Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators

We consider a generalization of the Kuramoto model in which the oscillators are coupled to the mean field with random signs. Oscillators with positive coupling are "conformists"; they are attracted to the mean field and tend to synchronize with it. Oscillators with negative coupling are "contrarians"; they are repelled by the mean field and prefer a phase diametrically opposed to it. The model is simple and exactly solvable, yet some of its behavior is surprising. Along with the stationary states one might have expected (a desynchronized state, and a partially-synchronized state, with conformists and contrarians locked in antiphase), it also displays a traveling wave, in which the mean field oscillates at a frequency different from the population's mean natural frequency.     

Feasibility of controlling speed-dependent low-frequency brake vibration amplification by modulating actuation pressure

In this article, a feasibility study of controlling the low frequency torque response of a disc brake system with modulated actuation pressure (in the open loop mode) is conducted. First, a quasi-linear model of the torsional system is introduced, and analytical solutions are proposed to incorporate the modulation effect. Tractable expressions for three different modulation schemes are obtained, and conditions that would lead to a reduction in the oscillatory amplitudes are identified. Second, these conditions are evaluated with a numerical model of the torsional system with clearance nonlinearity, and analytical solutions are verified in terms of the trends observed. Finally, a laboratory experiment with a solenoid valve is built to modulate actuation pressure with a constant duty cycle, and time–frequency domain data are acquired. Measurements are utilized to assess analytical observations, and all methods show that the speed-dependent brake torque amplitudes can be altered with an appropriate modulation of actuation pressure.     

Frequency-division multiplexing of optical-fibre sensors using a frequency-modulated source

Three basic configurations, namely, (i) parallel with a common reference, (ii) parallel with separate references and (iii) series, are studied for a multiplexed system of optical-fibre sensors. With a frequency-modulated laser source, each sensor of a different predetermined path imbalance results in a different beat frequency at the detector and signals are multiplexed in the frequency domain. The cross-term problem arising from undesired interference associated with more than one sensor is described. A series configuration has more cross terms than a parallel configuration if there are four sensors or more and, consequently, suffers more signal power reduction if there are seven sensors or more. Several schemes are presented, which ensures the separation of cross terms from desired signals. In a parallel system with a common reference, signals and cross terms are allocated in the lower and in the higher region, respectively, or to every other line in the frequency domain. In a parallel system with separate references, sensors are made incoherent to each other to produce no cross terms. In a series system, more elaborate schemes are necessary. The estimated maximum number of sensors indicates that a parallel configuration should be used if there are 10 sensors or more to be multiplexed.     

Finite-bandwidth effects on the causal prediction of ultrasonic attenuation of the power-law form

Kramers-Kronig (K-K) relations exist as a consequence of causality, placing nonlocal constraints on the relationship between dispersion and absorption. The finite-bandwidth method of applying these relations is examined where the K-K integrals are restricted to the spectrum of the experimental data. These finite-bandwidth K-K relations are known to work with resonant-type data and here are applied to dispersion data consistent with a power-law attenuation coefficient (exponent from 1 to 2). Bandwidth-restricted forms of the zero and once-subtracted K-K relations are used to determine the attenuation coefficient from phase velocity. Analytically, it is shown that these transforms produce the proper power-law form of the attenuation coefficient as a stand-alone term summed with artifacts that are dependent on the integration limits. Calculations are performed to demonstrate how these finite-bandwidth artifacts affect the K-K predictions under a variety of conditions. The predictions are studied in a local context as a function of subtraction frequency, bandwidth, and power-law exponent. The K-K predictions of the power-law exponent within various decades of the spectrum are also examined. In general, the agreement between finite-bandwidth K-K predictions and exact values grows as the power-law exponent approaches 1 and with increasing bandwidth.     

