Abrupt Phase Changes Research Articles

Phasor Estimation From Phasorlets

The mathematical formulation for estimating phasors from phasorlets, obtained from signal segments of a fraction of a cycle, is established and the frequency responses of the phasorlet generator filters are evaluated. From the theory and the numerical simulations it is concluded that, when the signal segment involved in the phasorlet generation corresponds to a pure sinusoidal signal, this estimation technique offers the quickest measurement of its phasor, improving the speed of the well known one-cycle Fourier filter estimate. The new estimates were found very useful for detecting and locating abrupt changes in amplitude or phase between two sinusoidal states. However, before transients or impure sinusoids, the exactness and the dynamic behavior of this estimation method (which includes the one-cycle Fourier filter) will depend in great extent on the applied noise extraction technique, given the huge sensitivity to nonsinusoidal signals of the phasorlet generator filters.

Interaction of two lump solitons described by the Kadomtsev–Petviashvili I equation

The interaction of two lump solitons described by the Kadomtsev–Petviashvili I (KPI) equation is analysed using both exact and numerical methods. The numerical method is based on a third order Runge–Kutta method, and a Crank–Nicholson scheme. The main characteristic of a direct interaction when the two lumps are initially aligned along the x-axis is that they may separate in the y-direction, but then come back to the x-axis after collision; the dependence of the maximum separation in the y-direction on the relative velocity difference is described. Two lumps may also experience an abrupt phase change in the case of an oblique interaction.

Spin-dependent transmission through a mesoscopic ring with a quantum gate

We investigate the spin-dependent transmission through an Aharonov–Bohm ring with a quantum gate that is tuned by an uniform external magnetic field. The formula of spin-dependent transmission coefficient at zero temperature is obtained as a function of the flux, the magnetic field and Fermi energy in term of quantum waveguide theory. We found that for some special Fermi energies, spin-state electrons are driven into a perfect transmissive state or reflective state, which is not affected by the flux, when Zeeman energy of electron moving in the stub coincides with a level of the isolated stub. As Zeeman energy crosses the level of the stub, Aharonov–Bohm oscillations of spin-state conductance have no abrupt change of phase by π and are in phase. The effect of the magnetic field on transmission behavior of spin-state electrons are examined.

Components of the 2 f1- f2 distortion-product otoacoustic emission in a moth

The noctuoid moth Empyreuma affinis has a simple tympanal organ with only two receptor cells attached to the eardrum. As in vertebrates, the growth of distortion-product otoacoustic emissions (DPOAE) with increasing stimulus level is characterized by two distinct components. An initial increase of DPOAE level for f 2 levels in the range of 30–65 dB SPL is followed by a second steep growth of the DPOAE at f 2 levels above 65 dB SPL. Both components increase at a slope of about 2 dB/dB and the difference between both components was used to assess a mechanical gain of the tympanal organ of 17 dB ( n=23). At around 65 dB SPL, a notch in the level function coincides with an abrupt phase change of up to 180°. The sensitive component induced by f 2 levels below 65 dB SPL is selectively affected by application of ethyl ether and disappears more quickly than the high-level component during ongoing deterioration of the moth preparation.

Absence of an abrupt phase change from polycrystalline to amorphous in silicon with deposition temperature.

Using fluctuation electron microscopy, we have observed an increase in the mesoscopic spatial fluctuations in the diffracted intensity from vapor-deposited silicon thin films as a function of substrate temperature from the amorphous to polycrystalline regimes. We interpret this increase as an increase in paracrystalline medium-range order in the sample. A paracrystal consists of topologically crystalline grains in a disordered matrix; in this model the increase in ordering is caused by an increase in the grain size or density. Our observations are counter to the previous belief that the amorphous to polycrystalline transition is a discontinuous disorder-order phase transition.

Energy gap dependence of vibrational dephasing rates in a bath: a semigroup description

The quantum dynamical semigroup formalism provides an appealing general framework for discussing factors that affect pure vibrational dephasing rates in chemical systems. Within this framework, we formulate a Poisson model of pure vibrational dephasing which is more generally applicable than the commonly employed stochastic Gaussian dephasing model. In the limit of small and frequent phase changes, the Poisson model reduces to the stochastic Gaussian form. We find that for certain vibrational states of the lithium dimer in argon, the stochastic Gaussian model is valid, while for other states large and abrupt phase changes clearly require application of the Poisson model. In the former case, dephasing rates increase with the difference in quantum number between constituent vibrational states, while in the latter case, the dependence on quantum number difference or energy gap can become negligible. Recent experimental advances described by Amitay and Leone are expected to permit experimental tests of our theoretical predictions.

