Approximate Analytical Expressions of the Fundamental Peak Frequency and the Amplification Factor of S-wave Transfer Function in a Viscoelastic Layered Model

2018 ◽  
Vol 176 (4) ◽  
pp. 1433-1443
Author(s):  
Tran Thanh Tuan ◽  
Pham Chi Vinh ◽  
Abdelkrim Aoudia ◽  
Truong Thi Thuy Dung ◽  
Daniel Manu-Marfo
Keyword(s):  
Transfer Function ◽  
Amplification Factor ◽  
Peak Frequency ◽  
S Wave ◽  
Layered Model ◽  
Analytical Expressions

scholarly journals On the role of acoustic feedback in boundary-layer instability

2014 ◽  
Vol 372 (2020) ◽  
pp. 20130347 ◽  
Author(s):  
Xuesong Wu
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Acoustic Waves ◽  
Feedback Loop ◽  
Peak Frequency ◽  
S Wave ◽  
Flat Plates ◽  
Acoustic Coupling ◽  
Acoustic Feedback ◽  
Roughness Elements

In this paper, the classical triple-deck formalism is employed to investigate two instability problems in which an acoustic feedback loop plays an essential role. The first concerns a subsonic boundary layer over a flat plate on which two well-separated roughness elements are present. A spatially amplifying Tollmien–Schlichting (T–S) wave between the roughness elements is scattered by the downstream roughness to emit a sound wave that propagates upstream and impinges on the upstream roughness to regenerate the T–S wave, thereby forming a closed feedback loop in the streamwise direction. Numerical calculations suggest that, at high Reynolds numbers and for moderate roughness heights, the long-range acoustic coupling may lead to absolute instability, which is characterized by self-sustained oscillations at discrete frequencies. The dominant peak frequency may jump from one value to another as the Reynolds number, or the distance between the roughness elements, is varied gradually. The second problem concerns the supersonic ‘twin boundary layers’ that develop along two well-separated parallel flat plates. The two boundary layers are in mutual interaction through the impinging and reflected acoustic waves. It is found that the interaction leads to a new instability that is absent in the unconfined boundary layer.

Comparative analysis of properties for amplified coherent state and amplified squeezed vacuum

2020 ◽  
Vol 34 (33) ◽  
pp. 2050377
Author(s):  
Yan-Bei Cheng ◽  
Sheng-Guo Guan ◽  
Zu-Jian Wang ◽  
Xue-Xiang Xu
Keyword(s):  
Comparative Analysis ◽  
Coherent State ◽  
Amplification Factor ◽  
Annihilation Operator ◽  
Photon Number ◽  
Matrix Elements ◽  
Squeezed Vacuum ◽  
Quadrature Squeezing ◽  
Antibunching Effect ◽  
Analytical Expressions

Two “amplified” quantum states, that is, amplified coherent state (ACS) and amplified squeezed vacuum (ASV), are considered in this paper by applying operator [Formula: see text] on coherent state (CS) and squeezed vacuum (SV), respectively. Here [Formula: see text] [Formula: see text] denotes a amplification factor and [Formula: see text]) denote the creation (annihilation) operator. Along these two lines, we make a comparative analysis of properties for ACS and ASV. The considered properties include density matrix elements, Wigner function, mean photon number, second-order autocorrelation function, and quadrature squeezing. We derive analytical expressions and make numerical simulations for all the properties. The noteworthy results include: (1) the ACS has antibunching and squeezing characters; (2) the ASV will have the bunching and antibunching effect in small initial squeezing.

A Method to Directly Estimate S-Wave Site Amplification Factor from Horizontal-to-Vertical Spectral Ratio of Earthquakes (eHVSRs)

2020 ◽  
Vol 110 (6) ◽  
pp. 2892-2911
Author(s):  
Eri Ito ◽  
Kenichi Nakano ◽  
Fumiaki Nagashima ◽  
Hiroshi Kawase
Keyword(s):  
Amplification Factor ◽  
Strong Motion ◽  
Spectral Ratio ◽  
Site Amplification ◽  
Body Waves ◽  
Correction Function ◽  
Site Classification ◽  
Frequency Range ◽  
S Wave ◽  
Site Amplification Factor

ABSTRACT The main purpose of the site classification or velocity determination at a target site is to obtain or estimate the horizontal site amplification factor (HSAF) at that site during future earthquakes because HSAF would have significant effects on the strong-motion characteristics. We have been investigating various kinds of methods to delineate the S-wave velocity structures and the subsequent HSAF, as precisely as possible. After the advent of the diffuse field concept, we have derived a simple formula based on the equipartitioned energy density observed in the layered half-space for incident body waves. In this study, based on the diffuse field concept, together with the generalized spectral inversion technique (GIT), we propose a method to directly estimate the HSAF of the S-wave portion from the horizontal-to-vertical spectral ratio of earthquakes (eHVSRs). Because the vertical amplification is included in the denominator of eHVSR, it cannot be viewed as HSAF without correction. We used GIT to determine both the HSAF and the vertical site amplification factor (VSAF) simultaneously from strong-motion data observed by the networks in Japan and then deduced the log-averaged vertical amplification correction function (VACF) from VSAFs at a total of 1678 sites in which 10 or more earthquakes have been observed. The VACF without a category has a constant amplitude of about 2 in the frequency range from 1 to 15 Hz. By multiplying eHVSR by VACF, we obtained the simulated HSAF. We verified the effectiveness of this correction method using data from observation sites not used in the aforementioned averaging in the frequency range from 0.12 to 15 Hz.

