Calculation of transport coefficient profiles in modulation experiments as an inverse problem

Area of Science:

• Physics
• Chemical Engineering
• Applied Mathematics

Background:

• Calculating transport profiles from experimental data is an inverse problem.
• Inverse problems are prone to ill-conditioning and singularity issues.
• Standard advection-diffusion models are often used for these calculations.

Purpose of the Study:

• To propose a reformulation of transport profile calculations for periodically modulated experiments.
• To address the ill-conditioning and singularity issues inherent in inverse problems.
• To improve the accuracy and uncertainty assessment of transport codes.

Main Methods:

• A matricial approach is proposed as a reformulation.
• The method is applied within the context of the standard advection-diffusion model.
• Analysis focuses on the vanishing determinant of a 2x2 matrix.

Main Results:

• The matricial approach offers a solution for ill-conditioning in transport profile calculations.
• It provides insights into the accuracy of existing transport codes.
• The method facilitates a more precise assessment of transport profiles and their uncertainties.

Conclusions:

• The proposed matricial approach enhances the reliability of transport profile calculations.
• It offers a pathway to more accurate determination of transport phenomena.
• This work contributes to a better understanding of inverse problem methodologies in scientific computing.