472 research outputs found
Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks
Planetesimals in gaseous protoplanetary disks may grow by collecting dust
particles. Hydrodynamical studies show that small particles generally avoid
collisions with the planetesimals because they are entrained by the flow around
them. This occurs when , the Stokes number, defined as the ratio of the
dust stopping time to the planetesimal crossing time, becomes much smaller than
unity. However, these studies have been limited to the laminar case, whereas
these disks are believed to be turbulent. We want to estimate the influence of
gas turbulence on the dust-planetesimal collision rate and on the impact
speeds. We used three-dimensional direct numerical simulations of a fixed
sphere (planetesimal) facing a laminar and turbulent flow seeded with small
inertial particles (dust) subject to a Stokes drag. A no-slip boundary
condition on the planetesimal surface is modeled via a penalty method. We find
that turbulence can significantly increase the collision rate of dust particles
with planetesimals. For a high turbulence case (when the amplitude of turbulent
fluctuations is similar to the headwind velocity), we find that the collision
probability remains equal to the geometrical rate or even higher for , i.e., for dust sizes an order of magnitude smaller than in the laminar
case. We derive expressions to calculate impact probabilities as a function of
dust and planetesimal size and turbulent intensity
Universality of Velocity Gradients in Forced Burgers Turbulence
It is demonstrated that Burgers turbulence subject to large-scale
white-noise-in-time random forcing has a universal power-law tail with exponent
-7/2 in the probability density function of negative velocity gradients, as
predicted by E, Khanin, Mazel and Sinai (1997, Phys. Rev. Lett. 78, 1904). A
particle and shock tracking numerical method gives about five decades of
scaling. Using a Lagrangian approach, the -7/2 law is related to the shape of
the unstable manifold associated to the global minimizer.Comment: 4 pages, 2 figures, RevTex4, published versio
Clustering of passive impurities in MHD turbulence
The transport of heavy, neutral or charged, point-like particles by
incompressible, resistive magnetohydrodynamic (MHD) turbulence is investigated
by means of high-resolution numerical simulations. The spatial distribution of
such impurities is observed to display strong deviations from homogeneity, both
at dissipative and inertial range scales. Neutral particles tend to cluster in
the vicinity of coherent vortex sheets due to their viscous drag with the flow,
leading to the simultaneous presence of very concentrated and almost empty
regions. The signature of clustering is different for charged particles. These
exhibit in addition to the drag the Lorentz-force. The regions of spatial
inhomogeneities change due to attractive and repulsive vortex sheets. While
small charges increase clustering, larger charges have a reverse effect.Comment: 9 pages, 13 figure
Dynamics and statistics of heavy particles in turbulent flows
We present the results of Direct Numerical Simulations (DNS) of turbulent
flows seeded with millions of passive inertial particles. The maximum Taylor's
Reynolds number is around 200. We consider particles much heavier than the
carrier flow in the limit when the Stokes drag force dominates their dynamical
evolution. We discuss both the transient and the stationary regimes. In the
transient regime, we study the growt of inhomogeneities in the particle spatial
distribution driven by the preferential concentration out of intense vortex
filaments. In the stationary regime, we study the acceleration fluctuations as
a function of the Stokes number in the range [0.16:3.3]. We also compare our
results with those of pure fluid tracers (St=0) and we find a critical behavior
of inertia for small Stokes values. Starting from the pure monodisperse
statistics we also characterize polydisperse suspensions with a given mean
Stokes.Comment: 13 pages, 10 figures, 2 table
Finite-time Lyapunov exponents of deep neural networks
We compute how small input perturbations affect the output of deep neural
networks, exploring an analogy between deep networks and dynamical systems,
where the growth or decay of local perturbations is characterised by
finite-time Lyapunov exponents. We show that the maximal exponent forms
geometrical structures in input space, akin to coherent structures in dynamical
systems. Ridges of large positive exponents divide input space into different
regions that the network associates with different classes. These ridges
visualise the geometry that deep networks construct in input space, shedding
light on the fundamental mechanisms underlying their learning capabilities.Comment: 6 pages, 4 figure
The analytic structure of 2D Euler flow at short times
Using a very high precision spectral calculation applied to the
incompressible and inviscid flow with initial condition , we find that the width of its analyticity
strip follows a law at short times over eight decades. The
asymptotic equation governing the structure of spatial complex-space
singularities at short times (Frisch, Matsumoto and Bec 2003, J.Stat.Phys. 113,
761--781) is solved by a high-precision expansion method. Strong numerical
evidence is obtained that singularities have infinite vorticity and lie on a
complex manifold which is constructed explicitly as an envelope of analyticity
disks.Comment: 19 pages, 14 figures, published versio
Superdiffusion of massive particles induced by multi-scale velocity fields
We study drag-induced diffusion of massive particles in scale-free velocity
fields, where superdiffusive behavior emerges due to the scale-free size
distribution of the vortices of the underlying velocity field. The results show
qualitative resemblance to what is observed in fluid systems, namely the
diffusive exponent for the mean square separation of pairs of particles and the
preferential concentration of the particles, both as a function of the response
time.Comment: 5 pages, 5 figures. Accepted for publication in EP
Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks
Acceleration disturbances due to local gravity gradients in ASTROD I
The Astrodynamical Space Test of Relativity using Optical Devices (ASTROD)
mission consists of three spacecraft in separate solar orbits and carries out
laser interferometric ranging. ASTROD aims at testing relativistic gravity,
measuring the solar system and detecting gravitational waves. Because of the
larger arm length, the sensitivity of ASTROD to gravitational waves is
estimated to be about 30 times better than Laser Interferometer Space Antenna
(LISA) in the frequency range lower than about 0.1 mHz. ASTROD I is a simple
version of ASTROD, employing one spacecraft in a solar orbit. It is the first
step for ASTROD and serves as a technology demonstration mission for ASTROD. In
addition, several scientific results are expected in the ASTROD I experiment.
The required acceleration noise level of ASTROD I is 10^-13 m s^-2 Hz^{-1/2} at
the frequency of 0.1 mHz. In this paper, we focus on local gravity gradient
noise that could be one of the largest acceleration disturbances in the ASTROD
I experiment. We have carried out gravitational modelling for the current
test-mass design and simplified configurations of ASTROD I by using an
analytical method and the Monte Carlo method. Our analyses can be applied to
figure out the optimal designs of the test mass and the constructing materials
of the spacecraft, and the configuration of compensation mass to reduce local
gravity gradients.Comment: 6 pages, presented at the 6th Edoardo Amaldi Conference (Okinawa
Japan, June 2005); to be published in Journal of Physics: Conference Serie
Reach out, touch space
A quick look at the stellar week of outreach activitites that formed part of NAM202
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