Absolute Phase Shift Research Articles

Cognitive Activity Shifts the Attractors of Bimanual Rhythmic Coordination

The attractors of bimanual rhythmic coordination are given as the solutions of a motion equation in relative phase. How are those attractors affected by cognitive activity? In 3 experiments, participants (N = 10 in Experiments 1 and 2; N = 5 in Experiment 3) were required to produce in-phase or antiphase coordination while they either did or did not perform an information-reduction task. The average absolute deviation from in-phase (0°) and antiphase (180°) satisfying a particular parameterization of the motion equation was amplified by cognitive activity. That amplification of absolute phase shift was the same for both in-phase and antiphase coordination. Furthermore, the amplification (in degrees) increased linearly with the magnitude of cognitive activity (in bits). Cognitive activity had limited influence on the variability of relative phase and did not affect its average signed deviation. Collectively, the results suggest that cognitive activity produces a shift in the attractors of bimanual coordination dynamics that is directionally nonspecific and is independent of movement speed, detuning, and the in-phase—antiphase distinction.

Spatiotemporal organization of simple-cell receptive fields in area 18 of cat’s cortex

Spatiotemporal structures of receptive-fields (RF) have been studied for simple cells in area 18 of eat by measuring the temporal transfer function (TTF) over different locations (subregions) within the RF. The temporal characteristics of different subregions differed from each other in the absolute phase shift (APS) to visual stimuli. Two types of relationships can be seen: (i)The APS varied continuously from one subregion to the next: (ii) A 180 degrees -phase jump was seen as the stimulus position changed somewhere within the receptive field. Spatiotemporal receptive field profiles have been determined by applying reverse Fourier analysis to responses in the frequency domain. For the continuous type, spatial and temporal characteristics cannot be dissociated (space time inseparable) and the spatiotemporal structure is oriented. On the contrary, the spatial and temporal characteristics for the jumping type can be dissociated (space-time separable) and the structure is not oriented in the space-time plane. Based on the APSs measured at different subregions, the optimal direction of motion and optimal spatial frequency of neurons can be predicted.

Measurements of the phase shift on reflection for low-order infrared Fabry–Perot interferometer dielectric stack mirrors

A simple technique based on a Fizeau interferometer to measure the absolute phase shift on reflection for a Fabry-Perot interferometer dielectric stack mirror is described. Excellent agreement between the measured and predicted phase shift on reflection was found. Also described are the salient features of low-order Fabry-Perot interferometers and the demonstration of a near ideal low-order (1-10) Fabry-Perot interferometer through minimizing the phase dispersion on reflection of the dielectric stack. This near ideal performance of a low-order Fabry-Perot interferometer should enable several applications such as compact spectral imagers for solid and gas detection. The large free spectral range of such systems combined with an active control system will also allow simple interactive tuning of wavelength agile laser sources such as CO(2) lasers, external cavity diode lasers, and optical parametric oscillators.

Generalized Levinson theorem: Applications to electron-atom scattering.

A recent formulation provides an absolute definition of the zero-energy phase shift \ensuremath{\delta} for multiparticle single-channel scattering of a particle by a neutral compound target in a given partial wave l. This formulation, along with the minimum principle for the scattering length, leads to a determination of \ensuremath{\delta} that represents a generalization of Levinson's theorem. In its original form that theorem is applicable only to potential scattering of a particle and relates \ensuremath{\delta}/\ensuremath{\pi} to the number of bound states of that l. The generalized Levinson theorem relates \ensuremath{\delta}/\ensuremath{\pi} for scattering in a state of given angular momentum to the number of composite bound states of that angular momentum plus a calculable number that, for a system described in the Hartree-Fock approximation, is the number of states of that angular momentum excluded by the Pauli principle. Thus, for example, for electron scattering by Na, with its (1s${)}^{2}$(2s${)}^{2}$(2p${)}^{6}$3s configuration and with one L=0 singlet composite bound state, \ensuremath{\delta} would be \ensuremath{\pi}+2\ensuremath{\pi} for s-wave singlet scattering, 0+3\ensuremath{\pi} for s-wave triplet scattering, and 0+\ensuremath{\pi} for both triplet and singlet p-wave scattering; the Pauli contribution has been listed first. The method is applicable to a number of ${\mathit{e}}^{\ifmmode\pm\else\textpm\fi{}}$-atom and nucleon-nucleus scattering processes, but only applications of the former type are described here. We obtain the absolute zero-energy phase shifts for ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$-H and ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$-He scattering and, in the Hartree-Fock approximation for the target, for atoms that include the noble gases, the alkali-metal atoms, and, as examples, B, C, N, O, and F, which have one, two, three, four, and five p electrons, respectively, outside of closed shells. In all cases, the applications provide results in agreement with expectations. \textcopyright{} 1996 The American Physical Society.

