Exploration of anomalous diffusion phenomena by means of dynamical systems theory and scaling limits
| Project/Area Number |
16KT0021
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 特設分野 |
|---|
| Research Field |
Mathematical Sciences in Search of New Cooperation
|
|---|
| Research Institution | Keio University |
|---|
Principal Investigator |
Takahasi Hiroki 慶應義塾大学, 理工学部(矢上), 准教授 (00467440)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
佐々田 槙子 東京大学, 大学院数理科学研究科, 准教授 (00609042)
秋元 琢磨 東京理科大学, 理工学部物理学科, 准教授 (30454044)
|
|---|
| Project Period (FY) |
2016-07-19 – 2020-03-31
|
| Project Status |
Completed (Fiscal Year 2019)
|
| Budget Amount *help |
¥14,300,000 (Direct Cost: ¥11,000,000、Indirect Cost: ¥3,300,000)
Fiscal Year 2018: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
|
|---|
| Keywords | 力学系 / 異常拡散 / スケール極限 / 大偏差原理 / 可算マルコフシフト / 非一様双曲力学系 / 拡散制御理論 |
|---|
| Outline of Final Research Achievements |
The Large Deviation Principle in dynamical systems is considered to have an important connection with deterministic diffusion. We have succeeded in establishing the Large Deviation Principle for various dynamical systems which lack the uniform hyperbolicity structure. For stochastic models of diffusive phenomena, we have obtained fairly good results regarding ergodic properties of mean-square displacements, time-dependence of diffusion coefficients and refined analyses of diffusion exponents. We have discovered a new type of anomalous diffusion phenomenon in stochastically perturbed Hamiltonian systems.
|
| Academic Significance and Societal Importance of the Research Achievements |
力学系の大偏差原理や異常拡散現象の確率モデルに関し、研究期間内に多くの興味深い成果が得られた点で、学術的意義は高い。しかし、これらの個々の成果を融合、昇華させ、研究開始当初の主目標であったカオス拡散による異常拡散現象の数学的な理解につなげるには、さらなる時間と努力が必要であると思われる。これは今後の課題としたい。力学系理論、非線型物理学、確率論とそれぞれ異なる背景を持つ３人の研究者（高橋、秋元、佐々田）の間の研究交流の促進につながった点では、社会的な意義も十分にあったと考える。
|
Report
(5 results)
Research Products
(63 results)
