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Engineering educational research section Science Center for Engineering Education |
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IZUHARA Hirofumi
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Degree 【 display / non-display 】
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Doctor (Science) ( 2008.3 Hiroshima University )
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修士(理学) ( 2005.3 広島大学 )
Research Areas 【 display / non-display 】
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Natural Science / Basic mathematics
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Natural Science / Basic mathematics / Applied mathematics
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Natural Science / Applied mathematics and statistics
Papers 【 display / non-display 】
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An instability framework of Hopf–Turing–Turing singularity in 2-component reaction–diffusion systems Reviewed
Izuhara H., Kobayashi S.
Japan Journal of Industrial and Applied Mathematics 42 ( 1 ) 63 - 112 2025.1
Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：Japan Journal of Industrial and Applied Mathematics
This paper investigates pattern formation in 2-component reaction–diffusion systems with linear diffusion and local reaction terms. We propose a novel instability framework characterized by 0-mode Hopf instability, m and m + 1 mode Turing instabilities in 2-component reaction–diffusion systems. A normal form for the codimension 3 bifurcation is derived via the center manifold reduction, representing one of the main results in this paper. Additionally, we present numerical results on the bifurcation of certain reaction–diffusion systems and on the chaotic behavior of the normal form.
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Iida M., Izuhara H., Kon R.
Discrete and Continuous Dynamical Systems - Series B 28 ( 12 ) 6159 - 6178 2023.12
Authorship：Corresponding author Language：English Publishing type：Research paper (scientific journal) Publisher：Discrete and Continuous Dynamical Systems - Series B
Cross-diffusion may be an important driving force of pattern formation in population models. Recently, a relation between cross-diffusion and reaction-diffusion systems has been revealed from the mathematical modeling point of view. In this paper, we derive a predator–prey model with cross-diffusion from a simple reaction-diffusion system with two behavioral states in the predator population and examine whether cross-diffusion can induce spatial patterns in predator–prey models. We assume that the predators have identical behavioral characteristics except for their mobility and searching activity for preys: we consider two states, namely less mobile predators searching for preys more actively than mobile predators. Our analysis shows that cross-diffusion derived in this situation can induce spatial patterns if the prey-density-dependent conversion rate from less mobile state to mobile one increases more rapidly than that from mobile to less mobile at high prey density.
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SPATIAL SEGREGATION OF MULTIPLE SPECIES: A SINGULAR LIMIT APPROACH Reviewed International coauthorship
Izuhara H., Monobe H., Wu C.H.
Discrete and Continuous Dynamical Systems - Series B 28 ( 12 ) 6208 - 6232 2023.12
Authorship：Lead author Language：English Publishing type：Research paper (scientific journal) Publisher：Discrete and Continuous Dynamical Systems - Series B
The spatial segregation of the populations occurs commonly in ecology. One typical way to understand this phenomenon is to consider strong competition in some species. In this paper, we shall consider multiple-species competition-diffusion models. Under the condition that some interspecies competition rates are large, we show that the segregation phenomenon occurs. Furthermore, we derive some two-phase Stefan-like problems appearing as the singular limit, which may provide some modeling interpretation for free boundary problems studied in the literature.
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PARTIALLY OVERLAPPING TRAVELLING WAVES IN A PARABOLIC-HYPERBOLIC SYSTEM Reviewed International coauthorship
Bertsch M., Izuhara H., Mimura M., Wakasa T.
Discrete and Continuous Dynamical Systems - Series B 28 ( 12 ) 5934 - 5966 2023.12
Language：English Publishing type：Research paper (scientific journal) Publisher：Discrete and Continuous Dynamical Systems - Series B
We study the existence of travelling wave solutions of a one-dimensional parabolic-hyperbolic system for u(x, t) and v(x, t), which arises as a model for contact inhibition of cell growth. Compared to the scalar Fisher-KPP equation, the structure of the travelling wave solutions is surprisingly rich and strongly parameter-dependent. In the present paper we consider a parameter regime where the minimal wave speed is positive. We show that there exists a branch of travelling wave solutions for wave speeds which are larger than the minimal one. But the main result is more surprising: for certain values of the parameters the travelling wave with minimal wave speed is not segregated (a solution is called segregated if the product uv vanishes almost everywhere) and in that case there exists a second branch of “partially overlapping” travelling wave solutions for speeds between the minimal one and that of the (unique) segregated travelling wave.
