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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Stable law distributions are fundamental in describing phenomena like polymer dielectric behavior and semiconductor carrier motion.
  • Existing resources lack accurate tables and algorithms for estimating parameters in these relaxation models.

Purpose of the Study:

  • To present comprehensive tables of specific functions and their properties.
  • To provide accurate data for parameter estimation in relaxation models.
  • To facilitate the analysis of polymers and related materials.

Main Methods:

  • Generation of tables for functions Q(z) and V(z) over specified ranges of alpha.
  • Utilized a variety of methods to achieve six-place accuracy.
  • Developed algorithms for sequential parameter estimation.

Main Results:

  • Provided accurate numerical values for Q(z) and V(z) across broad alpha ranges.
  • Demonstrated the utility of the tables for parameter estimation.
  • Presented an illustrative example using existing literature data.

Conclusions:

  • The presented tables and methods offer a significant improvement for analyzing relaxation phenomena.
  • Accurate parameter estimation is now more accessible for models like the Williams-Watts model.
  • This work supports research in polymers, semiconductors, and statistical physics.