Configurations of axisymmetric quasi-force-free magnetic systems. I

General requirements imposed on a force-free magnetic system (an analog of a quasi-force-free magnet) are formulated. The advantages of a system in which the force-free winding is supplemented with an external zone with zero azimuth current and with dielectric reinforcement cylinders bearing residual forces are demonstrated. Examples of a force-free current distribution in a plane layer and in a thin winding are considered. Configurations without additional external bodies (shields) are analyzed. It is shown that the continuity of the flux function and its normal derivative is ensured in the solutions to a high degree of accuracy due to current drainage to the external zone.     

The influence of contacts on the VA-characteristics of thin-layfr systems with amorphous semiconductors

In the paper the VA-characteristics of a sandwich-type thin-layer system with amorphous semiconductor are discussed, where ohmic and non-ohmic contacts are considered. The VA-characteristics are derived which, in the case of ohmic contacts, lead to a linear dependence of the current on voltage and, in the case of non-ohmic contacts (where barriers are supposed), to a nonlinear dependence, so that VA-characteristics with negative resistance are possible as well. These VA-characteristics are compared with the experimental ones, measured on thin-layer metalamorphous Si-metal and metal-amorphous CdTe-metal structures.     

Impact on short length bars

A finite element method for the solution of an axisymmetric wave propagation problem of a bar of finite length is proposed. The results are obtained for a uniform bar with (i) a displacement input and (ii) a stress input. Also results are obtained for a discontinuous bar with stress input. They are compared with the existing finite difference solutions and experimental results. It is observed that the results are in close agreement. The study is then extended to the case of bars with an hemispherical end. The advantage of using the finite element method for such problems is indicated. Finally the results for a composite bar comprising a hallow cylinder and hemisphere are obtained by using the finite element method. Experiments are conducted to verify these results.     

Dynamic Analysis of Vibrating Systems with Nonlinearities

The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.     

多曲面反射体的计算机辅助设计及优化

研究了自由曲面反射式照明系统的设计理论和方法.根据反射器的尺寸、位置以及配光要求按点光源设计得到曲面型值点初始坐标后,将双三次B样条曲面引入照明系统的设计,反算出控制顶点.给出了空间任意一条入射光线与反射器区块的交点及其曲面法线向量的求法,为了提高光路追迹的效率,针对多曲面反射体给出了一种快速判断相交区块的算法.探讨了用阻尼最小二乘法对B样条曲面反射器进行优化设计的方法,通过优化运算修正控制顶点Z轴坐标,使得曲面在使用扩展光源时光形分布尽可能满足设计要求.     

Properties of planar Nb/α-Si/Nb Josephson junctions with various degrees of doping of the α-Si layer

The properties of Nb/??-Si/Nb planar Josephson junctions with various degrees of doping of the amorphous silicon layer are experimentally studied. Tungsten is used as a doping impurity. The properties of the Josephson junctions are shown to change substantially when the degree of doping of the ??-Si layer changes: a current transport mechanism and the shape of the current-voltage characteristic of the junctions change. Josephson junctions with SNS-type conduction are formed in the case of a fully degenerate ??-Si layer. The properties of such junctions are described by a classical resistive model. Josephson junctions with a resonance mechanism of current transport through impurity centers are formed at a lower degree of doping of the ??-Si layer. The high-frequency properties of such junctions are shown to change. The experimental results demonstrate that these junctions are close to SINIS-type Josephson junctions.     

Development of intermolecular potential models for electrolyte solutions using an electrolyte SAFT-VR Mie equation of state