In-Phase Resonances with Generic Transmission Zeros and Eigenvectors of Hamiltonian in Models of Single Channel Transport**The project supported by National Natural Science Foundation of China

We investigate the phase coherent transport in a single channel system. The theory that the transmission zeros lead to abrupt phase change and in-phase resonances is confirmed numerically in two tight-binding models. After calculating the eigenvalues and eigenvectors of the Hamiltonians we also confirmed that the same symmetry of the eigenvectors also leads to the abrupt phase change and in-phase resonances that equal the transmission zero.

Correlation betweenthe phase of transmission resonances and parity of bound states in aquantum dot

We investigate the phase of the transmission peaks of electrons in asingle-channel system with a quantum dot embedded between the leads.The quantum dot is modelled by a tight-binding Hamiltonian of acluster of a two- or three-dimensional lattice which is connected withone-dimensional leads. We derive an exact expression which relatesthe transmission amplitude to the bound states of the dot. It isconfirmed that the abrupt phase changes in the transmissionamplitude are associated with the transmission peaks and zeros. Thephase at the resonance peaks is related to the parity of thecorresponding bound states of the dot. On the basis of the exactexpression a possible explanation of the in-phase featuresdiscovered in the experiments is presented.

Transmission modulated by quantum gate in aharonov-casher ring

We study the electron transmission tuned by quantum gate in an Aharonov-Casher (AC) ring. Transmission probability is obtained as a function of the normalized textured electric fields and Fermi energy. We find that modulating electron wavefunction in the stub can drastically affects electron transmission through the ring system. As Fermi energy crosses every eigenenergy of the isolated stub, the phases of both anomalous and periodic oscillations of the AC conductance generally have abrupt change by π. On two sides of several special Fermi energies, both anomalous and periodic oscillations have no abrupt phase change and are in phase. The detailed characteristics of the anomalous oscillations are dependent on the difference between the tilt angle of the spin and that of textured electric field. By modulating external magnetic field applied to the stub, we present AC oscillations of spin-polarized conductance within adiabatic limit.

Friedel phases and phases of transmission amplitudes in quantum scattering systems

We illustrate the relation between the scattering phase appearing in the Friedel sum rule and the phase of the transmission amplitude for quantum scatterers connected to two one-dimensional leads. Transmission zero points cause abrupt phase changes $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$ of the phase of the transmission amplitude. In contrast, the Friedel phase is a continuous function of energy. We investigate these scattering phases for simple scattering problems and illustrate the behavior of these models by following the path of the transmission amplitude in the complex plane as a function of energy. We verify the Friedel sum rule for these models by direct calculation of the scattering phases and by direct calculation of the density of states.

Conductance oscillations through an aharonov-bohm ring with a quantum gate

Based on a one-dimensional quantum wave guide theory, we investigate the ballistic conductance through an Aharonov-Bohm ring with a quantum gate. The analytical expression of the conductance is exactly obtained as the function of magnetic flux penetrating the ring and Fermi energy of indcident electrons. When Fermi energy equals that of bound states in the isolated stub, the conductance is fixed at a constant value which is only determined by the geometric structure of the ring system. We have found that there are a new kind of conductance oscillations for some special mesoscopic ring systems. As Fermi energy of incident electrons crosses that of bound state in the isolated stub, the conductance oscillations have no abrupt change of phase by π and are in phase. This striking feature is not in ageement with that of previous experiments and theories. The mechanism causing this new feature is discussed.

Micromechanical responses to tones in the auditory fovea of the greater mustached bat's cochlea.

An extended region of the greater mustached bat's cochlea, the sparsely innervated (SI) zone, is located just basally to the frequency place of the dominant 61-kHz component of the echolocation signal (CF2). Anatomic adaptations in the SI zone are thought to provide the basis for cochlear resonance to the CF2 echoes and for the extremely sharp tuning throughout the auditory system that allows these bats to detect Doppler shifts in the echoes caused by insect wing beat. We measured basilar membrane (BM) displacements in the SI zone with a laser interferometer and recorded acoustic distortion products at the ear drum at frequencies represented in the SI zone. The basilar membrane in the SI region was tuned both to its characteristic frequency (62-72 kHz) and to the resonance frequency (61-62 kHz). With increasing stimulus levels, the displacement growth functions are compressive curves with initial slopes close to unity, and their properties are consistent with the mammalian cochlear amplifier working at high sound frequencies. The sharp basilar membrane resonance is associated with a phase lag of 180 degrees and with a shift of the peak resonance to lower frequencies for high stimulus levels. Within the range of the resonance, the distortion product otoacoustic emissions, which have been attributed to the resonance of the tectorial membrane in the SI region, are associated with an abrupt phase change of 360 degrees. It is proposed that a standing wave resonance of the tectorial membrane drives the BM in the SI region and that the outer hair cells enhance, fine tune, and control the resonance. In the SI region, cochlear micromechanics appear to be able to work in two different modes: a conventional traveling wave leads to shear displacement between basilar and tectorial membrane and to neuronal excitation for 62-70 kHz. In addition, the SI region responds to 61-62 kHz with a resonance based on standing waves and thus preprocesses signals which are represented more apically in the CF2 region of the cochlea.

