27 research outputs found

    Propagation of boundary-induced discontinuity in stationary radiative transfer

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    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)

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    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

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    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 H1H^1 solutions for Stationary Linearized Boltzmann Equations in a Small Convex Domain

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    In this article, we investigate the incoming boundary value problem for the stationary linearized Boltzmann equations in ΩR3 \Omega \subseteq \mathbb{R}^{3}. For a C2C^2 bounded domain with boundary of positive Gaussian curvature, the existence theory is established in H1(Ω×R3)H^{1}(\Omega \times \mathbb{R}^{3}) provided that the diameter of the domain Ω\Omega 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

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    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

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    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

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    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 W1,pW^{1,p} space for 1p<31 \leq p <3
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