Phase Difference Distribution Research Articles

Efficiency optimization and symmetry-breaking in a model of ciliary locomotion

A variety of swimming microorganisms, called ciliates, exploit the bending of a large number of small and densely packed organelles, termed cilia, in order to propel themselves in a viscous fluid. We consider a spherical envelope model for such ciliary locomotion where the dynamics of the individual cilia are replaced by that of a continuous overlaying surface allowed to deform tangentially to itself. Employing a variational approach, we determine numerically the time-periodic deformation of such surface which leads to low-Reynolds locomotion with minimum rate of energy dissipation (maximum efficiency). Employing both Lagrangian and Eulerian points of views, we show that in the optimal swimming stroke, individual cilia display weak asymmetric beating, but that a significant symmetry-breaking occurs at the organism level, with the whole surface deforming in a wavelike fashion reminiscent of metachronal waves of biological cilia. This wave motion is analyzed using a formal modal decomposition, is found to occur in the same direction as the swimming direction, and is interpreted as due to a spatial distribution of phase differences in the kinematics of individual cilia. Using additional constrained optimizations, as well as a constructed analytical ansatz, we derive a complete optimization diagram where all swimming efficiencies, swimming speeds, and amplitudes of surface deformation can be reached, with the mathematically optimal swimmer, of efficiency one-half, being a singular limit. Biologically, our work suggests therefore that metachronal waves may allow cilia to propel cells forward while reducing the energy dissipated in the surrounding fluid.

Quadrature phase-shifting interferometer with a polarization imaging camera

We present a new high-speed phase distribution measurement, in which a polarization imaging camera is applied to a quadrature phase-shifting interferometer. The polarization imaging camera composed of a polarizer-mask on a detector array can provide simultaneously two phase-shifted data in quadrature. Two sets of two phase-shifted data in quadrature are obtained before and after a change of the interferometer such as object displacement or environmental disturbances. Phase sum and difference distributions of the interferograms between two states with arbitrary phase-shift in the interferometer are calculated with the two sets of two phase-shifted data in quadrature. This phase calculation method in the pixel displaced phase-shift method has such advantage that phase-shifted data required for the calculation of phase distributions can be obtained by only two pixels in the polarizer-mask detector array, which means no reduction of the image resolution in the other direction. The principle of this technique and experimental results are presented.

A STUDY ON A GENERATION OF SIMULATED EARTHQUAKE GROUND MOTION CONSIDERING PHASE DIFFERENCE CHARACTERISTICS

The purpose of this paper is to present a superposition technique for seismic waves from consecutive earthquakes. Seismic waves from each earthquake are synthesized by the waveform generation methods proposed in previous papers. The consecutive seismic waveforms are superposed so as to match the positions on the time history axis with respect to a wave arriving from the border between fault planes, considering the relationship between the distribution of phase differences and the time history of the accelerogram. By analyzing the dynamic behavior of high-rise buildings using the proposed superposition technique, it is indicated that a proper evaluation of ground motions is important in the case of consecutive earthquakes.

晶体锥折射空心光束的位相差及偏振特性

Based on the principle of hollow ring achieved by conical refraction effect in biaxial crystal,the formula of phase difference distribution between every point and the minimal point in the hollow ring are deduced,and the regularity of phase difference distribution is obtained by means of simulations.The continuity in the circumference of polarization direction variation of each point in the hollow ring is proved.In the experiment,un-polarized He-Ne laser is adopted to perpendicular radiate KNbO3 crystal,then polarization characteristic of hollow beams achieved by conical refraction effect in biaxial crystal is tested.The result of theoretical analysis agrees well with experiment.

