American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Towards deconvolution to enhance the grid method for in-plane strain measurement
  • IPI Home
  • This Issue
  • Next Article
    Superiorization of EM algorithm and its application in Single-Photon Emission Computed Tomography(SPECT)
February  2014, 8(1): 247-257. doi: 10.3934/ipi.2014.8.247

The linearized problem of magneto-photoelasticity

Vladimir Sharafutdinov 1,

1. 

Sobolev Institute of Mathematics and Novosibirsk State University, 4 Koptyug Avenue, Novosibirsk, 630090, Russian Federation

Received  April 2013 Revised  September 2013 Published  March 2014

The equations of magneto-photoelasticity are derived for a nonhomogeneous background isotropic medium and for a variable gyration vector. They coincide with Aben's equations in the case of a homogeneous background medium and of a constant gyration vector. We obtain an explicit linearized formula for the fundamental solution under the assumption that variable coefficients of equations are sufficiently small. Then we consider the inverse problem of recovering the variable coefficients from the results of polarization measurements known for several values of the gyration vector. We demonstrate that the data can be easily transformed to a family of Fourier coefficients of the unknown function if the modulus of the gyration vector is agreed with the ray length.
Keywords: Photoelasticity, the Faraday rotation., geometric optics.
Mathematics Subject Classification: Primary: 34A55, 78A05; Secondary: 74E10, 74F1.
Citation: Vladimir Sharafutdinov. The linearized problem of magneto-photoelasticity. Inverse Problems & Imaging, 2014, 8 (1) : 247-257. doi: 10.3934/ipi.2014.8.247
References:
[1]

H. Aben, Magnetophotoelasticity - photoelasticity in a magnetic field,, Experimental Mechanics, 10 (1970), 97.   Google Scholar

[2]

H. Aben, Integrated Photoelasticity,, McGraw Hill, (1979).   Google Scholar

[3]

G. P. Clarc, H. W. McKenzie and P. Stanley, The magnetophotoelastic analysis of residual stresses in thermally toughened glass,, Proc. of the Royal Society of London A, 455 (1999), 1149.   Google Scholar

[4]

S. Gibson, G. W. Jewel and R. A. Tomlinson, Full-field pulsed magnetophototlasticity,, J. of Strain Analysis for Engineering Design, 41 (2006), 161.   Google Scholar

[5]

Yu. Kravtsov, "Quasi-isotropic'' approximation of geometric optics,, Dokl. Acad. Nauk SSSR, 183 (1968), 74.   Google Scholar

[6]

L. Landau and E. Lifshitz, Theoretical Physics. VIII Electrodynamics of Continuous Media,, (Russian) 2nd edition, (1982).   Google Scholar

[7]

H. Poincaré, Théory Mathématique de la Lumiére. Reprint of the 1889 and 1892 Originals,, Éditions Jacques, (1995).   Google Scholar

[8]

F. E. Puro, Magnetophotoelasticity as parametric tensor field tomography,, Inverse Problems, 14 (1998), 1315.   Google Scholar

[9]

V. A. Sharafutdinov, The method of integral photoelasticity in the case of weak optical anisotropy,, Eesti NSV Tead. Acad. Toimetised Fuus.-Mat., 38 (1989), 379.   Google Scholar

[10]

V. Sharafutdinov, Integral Geometry of Tensor Field,, VSP, (1994).  doi: 10.1515/9783110900095.  Google Scholar

show all references

References:
[1]

H. Aben, Magnetophotoelasticity - photoelasticity in a magnetic field,, Experimental Mechanics, 10 (1970), 97.   Google Scholar

[2]

H. Aben, Integrated Photoelasticity,, McGraw Hill, (1979).   Google Scholar

[3]

G. P. Clarc, H. W. McKenzie and P. Stanley, The magnetophotoelastic analysis of residual stresses in thermally toughened glass,, Proc. of the Royal Society of London A, 455 (1999), 1149.   Google Scholar

[4]

S. Gibson, G. W. Jewel and R. A. Tomlinson, Full-field pulsed magnetophototlasticity,, J. of Strain Analysis for Engineering Design, 41 (2006), 161.   Google Scholar

[5]

Yu. Kravtsov, "Quasi-isotropic'' approximation of geometric optics,, Dokl. Acad. Nauk SSSR, 183 (1968), 74.   Google Scholar

[6]

L. Landau and E. Lifshitz, Theoretical Physics. VIII Electrodynamics of Continuous Media,, (Russian) 2nd edition, (1982).   Google Scholar

