229 Q-NA ߥʡ
2009 ǯ 1 6 () 15:30 - 17:00
彣Ȣꥭѥ 3 3 3311 漼
Michael Plum (Department of Mathematics, Universitt Karlsruhe)
A computer-assisted band-gap proof for 3D photonic crystals
Photonic crystals are usually modelled by a spectral problem for Maxwell's equations with periodic electric permittivity. By Floquet-Bloch theory, the spectrum has band-gap structure, and the bands are characterized by families of eigenvalue problems on a periodicity cell, depending on a parameter $k$ varying in the Brillouin zone $K$. We propose a computer-assisted method for proving the presence of band-gaps: For $k$ in a finite grid in $K$, we obtain eigenvalue enclosures by variational methods, and then capture all $k \in K$ by a perturbation argument.

230 Q-NA ߥʡ
2009 ǯ 1 13 () 15:30 - 17:00
彣Ȣꥭѥ 3 3 3311 漼
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ܸǤ, ήΤߺѤ븽ݤͷ׻ˤƸ뤳ȤɸǤ. ήΤߺѤ븽ݤɽŪȤƤ, ¡ưȷή󤲤. դϿ¡ưˤư, ɤ俴¡Ϸή饹ȥ쥹ѷ. Τ褦ʸݤήΤϢ˻ۤȹͤ. ϢǤ, ư«郎и뤳ȤħȤʤ. ħˤ, Ϣοͷ׻ϺȤʤ뤬, 桹ΥήˡMPSˡ(γˡ)Ȥ߹碌ͷ׻ˡȯ, ͷ׻ǽˤ. ȯϢ׻ˡѤ, ήΤưݥ(ñ㲽¡ȷή)ʤɤθݤκƸԤä.
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