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Transmission conditions in one-dimensional model of a rectangular lattice of thin quantum waveguides. / Nazarov, S.A.
в: Journal of Mathematical Sciences, Том 219, № 6, 2016, стр. 994-1016.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Transmission conditions in one-dimensional model of a rectangular lattice of thin quantum waveguides
AU - Nazarov, S.A.
N1 - Nazarov, S.A. Transmission Conditions in One-Dimensional Model of a Rectangular Lattice of Thin Quantum Waveguides. J Math Sci 219, 994–1015 (2016). https://doi.org/10.1007/s10958-016-3160-z
PY - 2016
Y1 - 2016
N2 - We consider the transmission conditions at vertices of the graph modeling a periodic rectangular lattice of thin quantum waveguides described by the spectral Dirichlet problem for the Laplace operator. The type of transmission conditions is determined by the structure of the space B Rbo of bounded solutions to the boundary layer problem in a cross-shaped waveguide with a circular core of radius R. We describe all variants of the structure of the space B Rst of nondecaying solutions and present methods for constructing hardly probable and very probable examples. Based on the method of matched asymptotic expansion, we construct all possible transmission conditions. We discuss numerical methods for computing critical radii, construction of the space B Rst, and classification of “trapped”/“almost standing” waves.
AB - We consider the transmission conditions at vertices of the graph modeling a periodic rectangular lattice of thin quantum waveguides described by the spectral Dirichlet problem for the Laplace operator. The type of transmission conditions is determined by the structure of the space B Rbo of bounded solutions to the boundary layer problem in a cross-shaped waveguide with a circular core of radius R. We describe all variants of the structure of the space B Rst of nondecaying solutions and present methods for constructing hardly probable and very probable examples. Based on the method of matched asymptotic expansion, we construct all possible transmission conditions. We discuss numerical methods for computing critical radii, construction of the space B Rst, and classification of “trapped”/“almost standing” waves.
UR - https://link.springer.com/article/10.1007/s10958-016-3160-z
M3 - Article
VL - 219
SP - 994
EP - 1016
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 6
ER -
ID: 7635811