Phase-shifting interferometry with four interferograms using linear polarization modulation and a Ronchi grating displaced by only a small unknown amount

A method to reduce the number of captures needed in phase-shifting interferometry is proposed on the basis of grating interferometry and modulation of linear polarization. The case of four interferograms is considered. A common-path interferometer is used with two windows in the object plane and a Ronchi grating as the pupil, thus forming several replicated images of each window over the image plane. The replicated images, under proper matching conditions, superpose in such a way so that they produce interference patterns. Orders 0 and +1 and −1 and 0 form useful patterns to extract the optical phase differences associated to the windows. A phase of π is introduced between these orders using linear polarizing filters placed in the windows and also in the replicated windows, so two π-shifted patterns can be captured in one shot. An unknown translation is then applied to the grating in order to produce another shift in the each pattern. A second and final shot captures these last patterns. The actual grating displacement and the phase shift can be determined according to the method proposed by Kreis before applying proper phase-shifting techniques to finally calculate the phase difference distribution between windows. Related simulations and experimental results are given.

The masking of interaural delays

Four experiments measured discrimination of interaural time delay (ITD) thresholds for broadband noise in the presence of masking noise of the same bandwidth as the target (0.1-3 kHz for experiments 1-3 and 0-10 kHz for experiment 4). In experiments 1-3, listeners performed interaural two-interval two-alternative forced-choice (2I-2AFC) delay discrimination tasks with stimuli composed of delayed and masking noises mixed in proportions of delayed noise ranging between 1 and 0.05. Experiments 1-3 employed interaurally correlated, anticorrelated, and uncorrelated maskers, respectively. Experiment 4 measured centering accuracy for continuous noise with a range of interaural coherences (equivalent to proportion of delayed noise) obtained by mixing delayed and interaurally uncorrelated noises. Results indicate that in the presence of an interaurally correlated masker ITD thresholds doubled for every halving of the proportion of delayed noise power in the stimulus. This function became steeper as the masking noise changed from interaurally correlated, to uncorrelated, to anticorrelated. The results were compared to thresholds predicted by a model based on variations in the distribution of interaural phase differences of the stimulus components.

Phase Synchronization in Human EEG During Audio-Visual Stimulation

Synchrony of EEG data recorded under influence of audio-visual stimulation was investigated. Instantaneous phases were derived from Wavelet transform method. Phase synchronization is assessed quantitatively via measure derived from uniformity of phase difference distribution. EEG data came from 6 healthy volunteers repeatedly exposed to 20 min AVS program with intervals with stable stimulation at 4 and 17 Hz. Phase synchronization during AVS significantly increased in comparison to non stimulation conditions in all examined cortex locations. The lowest increases in synchronization occurred in the frontal areas. In central region no dumping in synchronization was recognizable in comparison to backward locations where visual processing centers are situated.

Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses

Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase differences from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example.

Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating

We present a new type of quadrature phase-shifting interferometer, which utilizes wave plates, a diffraction grating, and two lasers with different wavelengths, in order to acquire two sets of two quadrature fringe patterns in each wavelength formed on a single image sensor. This method for calculating with four phase-shifted fringe patterns gives us the phase sum and difference distributions between the phases in two wavelengths. This is also substantiated by results of our experiments.

Coherence, collective rhythm, and phase difference distribution in populations of stochastic genetic oscillators with cellular communication

An ensemble of stochastic genetic relaxation oscillators via phase-attractive or repulsive cell-to-cell communication are investigated. In the phase-attractive coupling case, it is found that cellular communication can enhance self-induced stochastic resonance as well as collective rhythms, and that different intensities of noise resulting from the fluctuation of intrinsic chemical reactions or the extrinsic environment can induce stochastic limit cycles with different amplitudes for a large cell density. In contrast, in the phase-repulsive coupling case, the distribution of phase differences among the stochastic oscillators can display such characteristic as unimodality, bimodality or polymodality, depending on both noise intensity and cell number, but the modality of phase difference distribution almost keeps invariant for an arbitrary noise intensity as the cell number is beyond a threshold.

