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.     

Air-lubrication of magnetic disk sliders

Steady-state and dynamic flying of a self-acting magnetic disk slider over a hard disk are considered. Some tasks for computations are formulated and the possibilities of developed numerical codes are illustrated. Numerical results of dynamic flying over a disk surface with an obstacle are in agreement with experimental data.     

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.     

The use of distributed pressure receivers based on elastic piezoelectric composite materials for measuring the hydrodynamic noise produced by a near-wall turbulence

Receiving electroacoustic transducers with sensing elements made of an elastic piezoelectric composite material are described. The parameters of a composite material that exhibits a bulk piezoelectric effect are presented. Results obtained by measuring the turbulent noise in a hydrodynamic channel with the use of piezoelectric composite receivers are reported. The results are compared with those of the noise measurements by a miniature piezoceramic receiver and are considered in the light of the known models of near-wall turbulence.     

Chemical bond model of lattice distortions in hexagonal layers

The lattice distortions of a hexagonal layer are discussed in terms of a simple model with isotropic interactions. If only nearest-neighbour interactions are considered, the only stable distorted structures are the MnP structure (with zig-zag chains) and the low-temperature NbS structure (with triangles of metal atoms). If also interactions with more distant atoms are considered, more complicated distortions, as observed in crystals with charge density waves, are possible.     

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.     

Experimental investigation of preset electrostatic fields in a quasi-electrode system

We describe the results of implementation and breadboard investigations of the method for obtaining constant electric fields of a preset form in a quasi-electrode system. We have constructed a prototype (12 cm in diameter and 30 cm in length) with 36 filamentary electrodes fed with potentials from divider systems with azimuthal distribution laws corresponding to cosθ′, cos2θ′, and cos3θ′ laws with the maximal voltages up to ±2.4 kV. As a result, the electric dipole, quadrupole, and sextupole fields are formed. These fields are analyzed for a 2D cross section of the prototype by physical simulation on a specially developed device with conducting paper. The distributions of the families of equipotential curves measured using the bridge circuit are considered and the strengths of the three types of electric fields are calculated. The results indicate the attainment of all predicted fields with preset parameters and a working area of the aperture of ≥84%. Some other favorable features are also outlined and a number of technical recommendations for producing such fields are given.     

Long-Wavelength Approximation for String Cosmology with Barotropic Perfect Fluid

The field equations derived from the low energy string effective action with a matter tensor describing a perfect fluid with a barotropic equation of state are solved iteratively using the long-wavelength approximation, i.e. the field equations are expanded by the number of spatial gradients. In the zero order, a quasi-isotropic solution is presented and compared with the general solution of the pure dilaton gravity. Possible cosmological models are analyzed from the point of view of the pre-big bang scenario. The second order solutions are found and their growing and decaying parts are studied.     

ANALYSIS OF NON-LINEAR DYNAMIC STABILITY FOR A ROTATING SHAFT-DISK WITH A TRANSVERSE CRACK

In this paper, the nonlinear dynamic stability of a rotating shaft-disk with a transverse crack is studied. The crack and the disk are located in arbitrary positions of the shaft respectively. Using the equivalent line-spring model, the deflections of the system with a crack are constructed by adding a deflection to the deflections of the uncracked system. The unstable regions are confirmed by Runge-Kutta method and the Floquet theory. The effects of crack depth, crack position, disk position, disk thickness and rotating speed on the principal unstable regions are discussed. The numerical results are compared with available data.     

Correcting for incomplete saturation and off-resonance effects in multiple-site saturation-transfer kinetic measurements

The effects of incomplete saturation and off-resonance irradiation on nuclear magnetic resonance saturation-transfer measurements of three-site chemical-exchange rates are discussed. A new method that uses double-saturation measurements is compared with two published methods, one that uses single-saturation measurements and one that uses a single-saturation measurement and a double-saturation measurement. Several formulas are compared for measuring the exchange rate constant k(DE) for exchange from a detected spin D to an exchanging spin E in the presence of exchange from spin D to a competing spin C. For each method, formulas are derived with corrections for incomplete saturation or off-resonance effects, with both corrections, and with neither correction. Exact formulas are available for three exchanging sites with incomplete saturation if there are no off-resonance effects. Off-resonance corrections are imperfect even with complete saturation.     

Smectic islands in antiferroelectric nanofilms

Heterochiral islands, in which topological dipoles are oppositely directed, are observed in freestanding antiferroelectric (SmC _A ^*) films. The topological dipoles in films with a transverse electric polarization and a planar molecule orientation at island boundaries are coplanar with an electric field. The topological dipoles in films with a longitudinal polarization and a planar orientation at island boundaries are perpendicular to an electric field. For a radial director orientation at island boundaries, the topological dipoles in films with a longitudinal polarization are coplanar with a field. Changing the orientation of an electric field, we can control the position of a topological defect at an island boundary and the orientation of a topological dipole. Heterochiral islands can form dimers with an anomalously small interisland distance.     

