Analytic analysis of irregular discrete universes

In this work we investigate the dynamics of cosmological models with spherical topology containing up to 600 Schwarzschild black holes arranged in an irregular manner. We solve the field equations by tessellating the 3-sphere into eight identical cells, each having a single edge which is shared by all cells. The shared edge is enforced to be locally rotationally symmetric, thereby allowing for solving the dynamics to high accuracy along this edge. Each cell will then carry an identical (up to parity) configuration which can however have an arbitrarily random distribution. The dynamics of such models is compared to that of previous works on regularly distributed black holes as well as with the standard isotropic dust models of the FLRW type. The irregular models are shown to have richer dynamics than that of the regular models. The randomization of the distribution of the black holes is done both without bias and also with a certain clustering bias. The geometry of the initial configuration of our models is shown to be qualitatively different from the regular case in the way it approaches the isotropic model.     

Auditory profile analysis of irregular sound spectra

The discrimination of changes in the shapes of sound spectra is reported. The change was always an intensity increment to the 948-Hz component of a multitone complex. First, the ability of naive listeners to learn to discriminate a change in a "regular" background or reference spectrum (equal-level tones equally spaced in logarithmic frequency) was measured as a function of the number of trials. On the average, threshold improved about 10 dB over 3000 trials, with about 50% of the decrease in threshold occurring during the first 750 trials. In a subsequent series of experiments, the overall pattern of spectral shape of the background was varied randomly. Two kinds of perturbations in spectral shape were employed: Randomly choosing the frequencies of the reference spectra and randomly choosing the amplitudes of the components of the reference spectra. The experimental manipulations involved fixing the random spectra across a block of trials, varying the reference spectra from interval to interval of each trial, and providing extensive practice in discriminating specific randomly perturbed reference spectra. The results of the spectrum-learning and random perturbation experiments provide insight into the roles of critical band filtering, sensory variability, and short-term and long-term memory representations in auditory profile analysis. Further, the appropriateness of the generalization of a simple energy detection model is discussed.     

Directionality of dog vocalizations

The directionality patterns of sound emission in domestic dogs were measured in an anechoic environment using a microphone array. Mainly long-distance signals from four dogs were investigated. The radiation pattern of the signals differed clearly from an omnidirectional one with average differences in sound-pressure level between the frontal and rear position of 3-7 dB depending from the individual. Frequency dependence of directionality was shown for the range from 250 to 3200 Hz. The results indicate that when studying acoustic communication in mammals, more attention should be paid to the directionality pattern of sound emission.     

Acoustic detection of manatee vocalizations

The West Indian manatee (trichechus manatus latirostris) has become endangered partly because of a growing number of collisions with boats. A system to warn boaters of the presence of manatees, that can signal to boaters that manatees are present in the immediate vicinity, could potentially reduce these boat collisions. In order to identify the presence of manatees, acoustic methods are employed. Within this paper, three different detection algorithms are used to detect the calls of the West Indian manatee. The detection systems are tested in the laboratory using simulated manatee vocalizations from an audio compact disk. The detection method that provides the best overall performance is able to correctly identify approximately 96% of the manatee vocalizations. However, the system also results in a false alarm rate of approximately 16%. The results of this work may ultimately lead to the development of a manatee warning system that can warn boaters of the presence of manatees.     

A corrected model of level-by-level analysis of three-layer irregular conical shells

An approach for level-by-level analysis is considered, and models for corrected investigation of stress-strain states in layers of generally irregular three-layer conical shells are developed on its basis. The models make it possible to take into account the features of a layer-inhomogeneous structure, the moment state of carrying layers, and the three-dimensional stressed state in the filler layer.     

Nonlinear analysis of a multi-cavity gyro-twystron

To preserve high gain, high efficiency and high power merits of gyroklystron, a gyro-twystron is designed using an electron beam with α(v_⊥/v_z) greater than unity. With a multi-cavity section of high gain, the length of the waveguide output section can be made shorter than the threshold length of the absolute instability without losing total system gain. Numerical simulations are carried out to analyze a ka-band gyro- twystron consisting of three TE₁₁₁ mode cavities and an output section of a TE₁₁ mode waveguide. Stability study is performed to ensure the tube without self-excited oscillations. With α=1.5, the 3-dB linear and saturated gain bandwidth in excess of 2 % can be obtained by stagger tuning for an 80 kV, 3 A electron beam with 5 % axial velocity spread. The maximum saturated gain is more than 55 dB at 33 % efficiency. By tapering the magnetic field of the last 2 cm of the interaction region, the efficiency can be increased to 43 % without degrading the bandwidth, which corresponds to an output power of 103 kW.     

