About: Location of the nodal set for thin curved tubes

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The Dirichlet Laplacian in curved tubes of arbitrary constant cross-section rotating together with the Tang frame along a bounded curve in Euclidean spaces of arbitrary dimension is investigated in the limit when the volume of the cross-section diminishes. We show that spectral properties of the Laplacian are, in this limit, approximated well by those of the sum of the Dirichlet Laplacian in the cross-section and a one-dimensional Schrodinger operator whose potential is expressed solely in terms of the first curvature of the reference curve. In particular, we establish the convergence of eigenvalues, the uniform convergence of eigenfunctions and locate the nodal set of the Dirichlet Laplacian in the tube near nodal points of the one-dimensional Schrodinger operator. As a consequence, we prove the %22nodal-line conjecture%22 for a class of non-convex and possibly multiply connected domains. The Dirichlet Laplacian in curved tubes of arbitrary constant cross-section rotating together with the Tang frame along a bounded curve in Euclidean spaces of arbitrary dimension is investigated in the limit when the volume of the cross-section diminishes. We show that spectral properties of the Laplacian are, in this limit, approximated well by those of the sum of the Dirichlet Laplacian in the cross-section and a one-dimensional Schrodinger operator whose potential is expressed solely in terms of the first curvature of the reference curve. In particular, we establish the convergence of eigenvalues, the uniform convergence of eigenfunctions and locate the nodal set of the Dirichlet Laplacian in the tube near nodal points of the one-dimensional Schrodinger operator. As a consequence, we prove the %22nodal-line conjecture%22 for a class of non-convex and possibly multiply connected domains. (en) Zabyvame se dirichletovskym laplacianem v krivych trubicich v limite scvrkavajiciho se prurezu. Ukazujeme, ze spektralni vlastnosti laplacianu lze v teto limite aproximovat jednodimensionalnim schroedingerovskym operatorem, jehoz potencial zavisi na krivosti referencni krivky trubice. Jako aplikaci dokazujeme Payneovu %22hypotesu o nodalnich carach%22 pro takovouto tridu nekonvexnich a pripadne i vicesouvislych oblasti. (cs)
Title	Location of the nodal set for thin curved tubes Location of the nodal set for thin curved tubes (en) Lokalisace nodalni mnoziny pro tenke krive trubice (cs)
skos:prefLabel	Location of the nodal set for thin curved tubes Location of the nodal set for thin curved tubes (en) Lokalisace nodalni mnoziny pro tenke krive trubice (cs)
skos:notation	RIV/61389005:_____/08:00311171!RIV09-AV0-61389005
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC06002), Z(AV0Z10480505)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2009
http://linked.open...aciTvurceVysledku	Krejčiřík, David
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	377040
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/08:00311171
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Dirichlet Laplacian; nodal set; tubes (en)
http://linked.open.../riv/klicoveSlovo	tubes nodal set Dirichlet Laplacian
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[006CB03D4D74]
http://linked.open...i/riv/nazevZdroje	Indiana University Mathematics Journal
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Doppler Institute for Mathematical Physics and Applied Mathematics
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	57
http://linked.open...iv/tvurceVysledku	Krejčiřík, David Freitas, P.
http://linked.open...ain/vavai/riv/wos	000254468900010
http://linked.open...n/vavai/riv/zamer	Jaderná fyzika a příbuzné obory v základním, aplikovaném a interdisciplinárním výzkumu
issn	0022-2518
number of pages	33 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Location of the nodal set for thin curved tubes Location of the nodal set for thin curved tubes Location of the nodal set for thin curved tubes Location of the nodal set for thin curved tubes

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