Lissajous Plot Research Articles

A Simple and Effective Method to Estimate the Model Parameters of Dielectric Barrier Discharge Ozone Chamber

This paper presents a simple yet effective method to determine the electrical model parameters of the dielectric barrier discharge (DBD) ozone chamber at frequencies above 20 kHz. The method is an alternative to the conventional Lissajous plot estimation method which appears to yield unsatisfactory results in this frequency range. Furthermore, the proposed technique allows for the chamber parameters to be determined at different frequencies-a flexibility which is not easily achievable using the typical Lissajous method. The measurement setup consists of a full-bridge inverter and a high-frequency variable inductor connected to the DBD chamber. The inductor can be adjusted to allow for parameter determination at different frequencies. The chamber parameters obtained from experimental results are validated by applying them in a high-voltage power supply for ozone generator.

Model prediction of non-symmetric normal stresses under oscillatory squeeze flow

The non-symmetric responses of normal stresses in oscillatory squeeze flow have been investigated with model calculations. The simplest and most widely used constitutive equations were employed to predict the non-symmetric normal stresses, which is a distinctive feature of oscillatory squeeze flow. The model prediction was compared with experimental data of polymer solution in terms of stress shape, Lissajous plot, stress decomposition, and Fourier transformation. The upper-convected Maxwell, Giesekus, and exponential Phan-Thien Tanner models predicted the nonsymmetric characteristics of normal stresses under oscillatory squeeze flow. The predictions showed fairly good agreement with experimental data. However, the upper-convected Maxwell model showed unrealistic result in the Lissajous plot of [stress vs. strain] and [stress vs. strain rate]. From stress decomposition, it could be confirmed that the non-symmetric nature arises from the elastic contribution of the normal stress, which was verified in both experiment and model calculation. This study is expected to provide useful insights for further understanding of the nonlinear and non-symmetric characteristics of oscillatory squeeze flow.

Surface shear rheology of hydrophobin adsorption layers: laws of viscoelastic behaviour with applications to long-term foam stability

The long-term stabilization of foams by proteins for food applications is related to the ability of proteins to form dense and mechanically strong adsorption layers that cover the bubbles in the foams. The hydrophobins represent a class of proteins that form adsorption layers of extraordinary high shear elasticity and mechanical strength, much higher than that of the common milk and egg proteins. Our investigation of pure and mixed (with added beta-casein) hydrophobin layers revealed that their rheological behavior obeys a compound rheological model, which represents a combination of the Maxwell and Herschel-Bulkley laws. It is remarkable that the combined law is obeyed not only in the simplest regime of constant shear rate (angle ramp), but also in the regime of oscillatory shear strain. The surface shear elasticity and viscosity, E(sh) and eta(sh), are determined as functions of the shear rate by processing the data for the storage and loss moduli, G' and G''. At greater strain amplitudes, the spectrum of the stress contains not only the first Fourier mode, but also the third one. The method is extended to this non-linear regime, where the rheological parameters are determined by theoretical fit of the experimental Lissajous plot. The addition of beta-casein to the hydrophobin leads to softer adsorption layers, as indicated by their lower shear elasticity and viscosity. The developed approach to the rheological characterization of interfacial layers allows optimization and control of the performance of mixed protein adsorption layers with applications in food foams.

Bimanual Fitts’ tasks: Kelso, Southard, and Goodman, 1979 revisited

The experiment was designed to replicate and extend to an integrated feedback condition the pattern of movement time results found by Kelso et al. (J Exp Psychol Hum Percept Perform 5:229-238, 1979a, Science 204:1029-1031, 1979b) where the simultaneous movement of one hand to a low ID target and the other to a higher ID target indicated "a tight coordinate coupling between the hands" (p. 229). In the present experiment, a control group was provided feedback that depicted the independent movement of the two limbs under low and higher indexes of difficulty (ID). A Lissajous group was provided integrated feedback in the form of a Lissajous plot. The results indicated a pattern of results for the control and Lissajous groups similar to that found by Kelso et al. for one and two-limb movements to the same difficulty targets. The control group also replicated the finding for two-limb movements to mixed ID tasks. However, the Lissajous group simultaneously produced disparate movement in the mixed target conditions. The results are consistent with recent findings indicating that when provided salient integrated feedback participants can effectively produce disparate movements of the two limbs.

Coordination dynamics of elliptic shape drawing: Effects of orientation and eccentricity

The aim of the present study was to show the effect of orientation on producing ellipses of various eccentricities. Ten right-handed adults were required to reproduce eight series of 84 ellipses on a graphic tablet at spontaneous speed. The ellipses displayed seven eccentricities, corresponding to the Lissajous plot produced by two orthogonal harmonic oscillators whose relative phase (RP) varied from 0° (a line) to 90° (a circle), and twelve orientations, the long axis of the ellipses aligned in a direction ranging from three to nine o’clock with respect to the body transverse plane. Results confirmed the participant’s preference for two eccentricities, 0° and 45°, that is, a line and an ellipse of intermediate eccentricity, respectively. Except for the circle, insensitive to orientation by definition, orientation became a cogent constraint: In the 10:30 o’clock direction, line drawing (0° RP) increased in variability and the intermediate ellipse (45° RP) was attracted towards a circle (90° RP). These findings suggest an interaction between orientation effects, putatively due to differences in the motion of the wrist and fingers, and eccentricity effects, which may pertain to preferences arising from the non-linear coupling between the effectors.

