27,294 research outputs found
Enhanced diffusion by reciprocal swimming
Purcell's scallop theorem states that swimmers deforming their shapes in a
time-reversible manner ("reciprocal" motion) cannot swim. Using numerical
simulations and theoretical calculations we show here that in a fluctuating
environment, reciprocal swimmers undergo, on time scales larger than that of
their rotational diffusion, diffusive dynamics with enhanced diffusivities,
possibly by orders of magnitude, above normal translational diffusion.
Reciprocal actuation does therefore lead to a significant advantage over
non-motile behavior for small organisms such as marine bacteria
Derivation of an integral of Boros and Moll via convolution of Student t-densities
We show that the evaluation of an integral considered by Boros and Moll is a
special case of a convolution result about Student t-densities obtained by the
authors in 2008
The smallest eigenvalue of Hankel matrices
Let H_N=(s_{n+m}),n,m\le N denote the Hankel matrix of moments of a positive
measure with moments of any order. We study the large N behaviour of the
smallest eigenvalue lambda_N of H_N. It is proved that lambda_N has exponential
decay to zero for any measure with compact support. For general determinate
moment problems the decay to 0 of lambda_N can be arbitrarily slow or
arbitrarily fast. In the indeterminate case, where lambda_N is known to be
bounded below by a positive constant, we prove that the limit of the n'th
smallest eigenvalue of H_N for N tending to infinity tends rapidly to infinity
with n. The special case of the Stieltjes-Wigert polynomials is discussed
Kinematics of the swimming of Spiroplasma
\emph{Spiroplasma} swimming is studied with a simple model based on
resistive-force theory. Specifically, we consider a bacterium shaped in the
form of a helix that propagates traveling-wave distortions which flip the
handedness of the helical cell body. We treat cell length, pitch angle, kink
velocity, and distance between kinks as parameters and calculate the swimming
velocity that arises due to the distortions. We find that, for a fixed pitch
angle, scaling collapses the swimming velocity (and the swimming efficiency) to
a universal curve that depends only on the ratio of the distance between kinks
to the cell length. Simultaneously optimizing the swimming efficiency with
respect to inter-kink length and pitch angle, we find that the optimal pitch
angle is 35.5 and the optimal inter-kink length ratio is 0.338, values
in good agreement with experimental observations.Comment: 4 pages, 5 figure
Drops with non-circular footprints
In this paper we study the morphology of drops formed on partially wetting
substrates, whose footprint is not circular. This type of drops is a
consequence of the breakup processes occurring in thin films when anisotropic
contact line motions take place. The anisotropy is basically due to hysteresis
effects of the contact angle since some parts of the contact line are wetting,
while others are dewetting. Here, we obtain a peculiar drop shape from the
rupture of a long liquid filament sitting on a solid substrate, and analyze its
shape and contact angles by means of goniometric and refractive techniques. We
also find a non--trivial steady state solution for the drop shape within the
long wave approximation (lubrication theory), and compare most of its features
with experimental data. This solution is presented both in Cartesian and polar
coordinates, whose constants must be determined by a certain group of measured
parameters. Besides, we obtain the dynamics of the drop generation from
numerical simulations of the full Navier--Stokes equation, where we emulate the
hysteretic effects with an appropriate spatial distribution of the static
contact angle over the substrate
A single-photon sampling architecture for solid-state imaging
Advances in solid-state technology have enabled the development of silicon
photomultiplier sensor arrays capable of sensing individual photons. Combined
with high-frequency time-to-digital converters (TDCs), this technology opens up
the prospect of sensors capable of recording with high accuracy both the time
and location of each detected photon. Such a capability could lead to
significant improvements in imaging accuracy, especially for applications
operating with low photon fluxes such as LiDAR and positron emission
tomography.
The demands placed on on-chip readout circuitry imposes stringent trade-offs
between fill factor and spatio-temporal resolution, causing many contemporary
designs to severely underutilize the technology's full potential. Concentrating
on the low photon flux setting, this paper leverages results from group testing
and proposes an architecture for a highly efficient readout of pixels using
only a small number of TDCs, thereby also reducing both cost and power
consumption. The design relies on a multiplexing technique based on binary
interconnection matrices. We provide optimized instances of these matrices for
various sensor parameters and give explicit upper and lower bounds on the
number of TDCs required to uniquely decode a given maximum number of
simultaneous photon arrivals.
To illustrate the strength of the proposed architecture, we note a typical
digitization result of a 120x120 photodiode sensor on a 30um x 30um pitch with
a 40ps time resolution and an estimated fill factor of approximately 70%, using
only 161 TDCs. The design guarantees registration and unique recovery of up to
4 simultaneous photon arrivals using a fast decoding algorithm. In a series of
realistic simulations of scintillation events in clinical positron emission
tomography the design was able to recover the spatio-temporal location of 98.6%
of all photons that caused pixel firings.Comment: 24 pages, 3 figures, 5 table
Multicanonical Recursions
The problem of calculating multicanonical parameters recursively is
discussed. I describe in detail a computational implementation which has worked
reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded
Z-compressed .tar file created by uufiles), figure file corrected
Testing Error Correcting Codes by Multicanonical Sampling of Rare Events
The idea of rare event sampling is applied to the estimation of the
performance of error-correcting codes. The essence of the idea is importance
sampling of the pattern of noises in the channel by Multicanonical Monte Carlo,
which enables efficient estimation of tails of the distribution of bit error
rate. The idea is successfully tested with a convolutional code
Shaking a Box of Sand
We present a simple model of a vibrated box of sand, and discuss its dynamics
in terms of two parameters reflecting static and dynamic disorder respectively.
The fluidised, intermediate and frozen (`glassy') dynamical regimes are
extensively probed by analysing the response of the packing fraction to steady,
as well as cyclic, shaking, and indicators of the onset of a `glass transition'
are analysed. In the `glassy' regime, our model is exactly solvable, and allows
for the qualitative description of ageing phenomena in terms of two
characteristic lengths; predictions are also made about the influence of grain
shape anisotropy on ageing behaviour.Comment: Revised version. To appear in Europhysics Letter
Are Simple Real Pole Solutions Physical?
We consider exact solutions generated by the inverse scattering technique,
also known as the soliton transformation. In particular, we study the class of
simple real pole solutions. For quite some time, those solutions have been
considered interesting as models of cosmological shock waves. A coordinate
singularity on the wave fronts was removed by a transformation which induces a
null fluid with negative energy density on the wave front. This null fluid is
usually seen as another coordinate artifact, since there seems to be a general
belief that that this kind of solution can be seen as the real pole limit of
the smooth solution generated with a pair of complex conjugate poles in the
transformation. We perform this limit explicitly, and find that the belief is
unfounded: two coalescing complex conjugate poles cannot yield a solution with
one real pole. Instead, the two complex conjugate poles go to a different
limit, what we call a ``pole on a pole''. The limiting procedure is not unique;
it is sensitive to how quickly some parameters approach zero. We also show that
there exists no improved coordinate transformation which would remove the
negative energy density. We conclude that negative energy is an intrinsic part
of this class of solutions.Comment: 13 pages, 3 figure
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