Recursion relations for the impedance of periodic layers

Previous numerical work is extended by deriving simple analytic expressions for the impedance of periodic layers over a wide frequency range within the reflection stop band (not just the center Bragg frequency) for an arbitrary number of periods in the structure, for arbitrary layer thicknesses (not just quarter-wave layers), for sizable absorption, and for arbitrary sizes of the refractive index differences. When the number of periods in the structure is infinite, exact expressions for impedance, which are valid for all frequencies in the reflection stop band, are derived. For a finite number of periods in the structure, it is shown that the asymptotic approach of the impedance toward its value for an infinite structure has a decaying exponential dependence. It is shown that the characteristic number of periods in this decaying exponential dependence is determined by the condition number of the transverse field matrix. Simple analytic expressions for the phase shift throughout the reflection stop band are derived, as well as simple analytic expressions to show that a small fractional error in the VCSEL cavity mode frequency can still result from a large fractional error in the cavity thickness if the layers in the Bragg mirror have a small refractive index difference. These simple analytic expressions are useful for design.     

On the best location of signal detectors

An event may occur anywhere in a planar area or on a linear region such as a route. One or more detectors are to be located within this region with the objective of maximizing the smallest probability of the detection of an event anywhere in the region. In other words, the minimum protection in the region is to be maximized. The probability that an event is detected by a detector is a decreasing function of the distance. For example, the probability may decrease with some power (say, 2) of distance, or this decrease could be approximately exponential with distance. Two solution procedures are proposed for the problem on a line segment: a mathematical programming model and a specially designed algorithm. The problem in an area is solved by a univariate search, a Demjanov-type algorithm, a mathematical programming model, and simulated annealing. Computational experience is reported.     

The finite element method for the mechanically based model of non‐local continuum

In this paper the finite element method (FEM) for the mechanically based non‐local elastic continuum model is proposed. In such a model each volume element of the domain is considered mutually interacting with the others, beside classical interactions involved by the Cauchy stress field, by means of central body forces that are monotonically decreasing with their inter‐distance and proportional to the product of the interacting volume elements. The constitutive relations of the long‐range interactions involve the product of the relative displacement of the centroids of volume elements by a proper, distance‐decaying function, which accounts for the decrement of the long‐range interactions as long as distance increases. In this study, the elastic problem involving long‐range central interactions for isotropic elastic continuum will be solved with the aid of the FEM. The accuracy of the solution obtained with the proposed FEM code is compared with other solutions obtained with Galerkins' approximation as well as with finite difference method. Moreover, a parametric study regarding the effect of the material length scale in the mechanically based model and in the Kr”oner–Eringen non‐local elasticity has been investigated for a plane elasticity problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Enhanced spectral resolution FFT for step-like signals

A method is presented for obtaining a sampled Fourier transform of a steplike signal with a spectral resolution greater than previously reported. The method is related to zero padding, which is used for enhancing the spectral resolution of an FFT of a limited duration signal. The new method involves final value padding when the extension function outside the observation window is a step, or it involves padding with a sampled exponential function when the extension function is a decaying exponential     

基于倏逝波衰减特性的空间频域滤波器研究

平面近场声全息方法在全息面大小有限时存在由于测量距离增大而造成全息面空间频域能量泄漏而引起的不适定性问题。本文利用不同空间频率的平面倏逝波的衰减只与倏逝波波长相关的特性，提出了一种基于倏逝波随测量距离变化可利用准则的新型空间滤波器，在不引起不适定性问题的同时最大限度的利用了有用的倏逝波信息。通过模拟比较利用不同范围的倏逝波信息的声场重建结果，论证了该滤波器的适用性和合理性。     

Deconvolution of kinetic decays and fitting of multiple exponential decay curves by the linear prediction method

A method based on linear prediction (LP) theory is employed in analyzing multiple exponential decay signals. A generalized LP method is also proposed to determine true system response in deconvolution problems when the convoluted signals have a decay time comparable to the duration of excitation pulse. These LP methods linearize the least-squares fit and require no prior knowledge of the exact number of the decaying exponents.     

