318 research outputs found
Stokes trapping and planet formation
It is believed that planets are formed by aggregation of dust particles
suspended in the turbulent gas forming accretion disks around developing stars.
We describe a mechanism, termed 'Stokes trapping', by which turbulence limits
the growth of aggregates of dust particles, so that their Stokes number
(defined as the ratio of the damping time of the particles to the Kolmogorov
dissipation timescale) remains close to unity. We discuss possible mechanisms
for avoiding this barrier to further growth. None of these is found to be
satisfactory and we introduce a new theory which does not involve the growth of
small clusters of dust grains.Comment: 30 pages, 4 figures. Revised version has improved concluding remarks,
extended discussion of sticking velocit
An exact-diagonalization study of rare events in disordered conductors
We determine the statistical properties of wave functions in disordered
quantum systems by exact diagonalization of one-, two- and quasi-one
dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we
find that the tails of the distribution of wave-function amplitudes are
described by the non-linear sigma-model. In two dimensions, the tails of the
distribution function are consistent with a recent prediction based on a direct
optimal fluctuation method.Comment: 13 pages, 5 figure
The impact of beam deconvolution on noise properties in CMB measurements: Application to Planck LFI
We present an analysis of the effects of beam deconvolution on noise
properties in CMB measurements. The analysis is built around the artDeco beam
deconvolver code. We derive a low-resolution noise covariance matrix that
describes the residual noise in deconvolution products, both in harmonic and
pixel space. The matrix models the residual correlated noise that remains in
time-ordered data after destriping, and the effect of deconvolution on it. To
validate the results, we generate noise simulations that mimic the data from
the Planck LFI instrument. A test for the full 70 GHz covariance in
multipole range yields a mean reduced of 1.0037. We
compare two destriping options, full and independent destriping, when
deconvolving subsets of available data. Full destriping leaves substantially
less residual noise, but leaves data sets intercorrelated. We derive also a
white noise covariance matrix that provides an approximation of the full noise
at high multipoles, and study the properties on high-resolution noise in pixel
space through simulations.Comment: 22 pages, 25 figure
A numerical study of wave-function and matrix-element statistics in the Anderson model of localization
Colliding Particles in Highly Turbulent Flows
We discuss relative velocities and the collision rate of small particles
suspended in a highly turbulent fluid. In the limit where the viscous damping
is very weak, we estimate the relative velocities using the Kolmogorov cascade
principle.Comment: 5 pages, no figures, v2 contains additional result
Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model
We discuss the localization behavior of localized electronic wave functions
in the one- and two-dimensional tight-binding Anderson model with diagonal
disorder. We find that the distributions of the local wave function amplitudes
at fixed distances from the localization center are well approximated by
log-normal fits which become exact at large distances. These fits are
consistent with the standard single parameter scaling theory for the Anderson
model in 1d, but they suggest that a second parameter is required to describe
the scaling behavior of the amplitude fluctuations in 2d. From the log-normal
distributions we calculate analytically the decay of the mean wave functions.
For short distances from the localization center we find stretched exponential
localization ("sublocalization") in both, 1d and 2d. In 1d, for large
distances, the mean wave functions depend on the number of configurations N
used in the averaging procedure and decay faster that exponentially
("superlocalization") converging to simple exponential behavior only in the
asymptotic limit. In 2d, in contrast, the localization length increases
logarithmically with the distance from the localization center and
sublocalization occurs also in the second regime. The N-dependence of the mean
wave functions is weak. The analytical result agrees remarkably well with the
numerical calculations.Comment: 12 pages with 9 figures and 1 tabl
Correlation Exponent and Anomalously Localized States at the Critical Point of the Anderson Transition
We study the box-measure correlation function of quantum states at the
Anderson transition point with taking care of anomalously localized states
(ALS). By eliminating ALS from the ensemble of critical wavefunctions, we
confirm, for the first time, the scaling relation z(q)=d+2tau(q)-tau(2q) for a
wide range of q, where q is the order of box-measure moments and z(q) and
tau(q) are the correlation and the mass exponents, respectively. The influence
of ALS to the calculation of z(q) is also discussed.Comment: 6 pages, 3 figure
Variable-range Projection Model for Turbulence-driven Collisions
We discuss the probability distribution of relative speed of
inertial particles suspended in a highly turbulent gas when the Stokes numbers,
a dimensionless measure of their inertia, is large. We identify a mechanism
giving rise to the distribution
(for some constant ). Our conclusions are supported by numerical simulations
and the analytical solution of a model equation of motion. The results
determine the rate of collisions between suspended particles. They are relevant
to the hypothesised mechanism for formation of planets by aggregation of dust
particles in circumstellar nebula.Comment: 4 pages, 2 figure
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