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.     

Optimal stroke patterns for Purcell's three-link swimmer

Stroke patterns for Purcell's three-link swimmer are optimized. We model the swimmer as a jointed chain of three slender rods moving in an inertialess flow. The swimmer is optimized for efficiency and speed. We were able to attain swimmer designs significantly more efficient than those previously suggested by authors who only consider geometric design rather than kinematic criteria. The influence of slenderness on optimality is considered as well.     

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.     

Two Mathematically Equivalent Versions of Maxwell’s Equations

This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory. Here, we first show that there are two versions of Maxwell’s equations. The new version fixes the clock of the field source for all inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant for all observers, but depends on the motion of the source. This approach allows us to account for radiation reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions about the structure of the source. The theory provides a new invariance group which, in general, is a nonlinear and nonlocal representation of the Lorentz group. This approach also provides a natural (and unique) definition of simultaneity for all observers.     

Nonparametric NMR spectroscopy

The parametric (or model-based) approach to NMR spectroscopy suffers from two general problems: it is sensitive to modeling errors and requires knowledge of the number of resonances present in the compound(s) under analysis. The nonparametric approach has neither of these drawbacks and it may also be computationally simpler than the parametric approach. However, if not applied properly, the nonparametric approach may yield significantly less accurate spectroscopic results than the parametric approach. In this paper we introduce a high-resolution nonparametric methodology for NMR spectroscopy based on the adaptive filter bank approach. The main salient feature of the new approach is that it provides 2D spectra versus both frequency and damping, as opposed to the classical 1D frequency spectra routinely used in NMR spectroscopy. To show the power of our new nonparametric approach we compare its performance with the ultimate performance of the parametric approach. We use both simulated and real NMR signals in our numerical performance study.     

How walls affect the dynamics of self-phoretic microswimmers

We study the effect of a nearby planar wall on the propulsion of a spherical phoretic micro-swimmer driven by reactions on its surface. An asymmetric coverage of catalysts on its surface which absorb reactants and generate products gives rise to an anisotropic interfacial flow that propels the swimmer. We analyse the near-wall dynamics of such a self-phoretic swimmer as a function of the asymmetric catalytic coverage of the surface. By an analysis of the fundamental singularities of the flow and concentration or electrostatic potential gradients generated we are able to obtain and rationalise a phase diagram of behaviours as a function of the characteristics of the swimmer surface. We find a variety of possible behaviours, from “bound states” where the swimmer remains near the wall to “scattering” or repulsive trajectories in which the swimmer ends far from the wall. The formation of some of the bound states is a purely wall-phoretic effect and cannot be obtained by simply mapping a phoretic swimmer to a hydrodynamic one.     

Study of particle tracking algorithms based on neural networks for stereoscopic tracking velocimetry

Stereoscopic-tracking velocimetry can offer an excellent potential for continuously monitoring three-dimensional flow fields for all three-component velocities in near-real-time. Requiring only the deployment of two solid-state cameras with directional freedom in test-section illumination and observation, the system can be built to be compact and robust. For flow velocimetry measurement, increasing the number density in particle seeding is much desirable for maximizing spatial resolution, that is, number of velocity data points of the captured field. The challenge, however, is how to successfully track numerous crisscrossing particles with speed and reliability. In our approach, the task of particle tracking is converted to an optimization problem for which neural networks are applied. Here we present the design and development of the neural networks for particle tracking as well as the investigation results based on both computer simulations and real experiments. The approach appears to be appropriate for near-real-time velocity monitoring, being able to provide reliable solutions achieved by the massive parallel-processing power of the neural networks.     

基于改进Hough变换的井盖目标检测与定位

市政井盖的实时告失对城市管理具有重大意义。针对图像的复杂背景,提出了改进的Hough变换算法。在经边缘提取的二值图上,利用轮廓跟踪找到所有的轮廓,接下来设计轮廓过滤器排除虚假目标,进而在轮廓链表上进行Hough变换从而确定目标可能出现的区域,最终获得准确的井盖区域定位。该方案有效地提高了传统Hough变换的处理速度,减少了无效采样和累积。实验结果表明,该算法在多种复杂背景、不同视角、不同拍摄时间和条件、目标被部分遮挡等情况下都有很好的定位效果。     

Cluster Expansion for Abstract Polymer Models. New Bounds from an Old Approach

We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients of our approach are: (i) a careful consideration of the Penrose identity for truncated functions, and (ii) the use of iterated transformations to bound tree-graph expansions.     

