$f^{-\alpha}$ Fluctuation in Nonintegral Dimensional Diffusion System
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概要
- 論文の詳細を見る
A homogeneous and isotropic diffusion system driven at a point is spherically symmetric, and its behavior is governed by a partial differential equation of two variables regardless of its dimension $N$. Since $N$ appears in this equation only as a coefficient, the equation does not lose its meaning even if it is nonintegral. Investigating the equation thus obtained, we found that the fluctuation at the point where the system is driven by white noise has a power spectrum proportional to $f^{-(2-N)}$ for $N<2$, and the solution to the diffusion equation diverges at that point for $N\geq 2$. Moreover, it is concluded that the discretized version of the nonintegral dimensional diffusion system provides an efficient method of generating $f^{-\alpha}$ fluctuations for any value of $\alpha$ from zero to two.
- INSTITUTE OF PURE AND APPLIED PHYSICSの論文
- 2003-05-15
著者
-
Akabane Hideo
Department Of Applied Electronics Tokyo Institute Of Technology
-
Agu Masahiro
Department Of Electrical And Electronic Engineering Ibaraki University
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OKAMOTO Yoshiwo
Department of Applied Electronics, Tokyo Institute of Technology
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Agu Masahiro
Department of Media and Telecommunications Engineering, Faculty of Engineering, Ibaraki University, Hitachi, Ibaraki 316-8511, Japan
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Okamoto Yoshiwo
Department of Electric Engineering, Chiba Institute of Technology, Tsudanuma 2-17-1, Narashino, Chiba 275-0016, Japan
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- $f^{-\alpha}$ Fluctuation in Nonintegral Dimensional Diffusion System