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A numerical study is carried out to investigate the energy harvesting from an inverted foil undergoing flow-induced pitching oscillation for reduced velocity Ur = 1–45 and damping ratio ζ = 0–0.295. The benchmark results with undamped foil (ζ = 0) indicate that the foil does not oscillate for Ur ≤ 27 but does oscillate with increasing amplitude for 27

Frequency-dependent magnetization characteristics potentially promote magnetic nanoparticles as prominent nanotracers for tomographic imaging. Owing to fast Neel dynamics relative to Brownian rotation of colloidal magnetic nanoparticles, we can demonstrate a two-dimensional image reconstruction from the Neel and Brownian relaxation responses modulated by external oscillatory field bursts with two distinctive frequencies. To realize a micrometer-scale resolution, a field-free-point (FFP) is manipulated to move in a dense Lissajous trajectory by low-frequency perpendicular sinusoidal fields across a steep field gradient between two permanent magnets. Instead of directly recording the resulting harmonic responses, we use an orthogonal high-frequency field to probe the time-varying FFP movement coupled with the moment relaxation. The proposed method achieves high spatial resolution, irrespective of the nonlinearity of the magnetization response, making it practical for bioanalytical imaging of cells and small animal models.

Columnar pattern discharges and multipulse uniform discharges were generated in atmospheric helium with a background air pressure of 40 Pa to study the effect of discharge behaviors on the equivalent capacitance between the electrodes. Applied voltages, discharge currents, Lissajous figures, and discharge images from the bottom of the electrode under various applied voltages were measured. Based on the Lissajous figures, the equivalent capacitances between electrodes and the transferred charge were calculated. It was found that the equivalent capacitance is about 9.6 pF at the applied voltages below the discharge inception voltage, and increases from 13.2 pF at the incipient discharge voltage to 21.4 pF at a applied voltage above the discharge inception voltage, at which a multipulse uniform glow discharge covering the entire electrode surface appears, with an equivalent capacitance increase in 62%. If the applied voltage is decreased from the incipient discharge voltage, columnar patterned discharges below the incipient discharge voltage will appear; it increased from 9.6 pF of a single column discharge to 13.1 pF of a local uniform discharge, with an increase in 36%. At applied voltages further below the inception voltage, the discharge disappears and the equivalent capacitance returns to 9.6 pF. The correlation coefficient between the equivalent capacitance and the transferred charge was calculated under various discharge behaviors. The results show that the transferred charge during discharges caused the change of the equivalent capacitance between electrodes. From this understanding, an amendment is proposed for a previously simplified electrical equivalent circuit.

Oscillatory shearing is a popular method to understand transient nonlinear rheology. Various viscoelastic metrics have been used to analyze oscillatory rheology with different perspectives. We present a translation between various viscoelastic metrics for oscillatory rheology, using the framework of sequence of physical processes (SPPs) as a basis. The relation between the SPP metrics and Fourier-based metrics, such as Fourier sine and cosine coefficients, and large and minimum strain and rate metrics is provided. The meaning of the curvature in elastic and viscous Lissajous figures is explained with the sign of the SPP viscoelastic metrics. A low dimensional interpretation of the SPP framework is presented, featuring the center, size, and orientation of a deltoid in a transient Cole-Cole plot. Finally, we show how statistical information regarding the amount of change exhibited by the SPP metrics over a period of oscillation can be used to enhance the presentation and understanding of traditionally performed amplitude sweep experiments.

This work presents a multiparticle Monte Carlo simulation model in one dimension with adaptive time steps to investigate the time dependent physics of the single dielectric surface multipactor. Using this model, we study multipactor discharge on a dielectric with two carrier frequencies. We find that the saturation level and the oscillation pattern of the normal surface field with a parallel rf field of two carrier frequencies are different from those of single carrier frequency. Closed Lissajous curves are obtained to describe the temporal relationship between the fields normal and parallel to the surface in the ac saturation state.