Generic Transmission Zeros and In-Phase Resonances in Time-Reversal Symmetric Single Channel Transport

We study phase coherent transport in a single channel system using the scattering matrix approach. It is shown that identical vanishing of the transmission amplitude occurs generically in quasi-1D systems if the time-reversal is a good symmetry. The transmission zeros naturally lead to abrupt phase changes (without any intrinsic energy scale) and in-phase resonances, providing insights to recent experiments on phase coherent transport through a quantum dot.

Application of eddy viscosity closure models for the M 2 tide and tidal currents in the Yellow Sea and the East China Sea

A three-dimensional mode-splitting, σ-coordinate barotropic finite-difference model, with subgrid scale diffusion represented using a range of eddy viscosity closure models, is used to examine M 2 tidal elevation and currents in the Yellow Sea and the East China Sea. Four eddy viscosity formulations are considered: q 2- q 2 l turbulence energy model (Blumberg and Mellor, 1987), Prandtl mixing length model, Davies and Furnes’ (1980) simple flow-related model with mixing length which includes the bottom boundary layer thickness, and a time and space invariant eddy viscosity with 650 cm 2/s. The bottom friction at the sea bed is given in a quadratic form using a constant bottom friction coefficient, c f and near-bottom velocities. A series of M 2 tide model runs were carried out and optimal values of c f were determined through the comparison with tidal elevation amplitudes and phases at 203 stations. From these comparisons it is shown that the M 2 tidal charts computed with a range of eddy viscosity formulations are in good agreement with each other when optimal values of c f are chosen; comparing with M 2 tidal current amplitudes and phases at 15 stations, it is shown that tidal current distributions and its profiles are in reasonably good agreement with winter-time observations in the central part of the Yellow Sea; relatively poor results are obtained near the Chinese coast where non-tidal effects such as abrupt changes in tidal current phase in the vertical due to large freshwater discharge are pronounced. It is noted that the bottom friction coefficient has a major influence on tidal elevation and tidal currents and optimal values of bottom friction coefficient are closely related to the near-bottom eddy viscosity. The considered eddy viscosity closure models appear to work well for tidal problem when the bottom friction parameter is optimized. Results indicate that for a barotropic tide the Prandtl mixing length model which can account of the boundary layer thickness could be an useful alternative to a highly complex q 2- q 2 l model.

Joint synchronization in Eureka 147 DAB system based on abrupt phase change detection

We present a joint symbol, frame, and carrier synchronization method for the Eureka 147 DAB signal. Symbol timing is determined first by detecting an abrupt change in the phase angle of the complex product between the last quarter of a useful symbol and its cyclic extension in the guard interval. The detection of this abrupt change is based an the maximal likelihood (hit) principle. Frequency offset of fractional carrier spacing is estimated from the phase angle of the autocorrelation after symbol timing is estimated. Coarse frame synchronization and null symbol detection can also be achieved through this correlation information. Frequency offset of integral carrier spacing is determined from the convolution outputs between a received phase reference symbol and several locally generated but frequency-shifted phase reference symbols. We found the length of a guard interval is the most important parameter for the synchronization algorithm to work. Simulation results show that the performance of this synchronization method approaches to the ideal synchronization case in both an additive white Gaussian noise (AWGN) channel and a two-path Rayleigh fading channel.

Diel vertical migration in stratified tidal flows: Implications for plankton dispersal

This paper examines the kinematics of the horizontal motion induced in marine plankton which undergo diel vertical migration (DVM) in oscillatory tidal currents with depth varying amplitude and phase. Particular attention is paid to the transport-producing effects of DVM in shallow, stratified seas where frictional decoupling associated with a reduction in the vertical eddy viscosity in the pycnocline can cause abrupt changes in tidal phase across the pycnocline. M 2 -period tidal currents, horizontal displacements of up to 5 upper layer tidal excursions can be produced over a 15-day cycle and in S 2 -period currents, net unidirectional horizontal transport at a rate of up to 1 tidal excursion per tidal cycle is possible. The transport producing effects of DVM in spatially varying tidal fields are illustrated by the case of the northwest European shelf and with the example of an idealized stratified gulf. The results have potentially far reaching consequences since marine zooplankton and phytoplankton capable of DVM are often concentrated in the pycnocline and, for those organisms with swimming behavior unaffected by the temperature/salinity gradient at the pycnocline, vertical excursions of just a few meters would be sufficient to allow significant horizontal transport.

