Modified Szabo's wave equation models for lossy media obeying frequency power law

Szabo's models of acoustic attenuation [Szabo, J. Acoust. Soc. Am. 96(1), 491-500 (1994)] comply well with the empirical frequency power law involving noninteger and odd-integer exponent coefficients while guaranteeing causality, but nevertheless encounter the troublesome issues of hypersingular improper integral and obscurity in implementing initial conditions. The purpose of this paper is to ease or remove these drawbacks of the Szabo's models via the Caputo fractional derivative concept. The positive time-fractional derivative is also introduced to include the positivity of the attenuation processes.     

Limits of applicability of the Kramers-Kronig relations in the presence of an additional light wave

We analyze the possibility of applying the Kramers-Kronig relations to media with substantial spatial diffusion of the permittivity, in which case additional light waves of the Pekar type emerge. The calculations are done within a broad range of values of the exciton damping constant G with and without a “dead layer” at the crystal surface. We establish the condition in which the use of the Kramers-Kronig relations in calculating the optical constants of the substance yields correct results. Zh. éksp. Teor. Fiz. 114, 1393–1406 (October 1998)     

Finite-bandwidth Kramers-Kronig relations for acoustic group velocity and attenuation derivative applied to encapsulated microbubble suspensions

Kramers-Kronig (KK) analyses of experimental data are complicated by the conflict between the inherently bandlimited data and the requirement of KK integrals for a complete infinite spectrum of input information. For data exhibiting localized extrema, KK relations can provide accurate transforms over finite bandwidths due to the local-weighting properties of the KK kernel. Recently, acoustic KK relations have been derived for the determination of the group velocity (cg) and the derivative of the attenuation coefficient (alpha') (components of the derivative of the acoustic complex wave number). These relations are applicable to bandlimited data exhibiting resonant features without extrapolation or unmeasured parameters. In contrast to twice-subtracted finite-bandwidth KK predictions for phase velocity and attenuation coefficient (components of the undifferentiated wave number), these more recently derived relations for cg and alpha' provide stricter tests of causal consistency because the resulting shapes are invariant with respect to subtraction constants. The integrals in these relations can be formulated so that they only require the phase velocity and attenuation coefficient data without differentiation. Using experimental data from suspensions of encapsulated microbubbles, the finite-bandwidth KK predictions for cg and alpha' are found to provide an accurate mapping of the primary wave number quantities onto their derivatives.     

Consequences of the Kramers-Kronig relations for light diffraction on thick gratings

Diffraction of monochromatic light on a grating leads to the attenuation of the transmitted beam of diffraction order zero. In the case of a thick grating the diffraction efficiency, and hence the effective attenuation coefficient, is a fast-varying function of the Bragg mismatch angle. According to Kramers-Kronig theory, the transmitted beam encounters a phase shift that also depends on the mismatch angle. This phase shift is measured for holographic gratings in a photoaddressable block copolymer and compared with analytical calculations.     

Causality study and numerical response of the magnetic permeability as a function of the frequency of ferrites using Kramers-Kronig relations

In this paper, the numerical treatment of magnetic loss of NiZn, MnZn, Ni₂Y, and NiZnCu ferrite and their composites, by using Krameres-Kronig relations, is investigated. The complex magnetic permeability spectra for ferromagnetic materials have been studied. Due to the principle of causality and time independence in the relation between magnetic induction B and magnetic field H, the real and the imaginary part of the complex magnetic permeability are mutually dependent, and the correlation is given by the Krameres-Kronig equations. Through them, it is possible to measure the real component of the complex magnetic permeability, assuming the real component is given, and by the Hilbert transform, the imaginary part of the magnetic permeability can be calculated. Magnetic circuit model has been studied theoretically, focusing on the model's poles in the complex plane to verify the principle of causality and the temporary independence.     

Optimization of angular and frequency compounding in ultrasonic attenuation estimations

Previous reports have shown that the variance in ultrasound attenuation measurements is reduced when spatial and frequency compounding were applied in data acquisition and analysis. This paper investigates factors affecting the efficiency of compound attenuation imaging methods. A theoretical expression is derived that predicts the correlation between attenuation versus frequency slope (beta) estimates as a function of the increment between measurement frequencies (deltaf ) and the angular separation between beam lines (Delta (theta)). Theoretical results are compared with those from attenuation measurements on tissue-mimicking phantoms and from simulation data. Both predictions and measurement results show that the correlation between beta estimates as a function of (Delta f ) is independent of the length of the radio frequency (rf) data segment over which beta is derived. However, it decreases with an increase in the length of the data segment used in power spectra estimates. In contrast, the correlation between beta estimates as a function of delta(theta) decreases when the rf data segment length is longer or the frequency of the signal is higher. O 2005 Acoustical Society of America.     