The thermal memristor is the equivalent of the electrical memristor but in the thermal domain. The defining characteristic of the electrical memristor is the pinched Lissajous-type i-v curve (current to voltage difference); therefore, analogous behavior in the q-T curve (heat flux to temperature difference) should be the distinguishing feature of a thermal memristor. Herein, we propose a theoretical framework to realize thermal memristor devices using a solid-solid phase change material, tungsten doped vanadium dioxide. We show that by adding a periodic thermal input to the device, it is possible to obtain the characteristic pinched Lissajous type q-T curve that is indicative of the existence of a thermal memristor.

The vibration assisted polishing has widely application fields because of higher machining frequency and better polishing quality, especially the polishing with the non-resonant mode that is regarded as a kind of promising polishing method. This paper reports a novel vibration assisted polishing device, consisting of the flexible hinge mechanism driven by the piezoelectric actuators, which is suitable for polishing planes or curve surfaces with slow curvature. Firstly, the generation methods of vibration trajectory are investigated for the same frequency and different frequency signals’ inputs, respectively, and then the types of elliptic and Lissajous’s vibration trajectories are generated respectively. Secondly, a flexural mechanism consisting of the right circular flexible hinges and the leaf springs is developed to produce two-dimensional vibration trajectory. Statics and dynamics investigating of this flexible mechanism are finished in detail. The analytical models about input and output compliances of the flexural mechanism are established according to the matrix-based compliance modeling, and the dynamic model of the flexural mechanism based on the Euler-Lagrange equation is also presented. The finite element model of the flexural mechanism was established to carry out the numerical simulation in order to testify the rationality of device design. Finally, the polishing experiment is carried out to prove the effectiveness of the vibration device. The experimental results show that this novel vibration assisted polishing device developed in this study can remove more effectively the cutting marks left by last process and obviously reduce the workpiece surface roughness.

The (low frequency) zonal flow-ion temperature gradient (ITG) wave system, constructed on Braginskii's fluid model in tokamak, is shown to be a reaction-diffusion-advection system; it is derived by making use of a multiple spatiotemporal scale technique and two-dimensional (2D) ballooning theory. For real regular group velocities of ITG waves, two distinct temporal processes, sharing a very similar meso-scale radial structure, are identified in the nonlinear self-organized stage. The stationary and quasi-stationary structures reflect a particular feature of the poloidal group velocity. The equation set posed to be an initial value problem is numerically solved for JET low mode parameters; the results are presented in several figures and two movies that show the spatiotemporal evolutions as well as the spectrum analysis—frequency-wave number spectrum, auto power spectrum, and Lissajous diagram. This approach reveals that the zonal flow in tokamak is a local traveling wave. For the quasi-stationary process,...

A simple optical multiple reflection system is developed with two cylindrical concave mirrors at an appropriate spacing. The two cylindrical mirrors have different focal lengths and their principal sections are orthogonal. The alternate focusing of the two cylindrical mirrors at different direction keep the reflecting spots small. The reflecting spots fall on Lissajous patterns on the cylindrical mirrors. The mathematics for this optical system is described and the calculated coordinates of beam spots are very close matches of the experimental observations. The cylindrical mirror optical system is easy to construct and align, with a suitable method for obtaining long optical paths and a large number of passes in small volumes. In a photoacoustic spectrometer the beam family enhance the effective power in the photoacoustic cell and thus the signal-to-noise ratio of photoacoustic signal. An experimental result for photoacoustic spectrum of HDSe gas is given.

The chemical products of air plasma generated by dielectric barrier discharge were investigated in this paper, which played a key role in its applications. The results showed that the high applied voltage and low flow rate contributed a transition from ozone to nitric oxide mode. In order to investigate the relationship between the physical characteristic and a chemical product, the real energy density based on the ICCD image and Lissajous figure, a plausible parameter, was proposed. It was found that when the energy density increased beyond a critical value (∼10 mJ·cm−2), the mode transition occurred, which illustrated that the high value of energy density was favorable for the generation of nitrogen oxides but not for the ozone generation. The N2O density increased and the O3 density decreased at the flow rate of 480 L/h with the increase in energy density. When the flow rate was fixed at 60 L/h, the NO density increased with the increase in energy density while other parameters changed slightly and irr...

