Effective swimming strategies in low Reynolds number flows

The optimal strategy for a microscopic swimmer to migrate across a linear shear flow is discussed. The two cases, in which the swimmer is located at large distance, and in the proximity of a solid wall, are taken into account. It is shown that migration can be achieved by means of a combination of sailing through the flow and swimming, where the swimming strokes are induced by the external flow without need of internal energy sources or external drives. The structural dynamics required for the swimmer to move in the desired direction is discussed and two simple models, based respectively on the presence of an elastic structure, and on an orientation dependent friction, to control the deformations induced by the external flow, are analyzed. In all cases, the deformation sequence is a generalization of the tank-treading motion regimes observed in vesicles in shear flows. Analytic expressions for the migration velocity as a function of the deformation pattern and amplitude are provided. The effects of thermal fluctuations on propulsion have been discussed and the possibility that noise be exploited to overcome the limitations imposed on the microswimmer by the scallop theorem have been discussed.Comment: 14 pages, 5 figure

Cosmological parameter estimation using Very Small Array data out to ℓ= 1500

We estimate cosmological parameters using data obtained by the Very Small Array (VSA) in its extended configuration, in conjunction with a variety of other cosmic microwave background (CMB) data and external priors. Within the flat Λ cold dark matter (ΛCDM) model, we find that the inclusion of high-resolution data from the VSA modifies the limits on the cosmological parameters as compared to those suggested by the Wilkinson Microwave Anisotropy Probe (WMAP) alone, while still remaining compatible with their estimates. We find that Ωbh2= 0.0234+0.0012−0.0014, Ωdmh2= 0.111+0.014−0.016, h= 0.73+0.09−0.05, nS= 0.97+0.06−0.03, 1010AS= 23+7−3 and τ= 0.14+0.14−0.07 for WMAP and VSA when no external prior is included. On extending the model to include a running spectral index of density fluctuations, we find that the inclusion of VSA data leads to a negative running at a level of more than 95 per cent confidence ( nrun=−0.069 ± 0.032 ), something that is not significantly changed by the inclusion of a stringent prior on the Hubble constant. Inclusion of prior information from the 2dF galaxy redshift survey reduces the significance of the result by constraining the value of Ωm. We discuss the veracity of this result in the context of various systematic effects and also a broken spectral index model. We also constrain the fraction of neutrinos and find that fν < 0.087 at 95 per cent confidence, which corresponds to mν < 0.32 eV when all neutrino masses are equal. Finally, we consider the global best fit within a general cosmological model with 12 parameters and find consistency with other analyses available in the literature. The evidence for nrun < 0 is only marginal within this model

The long-time dynamics of two hydrodynamically-coupled swimming cells

Swimming micro-organisms such as bacteria or spermatozoa are typically found in dense suspensions, and exhibit collective modes of locomotion qualitatively different from that displayed by isolated cells. In the dilute limit where fluid-mediated interactions can be treated rigorously, the long-time hydrodynamics of a collection of cells result from interactions with many other cells, and as such typically eludes an analytical approach. Here we consider the only case where such problem can be treated rigorously analytically, namely when the cells have spatially confined trajectories, such as the spermatozoa of some marine invertebrates. We consider two spherical cells swimming, when isolated, with arbitrary circular trajectories, and derive the long-time kinematics of their relative locomotion. We show that in the dilute limit where the cells are much further away than their size, and the size of their circular motion, a separation of time scale occurs between a fast (intrinsic) swimming time, and a slow time where hydrodynamic interactions lead to change in the relative position and orientation of the swimmers. We perform a multiple-scale analysis and derive the effective dynamical system - of dimension two - describing the long-time behavior of the pair of cells. We show that the system displays one type of equilibrium, and two types of rotational equilibrium, all of which are found to be unstable. A detailed mathematical analysis of the dynamical systems further allows us to show that only two cell-cell behaviors are possible in the limit of $t\to\infty$, either the cells are attracted to each other (possibly monotonically), or they are repelled (possibly monotonically as well), which we confirm with numerical computations

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Surface effects in nucleation and growth of smectic B crystals in thin samples

We present an experimental study of the surface effects (interactions with the container walls) during the nucleation and growth of smectic B crystals from the nematic in free growth and directional solidification of a mesogenic molecule ($C_4H_9-(C_6H_{10})_2CN$) called CCH4 in thin (of thickness in the 10 $\mu$m range) samples. We follow the dynamics of the system in real time with a polarizing microscope. The inner surfaces of the glass-plate samples are coated with polymeric films, either rubbed polyimid (PI) films or monooriented poly(tetrafluoroethylene) (PTFE) films deposited by friction at high temperature. The orientation of the nematic and the smectic B is planar. In PI-coated samples, the orientation effect of SmB crystals is mediated by the nematic, whereas, in PTFE-coated samples, it results from a homoepitaxy phenomenon occurring for two degenerate orientations. A recrystallization phenomenon partly destroys the initial distribution of crystal orientations. In directional solidification of polycrystals in PTFE-coated samples, a particular dynamics of faceted grain boundary grooves is at the origin of a dynamical mechanism of grain selection. Surface effects also are responsible for the nucleation of misoriented terraces on facets and the generation of lattice defects in the solid.Comment: 15 pages, 24 figures, submitted to PR

A circle swimmer at low Reynolds number

Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys. Rev. E 69, 062901 (2004)). Our model consists of three solid spheres arranged in a triangular configuration, joined by two links of time-dependent length. For small strokes, we discuss the motion of the swimmer as a function of the separation angle between its links. We find that swimmers describe either clockwise or anticlockwise circular motion depending on the tilting angle in a non-trivial manner. The symmetry of the swimmer leads to a quadrupolar decay of the far flow field. We discuss the potential extensions and experimental realisation of our model.Comment: 9 pages, 9 Figure

Contact line dynamics in binary lattice Boltzmann simulations

We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents, and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface velocity.Comment: 10 pages, 5 figure

Modelling capillary filling dynamics using lattice Boltzmann simulations

We investigate the dynamics of capillary filling using two lattice Boltzmann schemes: a liquid-gas model and a binary model. The simulation results are compared to the well-known Washburn's law, which predicts that the filled length of the capillary scales with time as $l \propto t^{1/2}$. We find that the liquid-gas model does not reproduce Washburn's law due to condensation of the gas phase at the interface, which causes the asymptotic behaviour of the capillary penetration to be faster than $t^{1/2}. The binary model, on the other hand, captures the correct scaling behaviour when the viscosity ratio between the two phases is sufficiently high.Comment: 9 pages, 7 figures, DSFD 2007 proceeding

Capillary filling in patterned channels

We show how the capillary filling of microchannels is affected by posts or ridges on the sides of the channels. Ridges perpendicular to the flow direction introduce contact line pinning which slows, or sometimes prevents, filling; whereas ridges parallel to the flow provide extra surface which may enhances filling. Patterning the microchannel surface with square posts has little effect on the ability of a channel to fill for equilibrium contact angle $\theta_e \lesssim 30^{\mathrm{o}}$. For $\theta_e \gtrsim 60^{\mathrm{o}}$, however, even a small number of posts can pin the advancing liquid front.Comment: 4 pages, 4 figure