ABSTRACT

We present a theoretical framework and parameterisation of intermolecular potentials for aqueous electrolyte solutions using the statistical associating fluid theory based on the Mie interaction potential (SAFT-VR Mie), coupled with the primitive, non-restricted mean-spherical approximation (MSA) for electrolytes. In common with other SAFT approaches, water is modelled as a spherical molecule with four off-centre association sites to represent the hydrogen-bonding interactions; the repulsive and dispersive interactions between the molecular cores are represented with a potential of the Mie (generalised Lennard-Jones) form. The ionic species are modelled as fully dissociated, and each ion is treated as spherical: Coulombic ion–ion interactions are included at the centre of a Mie core; the ion–water interactions are also modelled with a Mie potential without an explicit treatment of ion–dipole interaction. A Born contribution to the Helmholtz free energy of the system is included to account for the process of charging the ions in the aqueous dielectric medium. The parameterisation of the ion potential models is simplified by representing the ion–ion dispersive interaction energies with a modified version of the London theory for the unlike attractions. By combining the Shannon estimates of the size of the ionic species with the Born cavity size reported by Rashin and Honig, the parameterisation of the model is reduced to the determination of a single ion–solvent attractive interaction parameter. The resulting SAFT-VRE Mie parameter sets allow one to accurately reproduce the densities, vapour pressures, and osmotic coefficients for a broad variety of aqueous electrolyte solutions; the activity coefficients of the ions, which are not used in the parameterisation of the models, are also found to be in good agreement with the experimental data. The models are shown to be reliable beyond the molality range considered during parameter estimation. The inclusion of the Born free-energy contribution, together with appropriate estimates for the size of the ionic cavity, allows for accurate predictions of the Gibbs free energy of solvation of the ionic species considered. The solubility limits are also predicted for a number of salts; in cases where reliable reference data are available the predictions are in good agreement with experiment.     

The coordinate of a singular point of the time correlation functions for a heteronuclear spin system of a crystal

The singularities of the time autocorrelation functions (ACFs) for a heteronuclear spin system of a crystal are investigated. Exact expressions are obtained for ten moments of the spectra of ACFs in the approximation of a self-consistent fluctuating field (SCFF) with arbitrary axial symmetry. These expressions are applied to determine the coordinate of the lowest singular point of these functions on the imaginary-time axis for a spin system with a dipole-dipole interaction (DDI). The leading corrections to this coordinate due to the correlation of local fields in real crystals are calculated. These corrections are determined by lattice sums with triangles of four bonds and pairs of four bonds. Numerical values of the coordinate are obtained for a LiF crystal in a magnetic field directed along three crystallographic axes. An increase in the coordinate of the singular point, which follows from the theory and leads to a faster falloff of the wings of the ACF spectra, qualitatively agrees with experiment.     

The Navier-Stokes limit of stationary solutions of the nonlinear Boltzmann equation

We consider the flow of a gas in a channel whose walls are kept at fixed (different) temperatures. There is a constant external force parallel to the boundaries which may themselves also be moving. The system is described by the stationary Boltzmann equation to which are added Maxwellian boundary conditions with unit accommodation coefficient. We prove that when the temperature gap, the relative velocity of the planes, and the force are all sufficiently small, there is a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of the corresponding compressible Navier-Stokes equations with no-slip voundary conditions. Corrections to this Maxwellian are obtained in powers of the Knudsen number with a controlled remainder.     

The conductivity of the spin-polarized two-dimensional electron gas: Exchange/correlation and strong disorder effects

The conductivity of a spin-polarized two-dimensional electron gas is calculated and compared with the conductivity of the unpolarized electron gas. Disorder effects are considered within the self-consistent current relaxation theory, which gives rise to a crossover point from metallic to insulating behavior. Many-body effects due to exchange and correlation are taken into account and are described by a local-field correction. Our calculations are in good agreement with recent experimental results on the magnetoresistance of silicon inversion layers.     

A theoretical investigation of flow-induced instabilities in compliant coatings

The flow-induced instabilities of a fairly general class of compliant coatings are investigated theoretically. The coatings are of finite length and consist of elastic plates or membranes stretched over a fluid substrate having a density which may be different from the main flow. Provision is also made for the plate to be backed by an elastic foundation of arbitrary spring stiffness. Fairly standard aeroelastic methods are followed. The aerodynamic forces generated by the main flow are calculated by using thin aerofoil theory with a correction factor to allow for the presence of a boundary layer. The pressure induced in the substrate fluid is calculated by assuming potential flow and applying the method of images. A single-mode analysis shows that coatings with laminar boundary layers suffer a divergence-type instability in contrast to turbulent boundary layers which always give rise to a flutter-type instability with a higher critical velocity. The order of the most dangerous mode is calculated and found to rise with an increase in equivalent spring stiffness for fixed tension or flexural rigidity. Results are presented for plates and membrane coatings with an air stream over air and water substrates. Taking account of the substrate fluid dynamics reduces the growth rate of the instability by an order of magnitude and completely suppresses flutter with water substrates. Single-, double- and triple-mode analyses are carried out and the results compared. The critical velocity is adequately predicted by single-mode analysis but a coupling of odd and even modes can lead to flutter even with a laminar boundary layer.     

