Fluctuation spreading from random environments to random walks
| Project/Area Number |
16K17620
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Nihon University |
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Principal Investigator |
KUBOTA Naoki 日本大学, 理工学部, 助教 (20754972)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 不規則媒質中の乱歩 / ファーストパッセージパーコレーション / フロッグモデル / 大偏差原理 / レート関数 / 連続性 / ランダムポテンシャル中の乱歩 / 確率論 |
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| Outline of Final Research Achievements |
Media that exist in the natural world often have complex and random structure, and “random walks in random environments” are one of the mathematical models describing particles moving in such media. In this research, we treated the above model and studied how the randomness for the structure of the media affects the behavior of the random walk. As a result, we obtained that the diffusivities for two different media are very close if their strengths of randomness are very similar (for instance, the ease of forming cavities in a sponge). To obtain this result, we investigated several related models and got new properties for the behaviors of those models.
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| Academic Significance and Societal Importance of the Research Achievements |
不規則な構造を持つ媒質中における粒子の挙動は，数学的・物理的に未解明な部分が多い．特に，粒子の拡散度合を特徴付ける性質についてはほとんど何もわかっていない．この未知の領域に対して，「不規則性の状態が近い媒質においては粒子の拡散度合も近くなる」という連続性の問題を本研究では解決することに成功した．また，不規則媒質中の乱歩の挙動は感染症の拡大やインターネット上の情報拡散にも深く関連していることから，これらの現実的な拡散現象の問題にも，本研究結果や解析手法の応用が期待できる．さらに，様々な数理モデルを関連付け研究を行ったため，本研究は実社会における幅広い拡散現象の解析にも役立つと思われる．
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Report
(6 results)
Research Products
(25 results)
