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

Efficiency of initiating cell adhesion in hydrodynamic flow

We theoretically investigate the efficiency of initial binding between a receptor-coated sphere and a ligand-coated wall in linear shear flow. The mean first passage time for binding decreases monotonically with increasing shear rate. Above a saturation threshold of the order of a few 100 receptor patches, the binding efficiency is enhanced only weakly by increasing their number and size, but strongly by increasing their height. This explains why white blood cells in the blood flow adhere through receptor patches localized to the tips of microvilli, and why malaria-infected red blood cells form elevated receptor patches (knobs).Comment: 4 pages, Revtex, 4 Postscript figures included, to appear in PR

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

Monotonicity and logarithmic convexity relating to the volume of the unit ball

Let $\Omega_n$ stand for the volume of the unit ball in $\mathbb{R}^n$ for $n\in\mathbb{N}$. In the present paper, we prove that the sequence $\Omega_{n}^{1/(n\ln n)}$ is logarithmically convex and that the sequence $\frac{\Omega_{n}^{1/(n\ln n)}}{\Omega_{n+1}^{1/[(n+1)\ln(n+1)]}}$ is strictly decreasing for $n\ge2$. In addition, some monotonic and concave properties of several functions relating to $\Omega_{n}$ are extended and generalized.Comment: 12 page

Individual differences in white matter microstructure reflect variation in functional connectivity during action choice.

The relation between brain structure and function is of fundamental importance in neuroscience. Comparisons between behavioral and brain imaging measures suggest that variation in brain structure correlates with the presence of specific skills[1-3]. Behavioral measures, however, reflect the integrated function of multiple brain regions. Rather than behavior, a physiological index of function could be a more sensitive and informative measure with which to compare structural measures. Here, we test for a relationship between a physiological measure of functional connectivity between two brain areas during a simple decision making task and a measure of structural connectivity. Paired-pulse transcranial magnetic stimulation indexed functional connectivity between two regions important for action choices: premotor and motor cortex. Fractional anisotropy (FA), a marker of microstructural integrity, indexed structural connectivity. Individual differences in functional connectivity during action selection show highly specific correlations with FA in localised regions of white matter interconnecting regions including the premotor and motor cortex. Probabilistic tractography[4, 5], a technique for identifying fibre pathways from diffusion-weighted imaging (DWI), reconstructed the anatomical networks linking the component brain regions involved in making decisions. These findings demonstrate a relationship between individual differences in functional and structural connectivity within human brain networks central to action choice

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

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

Generalized-ensemble Monte carlo method for systems with rough energy landscape

We present a novel Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor and is another version of the so-called generalized-ensemble techniques. The effectiveness of the new approach is demonstrated for the system of a small peptide, an example of the frustrated system with a rugged energy landscape.Comment: Latex; ps-files include

Collective chemotactic dynamics in the presence of self-generated fluid flows

In micro-swimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by self-generated flows. A kinetic theory coupling run-and-tumble chemotaxis to the flows of collective swimming shows separate branches of chemotactic and hydrodynamic instabilities for isotropic suspensions, the first driving aggregation, the second producing increased orientational order in suspensions of "pushers" and maximal disorder in suspensions of "pullers". Nonlinear simulations show that hydrodynamic interactions can limit and modify chemotactically-driven aggregation dynamics. In puller suspensions the dynamics form aggregates that are mutually-repelling due to the non-trivial flows. In pusher suspensions chemotactic aggregation can lead to destabilizing flows that fragment the regions of aggregation.Comment: 4 page

Reaction-Diffusion Process Driven by a Localized Source: First Passage Properties

We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at the origin by a source which is turned on at time t=0. When a diffusing atom collides with an immobile atom, the two atoms form an immobile stable molecule. The region occupied by molecules is asymptotically spherical with radius growing as t^{1/d} in d>=2 dimensions. We investigate the survival probability that a diffusing atom has not become a part of a molecule during the time interval t after its injection and the probability density of such a particle. We show that asymptotically the survival probability (i) saturates in one dimension, (ii) vanishes algebraically with time in two dimensions (with exponent being a function of the dimensionless flux and determined as a zero of a confluent hypergeometric function), and (iii) exhibits a stretched exponential decay in three dimensions.Comment: 7 pages; version 2: section IV is re-written, references added, 8 pages (final version