Vibrational properties of hierarchical systems

The vibrational properties of one-dimensional hierarchical systems are investigated and results are obtained for both their eigenvalues and eigenvectors. Two cases are considered, the first one with a hierarchy of spring constants and the latter with a hierarchy in the masses. In both cases the eigenspectrum is found to be a zero-measure, two-scale Cantor set with a fractal dimension between 0 and 1. The scaling properties of the spectra are calculated using renormalization group techniques and are verified by extensive numerical work. The low-frequency density of states and low-temperature specific heat are calculated and a singularity is found in the scaling behavior. The eigenvectors are found to be either extended or critical and self-similar. A transfer matrix formalism is introduced to calculate the scaling properties of the envelope of the critical eigenvectors. Furthermore, a connection is established between the hierarchical vibration and diffusion problems, as well as to the same problems in random systems, thus showing the universality of the observed features.     

MODELLING AND CONTROL WITH PIEZOACTUATORS FOR A SIMPLY SUPPORTED BEAM UNDER A MOVING MASS

In the paper, the dynamic modelling and control are presented for a simply supported beam under a moving mass. The equations of motion are obtained based on the Euler-Bernoulli beam theory by including the dynamic effect of a moving mass travelling along a vibrating path. The equations of motion are discretized by using the assumed modes method with the static deflection of the beam. In order to reduce the deflection of the beam under a moving mass, a controller with full state feedback is designed based on linearized equations of motion. Two piezoelectric actuators are bonded along the bottom of the beam at different locations determined by the minimization of an optimal cost functional. Numerical simulations are performed with respect to different constant velocities and different moving masses. The controller with two piezoelectric actuators shows excellent performance under unknown disturbances to the system.     

六自由度机构位姿的单相机照相测量研究

用单相机对新型的六自由度机构样机的六个自由度位移进行了非接触式照相测量。简要回顾了照相法的研究概况及该测量研究的工作背景;介绍了相机标定原理及具体标定方法。建立了被测样机的CAD模型,进行了自由度位移仿真,将仿真结果作为理想数据与实测数据进行比较,从而获得测量误差,并对测量误差进行了初步分析。探讨了单相机照相测量法的应用前景。     

Spectral energy balance in dry convective boundary layers

Three-dimensional large-eddy simulations (LES) of the convective boundary layer over a domain of approximately 6 km are performed with the UCLA LES model. Simulations are forced with a constant surface heat flux and prescribed subsidence, and are run to equilibrium. Sub-grid scale fluxes are parameterised with the Smagorinsky–Lilly scheme. A range of grid spacings from 40 down to 5 m are employed. Kinetic energy spectra and the various terms in the kinetic energy spectral budget – heat flux, nonlinear transfer, pressure, and dissipation – are computed using two-dimensional discrete Fourier transforms at every vertical level. Despite the fact that isotropic grid spacings of down to 5 m (grid sizes of 1152²×400) were used, an inertial range with a ?5/3 spectrum is not obtained. Rather, shallower energy spectral slopes that are closer to ?4/3 are found. The shallower spectra are shown to possibly result from the injection of kinetic energy over a wide range of scales via a very broad heat flux spectrum. Only with the highest resolution (Δx = 5 m) does the total heat flux begin to converge and the possibility of local isotropy emerge at small scales. Dependence on surface heat flux and domain size is considered. Preliminary sub-grid scale sensitivity results are obtained through comparison with the turbulent kinetic energy sub-grid scale model.