Signal averaging with a stabilized dual beam Mach Zehnder interferometer: Monitoring changes in gas density

A traditional Mach Zehnder interferometer has been fitted with a feedback loop that maintains a constant and known phase difference between the two optical beams. This stabilization is necessary so that signal averaging will not distort the signal. To increase sensitivity for small phase shifts and determine absolute phase shifts when large phase shifts are involved a dual beam technique, which uses circularly polarized monochromatic light, is implemented. In one arm of the interferometer a phase shift of 90° between the two polarization orientations is introduced via a quarter wave plate. Two photodiodes independently detect the polarized light beams that maintain a 90° phase difference. One of these signals provides the input for the stabilization while the other (with enhanced sensitivity) is used to monitor the density. Unambiguous phase shifts are calculated from the information contained in both signals. The interferometer is being used to monitor gas density changes resulting from vibrational to translational energy transfer.

Phaseshifts, total elastic cross sections and resonances in Ar-Ar scattering

The authors have performed systematic quantal calculations of Ar-Ar elastic scattering events using accurate pair potentials. Specifically, they have calculated a large number of partial wave phaseshifts, total cross sections and resonance energies over a range covering most of the glory region. The cross sections from two accurate potentials are compared over one glory oscillation and over a region including several shape resonances. The resonance energies obtained from these two potentials also are compared. The authors discuss the inappropriateness of using Levinson's theorem to define the absolute scale of the phaseshifts for realistic atomic potentials. As an alternative, the authors define an 'absolute phaseshift' that explicitly accounts for the difference in phase between the true wavefunction and its free particle counterpart.

Core-level x-ray photoemission: Deviations from threshold behavior.

We present a systematic numerical study of core-level x-ray photoemission intensity in metals, with emphasis upon studying the deviations from behavior asymptotically close to threshold. For a model with a contact potential and linear conduction-electron dispersion, we have evaluated the photoemission intensity for core-hole phase shifts \ensuremath{\delta}(0) between 0.05\ensuremath{\pi} and 0.5\ensuremath{\pi}. We find the following results. (i) The asymptotic regime extends out to 0.01 to 0.1 times the conduction bandwidth (D) from threshold. The range of the asymptotic regime decreases with increasing (absolute) phase shift. (ii) The linear relation between the integrated photoemission intensity and the asymptotic form holds for all phase shifts above \ensuremath{\sim}0.1D. Due to our normalization procedure we cannot say whether it holds below this value. (iii) Discrepancies exist between numerical estimates of the deviations from asymptotic behavior and approximate analytic estimates. (iv) A definition of the frequency-dependent threshold singularity exponent \ensuremath{\alpha}(\ensuremath{\omega}) in terms of a moment of the photoemission intensity is stable out to the conduction-band edge and may prove useful to experimentalists attempting to extract exponents from their data.

Differential reflectivity and differential phase shift: Applications in radar meteorology

The differential scattering properties of classes of hydrometeors at linear orthogonal polarizations provide potentially important differences which may be exploited for radar measurements of precipitation. The ratio of the reflectivity at horizontal (ZH) and vertical (Zv) polarizations may be combined with other radar measurements such as absolute reflectivity and differential phase shift to determine drop size distributions. Previous model calculations of differential reflectivity ZDR = 10 log (ZH/Zy) were made using Gans' theory of scattering by spheroids. New calculations, using Waterman's T‐matrix method, are in excellent agreement with Gans' theory for raindrops at S‐band wavelengths. The ZDR‐differential phase shift combination, which need not depend on any absolute measurements, is shown to be a reasonable radar method for measuring two‐parameter raindrop size distributions. Finally, calculations of ZDR for oblate hailstones indicate the possibility of uniquely detecting large, dry hail when the hail is falling with preferred orientation.

Use of Channeled Spectra to Measure Absolute Phase Shift and Dispersion in Two Beam Interferometry

An application of channeled spectra to two beam interferometry is described in which the optical path to be measured produces a shift of the channeled spectrum from a distribution that is preset in order to minimize the errors involved. This provides an absolute measurement of the phase and dispersion localized at the slit of the spectrometer with an improvement in accuracy over monochromatic or two wavelength interferometry. Examples include a time resolved channeled spectrum of the electron, ion, and neutral densities behind a strong shock wave in argon.

Travel time in the cochlea and its determination from cochlear-microphonic data.

A correlation between the behavior of the interscala cochlear-microphonic phase and the absolute phase shift between microphonic and sound at the eardrum is presented. It is shown that absolute phase can be interpreted with confidence over a limited frequency region for a given electrode location. Within this region the travel time in the cochlea, as manifested by microphonic measurements, is frequency independent.