Nonlinear time series analysis of electrocardiograms

In recent years there has been an increasing number of papers in the literature, applying the methods and techniques of Nonlinear Dynamics to the time series of electrical activity in normal electrocardiograms (ECGs) of various human subjects. Most of these studies are based primarily on correlation dimension estimates, and conclude that the dynamics of the ECG signal is deterministic and occurs on a chaotic attractor, whose dimension can distinguish between healthy and severely malfunctioning cases. In this paper, we first demonstrate that correlation dimension calculations must be used with care, as they do not always yield reliable estimates of the attractor's "dimension." We then carry out a number of additional tests (time differencing, smoothing, principal component analysis, surrogate data analysis, etc.) on the ECGs of three "normal" subjects and three "heavy smokers" at rest and after mild exercising, whose cardiac rhythms look very similar. Our main conclusion is that no major dynamical differences are evident in these signals. A preliminary estimate of three to four basic variables governing the dynamics (based on correlation dimension calculations) is updated to five to six, when temporal correlations between points are removed. Finally, in almost all cases, the transition between resting and mild exercising seems to imply a small increase in the complexity of cardiac dynamics. (c) 1995 American Institute of Physics.     

非规则封闭空间声场建模的Chebyshev-变分法及其固有声学特性分析

针对非规则封闭空间声场建模问题,提出了一种基于Chebyshev-变分原理的声场建模方法。该方法首先选取包络非规则声场的矩形空间并将此矩形空间内的声压函数展开成三重Chebyshev级数形式,然后通过坐标变换得到定义域空间中的声场势能和声场动能,最后按照里茨方法对声场的拉格朗日泛函进行求解,得到声场的特征方程并求得声场固有频率和模态。通过与曲面声场的数值结果对比,验证了本建模方法的正确性和有效性。在此基础上研究具有不同倾角的梯形声场固有特性,分析内部凹槽深度对\     

Modeling and acoustic analysis of irregular sound enclosure by using Chebyshev-variational method

A modeling method for irregular sound enclosures was proposed based on the Chebyshev-variational theory. A rectangular space was first assumed to bound the irregular sound space and the sound pressure in the rectangular space expressed as a triple-Chebyshev series. Next, a coordinate transformation was performed and the Lagrangian functional of the irregular sound space obtained. Finally, the Lagrangian functional was solved under the Ritz method framework, and the enclosure's acoustic characteristic equation deduced and the eigenpairs obtained. The accuracy of the present method was validated according to agreement between the present results and finite element results for an enclosure with a curved surface.Furthermore, the acoustic characteristics of a trapezoidal enclosure and an enclosure with an inner groove were investigated. The results showed that the mode shapes of the trapezoidal sound space changed with increased inclination angle and the natural frequencies, except the first order, of the sound space with a rectangular inner groove decreased with increased groove depth.     

Evaluation of effects of irregular shape on quantitative XRF analysis of metal objects

Quantitative XRF analysis of metal alloys can be obtained by using the general fundamental parameter method based on the comparison of x‐ray line fluorescence intensities with those obtained from reference standard pellets in identical experimental conditions. Corrections for auto absorption and secondary excitation effects are fundamental to obtaining quantitative results. When analyzing a real object with irregular, or at least nonpellet‐shaped, geometry and/or of incorrect positioning, an additional correction factor for x‐ray fluorescence line intensities must be entered. In this paper we review the problem of the contributions to the error specific to an irregular surface or incorrect positioning intrinsic to the fundamental parameter method, in the more enlarged context of considering a real experimental setup in which irradiation and detection angles are not exactly constant, as assumed in the fundamental parameter method. They are accounted for by the corrective irregular shape factors. In principle, these factors must be separately calculated for each value of excitation and characteristic x‐ray energies, and the relative precision in the quantitative determination of elemental concentrations with the fundamental parameter method can be estimated from the relative amplitude of the variation of shape factor values depending on the exciting energy spectrum. One obtains the result that the correction due to irregular shape or incorrect positioning of the object under examination tends to the limit 1, or, more generally, to a constant value independent of the excitation and emission x‐ray energies in the limiting case where the direction of the exciting radiation coincides with that of the detected fluorescence x‐rays. The results of calculations of the relative precision of XRF quantitative analysis are shown for gold‐based alloy objects in some specific cases of surface roughness and positioning of the object. Dispersion around the nominal values for the angles of incoming and outgoing x‐ray directions is assumed as determined by the geometric conditions in two selected instrumental setups. A nominal value of 45° was assumed for both the angles in the first case. In the second case, we considered an irradiation setup where the condition of coincidence for incoming and outgoing x‐ray directions is nearly achieved by employing an annular silicon drift detector (SDD) with a central hole, which allows the passage of the exciting x‐rays. An interesting result obtained in the latter case is that, looking only at the dependence on the irregular shape, an attainable precision on the order of <1‰ can be achieved. In view of the possible applications of quantitative XRF analysis to jewellery, employing SDD detectors capable of very high counting rates should allow a statistical error under the above‐mentioned limit in a reasonably short measuring time. However, concerning the error deriving from intrinsic x‐ray tube instability, an investigation aimed at achieving a stable enough system is still needed. Copyright © 2006 John Wiley & Sons, Ltd.     

