Geometry and violent events in turbulent pair dispersion

The statistics of Lagrangian pair dispersion in a homogeneous isotropic flow is investigated by means of direct numerical simulations. The focus is on deviations from the Richardson eddy-diffusivity model and in particular on the strong fluctuations experienced by tracers. Evidence is obtained that the distribution of distances attains an almost self-similar regime characterized by a very weak intermittency. The timescale of convergence to this behavior is found to be given by the kinetic energy dissipation time measured at the scale of the initial separation. Conversely the velocity differences between tracers are displaying a strongly anomalous behavior whose scaling properties are very close to that of Lagrangian structure functions. These violent fluctuations are interpreted geometrically and are shown to be responsible for a long-term memory of the initial separation. Despite this strong intermittency, it is found that the mixed moment defined by the ratio between the cube of the longitudinal velocity difference and the distance attains a statistically stationary regime on very short timescales. These results are brought together to address the question of violent events in the distribution of distances. It is found that distances much larger than the average are reached by pairs that have always separated faster since the initial time. They contribute a stretched exponential behavior in the large-value tail of the inter-tracer distance probability distribution. At large times this tail is found to be closer to a pure exponential than to the form obtained from the Richardson diffusive approach. At the same time, the distance distribution displays a time-dependent power-law behavior at very small values, which is interpreted in terms of fractal geometry. It is argued and demonstrated numerically that the exponent converges to one at large time, again in conflict with Richardson’s distribution.     

Elastic rod model of a supercoiled DNA molecule

We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod-like chain, involving two elastic constants, the bending and the twist rigidities. Writing this model in terms of Euler angles, we show that the corresponding Hamiltonian is singular and needs a small distance cut-off, which is a natural length scale giving the limit of validity of the model, of the order of the double-helix pitch. The rod-like chain in the presence of the cut-off is able to reproduce quantitatively the experimentally observed effects of supercoiling on the elongation-force characteristics, in the small supercoiling regime. An exact solution of the model, using both transfer matrix techniques and its mapping to a quantum mechanics problem, allows to extract, from the experimental data, the value of the twist rigidity. We also analyse the variation of the torque and the writhe-to-twist ratio versus supercoiling, showing analytically the existence of a rather sharp crossover regime which can be related to the excitation of plectoneme-like structures. Finally we study the extension fluctuations of a stretched and supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle, and we compare the theoretical predictions to some preliminary experimental data. Received 1 April 1999 and Received in final form 4 January 2000     

Time dependence of vacuum arc parameters

Time-resolved investigations of the expanded plasma of vacuum arc cathode spots are described, including the study of the ion charge state distribution, the random cathode spot motion, and the crater formation. It was found that the ion charge state distribution changes over a timescale on the order of hundreds of microseconds. For the random spot motion two timescales were observed: a very short spot residence time of tens of nanoseconds which gives, combined with the step width, the diffusion parameter of the random motion, and a longer timescale on the order of 100 μs during which the diffusion parameter changes. Crater formation studies by scanning electron microscopy indicate the occurrence of larger craters at the end of crater chains. The existence of a timescale much longer than the elementary times for crater formation and spot residence can be explained by local heat accumulation     

Quantum dynamics on a lossy non-Hermitian lattice

We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice,in which the particle can leak out with certain rate whenever it visits one of the two sublattices.Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained.In one regime,the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases.However,in the other regime,we find that the resultant distribution of local decay probability is very counterintuitive,in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker.We then analyze the energy spectrum of the non-Hermitian lattice with pure loss,and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of the edge states,which are topologically protected and can be well predicted by the non-Bloch winding number.The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides.     

阵列型LED灯具远场距离分析

LED灯具通常为阵列式排布的面光源,为实现对灯具光强分布进行准确测量,照度探测器需要距离待测灯具足够远,使得面光源可近似为点光源,该距离即为远场距离。针对目前对远场距离进行规定的多项国家标准相互间不统一,且标准只考虑灯具发光面最大尺寸单一参数等问题,对阵列排布式LED灯具的远场距离进行研究,计算了不同配光分布、阵列排布方式、阵列密度、阵列尺寸下灯具的远场距离,并详细分析各参数对远场距离的影响,给出远场距离设定的建议,为确定阵列型LED灯具远场距离的光强分布的准确测量提供参考。     

弱酸试纸法测量功率超声珩磨空化声场的研究*

为了简便、直观地测量功率超声珩磨磨削区的空化声场强度及分布情况,提出了利用弱酸PH试纸测量磨削区空化声场的方法。利用超声空化效应产生的弱酸空化泡在PH试纸表面溃灭后,形成深浅和分布不同的变色区域,间接地表征油石表面空化声场的强弱和分布规律。通过对比不同超声频率、测试距离和时间,得出了最佳测试距离和时间。结果表明,当超声频率为18.6 kHz,距离为10 mm时,测得油石表面的空化声场强度和分布最佳。该方法可形象地评价功率超声珩磨磨削区空化声场的强度和分布情况,具有一定的实际应用价值。     