A nakagami fading phase difference distribution and its impact on BER performance

We propose a new model for investigating the impact of complex imperfect channel state information (CSI) over Nakagami-m fading channels. The phase difference between two correlated complex Nakagami random variables (RVs) is proposed and its statistical properties are investigated. A closed-form expression for the distribution is obtained using an approach from [1] and depends on the Nakagami-m parameter and the power correlation coefficient (p) between two correlated complex RVs. A simple approximation is given when p is close to unity. The proposed phase difference is shown to accurately approximate that of the Ricean. We derive the joint density function of this phase difference and its associated correlated envelopes. This is given in a closed form in terms of a generalized hypergeometric function, but the RVs can be easily generated for simulation. We analyze the impact of imperfect CSI on the bit error rate (BER) of uncoded and coded modulation. For uncoded modulation, the average BER and a closed-form expression of the asymptotic BER or error floor are obtained. For coded modulation, we determine the error free feedback bound of bit-interleaved coded modulation with iterative decoding for both perfect and imperfect CSI. We show that imperfect phase estimation is the major cause of the error floor.

Indoor sound field feature matching for robot’s location and orientation detection

In this work, an indoor sound field feature matching method is proposed and is applied to detect a mobile robot’s location and orientation. The sound field feature, captured from a sound source to a pair of microphones, contains the dynamic of the propagation path. Because of the complexity of indoor environment, the features from different path can be distinguished using appropriate models. Gaussian mixture models are utilized in this paper to characterize the phase difference and magnitude ratio distributions between the microphone pair in consecutive data frames. The application provides an alternative thinking compared with traditional methods such as direction of arrival (DOA) using propagation delay. They usually suffer from reverberation, non-line-of-sight and microphone mismatch problems. The experimental results show the method not only has a high recognition rate for robot’s location and orientation, but also is robust against environmental noise.

Object recognition by use of polarimetric phase-shifting digital holography

Pattern recognition by use of polarimetric phase-shifting digital holography is presented. Using holography, the amplitude distribution and phase difference distribution between two orthogonal polarizations of three-dimensional (3D) or two-dimensional phase objects are obtained. This information contains both complex amplitude and polarimetric characteristics of the object, and it can be used for improving the discrimination capability of object recognition. Experimental results are presented to demonstrate the idea. To the best of our knowledge, this is the first report on 3D polarimetric recognition of objects using digital holography.

Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.

Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources

To address the problem of volume conduction and active reference electrodes in the assessment of functional connectivity, we propose a novel measure to quantify phase synchronization, the phase lag index (PLI), and compare its performance to the well-known phase coherence (PC), and to the imaginary component of coherency (IC). The PLI is a measure of the asymmetry of the distribution of phase differences between two signals. The performance of PLI, PC, and IC was examined in (i) a model of 64 globally coupled oscillators, (ii) an EEG with an absence seizure, (iii) an EEG data set of 15 Alzheimer patients and 13 control subjects, and (iv) two MEG data sets. PLI and PC were more sensitive than IC to increasing levels of true synchronization in the model. PC and IC were influenced stronger than PLI by spurious correlations because of common sources. All measures detected changes in synchronization during the absence seizure. In contrast to PC, PLI and IC were barely changed by the choice of different montages. PLI and IC were superior to PC in detecting changes in beta band connectivity in AD patients. Finally, PLI and IC revealed a different spatial pattern of functional connectivity in MEG data than PC. The PLI performed at least as well as the PC in detecting true changes in synchronization in model and real data but, at the same token and like-wise the IC, it was much less affected by the influence of common sources and active reference electrodes.

Laser-scanning angle deviation microscopy

A microscope manifesting a dynamic range of several microns and an axial (or height) resolution of 1nm is presented. It is based on the method of angle deviation due to nonfocal plane reflection and the application of surface plasmon resonance effect as well as the technique of heterodyne interferometry. The deviation angle and the induced phase difference between two rays are proportional to the departure from the focal plane. Using the common-path heterodyne interferometry to scan the specimen and measure the phase difference distribution, the surface profile would be obtained in real time.

