Speaker: Katarzyna Gorska, Institute of Nuclear Physics, Polish Academy of Sciences, Krakow, Poland

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

YouTube : https://youtu.be/GIwa-fql8xQ  

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: memory effects subordination, operational method

Abstract: The integral decomposition method is widely used to construct solutions to the Volterra-like evolution equations exemplified by those describing anomalous diffusion phenomena and non-Debye dielectric relaxations. In this seminar I present the integral decomposition method as it is emerges from the operational methods involving the Efros theorem. The probabilistic interpretation of integral decomposition (if allowed) guides us to subordination which encodes memory effects. Splitting the integral decomposition on the convolution of so-called parent and leading processes is ambiguous, however, if the parent process is fixed its partner leading process appears to be unique. Commonly assumed parent process given by the Brownian motion is not the only possibility. I illustrate this with the example of the generalized (memory dependent) Cattaneo-Vernotte equation for which I construct two distinct subordinations. For the first of them the parent process is given by the Gaussian, while for the second one I use the fundamental solution to the Cattaneo-Vernotte equation describing diffusion obeying the finite propagation speed. Non-uniqueness in the choice of parent and leading processes is also visible in the case of standard non-Debye relaxation patterns. For example, the Havriliak-Negami relaxation can be expressed as the subordination either of the Debye model or the Cole-Davidson one.

Biography: Katarzyna Gorska is full professor at the Theoretical Physics Division of the Institute of Nuclear Physics of the Polish Academy of Sciences in Krakow, Poland. Graduated from the Nicolaus Copernicus University in Toru\'n, she earned her PhD in theoretical physics there and completed postdoctoral fellowships at the Sorbonne University (Campus Paris 6) and the University of S\~ao Paulo. She served as a visiting scientist at research centers and universities in Europe (France, Italy), South and North America (Brazil, USA, Canada). She has authored or co-authored over 60 scientific publications. Her main research interests include transport phenomena, diffusion, heat transfer, dielectric relaxation, evolutionary equations, fractional calculus, stable distributions in probability and physics, integral transformations, umbral calculus, and special functions. Her other scientific interest (sometimes treated as a hobby) are foundations of quantum mechanics, in particular mathematical theory of coherent states.

Bibliography

[1]  K. Gorska, A. Horzela, E. K. Lenzi, G. Pagnini, and T. Sandev, Generalized Cattaneo (telegrapher’s) equations in modeling anomalous diffusion phenomena, Phys. Rev. E 102 (2020) 022128.
[2] K. Gorska, Integral decomposition for the solutions of the generalized Cattaneo equation, Phys. Rev. E 104 (2021) 024113.
[3] K. Gorska and A. Horzela, Subordination and memory dependent kinetics in diffusion and relaxation phenomena, Fract. Calc. Appl. Anal. 26 (2023) 480.
[4] T. Pietrzak, A. Horzela, and K. G´orska, The generalized telegraph equation with moving harmonic source: Solvability using the integral decomposition technique and wave aspects, Int. J. Heat Mass Transf. 225 (2025) 125373.
[5] K. Gorska, Operational solution for the generalized Fokker-Planck and generalized diffusion-wave equations, Phys. Rev. E 111 (2025) 024103