27 research outputs found
Propagation of boundary-induced discontinuity in stationary radiative transfer
We consider the boundary value problem of the stationary transport equation
in the slab domain of general dimensions. In this paper, we discuss the
relation between discontinuity of the incoming boundary data and that of the
solution to the stationary transport equation. We introduce two conditions
posed on the boundary data so that discontinuity of the boundary data
propagates along positive characteristic lines as that of the solution to the
stationary transport equation. Our analysis does not depend on the celebrated
velocity averaging lemma, which is different from previous works. We also
introduce an example in two dimensional case which shows that piecewise
continuity of the boundary data is not a sufficient condition for the main
result.Comment: 15 pages, no figure
Spectral analysis on the elastic Neumann-Poincaré operator (Analysis of inverse problems through partial differential equations and related topics)
The elastic Neumann-Poincaré (eNP) operator is a boundary integral operator that appears naturally when we solve classical boundary value problems for the Lame system using layer potentials, and there is rapidly growing interest in its spectral properties recently in relation to cloaking by anomalous localized resonance (CALR). In this workshop, the speaker reported two results on the spectrum of the eNP operator. The first one is the polynomial compactness of the three-dimensional eNP operator on a C¹, α surface for a > 0, which describes a distribution of eigenvalues. The second one is on the essential spectrum of the two-dimensional eNP operator on a curve which is smooth except at a corner
Spectral structure of the Neumann--Poincar\'e operator on tori
We address the question whether there is a three-dimensional bounded domain
such that the Neumann--Poincar\'e operator defined on its boundary has
infinitely many negative eigenvalues. It is proved in this paper that tori have
such a property. It is done by decomposing the Neumann--Poincar\'e operator on
tori into infinitely many self-adjoint compact operators on a Hilbert space
defined on the circle using the toroidal coordinate system and the Fourier
basis, and then by proving that the numerical range of infinitely many
operators in the decomposition has both positive and negative values.Comment: 14 page
On the Existence of solutions for Stationary Linearized Boltzmann Equations in a Small Convex Domain
In this article, we investigate the incoming boundary value problem for the
stationary linearized Boltzmann equations in . For a bounded domain with boundary of positive Gaussian
curvature, the existence theory is established in provided that the diameter of the domain is small
enough.Comment: 19 pages, 1 figur
入射境界条件下での輸送方程式の解の正則性について
京都大学0048新制・課程博士博士(情報学)甲第21212号情博第665号新制||情||115(附属図書館)京都大学大学院情報学研究科先端数理科学専攻(主査)教授 磯 祐介, 教授 木上 淳, 助手 藤原 宏志学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA
Factors influencing the induction of adventitious bud and callus in the brown alga Sargassum horneri (Turner) C. Agardh
A high frequency of callus induction and propagation from leaf explants of the brown alga Sargassum horneri was achieved within 2 months of culture when grown in medium supplemented with 5 μM uniconazole, which is a triazole-type inhibitor of cytochrome P450 enzymes. Adventitious buds were efficiently formed from the pigmented callus after transfer to medium without uniconazole, indicating that treatment with uniconazole was more beneficial for regeneration of the alga. Favorable culture conditions for induction of adventitious buds and calli included temperatures of 15 to 25 °C and light levels of 20 to 200 μmol photons m−2 s−1. Blue light promoted the production of adventitious buds and calli. The frequency of formation of adventitious buds and calli in explants from thalli with one leaf was more than 90 %, while it was 10 % only when explants were sourced from thalli with 9 to 11 leaves. These findings will be useful for clonal propagation and storage of seed materials for mariculture of Sargassum species
On the Existence and Regularity for Stationary Boltzmann Equation in a Small Domain
In this article, we study the stationary Boltzmann equation with the incoming
boundary condition for the hard potential cases. Assuming the smallness of the
domain and a suitable normal curvature condition on the boundary, we find a
suitable solution space which is a proper subset of the space for