A large gap of radio frequency dielectric barrier atmospheric pressure glow discharge

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.

Bimanual 1:1 with 90° continuous relative phase: difficult or easy!

The purpose of the present experiment was to observe the performance of participants attempting to produce a 1:1 bimanual coordination pattern with 90 degrees relative phase between the arms when feedback concerning the movement of the two limbs was integrated within a Lissajous plot and when this information was withdrawn. One group was paced with an auditory metronome and the other was encouraged to increase frequency when they fell below the goal frequency. We predicted that providing a salient integrated feedback display without a metronome would allow participants to effectively tune-in the goal relative phase pattern within several minutes; instead of several days as typically found in the literature when the metronome was used. The data indicated remarkably effective performances after 5 min of practice when the metronome was not used, with motion of both limbs harmonic in nature, and continuous relative phase errors (approximately 10 degrees) and standard deviation of continuous relative phase (approximately 10 degrees) relatively small. This seems remarkable given that this coordination pattern has proven relatively difficult to perform under normal and Lissajous feedback conditions even after several days of practice. As predicted relative phase errors and variability increased substantially when the metronome was used. When the extrinsic feedback was withdrawn all participants tended to drift from the required 90 degrees relative phase, but the cycle duration variability in the two limbs remained stable and limb motion remained harmonic in nature. The current findings suggest that some of the difficulty typically associated with producing various relative phase patterns is due to the less than optimal perceptual information available in the various testing situations and the use of pacing metronomes.

A geometrical interpretation of large amplitude oscillatory shear response

Although the stress of oscillatory shear flow can be decomposed into elastic and viscous parts in the linear regime, it is not yet known how to decompose the stress of a large amplitude oscillatory shear (LAOS) flow. We developed a method of analyzing LAOS data, which decomposes the stress into elastic and viscous components on the basis of a sound mathematical and physical foundation. This method is based on the symmetry of the stress and is a generalization of linear viscoelasticity from the viewpoint of geometry. The proposed method is more powerful than previous methods such as Fourier transform analysis and the Lissajous plot, in that it is more sensitive to the presence of nonlinearities and it is easier to determine nonlinear parameters.

Assessing thoracoabdominal asynchrony.

The traditional method of derivation of phase difference between ribcage and abdomen breathing movements from a Lissajous plot is shown to be unsatisfactory for assessing the degree of asynchrony. The signal processing technique of cross-correlation is introduced as a better, statistically based approach. Even so, examination of the latent structure of a Lissajous figure leads to the concept of movement sum and difference components along its principal axes. This more general form of analysis is used for indicating relative changes in tidal volume during postoperative monitoring of Cheyne-Stokes breathing with obstructive apnoea, as well as tracking the degree of asynchrony. The theoretical and practical limitations of inductive plethysmography calibrations are such that the proposed methods of uncalibrated non-invasive respiratory monitoring are also preferable as research tools.

Two-dimensional representation of three-dimensional pelvic motion during human walking: An example of how projections can be misleading

We investigated the movements of skin markers located on the anterior and posterior surfaces of the pelvis during normal walking. Plots of the vertical versus horizontal displacements of the body-surface markers for a single gait cycle yield characteristic horizontal figure-of-eight patterns, often referred to as Lissajous figures. Some literature citations indicate that these figure-of-eight plots represent movement of the body center of mass in the plane perpendicular to the line of progression. We show evidence suggesting that the Lissajous plot for the body center of mass is U-shaped and that the observed figure-of-eight pattern is due to the location of the marker on the body surface coupled with pelvic rotation. A simple rigid-body model is used to demonstrate that pelvic rotation about the vertical axis can appear as horizontal translations in a planar projection. Even small rotations about the vertical axis are observable in the phase relation between horizontal and vertical displacements of surface markers in the projection. As a result, Lissajous plots of vertical versus horizontal displacements, particularly for points on the exterior of a rigid body, may be strongly influenced by rotations. We demonstrate that Lissajous patterns for the model are similar to patterns for the human pelvis during walking and that pelvic rotation has a large influence on Lissajous patterns (vertical movement vs medial-lateral) plotted from pelvic marker data. This demonstration illustrates how two-dimensional representations of three-dimensional movement can lead to incorrect interpretations.

Magnetic hysteresis loops as Lissajous plots of relaxationally delayed response to periodic field variation

We have studied the nature of the response function (magnetisation) arising in response to a periodic perturbation (magnetic field) on Ising systems, using the Monte Carlo simulation (for a three dimensional Ising system) and also solving the mean field equation of Ising dynamics. The hysteresis loop is identified here as the Lissajous plot of the response function versus the perturbing field. It is observed that the response function is always periodic with the same frequency as that of the perturbing field and gets delayed in general due to relaxation. This equality in the frequency gives rise to the quadratic equation of the Lissajous figures (double valuedness and stability of magnetisation in the hysteresis loop) and the delay gives rise to the nonvanishing width of the Lissajous figures (nonvanishing hysteresis loss). We have also studied the scaling behaviour for the hysteresis loop area A, obtained from the mean field solution of the Ising dynamics and from the Monte Carlo study of a three dimensional Ising system. The scaling function is observed to be Lorentzian in form in the mean field case, while the scaling function is an exponentially decaying one multiplied by a power law function, in the case of (Monte Carlo results for) the three dimensional Ising systems. Additionally, we have studied the dynamic phase transition for the three dimensional Ising system and the tricritical point in the phase diagram has been located.