Gaussian Amplitude Distribution Research Articles

Diffractive Focusing of a Gaussian Beam

The problem of diffraction of a spherical wave with Gaussian amplitude distribution on two infinitesimally thin and ideally reflecting screens with apertures on an optical axis is solved within the framework of the quasi-optical approximation. It is shown theoretically and experimentally that when a Gaussian beam illuminates such a type of bicomponent diffraction system with small Fresnel numbers in a near zone of the second screen, the effect of diffractive multifocal focusing of radiation is observed. In this case, the diffraction picture from the second screen in the focal planes represents the circular nonlocal bands of the Fresnel zones with a bright narrow peak at the center, whose intensity can exceed by six times the value of the incident wave intensity. The energy efficiency of diffractive focusing of Gaussian beams by the bicomponent diffraction system can be as high as 70%. The diffractive method proposed allows the focusing of wide-aperture beams without using classical refraction elements such as lenses and prisms, and it is applicable to both low-intensity and high-power radiation.

Multiple-pattern linear antenna arrays with singleprefixed amplitude distributions: modifiedWoodward-Lawson synthesis

The authors describe the design of linear antenna arrays that generate multiple radiation patterns by switching between different excitation phase distributions while maintaining a constant pre-established amplitude distribution. Examples are given of antennas with uniform or Gaussian amplitude distributions that, depending on their phase distribution, generate a sum pattern, a flat-topped beam or a cosec-squared pattern.

Diffraction of atoms by a standing wave at Gaussian initial momentum distribution of amplitudes

The role of the initial-state preparation in the coherent diffraction of atoms in the field of a standing wave is considered. It is shown that the time evolution of the atomic wave packet with a Gaussian initial momentum distribution of amplitudes, due to the constructive quantum-mechanical interference, occurs practically without transformation of the initial Gaussian form. Depending on the phases of the initial momentum distribution components, the increment of the atomic momentum can vary from a maximum possible value (determined by the limiting speed of stimulated photon re-emission) to zero. Consequently, the standing wave presents an effective mirror for Gaussian atoms, the reflection angle being controllable.

Electronic noise in magnetic tunnel junctions

We have studied bias and magnetic field dependence of voltage noise in metallic magnetic tunnel junctions with areal dimensions on the order of 1 μm. We generally observe noise with Gaussian amplitude distribution and pure 1/f power spectra at low frequencies. The 1/f noise scales with bias voltage as V2. Two kinds of deviations from this low frequency behavior have been observed. One is at fixed magnetic field when the junction bias reaches above a critical value, the other occurs at a fixed bias when the external magnetic field brings the sample to certain magnetic configurations. In both cases the noise spectra become dominated by Lorentzian noise and in both cases we have observed two level fluctuators in the time domain. We attribute the bias dependent noise to charge traps in the tunnel barrier. The field dependent noise is associated with the switching of the magnetization direction of portions of the top electrode, which we believe to be reversible.

Simulation of self-focusing by an array on a crack in an immersed specimen

An ultrasonic measurement model is developed to simulate self-focusing by a curved array of transducers on an interior crack. The far field radiated by each transducer element is modeled by rays with a Gaussian distribution of amplitudes over the beam width. The ray tracing method is used to determine the focused wave field in the immersed specimen and the travel times from each array element to the crack. The self-focusing array is modeled for both sonification and reception focusing. The transducers in the array are excited with the appropriate time delays to achieve sonification focusing. After the incident wave field on the crack has been obtained, the crack opening volume is calculated. For a pair of transducers, a reciprocal identity for two media in contact is used to determine the amplitudes of signals scattered back from the crack. The field transmitted and received by the entire array is obtained by superposition. Reception focusing is used to adjust the differences in signal arrival times for in-phase signal summation. Considerable signal amplification can be achieved by the self-focusing procedure, as has been shown by comparison of scattered fields.

Noise and modulated photocurrents in amorphous semiconductors

A theory describing the current noise power spectral density SI(f) due to trapping processes in bulk amorphous semiconductors is presented. The analysis is based on an exact R–C equivalent circuit model developed previously to describe small signal-modulated photoconductivity (MPC). It is shown that `shot' noise-like fluctuations in trapping and release rates give rise to a net noise current spectral density equivalent to the sum of the `thermal' noise components associated with each `resistor', and further that the frequency dependence of SI(f) is identical to that of the real part of the modulated photocurrent response. Noise and MPC data obtained experimentally from the same undoped a-Si:H sample are presented, and support the theory in cases where the noise exhibits a Gaussian amplitude distribution. A brief description of observed nonstationary noise `bursts' is presented.

