Simulation of Power-Law Relaxations by Analog Circuits: Fractal Distribution of Relaxation Times and Non-integer Exponents

Kazuhiro SAITO; Michio SUGI

Simulation of Power-Law Relaxations by Analog Circuits: Fractal Distribution of Relaxation Times and Non-integer Exponents

Kazuhiro SAITO, Michio SUGI

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Power-law decay of current for the application of step-function voltage observed for amorphous materials can be expressed by an admittance s^a(0a1) of a linear diode using complex angular frequency s. It is shown that power-law decay can be interpreted as a superposition of exponential decays having fractally distributed relaxation times and simulated using RC networks. By use of a similar manner, admittance s^-b (0b1) showing the relation of duality can be simulated using RL networks. According to these methods, we can synthesize the admittance involving non-integer exponents systematically.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E76-A No.2 pp.204-209

Publication Date: 1993/02/25

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Type of Manuscript: PAPER

Category: Analog Circuits and Signal Processing

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Kazuhiro SAITO, Michio SUGI, "Simulation of Power-Law Relaxations by Analog Circuits: Fractal Distribution of Relaxation Times and Non-integer Exponents" in IEICE TRANSACTIONS on Fundamentals, vol. E76-A, no. 2, pp. 204-209, February 1993, doi: .
Abstract: Power-law decay of current for the application of step-function voltage observed for amorphous materials can be expressed by an admittance s^a(0a1) of a linear diode using complex angular frequency s. It is shown that power-law decay can be interpreted as a superposition of exponential decays having fractally distributed relaxation times and simulated using RC networks. By use of a similar manner, admittance s^-b (0b1) showing the relation of duality can be simulated using RL networks. According to these methods, we can synthesize the admittance involving non-integer exponents systematically.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e76-a_2_204/_p

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@ARTICLE{e76-a_2_204,
author={Kazuhiro SAITO, Michio SUGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Simulation of Power-Law Relaxations by Analog Circuits: Fractal Distribution of Relaxation Times and Non-integer Exponents},
year={1993},
volume={E76-A},
number={2},
pages={204-209},
abstract={Power-law decay of current for the application of step-function voltage observed for amorphous materials can be expressed by an admittance s^a(0a1) of a linear diode using complex angular frequency s. It is shown that power-law decay can be interpreted as a superposition of exponential decays having fractally distributed relaxation times and simulated using RC networks. By use of a similar manner, admittance s^-b (0b1) showing the relation of duality can be simulated using RL networks. According to these methods, we can synthesize the admittance involving non-integer exponents systematically.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Simulation of Power-Law Relaxations by Analog Circuits: Fractal Distribution of Relaxation Times and Non-integer Exponents
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 204
EP - 209
AU - Kazuhiro SAITO
AU - Michio SUGI
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E76-A
IS - 2
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - February 1993
AB - Power-law decay of current for the application of step-function voltage observed for amorphous materials can be expressed by an admittance s^a(0a1) of a linear diode using complex angular frequency s. It is shown that power-law decay can be interpreted as a superposition of exponential decays having fractally distributed relaxation times and simulated using RC networks. By use of a similar manner, admittance s^-b (0b1) showing the relation of duality can be simulated using RL networks. According to these methods, we can synthesize the admittance involving non-integer exponents systematically.
ER -