MATHEMATICAL FOUNDATIONS OF RENORMALIZATION GROUP THEORY AND ITS APPLICATIONS

重整化群理论的数学基础及其应用

基本信息

批准号：
09640304
负责人：
ITO Keiichi R.
金额：
$ 1.54万
依托单位：
SETSUNAN UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640304/
关键词：
Renormalization Group Random Walk Critical Temperature O (N) Spin Model Navier-Stokes equaion Viscosity Kormogorov law Dissipation O(N)Spin Model くり込み群関数行列式乱歩 O(N)スピン模型 polymer exponsicn ナヴィエ・ストークス方程式 Kolmogorov則モンテカルロ法

项目摘要

1. ITO and TAMURA (Kanazawa Univ.) studied classical 0(N) symmetric spin model by renormal ization group ( block spin transformation) method. They first showed that the correlation functions can be described by self-avoiding walks which enabled them to obtain almost optimal bounds for the critical temperatures. In the second stage, they argued the integrability of the functional de-terminent det^<N/2>(1+<approximately equal>92iGpsi/ROO<N>) with respect to psi, , where psi is the auxially field introcuced for Fourier Transformation. Using the technique called the polymer (cluster) expansion , they showed that the inverse critical temperature beta_C obeys the bound beta_C <bounded integral>1 N log N in two dimensions, which implies the existence of strong deviation. (beta_C-N for the dimension more than or equal to 3.) This method is expected to establish a complete proof of the conjecture beta_C = *by applying the present method recursively to the model. One typical problem in this approach is that there appear complicated non-local interactions after the transformations. So we need to control the main part of the flow. Some partial results are obtained and will be published soon.2. Teramoto investigated flow of non-compressible viscous fluid around a cyclinder by using cylindrical coordinate. He established that the equation exhibits global solution in time if the initial condition is sufficiently close to the stational current.3. Teramoto and Ito investigated properties of turbulence, among them, the Kolmogorov law about the dissipation of energy and deviation from it. They tried to derive the deviation from the Navier-Stokes equation but they could not obtain concrete results this year.

1。ITO和Tamura（Kanazawa Univ。）通过肾小效组（块旋转转换）方法研究了经典0（n）对称自旋模型。他们首先表明，可以通过自我避免的步行来描述相关函数，从而使他们能够在临界温度下获得几乎最佳的界限。在第二阶段，他们争论了功能性脱离术语det^<n/2>（1+ <大约等于> 92igpsi/roo <n>），相对于PSI，PSI是辅助场，用于傅立叶变换。他们使用称为聚合物（群集）膨胀的技术，表明临界温度beta_c在二维中遵守结合的beta_c <边界beta_c <边界积分> 1 n log n，这意味着存在强偏差。（对于尺寸的beta_c-n超过或等于3。）此方法有望通过将当前方法递归地应用于模型来建立猜想的beta_c = *的完整证明。在这种方法中，一个典型的问题是转化后出现复杂的非本地相互作用。因此，我们需要控制流的主要部分。获得了一些部分结果，并将很快发布2。 Teramoto通过使用圆柱坐标研究了不可压缩的粘性流体的流动。他确定，如果初始条件足够接近原子电流，则该方程式会在及时显示全球解决方案3。 Teramoto和ITO调查了湍流的特性，其中包括Kolmogorov法律，涉及能量耗散和偏离湍流。他们试图从Navier-Stokes方程中得出偏差，但今年无法获得具体的结果。