Choosing the amplitude interval for a proportional counter at a low signal level

A procedure is described for choosing the optimum pulse amplitude interval for a proportional counter when the useful signal level is comparable with the natural background level. It is shown that the optimum interval for counter pulses having a Gaussian amplitude distribution function corresponds to 1.4σ. The application of the procedure is demonstrated in a test example with processing of the iron K α x-ray spectrum.

Current-phase relation of high-T/sub c/ bicrystal and step-edge Josephson junctions

The real and imaginary part of the rf impedance of a phase-biased weak link based on YBa/sub 2/Cu/sub 3/O/sub 7-x/ thin films were investigated experimentally at 77 K. The investigated weak links were step-edge or bicrystal Josephson junctions incorporated into a washer type superconducting ring with a small inductance L=80...300 pH. The ring was inductively coupled to a tank circuit with a resonant frequency of about 23 MHz. The phase shift /spl alpha/ between the rf voltage and rf current through the tank circuit was found to be a convenient measure of the change of inductance of a weak link. From the dependence of /spl alpha/ on the magnetic flux in the ring one can deduce the current-phase relation I(/spl phi/)=I/sub c/ f(/spl phi/) of the weak link. The influence of thermal noise on f(/spl phi/) was estimated numerically using a Gaussian distribution of the noise amplitude. The experimentally observed dependence /spl alpha/(/spl phi/) for the bicrystal weak link can be sufficiently good described with f(/spl phi/)=sin (/spl phi/) and with a reasonable value of the noise amplitude. The step-edge junction shows remarkable deviation from the sinusoidal current-phase relation.

EMG activity in neck and back muscles during selected static postures in adult males and females

Surface electromyographic (EMG) amplitudes were gathered from 100 men and 100 women while maintaining the end range of nine motor tasks. Ratios of EMG amplitudes were used to characterise the activation patterns of 14 muscle groups of the back and trunk during 10 motor tasks. Procedures to identify electrode placement sites were developed to ensure reliability of all EMG recordings. Subcutaneous fat was estimated at each muscle site and a correction factor was used to account for signal attenuation due to the impedance attributable to adipose tissue thickness. Logarithmic transformations were performed to obtain a Gaussian distribution of the EMG amplitudes and muscle ratios. The transformed EMG amplitudes and transformed ratios were highly reliable between sessions across nine active motor tasks (Pearson's r and intra-class correlations ranged from 0.74 to 0.96). Significant gender differences were observed in the transformed EMG amplitudes and ratios of amplitudes in selected muscles and muscle pairs. It appears that the transformed EMG ratios represent a reliable means of assessing muscle recruitment patterns in a series of well-defined motor tasks in a large population of presumably normal adult male and female subjects. The acquisition of this large database under well-controlled conditions using defined criteria for each motor task provides a template to which individuals with injuries involving the neck and trunk musculature can be compared.

Relationship between temporal coherence and laser parameters in a two-longitudinal-mode HeNe laser

The relationship between the temporal coherenceg(1) (τ) and laser parameters - the output relative intensity (I1/I2) and the frequency widthδϕh of the longitudinal mode in a two-longitudinal-mode HeNe laser - is studied experimentally. The experimental results show that both the relative output intensity and the frequency width of the longitudinal mode have a great influence on the temporal coherenceg(1) (τ). Moreover, the spectral line-shape function of each longitudinal mode in a two-longitudinal mode HeNe laser is a Lorentzian function, with a frequency width of about 18.2 MHz. A model of the power spectrum with Gaussian amplitude distribution and equal frequency width of the longitudinal mode in a multi-longitudinal-mode gas laser is employed in the theoretical analysis. Good agreement between theory and experiment is obtained.

