Deriving stochastic crystal model from Hamiltonian dynamical system and the effect of relative effecacy
| Project/Area Number |
25800056
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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 | University of Tsukuba |
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Principal Investigator |
LIANG Song 筑波大学, 数理物質系, 准教授 (60324399)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 拡散過程 / 確率微分方程式 / 古典力学系 / 収束 / 強ポテンシャル / 経験分布 / 過程の収束 / １次元 / 総エネルギー / ノンランダム力学系 / 理想気体 / 等速運動 / 確率ハミルトン方程式 |
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| Outline of Final Research Achievements |
Put two heavy particles into an ideal gas environment, a system consists of infinitely many light particles with a certain initial distribution, and assume that the interactions between particles are non-random. In this research, the interactions between the heavy particles and the light particles are assumed to be of same type. We are interested in the problem of the limit behaviors of the heavy particles when the mass of the light particles converges to 0, under different settings.
We considered the stochastic differential equations corresponding to the cases with or without relative efficacy for the behaviors of heavy particles, and proved the convergences of the corresponding stochastic processes. This gives us the concrete expressions of the only candidate limit processes for each case. Also, we proved the convergence of the particle-environment model to this candidate for the case with relative efficacy.
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Report
(5 results)
Research Products
(7 results)