In this paper, the full energy spectrum of nonlinear oscillations, known as the cnoidal waves, is studied in the framework of small-amplitude Korteweg de Vries and modified Korteweg de Vries (mKdV) theories based on the pseudoparticle motion in Helmholtz and Duffing potentials by employing the newly introduced pseudoenergy concept. The pseudoenergy dependence of various cnoidal oscillation parameters is then studied, and it is shown that superposition of cnoidal waves leads to familiar beating and Lissajous profiles. One of the most important aspects of the nonlinear oscillation is found to be the frequency dependence of the oscillation amplitude which mainly characterizes the nature of oscillations. It is shown that the developed method can be used to study the spectrum of oscillations and shock waves in the fully nonlinear Sagdeev pseudopotential and to directly calculate many dynamic parameters of the given nonlinear system. Current research may be helpful in understanding of basic excitations and inte...

In this paper, an optimized optical encoder based on generalized grating imaging is presented. A multiple-tracks analyser grating is proposed to eliminate the second and third harmonic signals, and a photodiodes array with optimized cell width is used to suppress the fifth harmonic signal. The photodiodes array also guarantees the consistency and stability of the encoder signals benefiting from single-field photoelectric scanning. High-quality encoder signals are expected to be obtained from the above optimization, thereby ensuring high encoder accuracy. In the experiment, measured encoder signals with the approximately ideal Lissajous figure are obtained. FFT analysis of the encoder signals shows that the second, third, and fifth harmonic distortions are smaller than 0.3%, 0.5%, and 0.1%, respectively. The calibration results of the optical encoder show that the positioning error within one signal period is ±0.12 μm, and the positioning error over 150 mm measuring range is within ±0.2 μm.

This paper describes refinements to an instrument for determining the viscoelastic properties of a solid material isothermally, with a single apparatus, over 10 decades of time and frequency. Torque is applied electromagnetically to a specimen fixed at one end. Specimen deformation is determined via a laser beam reflected from the other end upon a split diode detector. Phase resolution is improved by the use of a lock-in amplifier at high frequency and by the use of Lissajous figures to measure phase, allowing the study of materials of moderate loss (0.008≤ tan δ≤0.2) in addition to materials with high loss (tan δ≊1). The rigidity of the instrument is increased by modifications in the specimen support geometry. The range of equivalent frequency for torsion is from less than 10−6 Hz to more than 104 Hz. Digital methods are incorporated in the creep measurements and in the phase measurements.

Unwanted reflection of laser light from target windows can produce an additional component to the VISAR fringe record that can obscure and complicate the true signal. Accurately removing this so-called ghost component is essential for achieving high accuracy EOS measurements, especially when the true signal is only weakly reflected from the shock front. Independent of the choice of algorithm for processing the raw data into a complex fringe signal, we have found it beneficial to plot this signal as a Lissajous and seek the true center of this curve, since the ghost contribution is solved by a translation in the complex plane that recenters the Lissajous. For continuous velocity histories, we find that plotting the fringe visibility vs nonfringing intensity and optimizing linearity is a valuable tool for determining the proper ghost offsets. For discontinuous velocity histories, we have developed methods which relate the results of two VISARs having different velocity per fringe proportionalities to find the ghost offset.Unwanted reflection of laser light from target windows can produce an additional component to the VISAR fringe record that can obscure and complicate the true signal. Accurately removing this so-called ghost component is essential for achieving high accuracy EOS measurements, especially when the true signal is only weakly reflected from the shock front. Independent of the choice of algorithm for processing the raw data into a complex fringe signal, we have found it beneficial to plot this signal as a Lissajous and seek the true center of this curve, since the ghost contribution is solved by a translation in the complex plane that recenters the Lissajous. For continuous velocity histories, we find that plotting the fringe visibility vs nonfringing intensity and optimizing linearity is a valuable tool for determining the proper ghost offsets. For discontinuous velocity histories, we have developed methods which relate the results of two VISARs having different velocity per fringe proportionalities to find t...