Latitude dependence of the quasi‐biennial oscillation and quasi‐triennial oscillation characteristics of total ozone measured by TOMS

The 12‐month moving averages of total ozone mapping spectrometer (TOMS) total ozone data for 14 years (1979–1992) were examined for quasi‐biennial oscillation (QBO) and quasi‐triennial oscillation (QTO) and compared with stratospheric low‐latitude zonal wind and equatorial eastern Pacific sea surface temperature (SST). The equatorial ozone had a strong QBO with a period of ∼30 months, and its maxima tallied with westerly wind maxima. At other latitudes the ozone maxima spacings were often different from 30 months, more so in the northern hemisphere. A spectral analysis showed that both hemispheres had one peak at ∼20 months and another peak at ∼30 months, only up to ∼50° latitude. At higher latitudes these peaks shifted to ∼23 and ∼36 months. For 0°–50° the ∼30‐month periodicity in the northern hemisphere showed abrupt phase changes, while the southern latitudes showed a roughly gradual phase shift. The northern hemisphere had an additional periodicity at ∼4 years, roughly matching the SST. Analysis of the same data without 12‐month averaging showed the above characteristics more clearly and revealed additional peaks at ∼0.7 years (8–9 months) and ∼1.30 years (16–17 months). All of these peaks showed shifts (mostly increases) at higher latitudes.

Transmission through an Aharonov-Bohm ring with two quantum dots

We study the phase behavior of the oscillating conductance for a modified Aharonov-Bohm (AB) ring threaded by a magnetic flux, with a quantum dot embedded in each arm, respectively (dot-1 for studying and dot-0 for reference). Using Keldysh's nonequilibrium-Green-function the expressions for the current j and the transmission probability T( ϵ) are derived. For the AB ring with one dot, we show that the phase behavior of the AB oscillating is in agreement with the observation qualitatively. In particular, we can obtain an abrupt phase drop by π near the centre of the two succesive resonance peaks, thus explain that the corresponding points of the succesive peaks are in phase. For the AB ring with two dots, we find that the symmetrical positions of a peak are in phase; no phase change happens as passing a single resonance peak but an abrupt phase change by π occurs around some-where between the peak and the valley. These phase characters can be explained in terms of the transmission probability.

Unsteady Flow in Oscillating Turbine Cascades: Part 1—Linear Cascade Experiment

An experimental and computational study has been carried out on a linear cascade of low-pressure turbine blades with the middle blade oscillating in a torsion mode. The main objectives of the present work were to enhance understanding of the behavior of bubble-type flow separation and to examine the predictive ability of a computational method. In addition, an attempt was made to address a general modeling issue: Was the linear assumption adequately valid for such kind of flow? In Part 1 of this paper, the experimental work is described. Unsteady pressure was measured along blade surfaces using off-board mounted pressure transducers at realistic reduced frequency conditions. A short separation bubble on the suction surface near the trailing edge and a long leading-edge separation bubble on the pressure surface were identified. It was found that in the regions of separation bubbles, unsteady pressure was largely influenced by the movement of reattachment point, featured by an abrupt phase shift and an amplitude trough in the first harmonic distribution. The short bubble on the suction surface seemed to follow closely a laminar bubble transition model in a quasi-steady manner, and had a localized effect. The leading-edge long bubble on the pressure surface, on the other hand, was featured by a large movement of the reattachment point, which affected the surface unsteady pressure distribution substantially. As far as the aerodynamic damping was concerned, there was a destabilizing effect in the separated flow region, which was, however, largely balanced by the stabilizing effect downstream of the reattachment point due to the abrupt phase change.

Application of phase screens to ray chaos

In wave propagation in complex media, phase changes along the propagation path are often approximated by a series of abrupt phase changes at discrete planes called ‘‘phase screens.’’ It is shown here how phase screens can be used in an analogous way in ray-tracing problems. The total travel time of each ray is formulated as a sum over phase screen and free space contributions. Fermat’s principle is then applied to the travel time, yielding a discrete mapping. The mapping connects the ray position at one phase screen to that at each succeeding screen. Examples of the method are given for both nonchaotic and chaotic ray tracing problems. The ray-tracing solution is compared to the wave solution calculated by the parabolic equation. By letting the separation between phase screens go to zero, the connection between continuous propagation and propagation with discrete transitions at phase screens is shown. [Work supported by the Penn State Univ. Applied Res. Lab.]