Numerical solution of scattering problems--An alternative to the moment method

2005 ◽  
Author(s):  
L. Jones ◽  
R. Kleinman
Keyword(s):  
Numerical Solution ◽  
Moment Method ◽  
Scattering Problems ◽  
The Moment

Inverse Scattering Scheme Based on the Moment Method in the Spectral Domain, Part I: Theory

1992 ◽  
Vol 14 (1) ◽  
pp. 16-28 ◽  
Author(s):  
Se-Yun Kim ◽  
Hyun-Chul Choi ◽  
Jae-Min Lee ◽  
Jung-Woong Ra
Keyword(s):  
Inverse Scattering ◽  
Basis Function ◽  
Moment Method ◽  
Spectral Domain ◽  
Scattering Problems ◽  
Actual Mechanism ◽  
Spectral Components ◽  
Key Factor ◽  
The Moment ◽  
Measurement Location

Recently, electromagnetic and ultrasonic imaging of inhomogeneous objects by applying the moment-method procedures of forward scattering problems in the reverse sequence have been developed. In this paper, the inverse scattering formulation has been modified to be applicable in the spectral domain. Compared to previous schemes, the suggested formulation illustrates clearly the actual mechanism of the inverse scattering process by explicit separation of the contributions from several variables, such as the measurement location, basis function, and geometry of objects. The ill-posedness inherent in inverse scattering problems was also explained easily in this spectral scheme by the exponentially-decaying behavior of high-frequency spectral components of the scattered field. It implies that enlargement of the discretized cell size is a key factor in regularizing the ill-posedness. In particular, since the singular kernel to be integrated on each cell became regular in the modified scheme, various types of basis functions instead of pulse function were adopted without additional difficulties. This advantage is expected to play an important role in regularizing the noise effect by selecting polynomial basis function on the enlarged cells of discretization in the spectral inverse scattering scheme.

scholarly journals Spectral gap in random bipartite biregular graphs and applications

2021 ◽  
pp. 1-39
Author(s):  
Gerandy Brito ◽  
Ioana Dumitriu ◽  
Kameron Decker Harris
Keyword(s):  
Community Detection ◽  
Adjacency Matrix ◽  
Moment Method ◽  
Coding Theory ◽  
High Probability ◽  
Spectral Gap ◽  
Matrix Completion ◽  
Full Rank ◽  
The Moment ◽  
Deterministic Matrix

Abstract We prove an analogue of Alon’s spectral gap conjecture for random bipartite, biregular graphs. We use the Ihara–Bass formula to connect the non-backtracking spectrum to that of the adjacency matrix, employing the moment method to show there exists a spectral gap for the non-backtracking matrix. A by-product of our main theorem is that random rectangular zero-one matrices with fixed row and column sums are full rank with high probability. Finally, we illustrate applications to community detection, coding theory, and deterministic matrix completion.

Investigation of the Thermodynamic Properties of Anharmonic Crystals with Defects and Influence of Anharmonicity in Exafs by the Moment Method

1998 ◽  
Vol 12 (02) ◽  
pp. 191-205 ◽  
Author(s):  
Vu Van Hung ◽  
Nguyen Thanh Hai
Keyword(s):  
Thermal Expansion ◽  
Thermodynamic Properties ◽  
Phase Change ◽  
Specific Heat ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Moment Method ◽  
Adiabatic Compressibility ◽  
Relative Displacement ◽  
The Moment

By the moment method established previously on the basis of the statistical mechanics, the thermodynamic properties of a strongly anharmonic face-centered and body-centered cubic crystal with point defect are considered. The thermal expansion coefficient, the specific heat Cv and Cp, the isothermal and adiabatic compressibility, etc. are calculated. Our calculated results of the thermal expansion coefficient, the specific heat Cv and Cp… of W, Nb, Au and Ag metals at various temperatures agrees well with the measured values. The anharmonic effects in extended X-ray absorption fine structure (EXAFS) in the single-shell model are considered. We have obtained a new formula for anharmonic contribution to the mean square relative displacement. The anharmonicity is proportional to the temperature and enters the phase change of EXAFS. Our calculated results of Debye–Waller factor and phase change in EXAFS of Cu at various temperatures agrees well with the measured values.

Fictitious Domain Methods for the Numerical Solution of Two-Dimensional Scattering Problems

1998 ◽  
Vol 145 (1) ◽  
pp. 89-109 ◽  
Author(s):  
Erkki Heikkola ◽  
Yuri A. Kuznetsov ◽  
Pekka Neittaanmäki ◽  
Jari Toivanen
Keyword(s):  
Numerical Solution ◽  
Fictitious Domain ◽  
Two Dimensional ◽  
Scattering Problems ◽  
Fictitious Domain Methods
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