In this paper, we report a method for atomic force microscopy surface modifications with single-tone and multiple-resolution Lissajous trajectories. The tip mechanical scratching experiments with two series of Lissajous trajectories were carried out on monolayer films. The scratching processes with two scan methods have been illustrated. As an application, the tip-based triboelectrification phenomenon on the silicon dioxide surface with Lissajous trajectories was investigated. The triboelectric charges generated within the tip rubbed area on the surface were characterized in-situ by scanning Kelvin force microscopy. This method would provide a promising and cost-effective approach for surface modifications and nanofabrication.

A 2-degree of freedom microelectromechanical systems nanopositioner designed for on-chip atomic force microscopy (AFM) is presented. The device is fabricated using a silicon-on-insulator-based process and is designed as a parallel kinematic mechanism. It contains a central scan table and two sets of electrostatic comb actuators along each orthogonal axis, which provides displacement ranges greater than ±10 μm. The first in-plane resonance modes are located at 1274 Hz and 1286 Hz for the X and Y axes, respectively. To measure lateral displacements of the stage, electrothermal position sensors are incorporated in the design. To facilitate high-speed scans, the highly resonant dynamics of the system are controlled using damping loops in conjunction with internal model controllers that enable accurate tracking of fast sinusoidal set-points. To cancel the effect of sensor drift on controlled displacements, washout controllers are used in the damping loops. The feedback controlled nanopositioner is successfully used to perform several AFM scans in contact mode via a Lissajous scan method with a large scan area of 20 μm × 20 μm. The maximum scan rate demonstrated is 1 kHz.

This Letter observes collapse and intensification of the two parameter (b,c) ‘‘Lissajous‐elliptic’’ vortex ring. Laboratory and direct numerical studies of this ring are proposed to elucidate near‐singular and intermittent fluid phenomena at very high Reynolds number. Quantifications of single filament Biot–Savart numerical simulations with various core ‘‘radii’’ show that collapse may be nonmonotonic in time. In the collapsing region, the largest positive strain‐rate eigenvalue, α, is off the filament and exhibits self‐similar, singular‐like behavior. A signature of collapse is found in the local approach to zero of the filament energy density in the collapsing regions.

Interest in the production of printed electronics using a roll-to-roll system has gradually increased due to its low mass-production costs and compatibility with flexible substrate. To improve the accuracy of roll-to-roll manufacturing systems, the movement of the web needs to be measured precisely in advance. In this paper, a novel measurement method is developed to measure the displacement and velocity of the web precisely and directly. The proposed algorithm is based on the traditional single field encoder principle, and the scale grating has been replaced with a printed grating on the web. Because a printed grating cannot be as accurate as a scale grating in a traditional encoder, there will inevitably be variations in pitch and line-width, and the motion of the web should be measured even though there are variations in pitch and line-width in the printed grating patterns. For this reason, the developed algorithm includes a precise method of estimating the variations in pitch. In addtion, a method of correcting the Lissajous curve is presented for precision phase interpolation to improve measurement accuracy by correcting Lissajous circle to unit circle. The performance of the developed method is evaluated by simulation and experiment. In the experiment, the displacement error was less than 2.5 μm and the velocity error of 1σ was about 0.25%, while the grating scale moved 30 mm.

The concept of the simplest equivalent circuit for a dielectric barrier discharge (DBD) is critically reviewed. It is shown that the approach is consistent with experimental data measured either in large-scale sinusoidal-voltage driven or miniature pulse-voltage driven DBDs. An expression for the charge transferred through the gas gap q(t) is obtained with an accurate account for the displacement current and the values of DBD reactor capacitance. This enables (i) the significant reduction of experimental error in the determination of q(t) in pulsed DBDs, (ii) the verification of the classical electrical theory of ozonizers about maximal transferred charge q(max), and (iii) the development of a graphical method for the determination of q(max) from charge-voltage characteristics (Q-V plots, often referred as Lissajous figures) measured under pulsed excitation. The method of graphical presentation of q(max) is demonstrated with an example of a Q-V plot measured under pulsed excitation. The relations between the discharge current j(R)(t), the transferred charge q(t), and the measurable parameters are presented in new forms, which enable the qualitative interpretation of the measured current and voltage waveforms without the knowledge about the value of the dielectric barrier capacitance C(d). Whereas for quantitative evaluation of electrical measurements, the accurate estimation of the C(d) is important.