Thermal waves scattering by a subsurface sphere in a semi-infinite exponentially graded material using non-Fourier's model

In this study, the multiple scattering of thermal waves and temperature distribution resulting from a subsurface sphere in a semi-infinite exponentially graded material are investigated, and the analytical expression of the temperature at the surface of the graded material is obtained. Non-Fourier heat conduction equation is applied to solve the temperature at the surface, and the image method is used to satisfy the semi-infinite boundary condition of graded material. The thermal wave fields are expressed using wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the sphere. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented for the first time. The temperature distribution and phase difference at the surface of the semi-infinite material with different parameters are graphically presented. Analyses show that the hyperbolic heat conduction equation cannot be regarded as a continuation of the parabolic heat conduction equation at very short time scale. The effects of the incident wave number, the structural and physical parameters on the distribution of temperature and phase difference in the semi-infinite material are also examined.

A Robust Statistical-Based Speaker's Location Detection Algorithm in a Vehicular Environment

This work presents a robust speaker's location detection algorithm using a single linear microphone array that is capable of detecting multiple speech sources under the assumption that there exist nonoverlapped speech segments among sources. Namely, the overlapped speech segments are treated as uncertainty and are not used for detection. The location detection algorithm is derived from a previous work (2006), where Gaussian mixture models (GMMs) are used to model location-dependent and content and speaker-independent phase difference distributions. The proposed algorithm is proven to be robust against the complex vehicular acoustics including noise, reverberation, near-filed, far-field, line-of-sight, and non-line-of-sight conditions, and microphones' mismatch. An adaptive system architecture is developed to adjust the Gaussian mixture (GM) location model to environmental noises. To deal with unmodeled speech sources as well as overlapped speech signals, a threshold adaptation scheme is proposed in this work. Experimental results demonstrate high detection accuracy in a noisy vehicular environment.

Phase correlation of foreign exchange time series

Correlation of foreign exchange rates in currency markets is investigated based on the empirical data of USD/DEM and USD/JPY exchange rates for a period from February 1 1986 to December 31 1996. The return of exchange time series is first decomposed into a number of intrinsic mode functions (IMFs) by the empirical mode decomposition method. The instantaneous phases of the resultant IMFs calculated by the Hilbert transform are then used to characterize the behaviors of pricing transmissions, and the correlation is probed by measuring the phase differences between two IMFs in the same order. From the distribution of phase differences, our results show explicitly that the correlations are stronger in daily time scale than in longer time scales. The demonstration for the correlations in periods of 1986–1989 and 1990–1993 indicates two exchange rates in the former period were more correlated than in the latter period. The result is consistent with the observations from the cross-correlation calculation.

Horizontal variability in chlorophyll fluorescence and potential temperature

Chlorophyll fluorescence and temperature were measured with a horizontal resolution of 4 m on two isopycnals and two isobars along a 1000 km meridional transect in the eastern North Pacific. Probability density functions (PDFs) of the magnitude of fluctuations in temperature and fluorescence are compared at each of a large range of length scales. While they are nearly identical at larger scales, the shapes of the PDFs of fluorescence and temperature differ significantly at small scales (∼1 km and less). This difference may indicate that at these scales, temperature and fluorescence distributions are controlled by distinct mechanisms. By comparing the phase of wavelet transforms of each of these two tracers, the tendency for temperature and fluorescence gradients to line up is investigated over a large range of spatial scales. At horizontal length scales of order 10 km and larger, the wavelet phase difference between temperature and fluorescence tends to be close to 0° or 180°—that is, the gradients tend to align, either in phase or 180° out of phase. At smaller scales, the distribution of phase difference on isopycnals is uniform—there is no tendency for gradients to coincide. Simple stirring models demonstrate that the locations of enhanced gradients in all tracers would be expected to coincide where the strain has been greatest. However, the directions of enhanced gradients formed in this way may be either parallel or antiparallel, depending on initial conditions and on the direction of the strain. These analyses suggest the horizontal distributions of temperature and fluorescence at large scales were both governed by advective processes. At intermediate scales, of order 1–10 km, a renovating wave model suggests that gradient alignment could be destroyed by turbulent diffusion or by rapid local phytoplankton growth.