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 $St$, 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 $St\geq 0.1$, 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 $\psi_0(x_1, x_2) = \cos x_1+\cos 2x_2$, we find that the width $\delta(t)$ of its analyticity strip follows a $\ln(1/t)$ 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

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