Simultaneous monitoring of origin and scale of a shifted exponential process with unknown and estimated parameters

The distribution of consumer lifetimes, high-voltage of current in semiconductor transistors, and the risk associated with monitoring health care often come with a threshold. A two-parameter (or shifted) exponential distribution is, in general, regarded as a better statistical model in such situations compared with a traditional (one-parameter) exponential model. Research on inferential problems associated with two-parameter exponential distributions, including monitoring schemes for the parameters of this model, is active. Currently, all existing monitoring schemes for origin and scale parameters of a shifted exponential distribution assume that the process parameters are known (Case-K). The actual values of the process parameters are, however, rarely known in practice. The traditional method of estimating parameters from a set of a (Phase-I) reference sample and plug them in for Phase-II monitoring affects the performance of a monitoring scheme. Skewed processes, like the two-parameter exponential process, exacerbate this problem. The present article shows that even a reference sample of size 50,000 cannot guarantee nominal in-control performances of monitoring schemes when the actual process parameters are unknown (Case-U). To address this problem, we develop monitoring schemes based on max and distance statistics for simultaneously monitoring the two parameters of a shifted exponential process in Case-U. We show that the proposed schemes perform well. We illustrate the practical application of the proposed procedures by analyzing data about the production of an electronic component.     

远场水下爆炸作用下舰船设备冲击响应一体化动力学模型

提出了一种远场水下爆炸作用下舰船设备冲击响应一体化动力学模型。该模型将动态设计分析方法(DDAM)与Taylor平板理论相结合,使得对舰船设备冲击响应分析更为高效。将船体外壳看做平板,将船体各层甲板和设备看做附加在平板上的多个质量,将水下爆炸冲击波看做指数衰减波,形成了一维分析模型。能够根据水下爆炸当量、爆距、舰艇吨位、总尺度、结构和设备质量与支撑刚度等参数预测舰船与设备的冲击响应。预测结果与舰船缩比模型水下爆炸试验结果进行了对比。从总体上看,船体冲击响应谱的趋势和量级一致。     

Spatial statistics of natural-terrain imagery. I. Non-Gaussian IR backgrounds and long-range correlations

We report on an analysis of statistical correlations in midwave IR imagery acquired from an airborne sensor flying over dense forest and sparsely covered terrain. We test for wide-sense stationarity, compute ensemble histograms, and estimate the autocovariance functions with associated error bars. We find that the statistics are stationary but non-Gaussian. Contrary to previous studies, we do not find that the correlations are described by decaying exponential functions. In fact, we find evidence for long-range correlations in the imagery, with autocovariance functions described by a relatively simple formula with power-law falloff.     

Elastic half space with inhomogeneous coating under the action of tangential forces

We study a three-dimensional problem of the theory of elasticity for an inhomogeneous half space loaded by tangential forces distributed in a circular domain of its surface. The half space consists of a homogeneous base and a surface inhomogeneous layer whose Poisson’s ratio is constant and the dependence of Young’s modulus on the distance from the surface of the half space is described by an exponential function. We compare the solution of the problem of the theory of elasticity taking into account the continuous dependence of Young’s modulus on the coordinate with the solution of the problem in which the inhomogeneous layer is replaced by a stack of homogeneous layers.     

Some estimates on solutions of mixed problems for mixtures

Abstract

Our study is dedicated to a composite, which, in fact, is a mixture of two thermoelastic micropolar bodies. We formulate the mixed initial boundary value problem in this context and define the domain of influence for given data. For any solution of the mixed problem we associate a measure and prove a second-order differential inequality for it. Based on the maximum principle for the heat equation and on the second-order differential inequality, we establish an estimate which proves that the thermal and the mechanical effects, at large distance from the domain of influence, are dominated by an exponential decay.     

Studying bacterial metabolic states using Raman spectroscopy

Natural metabolic variability expected during characteristic growth phases in batch cultures of Escherichia coli and Staphylococcus epidermidis were studied by Raman spectroscopy. Spectral changes induced by metabolic changes found in the growth phases (i.e., lag, exponential, stationary, and decay) were identified. Maximum intensity of bands assigned to DNA and RNA bases are seen at the beginning of the exponential phase, when cells are metabolically active, and minimum intensities are seen when cells are decaying. High agreement in spectral variation due to growth phases was seen for all the trials that were performed, four growth cycles for E. coli and two for S. epidermidis. Batch cultures were monitored by standard plate counts to identify all growth phases, including decay. Spectral data were analyzed by principal component analysis (PCA) and discriminant analysis to identify similarities and differences and to estimate a classification performance based on growth phases. For the species evaluated, spectra during decay are grouped closer to each other and separated from lag, exponential, and stationary cells. These results suggest that Raman spectroscopy can be used to study metabolic states in bacteria and in particular cell viability.     