Coupled bending and torsional vibration of a beam with in-span and tip attachments

In this paper, the coupled flexural-torsional free and forced vibrations of a beam with tip and/or in-span attachments are studied. First, a mathematical model is established, which consists of a beam with several tip attachments, i.e, a tip mass of non-negligible dimensions, a linear spring grounding the tip mass, and a torsional spring connected at the end of the beam. The modal functions of this model and the orthogonality condition among them are derived. For the purpose of verification the properties of the tip attachments are changed, and the numerical results obtained are compared with those given in the relevant literature. Effects of tip mass and distributed mass in-span on natural frequencies and modes are investigated for two cantilever beams with different cross sections. An application of the orthogonality condition in the case of a beam with tip mass is also presented for a forced vibration example.     

Fluctuation spectra of free and supported membrane pairs

Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential. Additionally, such a compound system can be attached to a supporting substrate. We compare quasi-analytical results for tethers with analytical results for corresponding continuous models and investigate under what circumstances the discrete nature of the tethers actually influences the fluctuations. A tethered, supported membrane pair with similar bending rigidities and stiff tethers can possess a nonmonotonic fluctuation spectrum with a maximum. A nonmonotonic spectrum with a maximum and a minimum can occur for an either free or supported membrane pair of rather different bending rigidities and for stiff tethers. Typical membrane displacements are calculated for supported membrane pairs with discrete or continuous interacting potentials. Thereby an estimate of how close the constituent two membranes and the substrate typically approach each other is given. For a supported membrane pair with discrete or continuous interactions, the typical displacements of each membrane are altered with respect to a single supported membrane, where those of the membrane near the substrate are diminished and those of the membrane further away are enhanced.     

导电平板上任意缝隙填充各向异性介质时TM波散射和传输特性分析

简单介绍了用于分析任意口径问题的通用频域方法——广义网络原理,并利用边界积分法和广义网络原理分析导电平板上任意缝隙填充各向异性介质时TM波的散射及传输特性.由于缝隙填充各向异性介质的情形尚未见公开文献报道,作为验证,将本方法退化计算各向同性介质填充时缝隙的散射和传输特性,并与文献结果进行比较.最后,给出了缝隙填充各向异性介质时的算例.     

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.     

Electron correlations and single-particle physics in the integer quantum Hall effect

The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical results for the influences of interaction and disorder on the compressibility as a function of the particle density and the strength of the magnetic field are presented. Localization-delocalization transitions associated with a highly compressible region in the energy spectrum are found at half-integer filling factors. Coulomb blockade effects are found near integer fillings in the regions of low compressibility. Results are compared with recent experiments.     

Effect of pairwise dipole–dipole interaction among three-atom systems

We present an analysis of a system of three two-level atoms interacting with one another through dipole–dipole interaction. The interaction manifests between the excited state of one of the atoms and the ground state of its nearest neighbour. Steady-state populations of the density matrix elements are presented and are compared with a situation when only two atoms are present. It can be noticed that the third atom modifies the behaviour of the three atoms. Two configurations are analysed, one in which the three atoms are in a line, with no interaction between atoms at the end points and the other in which the atoms form a closed loop with one atom interacting with both its neighbours.     

Network Analysis of Millimeter-Wave Omnidirectional Periodic Dielectric Rod Antenna with Arbitrary Grating Profile

The radiation characteristics of the omnidirectional periodic circular dielectric rod leaky-wave antenna with arbitrary grating profile are investigated by the network method combining with staircase approximation. In the analysis, the arbitrary grating profiles are transformed to a multilayer rectangular periodic structure, which is represented by a radial transmission line with a series current source. As a result, the calculations are greatly simplified and the effects of grating profile on the performance of the grating antenna are systematically studied in a very efficient way. Some useftil guidelines for the design and fabrication of the omnidirectional dielectric grating antenna are thereby suggested.     

Analysis of continuous generation of electron beams in medium-pressure gases

Stationary and stable open discharges are obtained in air, helium, and helium with an admixture of a few percent of air. The structure of the generator of an electron beam with a wide set of cathode and insulator materials is described. The experiments are performed under an air pressure of hundreds of pascals and under a helium pressure of thousands of pascals. The current-voltage characteristics of the discharge are measured and the results on the maximal current density attained are compared with the available data.