Complex temporal decay: a complete analysis.

Area of Science:

• Physics
• Chemistry
• Materials Science
• Engineering

Background:

• Relaxation dynamics are crucial for understanding system responses and identifying microscopic models.
• Non-trivial decay curves, which cannot be fitted by a single exponential, present challenges in data analysis.
• Accurate modeling of decay processes is essential across various scientific disciplines.

Purpose of the Study:

• To contrast two distinct yet related methods for fitting non-trivial decay curves.
• To evaluate the efficacy of exponential decomposition versus the gamma probability density function for complex relaxation dynamics.
• To provide insights into selecting appropriate functions for analyzing experimental data that deviates from simple exponential decay.

Main Methods:

• Comparative analysis of exponential decomposition and gamma probability density function fitting techniques.
• Application of both methods to datasets exhibiting non-trivial decay behavior.
• Evaluation of fitting accuracy and model suitability for each approach.

Main Results:

• Demonstration of how both exponential decomposition and gamma probability density functions can model complex decay curves.
• Highlighting the strengths and limitations of each method in different scenarios.
• Quantification of the differences in parameterization and model interpretability between the two approaches.

Conclusions:

• Both exponential decomposition and gamma probability density functions offer viable alternatives to single exponential fitting for complex relaxation dynamics.
• The choice between these methods depends on the specific characteristics of the decay data and the desired level of microscopic insight.
• This work aids researchers in selecting appropriate analytical tools for diverse scientific and engineering applications involving relaxation phenomena.