[7]

H. Poincaré, Théory Mathématique de la Lumiére. Reprint of the 1889 and 1892 Originals,, Éditions Jacques, (1995).   Google Scholar

[8]

F. E. Puro, Magnetophotoelasticity as parametric tensor field tomography,, Inverse Problems, 14 (1998), 1315.   Google Scholar

[9]

V. A. Sharafutdinov, The method of integral photoelasticity in the case of weak optical anisotropy,, Eesti NSV Tead. Acad. Toimetised Fuus.-Mat., 38 (1989), 379.   Google Scholar

[10]

V. Sharafutdinov, Integral Geometry of Tensor Field,, VSP, (1994).  doi: 10.1515/9783110900095.  Google Scholar

[1]

Qian Liu, Shuang Liu, King-Yeung Lam. Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 0-0. doi: 10.3934/dcds.2020050
[2]

Bertold Bongardt. Geometric characterization of the workspace of non-orthogonal rotation axes. Journal of Geometric Mechanics, 2014, 6 (2) : 141-166. doi: 10.3934/jgm.2014.6.141
[3]

Manuel Gutiérrez. Lorentz geometry technique in nonimaging optics. Conference Publications, 2003, 2003 (Special) : 386-392. doi: 10.3934/proc.2003.2003.386
[4]

Gang Bao. Mathematical modeling of nonlinear diffracvtive optics. Conference Publications, 1998, 1998 (Special) : 89-99. doi: 10.3934/proc.1998.1998.89
[5]

Daomin Cao, Ezzat S. Noussair, Shusen Yan. On the profile of solutions for an elliptic problem arising in nonlinear optics. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 649-666. doi: 10.3934/dcds.2004.11.649
[6]

Hongyu Liu, Ting Zhou. Two dimensional invisibility cloaking via transformation optics. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 525-543. doi: 10.3934/dcds.2011.31.525
[7]

Danny Calegari, Alden Walker. Ziggurats and rotation numbers. Journal of Modern Dynamics, 2011, 5 (4) : 711-746. doi: 10.3934/jmd.2011.5.711
[8]

Arek Goetz. Dynamics of a piecewise rotation. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 593-608. doi: 10.3934/dcds.1998.4.593
[9]

Xavier Buff, Nataliya Goncharuk. Complex rotation numbers. Journal of Modern Dynamics, 2015, 9: 169-190. doi: 10.3934/jmd.2015.9.169
[10]

Michel Laurent, Arnaldo Nogueira. Rotation number of contracted rotations. Journal of Modern Dynamics, 2018, 12: 175-191. doi: 10.3934/jmd.2018007
[11]

Jean-Marie Souriau. On Geometric Mechanics. Discrete & Continuous Dynamical Systems - A, 2007, 19 (3) : 595-607. doi: 10.3934/dcds.2007.19.595
[12]

Christopher Cleveland. Rotation sets for unimodal maps of the interval. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 617-632. doi: 10.3934/dcds.2003.9.617
[13]

David Cowan. A billiard model for a gas of particles with rotation. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 101-109. doi: 10.3934/dcds.2008.22.101
[14]

Mads Kyed. On a mapping property of the Oseen operator with rotation. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1315-1322. doi: 10.3934/dcdss.2013.6.1315
[15]

Siwei Yu, Jianwei Ma, Stanley Osher. Geometric mode decomposition. Inverse Problems & Imaging, 2018, 12 (4) : 831-852. doi: 10.3934/ipi.2018035
[16]

Bruce Hughes. Geometric topology of stratified spaces. Electronic Research Announcements, 1996, 2: 73-81.

[17]

Gianne Derks. Book review: Geometric mechanics. Journal of Geometric Mechanics, 2009, 1 (2) : 267-270. doi: 10.3934/jgm.2009.1.267
[18]

Tim Kreutzmann, Andreas Rieder. Geometric reconstruction in bioluminescence tomography. Inverse Problems & Imaging, 2014, 8 (1) : 173-197. doi: 10.3934/ipi.2014.8.173
[19]

Andrew D. Lewis. The physical foundations of geometric mechanics. Journal of Geometric Mechanics, 2017, 9 (4) : 487-574. doi: 10.3934/jgm.2017019
[20]

Henk Broer, Konstantinos Efstathiou, Olga Lukina. A geometric fractional monodromy theorem. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 517-532. doi: 10.3934/dcdss.2010.3.517

2018 Impact Factor: 1.469

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences