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Title: Absolutely and uniformly convergent iterative approach to inverse scattering with an infinite radius of convergence

Abstract

A method and system for solving the inverse acoustic scattering problem using an iterative approach with consideration of half-off-shell transition matrix elements (near-field) information, where the Volterra inverse series correctly predicts the first two moments of the interaction, while the Fredholm inverse series is correct only for the first moment and that the Volterra approach provides a method for exactly obtaining interactions which can be written as a sum of delta functions.

Inventors:
 [1];  [1];  [1];  [1];  [2]
  1. Houston, TX
  2. Ames, IA
Publication Date:
Research Org.:
Ames Laboratory (AMES), Ames, IA
Sponsoring Org.:
USDOE
OSTI Identifier:
909331
Patent Number(s):
7,212,933
Application Number:
10/806,045
Assignee:
The University of Houston System (Houston, TX) AMES
DOE Contract Number:
W-7405-ENG-82
Resource Type:
Patent
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Kouri, Donald J, Vijay, Amrendra, Zhang, Haiyan, Zhang, Jingfeng, and Hoffman, David K. Absolutely and uniformly convergent iterative approach to inverse scattering with an infinite radius of convergence. United States: N. p., 2007. Web.
Kouri, Donald J, Vijay, Amrendra, Zhang, Haiyan, Zhang, Jingfeng, & Hoffman, David K. Absolutely and uniformly convergent iterative approach to inverse scattering with an infinite radius of convergence. United States.
Kouri, Donald J, Vijay, Amrendra, Zhang, Haiyan, Zhang, Jingfeng, and Hoffman, David K. Tue . "Absolutely and uniformly convergent iterative approach to inverse scattering with an infinite radius of convergence". United States. doi:. https://www.osti.gov/servlets/purl/909331.
@article{osti_909331,
title = {Absolutely and uniformly convergent iterative approach to inverse scattering with an infinite radius of convergence},
author = {Kouri, Donald J and Vijay, Amrendra and Zhang, Haiyan and Zhang, Jingfeng and Hoffman, David K},
abstractNote = {A method and system for solving the inverse acoustic scattering problem using an iterative approach with consideration of half-off-shell transition matrix elements (near-field) information, where the Volterra inverse series correctly predicts the first two moments of the interaction, while the Fredholm inverse series is correct only for the first moment and that the Volterra approach provides a method for exactly obtaining interactions which can be written as a sum of delta functions.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}

Patent:

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  • A method and system for solving the inverse acoustic scattering problem using an iterative approach with consideration of half-off-shell transition matrix elements (near-field) information, where the Volterra inverse series correctly predicts the first two moments of the interaction, while the Fredholm inverse series is correct only for the first moment and that the Volterra approach provides a method for exactly obtaining interactions which can be written as a sum of delta functions.
  • The authors determine an upper bound on the convergence radius m{sub conv} for the expansion in the current quark mass using the Dyson-Schwinger (DS) equation of QCD in the rainbow approximation. Using a gluon propagator, which has the form D{sub {mu}{nu}}(p) {approximately} {delta}{sub {mu}{nu}}{chi}{sup 2}e{sup {minus}p{sup 2}/{Delta}} at small p{sup 2} and the standard logarithmic form in the UV region the authors find that m{sub conv} increases with decreasing width {Delta} and increasing strength {chi}{sup 2}. For those values of {chi}{sup 2} and {Delta}, which have been shown to provide a good description of low energy hadronic phenomena, M{sub conv}more » lies around 400 MeV, which is clearly larger than the mass of the strange quark. The authors analysis also explains the rather low value of m{sub conv} {approx} 50...80 MeV in the Nambu-Jona-Lasinio model, which as itself can be regarded as a special case of the rainbow DS models, where the gluon propagator is a constant in momentum space.« less
  • A method is presented for determining the transient surface temperature of a solid when the temperature response as a function of time at an interior point within the solid is known. The method employs approximate iterative techniques suitable for the solution of one-dimensional transient thermal conduction problems in homogeneous or composite solids with constant thermal properties. An example problem is solved using a linear technique and a least-squares approach. This iteration technique exhibits a high degree of accuracy, rapid convergence, and excellent stability. In addition, an analytical expression is developed that predicts the computed surface noise resulting from fluctuations inmore » the input data.« less