Speedup of self-propelled helical swimmers in a long cylindrical pipe

Pipe-like confinements are ubiquitously encountered by microswimmers.Here we systematically study the ratio of the speeds of a force-and torque-free microswimmer swimming in the center of a cylindrical pipe to its speed in an unbounded fluid(speed ratio).Inspired by E.coli,the model swimmer consists of a cylindrical head and a double-helical tail connected to the head by a rotating virtual motor.The numerical simulation shows that depending on swimmer geometry,confinements can enhance or hinder the swimming speed,which is verified by Reynolds number matched experiments.We further developed a reduced model.The model shows that the swimmer with a moderately long,slender head and a moderately long tail experiences the greatest speed enhancement,whereas the theoretical speed ratio has no upper limit.The properties of the virtual motor also affect the speed ratio,namely,the constant-frequency motor generates a greater speed ratio compared to the constant-torque motor.     

Brownian ratchets driven by asymmetric nucleation of hydrolysis waves

We propose a stochastic process wherein molecular transport is mediated by asymmetric nucleation of domains on a one-dimensional substrate, in contrast with molecular motors that hydrolyze nucleotide triphosphates and undergo conformational change. We show that asymmetric nucleation of hydrolysis waves on a track can also result in directed motion of an attached particle. Asymmetrically cooperative kinetics between hydrolyzed and unhydrolyzed states on each lattice site generate moving domain walls that push a particle sitting on the track. We use a novel fluctuating-frame, finite-segment mean field theory to accurately compute steady-state velocities of the driven particle and to discover parameter regimes yielding maximal domain wall flux, leading to optimal particle drift.     

Adiabatic Brownian ratchets with the inclusion of inertia

Inertial corrections to the drift velocity of a Brownian particle have been calculated for two main classes of Brownian ratchets operating in the adiabatic regime of fluctuations of the potential energy: first, the stationary periodic potential and dichotomic fluctuations of an external force with zero average value (rocking ratchet) and, second, dichotomic fluctuations of the periodic potential itself. It has been shown that, in contrast to passive transport at which the inertial correction always reduces the effective mobility and diffusion coefficients, inertial corrections for Brownian ratchets can play a constructive role, increasing the drift velocity at least at high temperatures.     

Quantifying the distortion products generated by amplitude-modulated noise

When sinusoidal amplitude modulation (SAM) is applied to noise or tone carriers, the stimuli can generate audible distortion products in the region of the modulation frequency. As a result, when bandpass-filtered SAM noise is used to investigate temporal processing, a band of unmodulated noise is typically positioned at the modulation frequency to mask any distortion products. This study was designed to investigate the distortion products for bandpass noise carriers, and so reduce ambiguity about the form of this distortion and its role in perception. The distortion consists of two distortion-noise bands and a distortion tone at the modulation frequency. In the first two experiments, the level and phase of the distortion tone are measured using two different experimental paradigms. In the third experiment, modulation-frequency difference limens are measured for filtered SAM noise and it is shown that performance deteriorates markedly when the distortion tone is canceled. In a fourth experiment, masked threshold is measured at low frequencies for bands of high-frequency, unmodulated noise with the same levels and spectra as the SAM noises in the earlier experiments. The results confirm that unmodulated noise also produces quadratic distortion which may explain some aspects of earlier reports on remote masking.     

Optical compensation of geometrical distortion by a deformable mirror

An optical method for the real time correction of geometrical distortion is reported. It is based on the “fun-house-mirror effect”: An adjustable nonplanar mirror is introduced between object- and pupil-plane and generates a suitable (space-variant) shift of each pixel. The method is restricted to a certain class of distortions, which lead to continuous mirror surfaces (mirror must not break). We also investigate aberrations which are another restriction of the method. Our application was the improvement of TV-systems: before correction 20%, and after correction 50% of pixels had a distortion less or equal than one pixel distance.     

Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish

Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish,to increase the swimming efficiency and the swimming speed and control the motion direction more easily,is investigated by combining optimization algorithms,unsteady computational fluid dynamics and dynamic control in this study.The 3D computational fluid dynamics package contains the immersed boundary method,volume of fluid method,the adaptive multi-grid finite volume method and the control strategy of fish swimming.Through shape optimizations of various swimming speeds,the results show that the optimal caudal fins of different swimming modes are not exactly the same shape.However,the optimal fish of high swimming speed,whose caudal fin shape is similar to the crescent,also have higher efficiency and better maneuverability than the other optimal bionic fish at low and moderate swimming speeds.Finally,the mechanisms of vorticity creation of different optimal bionic fish are studied by using boundary vorticity-flux theory,and three-dimensional wake structures of self-propelled swimming of these fish are comparatively analyzed.The study of vortex dynamics reveals the nature of efficient swimming of the 3D bionic fish with the lunate caudal fin.     

On the geometrical interpretation of solitons

Rigid body motion along helical space curves is shown to generate a class of nonlinear partial differential equations solvable by the two component inverse scattering phenomenology and the associated class of pseudopotentials, prolongation and Lie-algebraic structures. The results unify the various soliton interpretations.     

