TY - JOUR
T1 - Spectral properties of high contrast band-gap materials and operators on graphs
AU - Kuchment, Peter
AU - Kunyansky, Leonid A.
PY - 1999
Y1 - 1999
N2 - The theory of classical waves in periodic high contrast photonic and acoustic media leads to the spectral problem –Δu = λεu, where the dielectric constant ε(x) is a periodic function which assumes a large value ε near a periodic graph Σ; in ℝ2 and is equal to 1 otherwise. Existence and locations of spectral gaps are of primary interest. The high contrast asymptotics naturally leads to pseudodifferential operators of the Dirichlet-to-Neumann type on graphs and on more general structures. Spectra of these operators are studied numerically and analytically. New spectral effects are discovered, among them the "almost discreteness" of the spectrum for a disconnected graph and the existence of "almost localized" waves in someconnected purely periodic structures.
AB - The theory of classical waves in periodic high contrast photonic and acoustic media leads to the spectral problem –Δu = λεu, where the dielectric constant ε(x) is a periodic function which assumes a large value ε near a periodic graph Σ; in ℝ2 and is equal to 1 otherwise. Existence and locations of spectral gaps are of primary interest. The high contrast asymptotics naturally leads to pseudodifferential operators of the Dirichlet-to-Neumann type on graphs and on more general structures. Spectra of these operators are studied numerically and analytically. New spectral effects are discovered, among them the "almost discreteness" of the spectrum for a disconnected graph and the existence of "almost localized" waves in someconnected purely periodic structures.
UR - http://www.scopus.com/inward/record.url?scp=0033245667&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0033245667&partnerID=8YFLogxK
U2 - 10.1080/10586458.1999.10504384
DO - 10.1080/10586458.1999.10504384
M3 - Article
AN - SCOPUS:0033245667
VL - 8
SP - 1
EP - 28
JO - Experimental Mathematics
JF - Experimental Mathematics
SN - 1058-6458
IS - 1
ER -