The effects of reaction delay in the Nagel-Schreckenberg traffic flow model

This paper studies a new model, which considers the effects of drivers reaction delay in the Nagel-Schreckenberg model. We studied the traffic flow properties in the new model under both periodic and open boundary conditions. The fundamental diagram, spatio-temporal patterns, density-density correlation functions, relaxation time, and distance headway distribution are investigated. Several interesting results are reported, for example, (i) the jam becomes less condensed when the delay effect is considered; (ii) the distance headway of the new model exhibits a multi-peak distribution when randomization p is small; (iii) for large p, the distribution of distance headway follows a power law in the new model; (iv) under open boundary conditions, the existence of a stationary jam near the left boundary will lower the flow rate.     

Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.     

Scaling behaviour in the fracture of fibrous materials

We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the percolation density scales with the system size L, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation. Received 24 June 1999     

Confined diffusion of hydrophilic probes inserted in lyotropic lamellar phases

The dynamic behaviour of three hydrophilic probes (two dyes and one fluorescently-labelled protein) inserted in the water layers of lyotropic lamellar phases has been studied by confocal fluorescence recovery experiments. Two different, ionic (AOT/NaCl/ H(2)O and non-ionic ( C(12)E(5) /hexanol/ H(2)O host systems were studied. The confinement effect has been carefully monitored using the swelling properties of the lamellar phases. In all cases, we measure the evolution of the probe diffusion coefficient in the layer plane D ( perpendicular) versus the separation between the membranes d(w). Depending on the composition of the lamellar phase, this distance can be continuously adjusted from 500A to about 20A. For all systems, we observe a first regime, called dilute regime, where the diffusion coefficient decreases almost linearly with 1/d (w) . In this regime, the Faxén theory for the friction coefficient of a spherical particle symmetrically dragged between two rigid walls can largely explain our results. More unexpectedly, when the membranes are non-ionic, and also quite flexible ( C(12)E(5) /hexanol in water), we observe the existence of a second, concentrated (or confined) regime, where the diffusion coefficient is nearly constant and different from zero for membrane separations smaller than the particle size. This new regime can be heuristically explained by simple arguments taking into account the membrane fluidity.     

Collective excitations of a degenerate Fermi vapour in a magnetic trap

We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law is obtained for the vapour in the collisional regime inside a spherical trap of frequency , with n the number of radial nodes and the orbital angular momentum. The low-energy excitations are also treated in the case of an axially symmetric harmonic confinement. The collisionless regime is discussed with main reference to a Landau-Boltzmann equation for the Wigner distribution function: this equation is solved within a variational approach allowing an account of non-linearities. A comparative discussion of the eigenmodes of oscillation for confined Fermi and Bose vapours is presented in an Appendix. Received 23 February 1999 and Received in final form 21 April 1999     

Subwavelength resolution in a two-dimensional photonic-crystal-based superlens

We experimentally and theoretically demonstrate single-beam negative refraction and superlensing in the valence band of a two-dimensional photonic crystal operating in the microwave regime. By measuring the refracted electromagnetic waves from a slab shaped photonic crystal, we find a refractive index of -1.94 that is very close to the theoretical value of -2.06. A scanning transmission measurement technique is used to measure the spatial power distribution of the focused electromagnetic waves that radiate from a point source. The full width at half maximum of the focused beam is measured to be 0.21 lambda, which is in good agreement with the finite difference time domain method simulations. We also report a subwavelength resolution for the image of two incoherent point sources, which are separated by a distance of lambda/3.     

Thermal radiation and near-field energy density of thin metallic films

We study the properties of thermal radiation emitted by a thin dielectric slab, employing the framework of macroscopic fluctuational electrodynamics. Particular emphasis is given to the analytical construction of the required dyadic Green's functions. Based on these, general expressions are derived for both the system's Poynting vector, describing the intensity of propagating radiation, and its energy density, containing contributions from non-propagating modes which dominate the near-field regime. An extensive discussion is then given for thin metal films. It is shown that the radiative intensity is maximized for a certain film thickness, due to Fabry-Perot-like multiple reflections inside the film. The dependence of the near-field energy density on the distance from the film's surface is governed by an interplay of several length scales, and characterized by different exponents in different regimes. In particular, this energy density remains finite even for arbitrarily thin films. This unexpected feature is associated with the film's low-frequency surface plasmon polariton. Our results also serve as reference for current near-field experiments which search for deviations from the macroscopic approach.     

