PROBLEMS ON THE HYDRODYNAMIC LIMIT AND RELATED TOPICS

流体力学极限问题及相关主题

• 批准号: 15540109
• 负责人: UCHIYAMA Kohei
• 金额: $ 2.18万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540109/
• 关键词: hydrodynamic limit; spectral gap; non-gradient system; principle of large deviations; fluctuation process; 流体力学; スケール極限; 排他過程; ランダムウォーク; Green関数; 局所平衡; スケーリング極限; 相対エントロピー; hydrodynamic limit; equilibrium fluctuation; spectral gap; non-line

In 2003 introducing a lattice gas model, called zero-range-exclusion model, which possesses two conservative quantities, we obtained an estimate of the spectral gap for the model [cf. An estimate of the spectral gap for zero-range-exclusion dynamics, Osaka Jour.Math. 141(no.4) (2004)]. This model is of non-gradient type and its spin values are unbounded so that there arise various interesting problems in the investigation of the hydrodynamic limit for the model.The estimate obtained, though not uniform in the density of the gas as those for many known models are, seems sufficiently accurate for dealing with the problems concerning its hydrodynamic limit. In fact based on our estimate we proved in 2004 that the fluctuations around the hydrodynamic scaling in the equilibrium converge to a process that is characterized as an infinite dimensional Ornstein-Uhlenbeck prosess [cf. Equilibrium fluctuations for zero-range-exclusion processes, Jour.Stat.Phys. (2004)]. We encountered a certain difficulty for proving the tightness of a sequence of the processes of finite size and resolved it by devising a trick by using a time reversed process.

在2003年引入了一个具有两个守恒量的格子气模型，称为零程排斥模型，我们得到了该模型的谱隙的估计[cf.零程排斥动力学的谱隙估计，Osaka Jour.Math. 141（no.4）（2004）]。该模型是非梯度型的，其自旋值是无界的，因此在研究该模型的流体动力学极限时会出现各种有趣的问题，所得到的估计虽然不象许多已知模型那样在气体密度上是均匀的，但对于处理与其流体动力学极限有关的问题似乎是足够精确的。事实上，基于我们的估计，我们在2004年证明了平衡中流体动力学标度周围的波动收敛到一个过程，该过程被表征为无限维的Ornstein-Uhlenbeck过程[cf.零程排斥过程的平衡涨落，《统计物理学杂志》（2004年）]。我们在证明有限大小过程序列的紧性时遇到了一定的困难，通过设计一个技巧，利用时间反演过程解决了这个困难。

项目成果

Heat escape

热量逸出

• 发表时间: 2003
• 期刊: Math. Ann. 327
• 作者: Kazuhiro Kurata;M.Maniwa;Kazuhiro Kurata;Minoru Murata
• 通讯作者: Minoru Murata

H.Tanemura, N.Yoshida: "Localization transition of d-friendly walkers"Probab.Th.Rel.Fields.. 125. 593-608 (2003)

H.Tanemura, N.Yoshida：“d 友好步行者的本地化转变”Probab.Th.Rel.Fields.. 125. 593-608 (2003)

Uniqueness theorems for parabolic equations and Martin BOUNDARY for elliptic equations in skew producl form

抛物线方程的唯一性定理和斜积形式椭圆方程的 Martin BOUNDARY

• 发表时间: 2005
• 期刊: J.Math.SOC.Japan 57
• 作者: H.Matsuzoe;J.Inoguchi;蔵野 正美;M.MURATA
• 通讯作者: M.MURATA

Uniqueness theorems for parabolic equations and Martin BOUNDARY for elliptic equations in skew product form

抛物线方程的唯一性定理和斜积形式椭圆方程的 Martin BOUNDARY

• 发表时间: 2005
• 期刊: J.Math.Soc.Japan 57
• 作者: M.Murata

Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems

• DOI: 10.1063/1.1765215
• 发表时间: 2004-02
• 期刊: Journal of Mathematical Physics
• 影响因子: 1.3
• 作者: M. Katori;H. Tanemura