• Previous Article
    Particle filtering, beamforming and multiple signal classification for the analysis of magnetoencephalography time series: a comparison of algorithms
  • IPI Home
  • This Issue
  • Next Article
    Identification of sound-soft 3D obstacles from phaseless data
February  2010, 4(1): 151-167. doi: 10.3934/ipi.2010.4.151

Gauge equivalence in stationary radiative transport through media with varying index of refraction

1. 

Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, United States

2. 

Department of Mathematics, Purdue University, 150 N University Street, West Lafayette, IN 47907

3. 

Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States

Received  April 2009 Revised  December 2009 Published  February 2010

Three dimensional anisotropic attenuating and scattering media sharing the same albedo operator have been shown to be related via a gauge transformation. Such transformations define an equivalence relation. We show that the gauge equivalence is also valid in media with non-constant index of refraction, modeled by a Riemannian metric. The two dimensional model is also investigated.
Citation: Stephen McDowall, Plamen Stefanov, Alexandru Tamasan. Gauge equivalence in stationary radiative transport through media with varying index of refraction. Inverse Problems and Imaging, 2010, 4 (1) : 151-167. doi: 10.3934/ipi.2010.4.151
[1]

Guillaume Bal, Alexandre Jollivet. Stability estimates in stationary inverse transport. Inverse Problems and Imaging, 2008, 2 (4) : 427-454. doi: 10.3934/ipi.2008.2.427

[2]

Guillaume Bal, Ian Langmore, François Monard. Inverse transport with isotropic sources and angularly averaged measurements. Inverse Problems and Imaging, 2008, 2 (1) : 23-42. doi: 10.3934/ipi.2008.2.23

[3]

Guillaume Bal, Alexandre Jollivet. Generalized stability estimates in inverse transport theory. Inverse Problems and Imaging, 2018, 12 (1) : 59-90. doi: 10.3934/ipi.2018003

[4]

John C. Schotland, Vadim A. Markel. Fourier-Laplace structure of the inverse scattering problem for the radiative transport equation. Inverse Problems and Imaging, 2007, 1 (1) : 181-188. doi: 10.3934/ipi.2007.1.181

[5]

Olivier Brahic. Infinitesimal gauge symmetries of closed forms. Journal of Geometric Mechanics, 2011, 3 (3) : 277-312. doi: 10.3934/jgm.2011.3.277

[6]

Keonhee Lee, Kazuhiro Sakai. Various shadowing properties and their equivalence. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 533-540. doi: 10.3934/dcds.2005.13.533

[7]

Olof Heden, Martin Hessler. On linear equivalence and Phelps codes. Advances in Mathematics of Communications, 2010, 4 (1) : 69-81. doi: 10.3934/amc.2010.4.69

[8]

Emmanuel Hebey. Solitary waves in critical Abelian gauge theories. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1747-1761. doi: 10.3934/dcds.2012.32.1747

[9]

Luis Barreira, Liviu Horia Popescu, Claudia Valls. Generalized exponential behavior and topological equivalence. Discrete and Continuous Dynamical Systems - B, 2017, 22 (8) : 3023-3042. doi: 10.3934/dcdsb.2017161

[10]

Andres del Junco, Daniel J. Rudolph, Benjamin Weiss. Measured topological orbit and Kakutani equivalence. Discrete and Continuous Dynamical Systems - S, 2009, 2 (2) : 221-238. doi: 10.3934/dcdss.2009.2.221

[11]

Michael C. Sullivan. Invariants of twist-wise flow equivalence. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 475-484. doi: 10.3934/dcds.1998.4.475

[12]

Olof Heden, Martin Hessler. On linear equivalence and Phelps codes. Addendum. Advances in Mathematics of Communications, 2011, 5 (3) : 543-546. doi: 10.3934/amc.2011.5.543

[13]

Giuseppe Buttazzo, Luigi De Pascale, Ilaria Fragalà. Topological equivalence of some variational problems involving distances. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 247-258. doi: 10.3934/dcds.2001.7.247

[14]

Nguyen Lam. Equivalence of sharp Trudinger-Moser-Adams Inequalities. Communications on Pure and Applied Analysis, 2017, 16 (3) : 973-998. doi: 10.3934/cpaa.2017047

[15]

Zemer Kosloff, Terry Soo. The orbital equivalence of Bernoulli actions and their Sinai factors. Journal of Modern Dynamics, 2021, 17: 145-182. doi: 10.3934/jmd.2021005

[16]

Mike Crampin, David Saunders. Homogeneity and projective equivalence of differential equation fields. Journal of Geometric Mechanics, 2012, 4 (1) : 27-47. doi: 10.3934/jgm.2012.4.27

[17]

Mrinal Kanti Roychowdhury, Daniel J. Rudolph. Nearly continuous Kakutani equivalence of adding machines. Journal of Modern Dynamics, 2009, 3 (1) : 103-119. doi: 10.3934/jmd.2009.3.103

[18]

Michael C. Sullivan. Invariants of twist-wise flow equivalence. Electronic Research Announcements, 1997, 3: 126-130.

[19]

Kurt Ehlers. Geometric equivalence on nonholonomic three-manifolds. Conference Publications, 2003, 2003 (Special) : 246-255. doi: 10.3934/proc.2003.2003.246

[20]

B. Kaymakcalan, R. Mert, A. Zafer. Asymptotic equivalence of dynamic systems on time scales. Conference Publications, 2007, 2007 (Special) : 558-567. doi: 10.3934/proc.2007.2007.558

2021 Impact Factor: 1.483

Metrics

  • PDF downloads (75)
  • HTML views (0)
  • Cited by (3)

[Back to Top]