What is it about?
Up to now, the X-ray diffraction theory grounded on the Takagi–Taupin equations with the first-order partial derivatives over the two coordinates within the X-ray scattering plane. In the work, the theoretical approach based on the first-order fractional Takagi–Taupin equations with the ‘quasitime variable’ of the order α ∈ (0, 1] along the crystal depth has been suggested and the corresponding X-ray Cauchy problem is formulated.
Featured Image
Why is it important?
Developing the comprehensive theory of the X-ray diffraction by distorted crystals remains to be topical of the mathematical physics.
Perspectives
A goal of our study is to establish the mathematical framework for processing the reference 2D imaging patterns data of the X-ray diffraction tomography and then to develop mathematical background for solving the inverse tomography problem based on the general concept of the fractional Takagi–Taupin equations. By using the mathematical framework and considering the results presented in this paper, we can claim that the fractional Takagi–Taupin equations approach is a good tool for obtaining digital structural crystal information from the reference 2D diffraction patterns tomography data. This would be a good topic for future research.
Murat Mamchuev
Read the Original
This page is a summary of: Towards to solution of the fractional Takagi–Taupin equations. The Green function method, Fractional Calculus and Applied Analysis, March 2023, Springer Science + Business Media,
DOI: 10.1007/s13540-023-00137-4.
You can read the full text:
Contributors
The following have contributed to this page
