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$^\circ$ 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

Microscale swimming: The molecular dynamics approach

The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of two-dimensional swimming bodies employing a variety of propulsion mechanisms -- motivated by biological and microrobotic designs -- is investigated, including the use of moving limbs, changing body shapes and fluid jets. The swimming efficiency and the nature of the induced, time-dependent flow fields are found to differ widely among body designs and propulsion mechanisms.Comment: 5 pages, 3 figures (minor changes to text