### Abstract

The problem regarding the distribution of relaxation times (DRT) is revisited and discussed from the view point of mathematics and computing algorithms. Although the algorithm in conventional DRT analysis software involves an implicit hypothesis that the DRT is a continuous real function with a continuous relaxation time, this hypothesis is not a principle of nature but a requirement of a mathematical equation used for analysis. Note that the DRT calculated using the conventional algorithm is a continuous distribution of relaxation times (CDRT). As per the CDRT hypothesis, the DRT is a set of discrete values. On the other hand, there is a model that involves the discrete distribution of relaxation times (DDRT). Thus, the fundamental difference between the CDRT and DDRT models originates from their basic hypothesis. Using modern computers, the DDRT can be beneficial for analyzing non-Debye-type spectra.

Original language | English |
---|---|

Pages (from-to) | 940021-940027 |

Number of pages | 7 |

Journal | journal of the physical society of japan |

Volume | 87 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*journal of the physical society of japan*,

*87*(9), 940021-940027. https://doi.org/10.7566/JPSJ.87.094002

**Distribution of relaxation time analysis for non-ideal immittance spectrum : Discussion and progress.** / Kobayashi, Kiyoshi; Suzuki, Tohru.

Research output: Contribution to journal › Article

*journal of the physical society of japan*, vol. 87, no. 9, pp. 940021-940027. https://doi.org/10.7566/JPSJ.87.094002

}

TY - JOUR

T1 - Distribution of relaxation time analysis for non-ideal immittance spectrum

T2 - Discussion and progress

AU - Kobayashi, Kiyoshi

AU - Suzuki, Tohru

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The problem regarding the distribution of relaxation times (DRT) is revisited and discussed from the view point of mathematics and computing algorithms. Although the algorithm in conventional DRT analysis software involves an implicit hypothesis that the DRT is a continuous real function with a continuous relaxation time, this hypothesis is not a principle of nature but a requirement of a mathematical equation used for analysis. Note that the DRT calculated using the conventional algorithm is a continuous distribution of relaxation times (CDRT). As per the CDRT hypothesis, the DRT is a set of discrete values. On the other hand, there is a model that involves the discrete distribution of relaxation times (DDRT). Thus, the fundamental difference between the CDRT and DDRT models originates from their basic hypothesis. Using modern computers, the DDRT can be beneficial for analyzing non-Debye-type spectra.

AB - The problem regarding the distribution of relaxation times (DRT) is revisited and discussed from the view point of mathematics and computing algorithms. Although the algorithm in conventional DRT analysis software involves an implicit hypothesis that the DRT is a continuous real function with a continuous relaxation time, this hypothesis is not a principle of nature but a requirement of a mathematical equation used for analysis. Note that the DRT calculated using the conventional algorithm is a continuous distribution of relaxation times (CDRT). As per the CDRT hypothesis, the DRT is a set of discrete values. On the other hand, there is a model that involves the discrete distribution of relaxation times (DDRT). Thus, the fundamental difference between the CDRT and DDRT models originates from their basic hypothesis. Using modern computers, the DDRT can be beneficial for analyzing non-Debye-type spectra.

UR - http://www.scopus.com/inward/record.url?scp=85052398676&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052398676&partnerID=8YFLogxK

U2 - 10.7566/JPSJ.87.094002

DO - 10.7566/JPSJ.87.094002

M3 - Article

AN - SCOPUS:85052398676

VL - 87

SP - 940021

EP - 940027

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 9

ER -