DIPNET: A General Distributed Parameter Network Analysis Program

The DIPNETcomputer program makes practical the simple and rapid solution of elaborate microwave networks on a time-sharing computer. Given a file of input data describing a DIstributed Parameter NET-work of electrical sections, the program finds the complex voltage and current phasors along the network over a prescribed range of frequencies. Sections may consist of a variety of transmission lines, lumped constants, sources, and active devices. Network configurations may include chains, side stubs, and two-path sections. The network size is practically unlimited, and may easily comprise hundreds of sections. Output data at selected points along the network may include phasors, their absolute magnitude and phase shift, and power flow. Normalization to designated phasors is provided for by the program. The output data may also include input resistance, reactance, impedance, and the admittance counterparts. Repeated sequences may be handled automatically. Network parameters may also be modified automatically, both those which depend on frequency and frequency-independent parameters.

Absolute Transition Probabilities in Ultraviolet Molecular Spectra

The radiative lifetimes of seventeen excited states in H2, N2, N2+, CO, CO+, NO, NO+, BF, CF, BCl, and CO2+ have been measured by the phase-shift technique of Lawrence. The measured lifetimes were derived from transitions in the 960-4500-Å region and range from 0.6 nsec in H2 to 118 nsec in CO2+. Particular attention has been paid to the understanding and elimination of possible sources of systematic errors in the absolute phase shift measurements. The lifetimes have been combined with measured and calculated emission intensities to derive electric dipole transition moments and absorption oscillator strengths for the diatomic band systems.

Correlation of visco-elastic properties of large arteries with microscopic structure. V. Effects of sinusoidal forcings at low and at resonance frequencies.

Nine aortas from recently killed dogs were sectioned into 21 or more ring segments supported horizontally on two hooks in Ringer's solution. One hook oscillated sinusoidally from .01 to 21 Hz to stretch the segments 1.2% in excess of 4 or more mean strain levels from 5 to 100%. The segments were kept at 4 temperature levels (0°, 20°, 37°, 60°C). The other hook was coupled to a force transducer. At frequencies below 1 Hz, the force registered was sinusoidal with the same frequency as the stretch which it led, unless the specimen contained demonstrably contracted smooth muscle; then the stress was nonlinear and lagged behind the strain at frequencies below .05 Hz. As frequencies rose above 1 Hz, the force amplitude rose to a maximum, resonating at frequency ω r , which was higher at higher initial strains. Concurrently the phase shift increased to 90° at another frequency ω 90 . When ω 90 = ω r , viscous losses were negligible, a fact confirmed by other data in this and other studies and generally implicating collagen. When ω 90 > ω r , viscous losses were appreciable, in agreement with other measurements and implicating either muscle or elastin. These two wall components could be distinguished from each other by responses to drugs and to changes in temperature. Absolute dynamic modulus, storage modulus, loss modulus, phase shift, and loss angle measured from stress-strain loops compared favorably with similar measurements published for other visco-elastic materials and with viscous and elastic constants obtained from stress-relaxation experiments on aorta.

Direct Measurements of Predissociation Probabilities in CH and CD Molecules

Quantitative measurements of nonradiative decay rates in the $C^{2}\ensuremath{\Sigma}^{+}$ state of CH and CD molecules are presented via absolute phase shift versus frequency data and are interpreted as direct measures of predissociation probabilities. The $C$-state decay rates measured in CH are approximately three times larger than those in CD and comparison with absorption oscillator strength measurements shows that the predissociation probabilities of the rotational levels observed in CH range from approximately 3\ifmmode\times\else\texttimes\fi{}${10}^{7}$ to 1.6\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{sec}}^{\ensuremath{-}1}$, i.e., approximately 3 to 18 times the radiative transition probability.

Phase Shifts and the Quantum-Mechanical Hamilton—Jacobi Equation

A method of obtaining absolute phase shifts by integration of the quantum-mechanical Hamilton—Jacobi equation is developed and applied to the example of particles interacting through a Lennard-Jones potential. A new expression for the absolute phase shift is obtained in terms of an irregular solution of the Schrödinger equation.

Absolute Definition of Phase Shift in the Elastic Scattering of a Particle from Compound Systems

The projection of the target wave function on the total wave function of a scattered particle interacting with the target system is used to define an absolute phase shift including any multiples of π. With this definition of the absolute phase shift, one can prove rigorously in the limit of zero energy for s-wave electrons scattered from atomic hydrogen that the triplet phase shift must approach a nonzero multiple of π. One can further show that at least one π of this phase shift is not connected with the existence of a bound state of the H− ion.

Latest Wave in Physical Optics*

An increased interest in physical optics started about 1930. The paper gives a personal selection of some special topics. First, light rays are shown to be different from the paths of the energy. The diffraction patterns of lens errors cannot even approximately be found from the geometric patterns. The new concept of partial coherence is treated next. It has been made possible by introducing a less stringent definition of incoherence. Total reflection causes an absolute phase shift strongly dependent on the angle of incidence. This explains a ray displacement predicted from wrong premises by Goos and Hänchen. Even the old relative phase shift, as in the Fresnel rhomb, gives rise to a new effect, namely, a destructive interference between the two halves issuing from a roof prism. Phase differences which are otherwise unobservable become visible on a coherent background, which is obtained in a simple and accurate way by diffraction.