用Kramers-Kronig关系求出反射镜的相位色散

光学元件相位色散在超短光脉冲的产生和传播中起着重要的作用,本文提出运用Kramers-Kronig关系,从反射谱直接求出反射镜的相位色散.文中对此法作了分析并以多层介质膜和铝膜反射镜为例子进行了讨论.     

On the ultrasonic attenuation in glasses at low temperatures

The ultrasonic attenuation in glasses at low temperatures is calculated using the model proposed by Anderson, Halperin, and Varma. It is found that the resonant absorption of sound by the localized two-level systems saturates and can be observed only if the sound amplitude is extremely small. A second contribution to the sound absorption is derived which arises from the relaxation of the localized excitations and does not saturate. Qualitative agreement with recent measurements of the ultrasonic attenuation in fused silica is obtained.     

On estimating the center frequency of ultrasonic pulses

In this paper we propose a new technique for estimating the center frequency of the ultrasound pulse from records of backscattering noise. We start by considering that the conventional maximum frequency method can be seen as a filtering (differentiator) of the pulse spectrum magnitude followed by a searching for the zero-crossing value. The new approach replaces the differentiator by a Hilbert transformer. We show in the paper that the proposed method has less variance than the maximum frequency method. In particular, we analyse the performance assuming that the real cepstrum method is used for extracting pulse spectrum magnitude. We give an upper bound for the variance reduction when practical criteria are applied for fitting the cepstrum cut-off frequency. The analytical work is verified by real and simulated data.     

Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ($ \ell = \frac{I} {J} $ \ell = \frac{I} {J} ) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipole-quadrupole interaction (ℓ). The dipole-quadrupole critical exponent δ_χ has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval $ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 $ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 for $ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 $ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 and $ h = \frac{H} {J} = 0 $ h = \frac{H} {J} = 0 parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicate that the effect of the ℓ parameter is similar to the external magnetic field (h). The critical exponent δ_ℓ are in good agreement with the universal value (δ _h = 5) of the external magnetic field.     

Analysis of errors in optical functions calculated from the Kramers-Kronig relations

The effect of errors in the measured reflection coefficient and in the calculated phase on the accuracy of calculations of optical functions is studied in the particular case of the Bi₁₂SiO₂₀ crystal, whose reflection spectra have been measured over a wide energy range (1.5–30 eV) with the help of a synchrotronradiation source. The four most common extrapolation models are compared. The effect of the physical and mathematical components on the accuracy with which optical functions are calculated is analyzed. Corresponding practical recommendations are offered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 25–29, March, 1989.     

功率超声治疗的机理及其频率问题

由于超声治疗的对象,目的不同,所应用的超声生物物理性－治疗机理也不同,不同的物理特性与工作频率有着密切关系,因此,必须正确地选择工作频率,解决好频率自动跟踪中遇到的一系列有关频率问题,才能使超声治疗设备安全,可靠地运行。     

On the measurement of frequency-dependent ultrasonic attenuation in strongly heterogeneous materials

This paper deals with the measurement of frequency-dependent ultrasonic attenuation in strongly heterogeneous materials, such as cementitious materials. To improve the measurement of this parameter on this kind of materials, a linear swept–frequency signal is used to drive an emitter transducer to conduct a through-transmission inspection in immersion. To filter out undesirable frequency content, time–frequency filtering and detection process are performed. The use of this method has been compared with two excitation techniques, the broadband and the narrowband pulses. The results obtained using the swept–frequency excitation together with the time–frequency filtering, allows the determination of the attenuation curves with high accuracy over a wide frequency range without the need for complicated equipment, and improves the effective bandwidth by using a unique pair of transducers.     

功率超声设备频率振幅自动控制研究

本文根据差动变量器桥式电路补偿电学臂的原理，采用锁相环（PLL）及模拟乘法器等技术，进行功率超声设备频率振幅自动控制，结果表明，这种控制方法具有频率跟踪范围宽，负载知应能力强及系统性能稳定等功效。     

The effect of grain size distribution on the frequency dependence of the ultrasonic attenuation in polycrystalline materials

An expression has been derived for the effect of the grain size distribution in polycrystalline materials on the frequency dependence of the ultrasonic attenuation. It has been shown that two specimens with the same mean grain size can have significantly different ultrasonic attenuations if their grain size distributions are different and that no unique solution in terms of the grain size exists for a particular ultrasonic attenuation against frequency curve. Qualitative agreement has been found between the theory and some of the experimental data available.