PROCESSING AND INTERPRETATION OF MAGNETOTELLURIC SOUNDINGS

Geophysics ◽  
1972 ◽  
Vol 37 (6) ◽  
pp. 1005-1021 ◽  
Author(s):  
G. Kunetz
Keyword(s):  
Transfer Function ◽  
Time Domain ◽  
Transfer Functions ◽  
Seismic Analysis ◽  
Magnetotelluric Soundings ◽  
Automatic Interpretation ◽  
Uniqueness Of The Solution ◽  
Experimental Values ◽  
The Time Domain ◽  
Analytical Expressions

A few methods in the processing and interpretation of magnetotelluric soundings over a stratified earth are investigated, with emphasis on the less commonly used time‐domain procedures. Analytical expressions of the theoretical transfer function between the magnetic‐ and electric‐field variations, both in frequency and time domain, are derived. Their properties are studied, and recursive algorithms are given for their numerical computation. On the other hand, a procedure is outlined which leads directly in the time domain to the experimental values of this transfer function. It is similar to the methods used in seismic analysis for signal determination and makes use of the auto‐ and crosscorrelation functions of the measured field variations. Finally, methods of interpretation, based either on a visual or on an automatic comparison of these theoretical and experimental transfer functions, are proposed. For the case of automatic interpretation, complementary geologic data should be used where possible to take care of the lack of uniqueness of the solution.

scholarly journals A Study on an Empirical Formula for Amplification Factor Based on Fundamental Peak Frequency and Amplitude of Microtremor H/V

2019 ◽  
Vol 19 (7) ◽  
pp. 7_41-7_55
Author(s):  
Hayato NISHIKAWA ◽  
Tatsuya NOGUCHI ◽  
Masakatsu MIYAJIMA ◽  
Takao KAGAWA
Keyword(s):  
Empirical Formula ◽  
Amplification Factor ◽  
Peak Frequency

scholarly journals Relativistic modeling of atmospheric occultations with time transfer functions

2021 ◽  
Vol 648 ◽  
pp. A46
Author(s):  
A. Bourgoin ◽  
M. Zannoni ◽  
L. Gomez Casajus ◽  
P. Tortora ◽  
P. Teyssandier
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Integral Form ◽  
Original Method ◽  
Electromagnetic Signal ◽  
Time Transfer ◽  
Spacetime Curvature ◽  
Covariant Description ◽  
Analytical Expressions ◽  
Optical Metric

Context. Occultation experiments represent unique opportunities to remotely probe the physical properties of atmospheres. The data processing involved in modeling the time and frequency transfers of an electromagnetic signal requires that refractivity be properly accounted for. On theoretical grounds, little work has been done concerning the elaboration of a covariant approach for modeling occultation data. Aims. We present an original method allowing fully analytical expressions to be derived up to the appropriate order for the covariant description of time and frequency transfers during an atmospheric occultation experiment. Methods. We make use of two independent powerful relativistic theoretical tools, namely the optical metric and the time transfer functions formalism. The former allows us to consider refractivity as spacetime curvature while the latter is used to determine the time and frequency transfers occurring in a curved spacetime. Results. We provide the integral form of the time transfer function up to any post-Minkowskian order. The discussion focuses on the stationary optical metric describing an occultation by a steadily rotating and spherically symmetric atmosphere. Explicit analytical expressions for the time and frequency transfers are provided at the first post-Minkowskian order and their accuracy is assessed by comparing them to results of a numerical integration of the equations for optical rays. Conclusions. The method accurately describes vertical temperature gradients and properly accounts for the light-dragging effect due to the motion of the optical medium. It can be pushed further in order to derive the explicit form of the time transfer function at higher order and beyond the spherical symmetry assumption.

Analysis of the Transfer Function of Large and Small Premixed Laminar Conical Flames

2017 ◽  
Author(s):  
R. Gaudron ◽  
M. Gatti ◽  
C. Mirat ◽  
T. Schuller
Keyword(s):  
Transfer Function ◽  
Practical Interest ◽  
Theoretical Models ◽  
Phase Lag ◽  
Velocity Perturbation ◽  
Flow Perturbation ◽  
Half Angle ◽  
Premixed Laminar ◽  
Analytical Expressions ◽  
Weak Influence

The Flame Transfer Function (FTF) of premixed laminar conical flames submitted to flowrate modulations is a configuration of fundamental and practical interest for improving the design of thermo-acoustically stable low power burners. Many theoretical models were developed for relatively large single flames based on labscale experiments, while most domestic and industrial burners operate with a collection of small injectors. Measurements of the FTF of laminar premixed methane/air conical flames are compared with analytical expressions deduced from kinematic descriptions of flame wrinkling when the burner size is reduced. The flame aspect ratio is kept constant corresponding to a flame tip half-angle α = 14.47° and the radius of the injector is reduced from R = 11 mm to R = 1.5 mm. Three different velocity perturbation models are tested, with and without an additional model accounting for the dynamics of the flame anchoring point. For the largest flames R = 11 mm and 7 mm, the best agreement is found for a FTF model with an incompressible velocity disturbance in the fresh reactants stream. The anchoring point dynamics has only a weak influence on the FTF gain and phase-lag plots of these flames. For the smallest flames (R = 1.5 mm), a FTF model based on a uniform flow perturbation yields the best match with experiments for the phase-lag plot, but none of the three velocity perturbation models reproduce the FTF gain evolution as measured in experiments. Including the contribution of the anchoring point dynamics to the FTF significantly changes the FTF gain predictions, but it does not allow to reproduce the main features observed in the measured gain curves and the phase-lag predictions worsen. It is concluded that an additional modeling effort is needed to adequatedly reproduce the FTF of small premixed laminar conical flames.

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