Abstract
We investigate the wave energy distribution in complex built-up structures it is clear where the semiclassical approximations are made at each stage of the derivation. We reformulate the boundary integral equations for the Helmholtz equation in terms of incoming and outgoing boundary waves independently of the boundary conditions and decomposing the green functions into singular and regular components. For demonstration purposes, we apply a semiclassical form of the operator (corresponding to a high-frequency approximation) to polygonal coupled-cavity configurations with abrupt changes of the material properties (such as wave speed and absorption coefficients at the interfaces between the cavities)
Keywords
Bogomolny transfer operator with multiple interfaces at which the material properties change discontinuously. We Boundary integral equations Green function formulate the transfer operator in such a way that it can in principle be made exact and
References
- M. Abramowitz, I. A. Stegun “Handbook of Mathematical Functions” Dover, New York (1972)
- H. Ben Hamdin “Boundary element and transfer operator methods for multi-component wave systems” PhD Thesis, School of Mathematical Sciences, Nottingham University, UK( 2012)
- H. Ben Hamdin, G. Tanner “Multi-component BEM for the Helmholtz equation - A normal derivative method” IOS Press, Shock and Vibration, 19 (2012) 957–967
- E.B. Bogomolny “Semiclassical quantization of multidimensional systems” Nonlinearity, 5(1992) 805–866
- P. A. Boasman “Semiclassical Accuracy for Billiards” Nonlinearity, 7 (1994) 485
- S. C. Creagh, H. Ben Hamdin and G. Tanner “In-out decomposition of boundary integral equations” J.Phys. A: Math. Theor., 46(2013)
- B. Georgeot, R. E. Prange “Exact and Quasiclassical Fredholm Solutions of Quantum Billiards” Phys. Rev. Lett.,74 (15) (1992) 2851–2854
- B. Georgeot, R. E. Prange “Fredholm Theory for
- Quasiclassical Scattering” Phys. Rev. Lett.,74 (21) (1995) 4110–4113
- T. Prosen “Exact quantum surface of section method” J. Phys. A:Math. Gen., 27(1994)L709– L714
- T. Prosen “General quantum surface-of-section
- method” J. Phys. A:Math. Gen., 28(1995) 4133–4155
Abstract
We investigate the wave energy distribution in complex built-up structures with multiple interfaces at which the material properties change discontinuously. We formulate the transfer operator in such a way that it can in principle be made exact, and it is clear where the semiclassical approximations are made at each stage of the derivation. We reformulate the boundary integral equations for the Helmholtz equation in terms of incoming and outgoing boundary waves independently of the boundary conditions and decomposing the green functions into singular and regular components. For demonstration purposes, we apply a semiclassical form of the operator (corresponding to a high-frequency approximation) to polygonal coupled-cavity configurations with abrupt changes of the material properties (such as wave speed and absorption coefficients at the interfaces between the cavities).
Keywords
References
- M. Abramowitz, I. A. Stegun “Handbook of Mathematical Functions” Dover, New York (1972)
- H. Ben Hamdin “Boundary element and transfer operator methods for multi-component wave systems” PhD Thesis, School of Mathematical Sciences, Nottingham University, UK( 2012)
- H. Ben Hamdin, G. Tanner “Multi-component BEM for the Helmholtz equation - A normal derivative method” IOS Press, Shock and Vibration, 19 (2012) 957–967
- E.B. Bogomolny “Semiclassical quantization of multidimensional systems” Nonlinearity, 5(1992) 805–866
- P. A. Boasman “Semiclassical Accuracy for Billiards” Nonlinearity, 7 (1994) 485
- S. C. Creagh, H. Ben Hamdin and G. Tanner “In-out decomposition of boundary integral equations” J.Phys. A: Math. Theor., 46(2013)
- B. Georgeot, R. E. Prange “Exact and Quasiclassical Fredholm Solutions of Quantum Billiards” Phys. Rev. Lett.,74 (15) (1992) 2851–2854
- B. Georgeot, R. E. Prange “Fredholm Theory for
- Quasiclassical Scattering” Phys. Rev. Lett.,74 (21) (1995) 4110–4113
- T. Prosen “Exact quantum surface of section method” J. Phys. A:Math. Gen., 27(1994)L709– L714
- T. Prosen “General quantum surface-of-section
- method” J. Phys. A:Math. Gen., 28(1995) 4133–4155
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | September 26, 2015 |
| Submission Date | September 26, 2015 |
| Published in Issue | Year 2015 |