8,131 research outputs found
Tumbling of a rigid rod in a shear flow
The tumbling of a rigid rod in a shear flow is analyzed in the high viscosity
limit. Following Burgers, the Master Equation is derived for the probability
distribution of the orientation of the rod. The equation contains one
dimensionless number, the Weissenberg number, which is the ratio of the shear
rate and the orientational diffusion constant. The equation is solved for the
stationary state distribution for arbitrary Weissenberg numbers, in particular
for the limit of high Weissenberg numbers. The stationary state gives an
interesting flow pattern for the orientation of the rod, showing the interplay
between flow due to the driving shear force and diffusion due to the random
thermal forces of the fluid. The average tumbling time and tumbling frequency
are calculated as a function of the Weissenberg number. A simple cross-over
function is proposed which covers the whole regime from small to large
Weissenberg numbers.Comment: 22 pages, 9 figure
Strongly coupled modes in a weakly driven micromechanical resonator
We demonstrate strong coupling between the flexural vibration modes of a
clamped-clamped micromechanical resonator vibrating at low amplitudes. This
coupling enables the direct measurement of the frequency response via
amplitude- and phase modulation schemes using the fundamental mode as a
mechanical detector. In the linear regime, a frequency shift of
is observed for a mode with a line width of
in vacuum. The measured response is well-described by the
analytical model based on the Euler-Bernoulli beam including tension.
Calculations predict an upper limit for the room-temperature Q-factor of
for our top-down fabricated micromechanical beam
resonators.Comment: 9 pages, 2 figure
Conserving Approximations in Time-Dependent Density Functional Theory
In the present work we propose a theory for obtaining successively better
approximations to the linear response functions of time-dependent density or
current-density functional theory. The new technique is based on the
variational approach to many-body perturbation theory (MBPT) as developed
during the sixties and later expanded by us in the mid nineties. Due to this
feature the resulting response functions obey a large number of conservation
laws such as particle and momentum conservation and sum rules. The quality of
the obtained results is governed by the physical processes built in through
MBPT but also by the choice of variational expressions. We here present several
conserving response functions of different sophistication to be used in the
calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio
Combining Hebbian and reinforcement learning in a minibrain model
A toy model of a neural network in which both Hebbian learning and
reinforcement learning occur is studied. The problem of `path interference',
which makes that the neural net quickly forgets previously learned input-output
relations is tackled by adding a Hebbian term (proportional to the learning
rate ) to the reinforcement term (proportional to ) in the learning
rule. It is shown that the number of learning steps is reduced considerably if
, i.e., if the Hebbian term is neither too small nor too
large compared to the reinforcement term
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Measuring the impact of observations on the predictability of the Kuroshio Extension in a shallow-water model
In this paper sequential importance sampling is used to assess the impact of observations on a ensemble prediction for the decadal path transitions of the Kuroshio Extension (KE). This particle filtering approach gives access to the probability density of the state vector, which allows us to determine the predictive power — an entropy based measure — of the ensemble prediction. The proposed set-up makes use of an ensemble that, at each time, samples the climatological probability distribution. Then, in a post-processing step, the impact of different sets of observations is measured by the increase in predictive power of the ensemble over the climatological signal during one-year. The method is applied in an identical-twin
experiment for the Kuroshio Extension using a reduced-gravity shallow water model. We investigate the impact of assimilating velocity observations from different locations during the elongated and the contracted meandering state of the KE. Optimal observations location correspond to regions with strong potential vorticity gradients. For the elongated state the optimal location is in the first meander of the KE. During the contracted state of the KE it is located south of Japan, where the Kuroshio separates from the coast
Multi-dimensional population modelling using frbpoppy: magnetars can produce the observed Fast Radio Burst sky
Fast Radio Bursts (FRBs) are energetic, short, bright transients that occur
frequently over the entire radio sky. The observational challenges following
from their fleeting, generally one-off nature have prevented identification of
the underlying sources producing the bursts. As the population of detected FRBs
grows, the observed distributions of brightness, pulse width and dispersion
measure now begin to take shape. Meaningful direct interpretation of these
distributions is, however, made impossible by the selection effects that
telescope and search pipelines invariably imprint on each FRB survey. Here we
show that multi-dimensional FRB population synthesis can find a single,
self-consistent population of FRB sources that can reproduce the real-life
results of the major ongoing FRB surveys. This means that individual observed
distributions can now be combined to derive the properties of the intrinsic FRB
source population. The characteristics of our best-fit model for one-off FRBs
agree with a population of magnetars. We extrapolate this model and predict the
number of FRBs future surveys will find. For surveys that have commenced, the
method we present here can already determine the composition of the FRB source
class, and potentially even its subpopulations.Comment: 12 pages, 4 figures, accepted by Astronomy & Astrophysic
Numerical simulations on the motion of atoms travelling through a standing-wave light field
The motion of metastable helium atoms travelling through a standing light
wave is investigated with a semi-classical numerical model. The results of a
calculation including the velocity dependence of the dipole force are compared
with those of the commonly used approach, which assumes a conservative dipole
force. The comparison is made for two atom guiding regimes that can be used for
the production of nanostructure arrays; a low power regime, where the atoms are
focused in a standing wave by the dipole force, and a higher power regime, in
which the atoms channel along the potential minima of the light field. In the
low power regime the differences between the two models are negligible and both
models show that, for lithography purposes, pattern widths of 150 nm can be
achieved. In the high power channelling regime the conservative force model,
predicting 100 nm features, is shown to break down. The model that incorporates
velocity dependence, resulting in a structure size of 40 nm, remains valid, as
demonstrated by a comparison with quantum Monte-Carlo wavefunction
calculations.Comment: 9 pages, 4 figure
Waiting and Residence Times of Brownian Interface Fluctuations
We report on the residence times of capillary waves above a given height
and on the typical waiting time in between such fluctuations. The measurements
were made on phase separated colloid-polymer systems by laser scanning confocal
microscopy. Due to the Brownian character of the process, the stochastics vary
with the chosen measurement interval . In experiments, the discrete
scanning times are a practical cutoff and we are able to measure the waiting
time as a function of this cutoff. The measurement interval dependence of the
observed waiting and residence times turns out to be solely determined by the
time dependent height-height correlation function . We find excellent
agreement with the theory presented here along with the experiments.Comment: 5 figure
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