Research output: Contribution to journal › Article
Bound states of waveguides with two right-angled bends. / Nazarov, S.A.; Ruotsalainen, K.; Uusitalo, P.
In: Journal of Mathematical Physics, No. 2, 2015, p. None.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Bound states of waveguides with two right-angled bends
AU - Nazarov, S.A.
AU - Ruotsalainen, K.
AU - Uusitalo, P.
PY - 2015
Y1 - 2015
N2 - © 2015 AIP Publishing LLC.We study waveguides with two right-angled bends. These waveguides are in shape of letter Z or alternatively C. For both cases, we assume the semi-infinite arms of waveguides to be of unit width. These arms are connected to each other by a rectangle with side lengths H and L. We consider the Dirichlet boundary value problem for Laplacian and study the spectrum of the corresponding operator. It is shown that the total multiplicity of the discrete spectrum depends on the parameters H and L. In particular, for the width H = 1, we compare the relation between the eigenvalues of both waveguides and moreover, we observe that the monotonicity in height L of the first eigenvalue of the Z-shaped waveguide is not achieved while the question of the monotonicity of the second eigenvalue remains open. The eigenvalues in the C-shaped waveguide are monotone. We construct and justify the asymptotics of the eigenvalues for the cases H = 1, L → ∞, H = 1, L → 1 + 0, and H, L → ∞.
AB - © 2015 AIP Publishing LLC.We study waveguides with two right-angled bends. These waveguides are in shape of letter Z or alternatively C. For both cases, we assume the semi-infinite arms of waveguides to be of unit width. These arms are connected to each other by a rectangle with side lengths H and L. We consider the Dirichlet boundary value problem for Laplacian and study the spectrum of the corresponding operator. It is shown that the total multiplicity of the discrete spectrum depends on the parameters H and L. In particular, for the width H = 1, we compare the relation between the eigenvalues of both waveguides and moreover, we observe that the monotonicity in height L of the first eigenvalue of the Z-shaped waveguide is not achieved while the question of the monotonicity of the second eigenvalue remains open. The eigenvalues in the C-shaped waveguide are monotone. We construct and justify the asymptotics of the eigenvalues for the cases H = 1, L → ∞, H = 1, L → 1 + 0, and H, L → ∞.
U2 - 10.1063/1.4907559
DO - 10.1063/1.4907559
M3 - Article
SP - None
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 2
ER -
ID: 4011765