Nonlinear Fourier analysis of localized wave fields

Summary The Fourier transform (FT) has long served as an indispensable means for analysing wave motion described by linear evlution equations. The methods are well known and include not only mathematical analysis but also the analysis of data as well. In recent years new spectral methods have been developed for analysing nonlinear evolution equations. Such methods are generalizations of the FT to specific nonlinear wave systems and are referred to as the spectral or scattering transform (ST). Herein we use numerical procedures for applying the ST directly to the analysis of localized data described by the Kortewegde Vries (KdV) equation on the infinite interval,i.e. the Cauchy problem in shallow water. In this context we emphasize the importance of the direct spectral transform (DST) as a wave number domain representation of nonlinear data. The numerical methods discussed for the KdV equation should be extendible to the large class of systems considered by Ablowitzet al., Calogero and Degasperis. We give examples of the spectral analysis of nonlinear, computer-generated data.

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Riassunto La ben nota trasformata di Fourier (FT) è di uso commune per analizzare moti ondosi descritti da equazioni di evoluzione lineari. Negli ultimi anni sono stati sviluppati nouvi metodi (detti trasformate spettrali o di scattering, ST) per l'analisi di equazioni di evoluzione non lineari basati sulla generalizzazione della FT agli specifici sistemi ondosi non lineari. Qui usiamo procedimenti numerici per applicare la ST direttamente all'analisi di dati localizzati descritti dall'equazione di Korteweg-deVries nell'intervallo infinito, cioè al problema di Cauchy in acqua bassa. In questo contesto sottolineiamo l'importanza della trasformata specttrale diretta come rappresentazione nel campo dei numeri d'onda di dati non lineari. I metodi numerici discussi, che a titolo di esempio sono qui applicati all'analisi spettrale di dati non lineari generati dal calcolatore, hanno l'interessante possibilità di essere estendibili ai problemi piú generali di propagazione ondosa.

     

Nonlinear analysis of high-harmonic slotted gyro-TWT amplifier

A nonlinear self-consistent simulation code is employed to investigate the behavior of the slotted gyrotron traveling-wave amplifier (gyro-TWT), in which an axis-encircling electron beam synchronously interacts with a high-order azimuthal mode in a magnetron-type waveguide. The efficiency of a fourth-harmonic device with an ideal 60 kV, 5 A beam is shown to reach 30% for α≡ν_⊥/ν_z=2. The growth rate for the π mode is roughly 25% larger than for the 2π mode. The efficiency increases for lower voltage and the device is found to be moderately sensitive to the radial spread of the beam's guiding center position and extremely sensitive to the axial velocity spread. For an ideal 60 kV, 5 A beam with α=1.5, the efficiency of a second-harmonic gyro-TWT is 42% and falls to 10% for an eighth-harmonic device. The design of a 35 GHz, 60 kV, 5A, α=1.5, eight-vane, fourth-harmonic gyro-TWT with 7% axial velocity spread is presented. It is predicted that this design will yield a peak output power of 90 kW, a peak efficiency of 30%, and 6.3% saturated bandwidth     

马赫曾德尔单频干涉仪非线性误差分析

 研究了马赫曾德尔单频干涉仪对可调谐激光器进行频率监测时非理想1/4波片和偏振分光镜引入的非线性误差。借助琼斯矩阵对干涉仪建模,理论推导了系统误差公式。理论分析和数值仿真发现：系统的非线性误差为一次谐波误差和二次谐波误差的线性叠加;系统中2个偏振分光镜倾斜角度的非对称主要导致一次谐波误差;波片倾斜角度误差、偏振分光镜倾斜角度误差以及波片相位延迟误差主要导致二次谐波误差,总二次谐波误差近似表现为此3类误差源独立产生的误差的线性叠加;当偏振分光镜消偏比较大时,其产生的误差可忽略。     

Nonlinear analysis of the gradient drift instability

An analytical study of the gradient drift instability in the equatorial electrojet of wavelengths in the order of one kilometer is presented. Different mechanisms, linear, non-local and turbulent, are found in the literature to explain the predominance of the 1 km wavelength in the electrojet. In the present work a simplified model is proposed in which the nonlinear evolution of three coupled modes is followed. By considering that one of the modes attains the stationary state, the evolution of the other two is obtained, and it is found that they follow equations of the Lotka–Volterra type. A stable stationary nonlinear solution for these equations is also found, and the conditions under which periodic solutions are possible are analyzed.