自回归状态空间模型下时变声速剖面跟踪方法

讨论了一种适用于浅海的时变声速剖面跟踪方法。该方法将时变水体声速剖面的反演问题建模为由描述声速剖面时变特性的状态方程与包含声压场局部测量信息的测量方程组成的状态-空间模型,提出利用自回归分析拟合方法将声速场扰动建模为高阶自回归演化模型,并通过集合卡尔曼滤波序贯地估计时间演化的海洋声速场。利用2001年亚洲海实验环境与声速测量数据,仿真分析了基于高阶自回归演化模型的时变声速剖面集合卡尔曼滤波估计方法。结果表明,相比于利用传统随机游走状态演化模型的估计方法,该改进方法可有效降低声速的跟踪误差,并且在较低信噪比条件下仍具有较好的跟踪性能。      

A novel video-based microsphere localization algorithm for low contrast silica particles under white light illumination

On the basis of a brief review of four common image recognition algorithms for microspheres made of polystyrene or melamine resin, we present a new microsphere localization method for low-contrast silica beads under white light illumination. We compare both the polystyrene and silica procedures with respect to accuracy and precision by means of an optical tweezers setup providing CMOS video microscopy capability. By that we demonstrate that our new silica algorithm achieves a relative position uncertainty of less than ±1 nm for micron-sized microspheres, significantly exceeding the precision of the other silica approaches studied. Second, we present an advancement of our single microsphere tracking method to scenarios where two polystyrene, melamine resin or silica microspheres are in close-to-contact proximity. While the majority of the analysis algorithms studied generate artefacts due to interference effects under these conditions, we show that our new approach yields accurate and precise results.     

Tracking of time-evolving sound speed profiles with an auto-regressive state-space model

An approach for time-evolving sound speed profiles tracking in shallow water is discussed.The inversion of time-evolving sound speed profiles is modeled as a state-space estimation problem,which includes a state equation for predicting the time-evolving sound speed profile and a measurement equation for incorporating local acoustic measurements.In the paper,auto-regression(AR) method is introduced to obtain a high-order AR evolution model of the sound speed field time variations,and the ensemble Kalman filter is utilized to track the sound speed field.To validate the approach,the accuracy in sound speed estimation is analyzed via a numerical implementation using the ASIAEX experimental environment and the sound velocity measurement data.Compared with traditional approaches based on the state evolution represented as a random walk,simulation results show the proposed AR method can effectively reduce the tracking errors of sound speed,and still keep good tracking performance at low signal-to-noise ratios.     

Product-State Approximations to Quantum States

We show that for any many-body quantum state there exists an unentangled quantum state such that most of the two-body reduced density matrices are close to those of the original state. This is a statement about the monogamy of entanglement, which cannot be shared without limit in the same way as classical correlation. Our main application is to Hamiltonians that are sums of two-body terms. For such Hamiltonians we show that there exist product states with energy that is close to the ground-state energy whenever the interaction graph of the Hamiltonian has high degree. This proves the validity of mean-field theory and gives an explicitly bounded approximation error. If we allow states that are entangled within small clusters of systems but product across clusters then good approximations exist when the Hamiltonian satisfies one or more of the following properties: (1) high degree, (2) small expansion, or (3) a ground state where the blocks in the partition have sublinear entanglement. Previously this was known only in the case of small expansion or in the regime where the entanglement was close to zero. Our approximations allow an extensive error in energy, which is the scale considered by the quantum PCP (probabilistically checkable proof) and NLTS (no low-energy trivial-state) conjectures. Thus our results put restrictions on the possible Hamiltonians that could be used for a possible proof of the qPCP or NLTS conjectures. By contrast the classical PCP constructions are often based on constraint graphs with high degree. Likewise we show that the parallel repetition that is possible with classical constraint satisfaction problems cannot also be possible for quantum Hamiltonians, unless qPCP is false. The main technical tool behind our results is a collection of new classical and quantum de Finetti theorems which do not make any symmetry assumptions on the underlying states.     

Speed Geometric Quantum Logical Gate Based on Double-Hamiltonian Evolution under Large-Detuning Cavity QED Model

We introduce the double-Hamiltonian evolution technique approach toinvestigate the unconventional geometric quantum logical gate with dissipation under the model of many identical three-level atoms in a cavity, driven by a classical field. Our concrete calculation is made for the case of two atoms for the large-detuning interaction of the atoms with the cavity mode. The main advantage of our scheme is of eliminating the photon flutuation in the cavity mode during the gating. The corresponding analytical results will be helpful for experimental realization of speed geometric quantum logical gate in real cavities.     

