Diffuse scattering on graphs

We formulate and analyze difference equations on graphs analogous to time-independent diffusion equations arising in the study of diffuse scattering in continuous media. Moreover, we show how to construct solutions in the presence of weak scatterers from the solution to the homogeneous (background p...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Linear algebra and its applications Jg. 496; S. 1 - 35
Hauptverfasser:	Gilbert, Anna C., Hoskins, Jeremy G., Schotland, John C.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier Inc 01.05.2016
Schlagworte:	Discrete mathematics in relation to computer science Equations of mathematical physics and other areas of application Graph algorithms Graphs and groups Graphs and matrices 68R Equations of mathematical physics and other areas of application 05C50 05C85 Graphs and groups Graphs and matrices Graph algorithms 05C25 35Q Discrete mathematics in relation to computer science
ISSN:	0024-3795, 1873-1856
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	We formulate and analyze difference equations on graphs analogous to time-independent diffusion equations arising in the study of diffuse scattering in continuous media. Moreover, we show how to construct solutions in the presence of weak scatterers from the solution to the homogeneous (background problem) using Born series, providing necessary conditions for convergence and demonstrating the process through numerous examples. In addition, we outline a method for finding Green's functions for Cayley graphs for both abelian and non-abelian groups. Finally, we conclude with a discussion of the effects of sparsity on our method and results, outlining the simplifications that can be made provided that the scatterers are weak and well-separated.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/j.laa.2016.01.012