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諸分野のための数学研究会
過去の記録 ～10/22｜次回の予定｜今後の予定 10/23～
| 開催情報 | 火曜日 10:30～11:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 儀我美一、石村直之(中央大学)、齊藤宣一、山本昌宏、三竹大寿(早稲田大学) |
| セミナーURL | https://www.math.sci.hokudai.ac.jp/coe/sympo/various/ |
| 目的 | 北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)の情報が掲載されております。 |
今後の予定
2026年11月20日(金)
14:00-15:00 数理科学研究科棟(駒場) 056号室
通常の曜日・時刻と異なります。
Dieter Bothe 氏 (ダルムシュタット工科大学)
Multicomponent Diffusion — Modelling and Analysis (English)
通常の曜日・時刻と異なります。
Dieter Bothe 氏 (ダルムシュタット工科大学)
Multicomponent Diffusion — Modelling and Analysis (English)
[ 講演概要 ]
Diffusion in fluid systems composed of several chemical species is a classical subject with a surprisingly rich mathematical structure. In contrast to scalar diffusion, the motion of the individual components is coupled through conservation laws, thermodynamic constraints, and interspecies interactions. This leads to strongly coupled systems of nonlinear partial differential equations, whose modelling and analysis are closely intertwined. The talk introduces the main ideas of multicomponent diffusion, from its physical and thermodynamic foundations to modern mathematical formulations. Particular emphasis is placed on the relation between physically meaningful constitutive laws and the qualitative properties of the resulting PDE systems, including the question of global regularity for large data.
Diffusion in fluid systems composed of several chemical species is a classical subject with a surprisingly rich mathematical structure. In contrast to scalar diffusion, the motion of the individual components is coupled through conservation laws, thermodynamic constraints, and interspecies interactions. This leads to strongly coupled systems of nonlinear partial differential equations, whose modelling and analysis are closely intertwined. The talk introduces the main ideas of multicomponent diffusion, from its physical and thermodynamic foundations to modern mathematical formulations. Particular emphasis is placed on the relation between physically meaningful constitutive laws and the qualitative properties of the resulting PDE systems, including the question of global regularity for large data.
2026年12月08日(火)
10:30-11:30 数理科学研究科棟(駒場) 056号室
Prashant Athavale 氏 (Clarkson University)
Total Variation Methods for Denoising and Inpainting Crystallographic Orientation Maps (English)
Prashant Athavale 氏 (Clarkson University)
Total Variation Methods for Denoising and Inpainting Crystallographic Orientation Maps (English)
[ 講演概要 ]
Electron backscatter diffraction (EBSD) provides spatial maps of crystal orientations in polycrystalline materials. These measurements often contain noise and missing data, complicating the identification of grains and their boundaries. In this talk, I will introduce the mathematical challenges of restoring orientation maps and present our work on total variation methods for denoising and hybrid methods for filling missing regions. Particular attention will be given to preserving grain boundaries while recovering useful microstructural information. I will also discuss ongoing work on using shape tensors and statistical comparisons of grain geometry to guide stopping criteria for denoising flows. The presentation will emphasize connections between variational methods, geometric representations, and materials imaging.
Electron backscatter diffraction (EBSD) provides spatial maps of crystal orientations in polycrystalline materials. These measurements often contain noise and missing data, complicating the identification of grains and their boundaries. In this talk, I will introduce the mathematical challenges of restoring orientation maps and present our work on total variation methods for denoising and hybrid methods for filling missing regions. Particular attention will be given to preserving grain boundaries while recovering useful microstructural information. I will also discuss ongoing work on using shape tensors and statistical comparisons of grain geometry to guide stopping criteria for denoising flows. The presentation will emphasize connections between variational methods, geometric representations, and materials imaging.