Motion and mixing for multiple ferromagnetic microswimmers

This paper concerns the interaction of several ferromagnetic microswimmers, their motion and the resulting fluid mixing. Each swimmer consists of two ferromagnetic beads joined by an elastic link, and is driven by an external, time-dependent magnetic field. The external field provides a torque on a swimmer and, together with the varying attraction between the magnetic beads, generates a time-irreversible motion leading to persistent swimming in a low Reynolds number environment. The aim of the present paper is to consider the interactions between several swimmers. A regime is considered in which identical swimmers move in the same overall direction, and their motion is synchronised because of driving by the external field. It is found that two swimmers tend to encircle one another while three undergo more complicated motion that may involve the braiding of swimmer trajectories. By means of approximations it is established that the interaction between pairs of swimmers gives circulatory motion which falls off with an inverse square law and is linked to their overall speed of motion through the fluid. As groups of two or more swimmers move through the fluid they process fluid, leaving behind a trail of fluid that has undergone mixing: this is investigated by following streak lines numerically.     

基于转镜同步跟踪系统的研究

为了研究高速飞行弹丸的运动姿态问题,提出转镜同步跟踪技术。在高速CCD相机主光轴方向放置一面转镜,将弹道线位置上飞行弹丸的运动姿态反射到高速CCD相机内实现同步跟踪。设计了基于高速CCD相机视场中点的转镜跟踪系统,建立了弹丸和转镜的运动模型,并利用MATLAB软件得到了其随时间变化的曲线,分析了相机和转镜空间位置对成像质量的影响。针对参数H=200 m,V=100 m/s,对系统存在的误差进行了分析,结果表明该系统可以实现对高速弹丸的同步跟踪。     

基于普尔钦斑点的人眼视线方向检测

分析了在人眼视线方向检测中普尔钦斑的成像机理,探讨了普尔钦斑的位置与眼球转动角度间的变化关系,发现普尔钦斑的位置随着眼球的转动而基本呈线性变化的规律。提出了仅利用普尔钦斑的偏移量来检测视线方向的新方法。该方法只需在拍摄得到的眼睛图像中寻找灰度特征明显的普尔钦斑即可准确判断出使用者的视线方向。实验证明,该方法简单有效,所需要的运算量小,可提高视线方向的检测速度和精度,能进一步简化检测装置。     

Implementation of autonomous visual tracking and landing for a low-cost quadrotor

This paper presents an implementation of a hybrid system consisting of a low-cost quadrotor and a small pushcart. The quadrotor is controlled with classical Proportional?Integral?Derivative (PID) controller for autonomous visual tracking and landing on the moving carrier. The vision-based tracking and landing approach utilizes enhancement of red, green and blue (RGB) color information rather than grayscale information of the helipad on the carrier, which shows fast and robust performance in different lighting conditions. This work is characteristic with utilizing the off-the-shelf affordable quadrotor and accomplishing the complex task using only the relative pixel position in image plane without communication between the quadrotor and carrier. The quadrotor's relative position to helipad is estimated with a frequency up to 30 Hz from the video stream, which enables the quadrotor to fly autonomously while performing real-time visual tracking and landing on the carrier. Series of experiments show that our system is easy to deploy and tune, simple and robust, also low-cost.     

Numerical Simulation of Polynomial-Speed Convergence Phenomenon

We provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for Markov processes. The hybrid method that we introduce is based on the coupling technique and renewal theory. We propose to replace some estimates in classical results about the ergodicity of Markov processes by numerical simulations when the corresponding analytical proof is difficult. After that, all remaining conclusions can be derived from rigorous analysis. Then we apply our results to seek numerical justification for the ergodicity of two 1D microscopic heat conduction models. The mixing rate of these two models are expected to be polynomial but very difficult to prove. In both examples, our numerical results match the expected polynomial mixing rate well.     

Cutting by a high power laser at a long distance without an assist gas for dismantling

As the applications of laser processing progress, new fields of use are being investigated, including dismantling with power lasers. To fulfil our dismantling requirements we propose a new laser method that we have called the laser dismantling (LD) process. This cutting method uses a high-power laser at a long distance, without an assist gas, and with a focal length of the system of 1 m to 10 m. Precision and accuracy in the process are not the same as for laser cutting for production and assembly. The first application of the laser dismantling process, on which we demonstrate our method, is the dismantling of obsolete nuclear plants with remote controlled, or automatic, robots in irradiated environments. For our demonstrator, the beam from a Nd:YAG laser was focused by a multimode optical fibre. The objectives of this paper are: to discuss the criteria for determining the theoretical feasibility of LD; to discuss issues related to future industrial implementation by introducing the process's basic principles; and to compare LD with classical laser processing, which differs not only in the consideration of cutting quality and speed, but also in the cutting irregularities that could be accepted.