A method of analyzing Faraday rotation data from pulsed magnetic field measurements is described. The method uses direct least-squares elliptical fitting to measured data. The least-squares fit conic parameters are used to rotate, translate, and rescale the measured data. Interpretation of the transformed data provides improved accuracy and time-resolution characteristics compared with many existing methods of analyzing Faraday rotation data. The method is especially useful when linear birefringence is present at the input or output of the sensing medium, or when the relative angle of the polarizers used in analysis is not aligned with precision; under these circumstances the method is shown to return the analytically correct input signal. The method may be pertinent to other applications where analysis of Lissajous figures is required, such as the velocity interferometer system for any reflector (VISAR) diagnostics. The entire algorithm is fully automated and requires no user interaction. An example of algorithm execution is shown, using data from a fiber-based Faraday rotation sensor on a capacitive discharge experiment.

A large gap was acquired between electrodes (up to 5.5 mm) of Ar atmospheric pressure glow discharge in radio frequency dielectric barrier discharge (rf-DBD). The discharge of Ar plasma was characterized by I-V curve and Lissajous plot, and the effective power of the discharge was calculated based on the measured Lissajous plot and found to be higher than 90% of the input power. To gain a thorough understanding of the mechanism, the rf-DBD with a single dielectric barrier layer operating in γ mode glow discharge of N2 plasma was diagnosed in spatial resolution through optical emission spectroscopy. It was concluded that secondary electron emission might be responsible for the sustainable glow discharge in the large gap rf-DBD plasma.

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are nonnatural and the forces are not derivable from a potential. The constant value $E$ of a preserved energy function can be used as an appropriate parameter for characterizing the behaviour of the solutions of these two systems. In the second part the existence of two--dimensional versions endowed with superintegrability is proved. The explicit expressions of the additional integrals are obtained in both cases. Finally it is proved that the orbits of the second system, that represents a nonlinear oscillator, can be considered as nonlinear Lissajous figures, 25 pages, 7 figures

A Lissajous figure and surfaces of section are presented which show a 4:7 nonlinear resonance between two selectively excited coordinates of a system containing 900 degrees of freedom. The significance of this work is; first, plots of this nature have never before been constructed for a multidimensional system this large; and second, the nonlinear resonance exists between two collective modes of the linear macromolecule.

The generation and measurement of subpicosecond electron beam pulses by the transverse-longitudinal combination gate system is described. The temporal property of the pulse gate is analyzed with the help of the longitudinal emittance diagram. Close agreement has been obtained between the calculated pulse width and the observed one which was measured by the Lissajous's figure method. A beam pulse of 0.2 ps (FWHM) was produced.

A general‐purpose electronic analog computer has been used extensively to construct the streamlines around two‐dimensional airfoil shapes immersed in an incompressible, nonrotating, nonviscous fluid. The computer generates a circular Lissajous pattern on a plotting table, and then transforms the coordinates of the circle into the airfoil shape by a conformal transformation. Two samples of the variety of airfoil shapes so constructed are shown. The accuracy of the process, which has been checked by a digital computer and a desk calculator, is quite satisfactory; the speed of the actual mapping process is highly advantageous to thorough exploration of a variety of airfoil shapes.

A new method is described for approximate measurement of the coefficient of correlation between two random variables which can be represented by time‐varying electrical voltages. This method makes use of simple analog‐computing elements to obtain the coefficient of linear regression of one variable on the other. Its use in connection with an oscilloscope display of the two variables is described, and the relation between these displays and the Lissajous figure formed by two sinusoids is discussed. A possible design for a directreading correlation meter is suggested.