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.

Dynamic Observer Method Based on Modified Green’s Functions for Robust and More Stable Inverse Algorithms

2008 ◽  
Author(s):  
Priscila F. B. Sousa ◽  
Ana P. Fernandes ◽  
Vale´rio Luiz Borges ◽  
George S. Dulikravich ◽  
Gilmar Guimara˜es
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Green's Functions ◽  
Transfer Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Original Method ◽  
Identification Algorithm ◽  
Transfer Function Model ◽  
Function Model

This work presents a modified procedure to use the concept of dynamic observers based on Green’s functions to solve inverse problems. The original method can be divided in two distinct steps: i) obtaining a transfer function model GH and; ii) obtaining heat transfer functions GQ and GN and building an identification algorithm. The transfer function model, GH, is obtained from the equivalent dynamic systems theory using Green’s functions. The modification presented here proposes two different improvements in the original technique: i) A different method of obtaining the transfer function model, GH, using analytical functions instead of numerical procedures, and ii) Definition of a new concept of GH to allow the use of more than one response temperature. Obtaining the heat transfer functions represents an important role in the observer method and is crucial to allow the technique to be directly applied to two or three-dimensional heat conduction problems. The idea of defining the new GH function is to improve the robustness and stability of the algorithm. A new dynamic equivalent system for the thermal model is then defined in order to allow the use of two or more temperature measurements. Heat transfer function, GH can be obtained numerically or analytically using Green’s function method. The great advantage of deriving GH analytically is to simplify the procedure and minimize the estimative errors.

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 Comparison of Hydrogen Micromix Flame Transfer Functions Determined Using RANS and LES

2019 ◽  
Author(s):  
Jonathan McClure ◽  
David Abbott ◽  
Parash Agarwal ◽  
Xiaoxiao Sun ◽  
Giulia Babazzi ◽  
...  
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Diffusion Flames ◽  
Design Tool ◽  
Preliminary Design ◽  
Flame Response ◽  
Combustion Systems ◽  
Acoustic Excitations ◽  
Analytical Expressions

Abstract Hydrogen has been proposed as an alternative fuel to meet long term emissions and sustainability targets, however due to the characteristics of hydrogen significant modifications to the combustion system are required. The micromix concept utilises a large number of miniaturised diffusion flames to improve mixing, removing the potential for local stoichiometric pockets, flash-back and autoignition. No publicly available studies have yet investigated the thermoacoustic stability of these combustion systems, however due to similarities with lean-premixed combustors which have suffered significant thermoacoustic issues, this risk should not be neglected. Two approaches have been investigated for estimating flame response to acoustic excitations of a single hydrogen micromix injector element. The first uses analytical expressions for the flame transfer function with constants obtained from RANS CFD while the second determines the flame transfer function directly using unsteady LES CFD. Results show the typical form of the flame transfer function but suggest micromix combustors may be more susceptible to higher frequency instabilities than conventional combustion systems. Additionally, the flame transfer function estimated using RANS CFD is broadly similar to that of the LES approach, therefore this may be suitable for use as a preliminary design tool due to its relatively low computational expense.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Trombone Transfer Functions: Comparison Between Frequency-Swept Sine Wave and Human Performer Input

2012 ◽  
Vol 37 (4) ◽  
pp. 447-454
Author(s):  
James W. Beauchamp
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Cutoff Frequency ◽  
Sine Wave ◽  
Nonlinear Propagation ◽  
Linear Filter ◽  
Wave System ◽  
General Effect ◽  
Filter Characteristic ◽  
High Pass

Abstract Source/filter models have frequently been used to model sound production of the vocal apparatus and musical instruments. Beginning in 1968, in an effort to measure the transfer function (i.e., transmission response or filter characteristic) of a trombone while being played by expert musicians, sound pressure signals from the mouthpiece and the trombone bell output were recorded in an anechoic room and then subjected to harmonic spectrum analysis. Output/input ratios of the signals’ harmonic amplitudes plotted vs. harmonic frequency then became points on the trombone’s transfer function. The first such recordings were made on analog 1/4 inch stereo magnetic tape. In 2000 digital recordings of trombone mouthpiece and anechoic output signals were made that provide a more accurate measurement of the trombone filter characteristic. Results show that the filter is a high-pass type with a cutoff frequency around 1000 Hz. Whereas the characteristic below cutoff is quite stable, above cutoff it is extremely variable, depending on level. In addition, measurements made using a swept-sine-wave system in 1972 verified the high-pass behavior, but they also showed a series of resonances whose minima correspond to the harmonic frequencies which occur under performance conditions. For frequencies below cutoff the two types of measurements corresponded well, but above cutoff there was a considerable difference. The general effect is that output harmonics above cutoff are greater than would be expected from linear filter theory, and this effect becomes stronger as input pressure increases. In the 1990s and early 2000s this nonlinear effect was verified by theory and measurements which showed that nonlinear propagation takes place in the trombone, causing a wave steepening effect at high amplitudes, thus increasing the relative strengths of the upper harmonics.

Structural-parametric model of an electroelastic actuator for nanomechanics

2020 ◽  
pp. 3-11
Author(s):  
S.M. Afonin
Keyword(s):  
Transfer Function ◽  
Piezoelectric Actuator ◽  
Transfer Functions ◽  
Piezoelectric Effect ◽  
Parametric Model ◽  
Elastic Compliance ◽  
Parametric Models ◽  
Piezo Actuator ◽  
Structural Scheme ◽  
Model Transfer

Structural-parametric models, structural schemes are constructed and the transfer functions of electro-elastic actuators for nanomechanics are determined. The transfer functions of the piezoelectric actuator with the generalized piezoelectric effect are obtained. The changes in the elastic compliance and rigidity of the piezoactuator are determined taking into account the type of control. Keywords electro-elastic actuator, piezo actuator, structural-parametric model, transfer function, parametric structural scheme

scholarly journals Determination of the Optimal Neural Network Transfer Function for Response Surface Methodology and Robust Design

2021 ◽  
Vol 11 (15) ◽  
pp. 6768
Author(s):  
Tuan-Ho Le ◽  
Hyeonae Jang ◽  
Sangmun Shin
Keyword(s):  
Response Surface Methodology ◽  
Transfer Function ◽  
Response Surface ◽  
Robust Design ◽  
Transfer Functions ◽  
Desirability Function ◽  
Likelihood Estimation ◽  
Statistical Simulation ◽  
Screening Procedure ◽  
Function Estimation

Response surface methodology (RSM) has been widely recognized as an essential estimation tool in many robust design studies investigating the second-order polynomial functional relationship between the responses of interest and their associated input variables. However, there is scope for improvement in the flexibility of estimation models and the accuracy of their results. Although many NN-based estimations and optimization approaches have been reported in the literature, a closed functional form is not readily available. To address this limitation, a maximum-likelihood estimation approach for an NN-based response function estimation (NRFE) is used to obtain the functional forms of the process mean and standard deviation. While the estimation results of most existing NN-based approaches depend primarily on their transfer functions, this approach often requires a screening procedure for various transfer functions. In this study, the proposed NRFE identifies a new screening procedure to obtain the best transfer function in an NN structure using a desirability function family while determining its associated weight parameters. A statistical simulation was performed to evaluate the efficiency of the proposed NRFE method. In this particular simulation, the proposed NRFE method provided significantly better results than conventional RSM. Finally, a numerical example is used for validating the proposed method.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

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