The linearized problem of magneto-photoelasticity

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

Abstract
Related Papers

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 and 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), 97-105.
[2]	H. Aben, Integrated Photoelasticity, McGraw Hill, New York - London 1979.
[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), 1149-1173.
[4]	S. Gibson, G. W. Jewel and R. A. Tomlinson, Full-field pulsed magnetophototlasticity, J. of Strain Analysis for Engineering Design, 41 (2006), 161-182.
[5]	Yu. Kravtsov, "Quasi-isotropic'' approximation of geometric optics, Dokl. Acad. Nauk SSSR, 183 (1968), 74-76.
[6]	L. Landau and E. Lifshitz, Theoretical Physics. VIII Electrodynamics of Continuous Media, (Russian) 2nd edition, Nauka, Moscow, 1982.
[7]	H. Poincaré, Théory Mathématique de la Lumiére. Reprint of the 1889 and 1892 Originals, Éditions Jacques, Sceaux, 1995.
[8]	F. E. Puro, Magnetophotoelasticity as parametric tensor field tomography, Inverse Problems, 14 (1998), 1315-1330. Éditions Jacques, Sceaux, (1995).
[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), 379-389.
[10]	V. Sharafutdinov, Integral Geometry of Tensor Field, VSP, Utrecht, the Netherlands, 1994. doi: 10.1515/9783110900095.

show all references

References:

[1]	H. Aben, Magnetophotoelasticity - photoelasticity in a magnetic field, Experimental Mechanics, 10 (1970), 97-105.
[2]	H. Aben, Integrated Photoelasticity, McGraw Hill, New York - London 1979.
[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), 1149-1173.
[4]	S. Gibson, G. W. Jewel and R. A. Tomlinson, Full-field pulsed magnetophototlasticity, J. of Strain Analysis for Engineering Design, 41 (2006), 161-182.
[5]	Yu. Kravtsov, "Quasi-isotropic'' approximation of geometric optics, Dokl. Acad. Nauk SSSR, 183 (1968), 74-76.
[6]	L. Landau and E. Lifshitz, Theoretical Physics. VIII Electrodynamics of Continuous Media, (Russian) 2nd edition, Nauka, Moscow, 1982.
[7]	H. Poincaré, Théory Mathématique de la Lumiére. Reprint of the 1889 and 1892 Originals, Éditions Jacques, Sceaux, 1995.
[8]	F. E. Puro, Magnetophotoelasticity as parametric tensor field tomography, Inverse Problems, 14 (1998), 1315-1330. Éditions Jacques, Sceaux, (1995).
[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), 379-389.
[10]	V. Sharafutdinov, Integral Geometry of Tensor Field, VSP, Utrecht, the Netherlands, 1994. doi: 10.1515/9783110900095.

[1]	Qian Liu, Shuang Liu, King-Yeung Lam. Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3683-3714. 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 and Continuous Dynamical Systems, 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 and Continuous Dynamical Systems, 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]	Michel Laurent, Arnaldo Nogueira. Rotation number of contracted rotations. Journal of Modern Dynamics, 2018, 12: 175-191. doi: 10.3934/jmd.2018007
[9]	Arek Goetz. Dynamics of a piecewise rotation. Discrete and Continuous Dynamical Systems, 1998, 4 (4) : 593-608. doi: 10.3934/dcds.1998.4.593
[10]	Xavier Buff, Nataliya Goncharuk. Complex rotation numbers. Journal of Modern Dynamics, 2015, 9: 169-190. doi: 10.3934/jmd.2015.9.169
[11]	Jean-Marie Souriau. On Geometric Mechanics. Discrete and Continuous Dynamical Systems, 2007, 19 (3) : 595-607. doi: 10.3934/dcds.2007.19.595
[12]	Christopher Cleveland. Rotation sets for unimodal maps of the interval. Discrete and Continuous Dynamical Systems, 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 and Continuous Dynamical Systems, 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 and Continuous Dynamical Systems - S, 2013, 6 (5) : 1315-1322. doi: 10.3934/dcdss.2013.6.1315
[15]	Fabrice Delbary, Kim Knudsen. Numerical nonlinear complex geometrical optics algorithm for the 3D Calderón problem. Inverse Problems and Imaging, 2014, 8 (4) : 991-1012. doi: 10.3934/ipi.2014.8.991
[16]	Siwei Yu, Jianwei Ma, Stanley Osher. Geometric mode decomposition. Inverse Problems and Imaging, 2018, 12 (4) : 831-852. doi: 10.3934/ipi.2018035
[17]	Bruce Hughes. Geometric topology of stratified spaces. Electronic Research Announcements, 1996, 2: 73-81.
[18]	Gianne Derks. Book review: Geometric mechanics. Journal of Geometric Mechanics, 2009, 1 (2) : 267-270. doi: 10.3934/jgm.2009.1.267
[19]	Tim Kreutzmann, Andreas Rieder. Geometric reconstruction in bioluminescence tomography. Inverse Problems and Imaging, 2014, 8 (1) : 173-197. doi: 10.3934/ipi.2014.8.173
[20]	Andrew D. Lewis. The physical foundations of geometric mechanics. Journal of Geometric Mechanics, 2017, 9 (4) : 487-574. doi: 10.3934/jgm.2017019

2021 Impact Factor: 1.483

Tools

Metrics

Other articles
by authors

on AIMS
Vladimir Sharafutdinov
on Google Scholar
Vladimir Sharafutdinov

[Back to Top]