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Related Experiment Video

Updated: Jan 1, 2026

15N CPMG Relaxation Dispersion for the Investigation of Protein Conformational Dynamics on the µs-ms Timescale
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Adaptive multi-parameter regularization approach to construct the distribution function of relaxation times.

Mark Žic1, Sergiy Pereverzyev2,3, Vanja Subotić4

  • 11Ruđer Bošković Institute, P.O. Box 180, 10000 Zagreb, Croatia.

GEM : International Journal on Geomathematics
|December 17, 2019
PubMed
Summary

This study introduces a new method for analyzing electrochemical impedance spectroscopy (EIS) data to determine the distribution function of relaxation times (DFRT). The technique enhances system process insights by employing regularized collocation and a novel parameter choice strategy.

Keywords:
DFRTEISIll-posed problemRegularization

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Area of Science:

  • Electrochemistry
  • Computational Science
  • Data Analysis

Background:

  • Electrochemical impedance spectroscopy (EIS) provides limited insight into complex system processes.
  • Distribution function of relaxation times (DFRT) offers a more detailed analysis of system timescales.
  • Extracting DFRT from noisy EIS data involves solving an ill-posed Fredholm integral equation.

Purpose of the Study:

  • To develop and implement a regularized collocation method for DFRT analysis.
  • To introduce an adjusted multiple parameter choice strategy for DFRT problem-solving.
  • To validate the proposed technique using synthetic and real-world EIS data.

Main Methods:

  • Implementation of regularized collocation for the DFRT problem, enabling symbolic computation.
  • Treatment of the regularized collocation as a multi-parameter regularization approach.
  • Adjustment and application of a multiple parameter choice strategy based on aggregating regularized approximants.

Main Results:

  • The proposed regularized collocation method successfully reproduces known exact DFRT from synthetic data.
  • The technique demonstrates robust performance in extracting timescale characteristics from EIS measurements.
  • Comparison with existing DRTtools software shows comparable and reliable data acquisition.

Conclusions:

  • The developed regularized collocation method provides a powerful tool for DFRT analysis.
  • The novel parameter choice strategy enhances the accuracy and reliability of DFRT extraction.
  • This approach offers a valuable alternative for detailed electrochemical system analysis.