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A new instability framework in 2-component reaction-diffusion systems
Hirofumi Izuhara, Shunsuke Kobayashi
arXiv 2023.11
Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)
Books 【 display / non-display 】
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辻川 亨, 出原 浩史（ Role： Joint author）
学術図書出版社 2024.3 （ ISBN:9784780612400 ）
Language：Japanese Book type：Scholarly book
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辻川 亨, 出原 浩史（ Role： Joint author）
学術図書出版社 2017.11
Language：Japanese Book type：Scholarly book
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Murray J. D. (James Dickson), 勝瀬 一登, 三村 昌泰, 瀬野 裕美, 吉田 雄紀, 青木 修一郎, 宮嶋 望, 半田 剛久, 清田 正紘, 河内 一樹, 中口 悦史, 梯 正之, 川崎 廣吉, 池田 幸太, 森下 喜弘, 出原 浩史, 関村 利朗, 昌子 浩登, 柴田 達夫, 上田 肇一, 本多 久夫, 稲葉 寿（ Role： Joint translator）
丸善出版 2016
Language：Japanese Book type：Scholarly book
MISC 【 display / non-display 】
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第31回日本数理生物学会大会報告
飯田雅人, 今隆助, 出原浩史
日本数理生物学会ニュースレター ( 96 ) 2 - 5 2022.2
Language：Japanese Publishing type：Meeting report
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半乾燥地域における植生パターンと数理モデル Invited
出原浩史
数理科学 数理モデリングと生命科学 59 ( 9 ) 51 - 57 2021.9
Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)
Presentations 【 display / non-display 】
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反応拡散系に現れる複雑ダイナミクス：分岐構造から探る起源 Invited
出原浩史
北陸応用数り研究会
Event date： 2025.2.20 - 2025.2.22
Presentation type：Oral presentation (invited, special)
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2成分反応拡散系における複雑ダイナミクスの起源 Invited
出原浩史
数学と現象 in 清里
Event date： 2025.2.2 - 2025.2.4
Presentation type：Oral presentation (invited, special)
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遅延を含むFisher-KPP方程式のsemi-waveについて Invited
出原浩史
RIMS共同研究「時間遅れ系と数理科学：理論と応用の新たな展開に向けて」
Event date： 2024.11.13 - 2024.11.15
Presentation type：Oral presentation (invited, special)
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遅延を含むFisher-KPP方程式のsemi-waveについて−数値計算の視点から− Invited
出原浩史
日本応用数理学会2024年度年会 正会員OS「時間遅れと数理」
Event date： 2024.9.14 - 2024.9.16
Presentation type：Oral presentation (invited, special)
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2成分反応拡散系の解の構造 Invited
出原浩史
数学と現象 in 伊香保
Event date： 2024.8.30 - 2024.9.1
Presentation type：Oral presentation (invited, special)
Awards 【 display / non-display 】
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熱コレ2022 最優秀動画賞
2022.10 日本機械学会 熱工学コンファレンス2022 様々な紙の燃え方
中村 愛美, 小林 温斗, 鈴木 啓介, 松岡 常吉, 出原 浩史, 桑名 一徳, 中村 祐二
Award type：Award from Japanese society, conference, symposium, etc.
Grant-in-Aid for Scientific Research 【 display / non-display 】
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不安定な燃え拡がり挙動の評価指標の検討
Grant number：24K07960 2024.04 - 2027.03
独立行政法人日本学術振興会 科学研究費基金 基盤研究(C)
Authorship：Coinvestigator(s)
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個体群の広がりを抑制する障害物問題とその解析
Grant number：23K03216 2023.04 - 2026.03
独立行政法人日本学術振興会 科学研究費基金 基盤研究(C)
Authorship：Coinvestigator(s)
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狭い空間における燃焼の数理モデルと理論解析
Grant number：21K03353 2021.04 - 2025.03
独立行政法人日本学術振興会 科学研究費基金 基盤研究(C)
Authorship：Principal investigator
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燃焼限界近傍における火炎の燃え拡がり方向を決めるメカニズムの解明
Grant number：20K05001 2020.04 - 2023.03
独立行政法人日本学術振興会 科学研究費補助金 基盤研究(C)
Authorship：Coinvestigator(s)
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燃焼モデルに現れるパターンの計算機支援解析
Grant number：17K14237 2017.04 - 2022.03
科学研究費補助金 若手研究(B)
Authorship：Principal investigator
Available Technology 【 display / non-display 】
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複雑現象の数理モデリングと計算機シミュレーション
自然・社会に現れるパターン形成の数理
機械学習と数理モデリングRelated fields where technical consultation is available：・複雑現象の数理モデリング
・数値シミュレーションMessage：・共同研究の希望テーマ：複雑現象を記述する数理モデルの構築とその応用
・数理モデルを用いた開発というニーズがあれば、ぜひ教えてください。