Kullback–Leibler Divergence of a Freely Cooling Granular Gas

Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original H-theorem hypotheses do not fit here and the H-functional presents some additional measure problems that are solved by the Kullback–Leibler divergence (KLD) of a reference velocity distribution function from the actual distribution. The right choice of the reference distribution in the KLD is crucial for the latter to qualify or not as a Lyapunov functional, the asymptotic “homogeneous cooling state” (HCS) distribution being a potential candidate. Due to the lack of a formal proof far from the quasielastic limit, the aim of this work is to support this conjecture aided by molecular dynamics simulations of inelastic hard disks and spheres in a wide range of values for the coefficient of restitution (α) and for different initial conditions. Our results reject the Maxwellian distribution as a possible reference, whereas they reinforce the HCS one. Moreover, the KLD is used to measure the amount of information lost on using the former rather than the latter, revealing a non-monotonic dependence with α.     

Reflector-based phase calibration of ultrasound transducers

Recently, the measurement of phase transfer functions (PTFs) of piezoelectric transducers has received more attention. These PTFs are useful for e.g. coding and interference based imaging methods, and ultrasound contrast microbubble research. Several optical and acoustic methods to measure a transducer’s PTF have been reported in literature. The optical methods require a setup to which not all ultrasound laboratories have access to. The acoustic methods require accurate distance and acoustic wave speed measurements. A small error in these leads to a large error in phase, e.g. an accuracy of 0.1% on an axial distance of 10 cm leads to an uncertainty in the PTF measurement of ±97° at 4 MHz. In this paper we present an acoustic pulse-echo method to measure the PTF of a transducer, which is based on linear wave propagation and only requires an estimate of the wave travel distance and the acoustic wave speed. In our method the transducer is excited by a monofrequency sine burst with a rectangular envelope. The transducer initially vibrates at resonance (transient regime) prior to the forcing frequency response (steady state regime). The PTF value of the system is the difference between the phases deduced from the transient and the steady state regimes. Good agreement, to within 7°, was obtained between KLM simulations and measurements on two transducers in a 1-8 MHz frequency range. The reproducibility of the method was ±10°, with a systematic error of 2° at 1 MHz increasing to 16° at 8 MHz. This work demonstrates that the PTF of a transducer can be measured in a simple laboratory setting.     

Arbitrary amplitude dust-acoustic solitary waves in a dusty plasma with flat-topped ion distribution

The properties of arbitrary amplitude dust-acoustic (DA) solitary waves (SWs) in a dusty plasma containing warm adiabatic dust fluid, isothermal electrons and ions following flat-topped velocity distribution is studied by the pseudo-potential approach. The effects of dust temperature and flat-trapped ions are found to significantly modify the basic features of DA-SWs as well modify the parametric regime for the existence of rarefactive solitary waves. The pseudo-potential for small amplitude limit is also analytically analyzed, and the numerical results are found to agree with analytical results.     

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the ‘fluctuation-dissipation theorem’, the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the ‘fluctuation-dissipation theorem’ is satisfied, and this verifies that satisfying ‘fluctuation-dissipation theorem’ indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.     

End-to-end diffusion coefficients and distance distributions from fluorescence energy transfer measurements: Enhanced resolution by using multiple donors with different lifetimes

We describe a method to improve the resolution of donor-to-acceptor distance distributions in molecules which are flexing on the timescale of the fluorescence lifetime. We measured the timedependent donor decays of two donor (D)-acceptor (A) pairs, where the donor lifetimes were substantially different. The donors were an indole residue (5.7 ns) and a naphthalene residue (24.4 ns). The same dansyl acceptor was used for both D-A pairs. The donor decays are complex due to both a distribution of D-A distances and D-A diffusion. Using the donor decay data for each D-A pair alone, it is difficult to resolve both the distance distribution and the D-to-A diffusion coefficient. However, these values are unambiguously recovered from global analysis of the data from both D-A pairs. The increased resolution from the global analysis is apparently the result of the complementary information content of the data for each D-A pair. The shorter-lived indole donor provides more information on the time-zero distance distribution because there is less time for D-A diffusion, and the longer-lived naphthyl donor is quenched to a greater extent than indole due to the longer time for diffusion-enhanced energy transfer. Simulations were also used to demonstrate the increased resolution of global analysis with different lifetime donors to obtain distance distribution parameters in the presence of D-A diffusion.     

大功率TEACO2非稳腔激光器的远场传输特性

针对大功率激光器的远场传输特性,提出了一种测量TEACO,远场光束传输特性的新方法,该法采用相对测量和绝对测量相结合的方式来获得高能激光器的绝对空间光强分布。利用该方法测试了2kW脉冲TEACO,非稳腔激光器在500m处的光强分布,并对测试结果进行了分析讨论。实验结果表明,此方法简单、易行,准确度较高,而且测量过程中考虑了大气湍流的影响,光斑强度相对分布上出现了平顶、破碎并出现旁瓣现象,实测大气透过率为81．5％,最大功率密度为1．59W／cm^2,光束的横向远场发散角达到0．64mrad,基本与理论计算结果相吻合。本研究将为评估激光系统的应用效果及系统的优化设计提供重要的参考。