Jpn. J. Appl. Phys. 39 (2000) pp. 4241-4244  |Next Article|  |Table of Contents|
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1/f Fluctuation in a Discrete One-Dimensional Diffusion System

Hideo Akabane, Yoshiwo Okamoto¹ and Masahiro Agu

(Received February 21, 2000; accepted for publication April 24, 2000)

A one-dimensional diffusion system is considered to be a convenient tool to generate 1/f fluctuations by a computer, since its frequency response to the driving force concentrated at one point is proportional to 1/√f. However, the frequency response of a discrete diffusion system depends not only on the spatial increment and time step but also on the type of finite difference used to approximate the derivative. In the present paper, we specify the conditions under which a discrete diffusion system has a frequency response strictly proportional to 1/√f.

KEYWORDS: 1/f fluctuation, one-dimensional diffusion system, continuous system, discrete system
URL: http://jjap.ipap.jp/link?JJAP/39/4241/
DOI: 10.1143/JJAP.39.4241

References | Citing Article (1)

1. J. B. Johnson: Phys. Rev. 26 (1925) 71[APS].
2. M. Sano, H. Nakauchi, H. Akabane and T. Musha: Jpn. J. Appl. Phys. 29 (1990) 2186[IPAP].
3. K. Tanaka and Y. Aizawa: Prog. Theor. Phys. 90 (1993) 547[IPAP].
4. R. F. Voss and J. Clarke: Phys. Rev. Lett. 36 (1976) 42[APS].
5. H. Akabane and M. Agu: Jpn. J. Appl. Phys. 37 (1998) L830[IPAP].
6. H. Furukawa: Phys. Rev. A 34 (1986) 2315[APS].
7. H. Jensen: Phys. Rev. 40 (1989) 7425[APS].
8. H. Akabane, K. Nakaya and M. Agu: to be published in Jpn. J. Appl. Phys.
9. J. Crank and P. Nicholson: Proc. Camb. Philos. Soc. (Math. Phys. Sci.) 43 (1947) 50.