scholarly journals Developing the Techniques for Solving the Inverse Problem in Photoacoustics

Atoms ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 24 ◽  
Author(s):  
Mioljub Nesic ◽  
Marica Popovic ◽  
Slobodanka Galovic
Keyword(s):  
Inverse Problem ◽  
Modulation Frequency ◽  
Back Propagation ◽  
Mathematical Physics ◽  
Measurement Range ◽  
High Accuracy ◽  
Parameter Determination ◽  
Minimum Volume ◽  
Self Consistent

In this work, theoretically/mathematically simulated models are derived for the photoacoustic (PA) frequency response of both volume and surface optically-absorbing samples in a minimum volume PA cell. In the derivation process, the thermal memory influence of both the sample and the air of the gas column are accounted for, as well as the influence of the measurement chain. Within the analysis of the TMS model, the influence of optical, thermal, and elastic properties of the sample was investigated. This analysis revealed that some of the processes, characterized by certain sample properties, exert their dominance only in limited modulation frequency ranges, which are shown to be dependent upon the choice of the sample material and its thickness. Based on the described analysis, two methods are developed for TMS model parameter determination, i.e., sample properties which dominantly influence the PA response in the measurement range: a self-consistent procedure for solving the exponential problems of mathematical physics, and a well-trained three-layer perceptron with back propagation, based upon theory of neural networks. The results of the application of both inverse problem solving methods are compared and discussed. The first method is shown to have the advantage in the number of properties which are determined, while the second one is advantageous in gaining high accuracy in the determination of thermal diffusivity, explicitly. Finally, the execution of inverse PA problem is implemented on experimental measurements performed on macromolecule samples, the results are discussed, and the most important conclusions are derived and presented.

scholarly journals Development and Comparison of the Techniques for Solving the Inverse Problem in Photoacoustics

2021 ◽  
Author(s):  
Mioljub Vojislav Nesic ◽  
Marica Popovic ◽  
Katarina Djordjevic ◽  
Vesna Miletic ◽  
Miroslava Jordovic-Pavlovic ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Frequency Response ◽  
Coefficient Of Thermal Expansion ◽  
Back Propagation ◽  
Mathematical Physics ◽  
Silicon Sample ◽  
Minimum Volume ◽  
Linear Coefficient ◽  
Self Consistent

Abstract In this work, theoretically/mathematically simulated (TMS) model is presented for the photoacoustic (PA) frequency response of a semiconductor in a minimum volume PA cell. By analyzing of the TMS model, the influences of thermal diffusivity and linear coefficient of thermal expansion on silicon sample PA frequency response were investigated and two methods were developed for their estimation. The first one is a self consistent inverse procedure (SCIP) for solving the exponential problems of mathematical physics, based on regression. The second one, a well trained three-layer perceptron with back propagation, based upon theory of artificial neural networks (ANN), is developed and presented. These two inverse problem solving concepts are applied to thermo-elastic characterization of silicon, compared and discussed in the domain of semiconductor characterization.

scholarly journals Accuracy of Doppler Determinations of Station Positions

1972 ◽  
Vol 48 ◽  
pp. 101-103
Author(s):  
R. J. Anderle
Keyword(s):  
Elevation Angle ◽  
High Elevation ◽  
Time Of Day ◽  
Satellite Observations ◽  
Standard Errors ◽  
Lower Elevation ◽  
Self Consistent

Locations of Doppler satellite observing stations have been revised to obtain a set which is more self-consistent and more consistent with the CIO pole. Residuals of satellite observations for 1970 have been analyzed using the new coordinates to determine mean and standard errors for five days of observations of latitude versus station, time of day, and elevation angle. The accuracy of the determination of latitude is about 4 meters at moderate and high elevation angles. But since more satellite passes occur at lower elevation angles, the accuracy of determination of a component of position based on five days of observation of one satellite is only about 2 meters.

scholarly journals The Degree of Oxidation of Graphene Oxide

Nanomaterials ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 560
Author(s):  
Alexandra Carvalho ◽  
Mariana C. F. Costa ◽  
Valeria S. Marangoni ◽  
Pei Rou Ng ◽  
Thi Le Hang Nguyen ◽  
...  
Keyword(s):  
Graphene Oxide ◽  
Ab Initio ◽  
State Of The Art ◽  
High Accuracy ◽  
Precise Determination ◽  
Photoemission Spectroscopy ◽  
Pristine Graphene ◽  
X Ray ◽  
Degree Of Oxidation

We show that the degree of oxidation of graphene oxide (GO) can be obtained by using a combination of state-of-the-art ab initio computational modeling and X-ray photoemission spectroscopy (XPS). We show that the shift of the XPS C1s peak relative to pristine graphene, ΔEC1s, can be described with high accuracy by ΔEC1s=A(cO−cl)2+E0, where c0 is the oxygen concentration, A=52.3 eV, cl=0.122, and E0=1.22 eV. Our results demonstrate a precise determination of the oxygen content of GO samples.

Electrochemical device based on nonspecific DNAzyme for the high-accuracy determination of Ca2+ with Pb2+ interference

2020 ◽  
pp. 107732
Author(s):  
Hui Wang ◽  
Qingyao Luo ◽  
Yiguang Zhao ◽  
Xuemei Nan ◽  
Fan Zhang ◽  
...  
Keyword(s):  
High Accuracy ◽  
Electrochemical Device ◽  
Accuracy Determination

Determination of an impulsive diffusion operator from interior spectral data

Analysis ◽  
2020 ◽  
Vol 40 (1) ◽  
pp. 39-45
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Potential Functions ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Impulsive Diffusion

AbstractIn the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions {q_{0}(x)} and {q_{1}(x)} can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.

scholarly journals An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Philip Trautmann
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Eikonal Equation ◽  
State Equation ◽  
High Accuracy ◽  
Well Posedness ◽  
Numerical Examples ◽  
Marquardt Method ◽  
Math Biol ◽  
Levenberg Marquardt

AbstractIn this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg–Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033–2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.

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