Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions

We consider the problem of inversion of elastic light scattering (ELS) measurements from polymeric emulsions, to obtain its particle size distribution (PSD) and its refractive index. The mathematical formulation results in a nonlinear inverse problem. A Fredholm integral equation of the first kind a...

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Publicado: 2007
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17415977_v15_n2_p123_Frontini
http://hdl.handle.net/20.500.12110/paper_17415977_v15_n2_p123_Frontini
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spelling paper:paper_17415977_v15_n2_p123_Frontini2023-06-08T16:26:59Z Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions We consider the problem of inversion of elastic light scattering (ELS) measurements from polymeric emulsions, to obtain its particle size distribution (PSD) and its refractive index. The mathematical formulation results in a nonlinear inverse problem. A Fredholm integral equation of the first kind appears with an unknown parameter in its kernel. We discuss the existence, uniqueness, and stability of the generalized solutions of the problem when it is stated as a minimization problem with a least square functional. First, we assume that the PSD is known, and for this case we prove that the solution exists and is unique as long as the relation between the measurements and the parameter is by an injective function. Then, we use this result to state sufficient conditions for the complete problem. The analysis of existence and uniqueness of the solution for the problem in hand is supported by numerical simulation. The Phillips-Tikhonov regularization method is proposed to stabilize the problem when noisy-data is available. 2007 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17415977_v15_n2_p123_Frontini http://hdl.handle.net/20.500.12110/paper_17415977_v15_n2_p123_Frontini
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We consider the problem of inversion of elastic light scattering (ELS) measurements from polymeric emulsions, to obtain its particle size distribution (PSD) and its refractive index. The mathematical formulation results in a nonlinear inverse problem. A Fredholm integral equation of the first kind appears with an unknown parameter in its kernel. We discuss the existence, uniqueness, and stability of the generalized solutions of the problem when it is stated as a minimization problem with a least square functional. First, we assume that the PSD is known, and for this case we prove that the solution exists and is unique as long as the relation between the measurements and the parameter is by an injective function. Then, we use this result to state sufficient conditions for the complete problem. The analysis of existence and uniqueness of the solution for the problem in hand is supported by numerical simulation. The Phillips-Tikhonov regularization method is proposed to stabilize the problem when noisy-data is available.
title Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions
spellingShingle Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions
title_short Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions
title_full Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions
title_fullStr Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions
title_full_unstemmed Analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions
title_sort analysis of the solution of the elastic light scattering inverse problem for polymeric emulsions
publishDate 2007
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_17415977_v15_n2_p123_Frontini
http://hdl.handle.net/20.500.12110/paper_17415977_v15_n2_p123_Frontini
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