High-Frequency Tuning Properties of Bullfrog Lagenar Vestibular Afferent Fibers

A common property of vertebrate acoustic sensors, including otoconial acoustic sensors in lower vertebrates, is steep slopes on the high- and low-frequency band edges of the amplitude tuning curves. Bullfrog otoconial acoustic fibers are responsive to sound and exquisitely responsive to substrate vibrations in the frequency range from 20 Hz to 300 Hz. The sum of the absolute values of the two band-edge slopes of the amplitude tuning curve of such a fiber typically ranges from 100 dB/decade to 160 dB/decade (sometimes as high as 220 dB/decade), implying typical dynamic order of at least five to eight. We wondered if such steep slopes and the high dynamic order implied by them reflect special adaptations in acoustic sensors or if they are inherent in all lower-vertebrate otoconial sensors excited in this frequency range. To address this question, we examined the amplitude tuning characteristics of afferent nerve fibers from a bullfrog otoconial vestibular sensor in the same frequency range. In this paper, we report observations of tuning for bullfrog lagenar vestibular fibers in the frequency range from 10 Hz to approximately 500 Hz. To make these observations, we stimulated the frog with random dorsoventral motion that exhibited Gaussian amplitude distribution and that was flat in velocity from 10 Hz to 1.0 kHz. For each afferent fiber studied, we used discrete cross-correlation (between stimulus waveform and axon spike train) and discrete Fourier transformation to compute an amplitude tuning curve. In contrast with the amplitude tuning curve. In contrast with the amplitude tuning curves from saccular and lagenar acoustic fibers, those from the lagenar vestibular fibers typically had band-edge slopes whose absolute values summed to approximately 20 dB/decade, implying typical dynamic order of one. We conclude that steep band-edge slopes and high dynamic order are indeed special features of acoustic sensors, not shared by vestibular sensors.

Reflection and transmission of the unequal mirrors interference wedge

Some interesting features of the interference wedge of thickness 5–200 μm are found which characterize its reflection and transmission when it is constructed of unequal-reflectivity mirrors. The analysis of the wedge's behaviour is made using equations derived by us for restricted laser beam illumination on the assumption of truncated Gaussian amplitude distribution and uniform phase distribution. It is shown that at resonant wavelengths the unequal-reflectivity mirrors interference wedge has a property of optical asymmetry in reflection for both contraincidences and that the earlier-reported phenomenon of spectrally controlled resurgence of light outside the nonresonantly reflected beam increases drastically to reach at resonance 60–70% of the reflected power. We ascertained that the wedge spectral selectivity is a function of the product of the reflectivities of its mirrors. Keeping one of them fixed and increasing the other, a higher wedge transmission may be obtained, but for a constant value of their product a maximum in transmission is achieved at equal reflectivities. Some of the dependences obtained have been checked experimentally.

Influence of surface roughness on the wetting angle

A this paper the influence of surface roughness on contact angles in the system of liquid Al wetting solid surfaces of Al2O3 has been studied. It was observed that contact angles of liquid Al vary significantly on different rough surfaces of Al2O3. A model is proposed to correlate contact angles with conventional roughness measurements and wavelengths by assuming a cosine profile of rough grooves with a Gaussian distribution of amplitudes. In comparison with the experimental results, the model provides a good estimate for describing the influence of surface roughness on contact angles of liquid Al on Al2O3.

Acoustic streaming induced in focused Gaussian beams

Axisymmetric flow equations for a viscous incompressible fluid are transformed into the vorticity transport and Poisson’s equations. They are numerically solved via a finite difference method imposing appropriate initial and boundary conditions. A model source of 1-cm radius and 5-cm focal length with Gaussian amplitude distribution radiates 5-MHz ultrasound beams in water. Numerical examples are shown for buildup of acoustic streaming along and across the acoustic axis. Evidently, hydrodynamic nonlinearity has an essential effect on the streaming generation in comparison with a linear flow case; the nonlinearity reduces the streaming velocity in the focal and prefocal region, whereas it tends to accelerate the flow in the postfocal region.

Conditional analysis of floating potential fluctuations at the edge of the Texas Experimental Tokamak Upgrade (TEXT-U)

Fluctuations in floating potential in the scrape-off layer and plasma edge were analyzed using a conditional statistical analysis technique. The floating potential fluctuations had a nearly Gaussian probability density function with the largest deviation from a Gaussian at the shear layer. The conditional averaging technique followed the statistical evolution of selected conditions in the floating potential signal. The decay rate of a conditional feature in time or space showed a small systematic variation with the amplitude of condition chosen. Either long-lived coherent structures are not present in statistically significant numbers, or the fluctuations are dominated by a large number of coherent structures with a nearly Gaussian distribution of fluctuation amplitudes, or conditional analysis using the amplitude of the floating potential as a condition is not a sensitive technique for identifying coherent structures.

