stress tensor, together with a drift
correction due to an inhomogeneous turbulence. The corresponding subgrid model,
which depends on the small scales velocity variance, generalizes the Boussinesq
eddy viscosity assumption. However, it is not anymore obtained from an analogy
with molecular dissipation but ensues rigorously from the random modeling of
the flow. This principle allows us to propose several subgrid models defined
directly on the resolved flow component. We assess and compare numerically
those models on a standard Green-Taylor vortex flow at Reynolds 1600. The
numerical simulations, carried out with an accurate divergence-free scheme,
outperform classical large-eddies formulations and provides a simple
demonstration of the pertinence of the proposed large-scale modeling
Symmetry-breaking phase-transitions in highly concentrated semen
New experimental evidence of self-motion of a confined active suspension is presented. Depositing fresh semen sample in an annular shaped micro- fluidic chip leads to a spontaneous vortex state of the fluid at sufficiently large sperm concentration. The rotation occurs unpredictably clockwise or counterclockwise and is robust and stable. Furthermore, for highly active and concentrated semen, richer dynamics can occur such as self-sustained or damped rotation oscillations. Experimental results obtained with systematic dilution provide a clear evidence of a phase transition toward collective motion associated with local alignment of spermatozoa akin to the Vicsek model. A macroscopic theory based on previously derived Self-Organized Hydrodynamics (SOH) models is adapted to this context and provides predictions consistent with the observed stationary motion
Fluid flow dynamics under location uncertainty
We present a derivation of a stochastic model of Navier Stokes equations that
relies on a decomposition of the velocity fields into a differentiable drift
component and a time uncorrelated uncertainty random term. This type of
decomposition is reminiscent in spirit to the classical Reynolds decomposition.
However, the random velocity fluctuations considered here are not
differentiable with respect to time, and they must be handled through
stochastic calculus. The dynamics associated with the differentiable drift
component is derived from a stochastic version of the Reynolds transport
theorem. It includes in its general form an uncertainty dependent "subgrid"
bulk formula that cannot be immediately related to the usual Boussinesq eddy
viscosity assumption constructed from thermal molecular agitation analogy. This
formulation, emerging from uncertainties on the fluid parcels location,
explains with another viewpoint some subgrid eddy diffusion models currently
used in computational fluid dynamics or in geophysical sciences and paves the
way for new large-scales flow modelling. We finally describe an applications of
our formalism to the derivation of stochastic versions of the Shallow water
equations or to the definition of reduced order dynamical systems
Looking for a theory of faster-than-light particles
Several principal aspects of a theoretical approach to the theory of
faster-than-light particles (tachyons) are considered in this note. They
concern the resolution of such problems of tachyon theory as the causality
violation by tachyons, the stability of the tachyon vacuum, and the stability
of ordinary particles against the spontaneous emission of tachyons, i.e. the
problems which are generally used as arguments against the possibility of such
particles. It is demonstrated that all these arguments contain nontrivial
loopholes which undermine their validity. A demand for a consistent tachyon
theory is formulated, and several ideas for its construction are suggested.Comment: 41 pages, 5 figure
Extensive divergence of transcription factor binding in Drosophila embryos with highly conserved gene expression
Extensive divergence of transcription factor binding in Drosophila embryos
with highly conserved gene expressionComment: 7 figures, 20 supplementary figures, 6 supplementary tables Paris M,
Kaplan T, Li XY, Villalta JE, Lott SE, et al. (2013) Extensive Divergence of
Transcription Factor Binding in Drosophila Embryos with Highly Conserved Gene
Expression. PLoS Genet 9(9): e1003748. doi:10.1371/journal.pgen.100374
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