A Wide Range Time Constant Measuring Technique

A method is presented and analyzed that allows the implementation of a technique for the direct measurement of the time constant of single and/or multiple event exponentially decaying signals of the form: Y = K exp (-?t). The decaying exponential signal is fed into monolithic comparators which detect two preselected voltage levels of the signal. By means of TTL logic circuitry the output of the comparators are converted into a pulse. The duration of the pulse is directly proportional to the time constant of the signal and can thus be measured by different means. The technique described is capable of a dynamic range with a lower limit of 50 ns and a measured higher limit of several milliseconds, however, there is no theoretical upper limit with this method. The accuracy of the measurements remains within 1 percent, utilizing standard inexpensive components. Both lower limit and accuracy can be improved by the use of selected components. Inaccuracies of the measurements due to temperature variations from 0 to 80°C could not be detected by standard laboratory methods.     

Spectral properties of the nonspherically decaying radiation generated by a rotating superluminal source

The focusing of the radiation generated by a polarization current with a superluminally rotating distribution pattern is of a higher order in the plane of rotation than in other directions. Consequently, our previously published [J. Opt. Soc. Am. A24, 2443 (2007)] asymptotic approximation to the value of this field outside the equatorial plane breaks down as the line of sight approaches a direction normal to the rotation axis, i.e., is nonuniform with respect to the polar angle. Here we employ an alternative asymptotic expansion to show that, though having a rate of decay with frequency (mu) that is by a factor of order mu(2/3) slower, the equatorial radiation field has the same dependence on distance as the nonspherically decaying component of the generated field in other directions: It, too, diminishes as the inverse square root of the distance from its source. We also briefly discuss the relevance of these results to the giant pulses received from pulsars: The focused, nonspherically decaying pulses that arise from a superluminal polarization current in a highly magnetized plasma have a power-law spectrum (i.e., a flux density S infinity mu(alpha)) whose index (alpha) is given by one of the values -2/3, -2, -8/3, or -4.     

具常重特征拟线性非严格双曲组的经典解的奇性形成

我们考虑具常重特征的非严格拟线性双曲组的Cauchy问题,在初值具有较弱衰减假设下,得到Cauchy问题解的奇性形成。     

Axially symmetric contact problem of pressing of an absolutely rigid ball into an elastic half space with inhomogeneous coating

We consider an axially symmetric contact problem of pressing of an absolutely rigid ball into an inhomogeneous half space formed by a homogeneous base and an inhomogeneous surface layer. The Poisson’s ratio of the layer is constant and its Young modulus is an exponential function of the distance from the surface of the half space. The solution of the problem of the theory of elasticity with continuous dependence of the Young modulus on the coordinate is compared with the solution of the problem in which the inhomogeneous layer is replaced with a package of homogeneous layers.     

Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source

We consider the nonspherically decaying radiation field that is generated by a polarization current with a superluminally rotating distribution pattern in vacuum, a field that decays with the distance R(P) from its source as R(P)(-1/2), instead of R(P)(-1). It is shown (i) that the nonspherical decay of this emission remains in force at all distances from its source independently of the frequency of the radiation, (ii) that the part of the source that makes the main contribution toward the value of the nonspherically decaying field has a filamentary structure whose radial and azimuthal widths become narrower (as R(P)(-2) and R(P)(-3), respectively) the farther the observer is from the source, (iii) that the loci on which the waves emanating from this filament interfere constructively delineate a radiation subbeam that is nondiffracting in the polar direction, (iv) that the cross-sectional area of each nondiffracting subbeam increases as R(P), instead of R(P)(2), so that the requirements of conservation of energy are met by the nonspherically decaying radiation automatically, and (v) that the overall radiation beam within which the field decays nonspherically consists, in general, of the incoherent superposition of such coherent nondiffracting subbeams. These findings are related to the recent construction and use of superluminal sources in the laboratory and numerical models of the emission from them. We also briefly discuss the relevance of these results to the giant pulses received from pulsars.     

Thermocapillary deformation of a locally heated liquid film moving under the action of a gas flow

We propose a two-dimensional model of a steady laminar flow of a liquid film in a channel in the presence of a cocurrent gas flow. An analytical solution for the problem of temperature distribution is obtained for a linear flow velocity profile. The linearized problem of thermocapillary deformation of the film surface caused by local heating at a constant heat flux is solved. It is established that a thermocapillary bump is formed in the region where a thermal boundary layer emerges on the film surface. Additional perturbations, decaying in the upstream direction, can be present on the free surface in front of the bump. A criterion determining this effect is found.     

Some features of the hydrodynamic characteristics of a high-voltage electric discharge in a liquid with a two-pulse power deposition law

An analysis is made of the external hydrodynamic problem of an underwater electric discharge with a two-pulse power deposition law in the channel. As a result of an analytic solution of the problem, it is shown that the pressure function at the channel wall is a series of pulses of decaying amplitude, while the pressure function for a fixed point in the wave field is a series of increasing pulses. Pis’ma Zh. Tekh. Fiz. 23, 58–61 (May 12, 1997)