Arithmetic coding in lossless waveform compression

A method for applying arithmetic coding to lossless waveform compression is discussed. Arithmetic coding has been used widely in lossless text compression and is known to produce compression ratios that are nearly optimal when the symbol table consists of an ordinary alphabet. In lossless compression of digitized waveform data, however, if each possible sample value is viewed as a "symbol" the symbol table would be typically very large and impractical. the authors therefore define a symbol to be a certain range of possible waveform values, rather than a single value, and develop a coding scheme on this basis. The coding scheme consists of two compression stages. The first stage is lossless linear prediction, which removes coherent components from a digitized waveform and produces a residue sequence that is assumed to have a white spectrum and a Gaussian amplitude distribution. The prediction is lossless in the sense that the original digitized waveform can be recovered by processing the residue sequence. The second stage, which is the subject of the present paper, is arithmetic coding used as just described. A formula for selecting ranges of waveform values is provided. Experiments with seismic and speech waveforms that produce near-optimal results are included.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The low-frequency scattering action of fish schools

Enhanced low-frequency scattering levels from a single fish at its swimbladder resonance and a frequency invariant return for an octave or so above have been predicted by simple monopole scattering models [Love (1977)]. These characteristics have also been measured, more or less, with fish schools [McCartney (1967)]. In this talk the ‘‘more or less’’ is explored by modeling the school as a number of monopole scatterers quasi-randomly distributed within an ellipsoidal volume, with and without mutual scattering taken into account. The swimbladder natural frequencies themselves are also taken to be random with a uniform PDF over a finite band. For a given realization, overall returns are computed in both the frequency and time domains. Computed fluctuations in aspect are compared with those for a Gaussian amplitude distribution. The influence of mutual scattering is shown as a function of the mean free path among individual fish. Finally, it is noted that though swimbladder gas volume and bulk modulus indicate a P5/6 hydrostatic pressure dependence, swimbladder natural frequencies typically vary as P1/2 [Weston (1967)]. [Work sponsored by Naval Undersea Warfare Center, New London Detachment.]

Statistical properties of highly excited quantum eigenstates of a strongly chaotic system

Statistical properties of highly excited quantal eigenstates are studied for the free motion (geodesic flow) on a compact surface of constant negative curvature (hyperbolic octagon) which represents a strongly chaotic system (K-system). The eigenstates are expanded in a circular-wave basis, and it turns out that the expansion coefficients behave as Gaussian pseudo-random numbers. It is shown that this property leads to a Gaussian amplitude distribution P(Ψ) in the semiclassical limit, i.e. the wave-functions behave as Gaussian random functions. This behaviour, which should hold for chaotic systems in general, is nicely confirmed for eigenstates lying 10 000 states above the ground state thus probing the semiclassical limit. In addition, the autocorrelation function and the path-correlation function are calculated and compared with a crude semiclassical Bessel-function approximation. Agreement with the semiclassical prediction is only found, if a local averaging is performed over roughly 1000 de Broglie wavelengths. On smaller scales, the eigenstates show much more structure than predicted by the first semiclassical approximation.

Energy-crossing number relations for braided magnetic fields.

This Letter derives lower bounds on the energy of braided magnetic fields, based on crossing number techniques pioneered by freedman and He. Mean crossing numbers are defined for magnetic fields inside a cylinder, for configurations with a uniform axial component the square of the crossing number provides a lower bound for the free magnetic energy. An energy-crossing number relation is also derived for a random field with Gaussian amplitude distribution, in the limit of small correlation lengths. These results provide information on the structure of solar coronal loops and on the problem of coronal heating

On-line estimation of myoelectric signal spectral parameters and nonstationarities detection.

In this communication, we present a method for detecting nonstationarities of random time series with an approximately Gaussian distribution of amplitudes. This method is suitable for real time implementation. Here we report some results obtained by applying them to a time series of spectral parameters of surface myoelectric signals, collected during voluntary isometric contractions of human muscles. Moreover, we describe the computerized system that we used to implement our detector of nonstationarity. This system is based on the TMS 320C25 DSP chip and realizes on-line estimation and display of spectral parameters, as well as detection of their nonstationarities, featuring a sampling frequency up to 20 k samples/s. A friendly user interface, fully menu driven, allows the user to select different options during the system's operation by means of hot keys. The accuracy of the system was tested by comparing its estimates with those of an off-line system, previously characterized, which we took as a reference. The estimates of spectral parameters obtained by means of the two systems were always consistent. The on-line stationarity detector was able to recognize rates of variation of the spectral parameters as small as 1%/s during contractions lasting 10-15 s. This sensitivity makes it suitable for clinical application. The set of results herein presented has been selected to highlight the main characteristics of the system.