Molecular ratchets: verification of the principle of detailed balance and the second law of dynamics

We argue that the recent experiments of Kelly et al. [Angew. Chem. Int. Ed. Engl. 36, 1866 (1997)] on molecular ratchets, in addition to being in agreement with the second law of thermodynamics, is a test of the principle of detailed balance for the ratchet. We suggest experiments, using an asymmetric ratchet, to further test the principle. We also point out methods involving a time variation of the temperature to give it a directional motion.     

The geometrical aspects of the bell inequalities

The Bell inequalities of the metric form are introduced. The quantum-mechanical correlations of the particles with s=1/2 and photons are described using the relative measure of probability on the concave surfaces. The relation of the proposed scheme with the Bayes theorem about conditional information entropy and J. von Neumann's postulates is discussed.     

Measuring the geometrical size of multiparticle processes

We examine the possibility of measuring the geometrical size of multiparticle processes. The mean-square impact parameter, 〈b²〉, of a process can be estimated by means of lower bounds which are determined from experiment. A bound of this type, which has been proposed by Webber, is found to be inadequate for the estimate. We propose several alternative bounds. One of them represents a considerable improvement over Webber's bound, with essentially no increase in the difficulty of the measurement. Another is a theoretically optimal bound which, however, requires an extremely high-statistics experiment. We also describe a method of deriving further bounds; and make estimates of the difference between the bounds and the true 〈b²〉.     

Symmetry properties of the large-deviation function of the velocity of a self-propelled polar particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.     

Numerical modeling of the swirling turbulent wake decay past a self-propelled body

Numerical analysis of the swirling turbulent wake degeneration past a self-propelled body has been carried out. It has been shown that starting from the distances of the order of 100 diameters from the body, the flow becomes practically shearless. A simplified mathematical model of the far swirling wake past a self-propelled body has been constructed.     

On the geometrical aspects of electromagnetism,I

The trajectory of a charged test particle under a Lorentz force is obtained as the geodesic of a riemannian four dimensional manifold. Originally, the geodesic equation is nonlinear in some vector field A′_μ. The nonlinearity is traded in for the correct characteristic $\text{e}\text{m}$ of the test particle through a gauge condition, imposed upon A′_μ, which turns the geodesic into the fully covariant linear and gauge invariant Lorentz equation. Fitting the $\text{e}\text{m}$ ratio inside the gauge leaves F′_μν independent of $\text{e}\text{m}$ and allows its identification with the E.-M. tensor F_μν. This four dimensional approach allows the identification of the fifth coordinate used in Kaluza's geometrization |1,2|. The gauge function appears as the sum of Hamilton-Jacobi function plus an additional term, related to the “length” of the trajectory. It is this latter term which guarantees the correct “normalisation” of the $\text{e}\text{m}$ ratio.     

A geometrical approach to the problem of integrability of Hamiltonian systems by separation of variables

We propose a geometrical approach to the problem of integrability of Hamiltonian systems of low dimensions using the Hamilton–Jacobi method of separation of variables, based on the method of moving frames. As an illustration we present a complete classification of all separable Hamiltonian systems defined in two-dimensional Riemannian manifolds of arbitrary curvature and a criterion for separability. Connections to bi-Hamiltonian theory are also found.     

A geometrical interpretation of the null sectional curvature

A geometrical interpretation is given for the null sectional curvature of degenerate planes in a Lorentzian manifold. This interpretation is based on a generalization to the indefinite case of the squaroids of Levi-Civita. Further, it is shown that a three-dimensional, conformally flat Lorentzian manifold has isotropic and spatially constant null sectional curvature if and only if it is locally a Robertson–Walker manifold.     

Automatic computation of the geometrical characteristics of a surface modified by a scanning nanohardness tester

A technique for automatic determination of the contact area of a remnant impression obtained by nanoindentation with regard to a surrounding relief is suggested. An algorithm on which the suggested technique is based and an algorithm to automatically correct scanning defects are described. The hardness values determined by dynamic nanoindentation and by direct measurement of the impression are compared.     

Calculation of cross sections of simultaneous ionization in ion-atom collisions by the generalized geometrical model

The geometrical model (GM) of ionization in ion—atom collisions [8, 9] was generalized to describe ionization of both colliding particles (simultaneous ionization) due to electron—electron interaction. The generalized GM (GGM) allows calculation of the cross sections for electron loss by an incident particle with simultaneous target ionization at collision velocities higher than characteristic electron velocities, accurate within a factor of two with respect to the Born or impulse approximation. An advantage of the GGM, except for its simplicity, is easy calculation of p(b) (p is the ionization probability and b is the impact parameter), which makes it possible to include the contribution of simultaneous ionization into more general approximate schemes for calculating cross sections of multielectron ionization of atoms or ions.     

Quantifying the nonlocality of Greenberger-Horne-Zeilinger quantum correlations by a bounded communication simulation protocol

The simulation of quantum correlations with finite nonlocal resources, such as classical communication, gives a natural way to quantify their nonlocality. While multipartite nonlocal correlations appear to be useful resources, very little is known on how to simulate multipartite quantum correlations. We present a protocol that reproduces tripartite Greenberger-Horne-Zeilinger correlations with bounded communication: 3 bits in total turn out to be sufficient to simulate all equatorial Von Neumann measurements on the tripartite Greenberger-Horne-Zeilinger state.