Tuning of the Dielectric Relaxation and Complex Susceptibility in a System of Polar Molecules: A Generalised Model Based on Rotational Diffusion with Resetting
The application of the fractional calculus in the mathematical modelling of relaxation processes in complex heterogeneous media has attracted a considerable amount of interest lately. The reason for this is the successful implementation of fractional stochastic and kinetic equations in the studies o...
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| Format: | Article |
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MDPI AG
2022-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/2/88 |
| _version_ | 1797480056114642944 |
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| author | Irina Petreska Ljupco Pejov Trifce Sandev Ljupco Kocarev Ralf Metzler |
| author_facet | Irina Petreska Ljupco Pejov Trifce Sandev Ljupco Kocarev Ralf Metzler |
| author_sort | Irina Petreska |
| collection | DOAJ |
| description | The application of the fractional calculus in the mathematical modelling of relaxation processes in complex heterogeneous media has attracted a considerable amount of interest lately. The reason for this is the successful implementation of fractional stochastic and kinetic equations in the studies of non-Debye relaxation. In this work, we consider the rotational diffusion equation with a generalised memory kernel in the context of dielectric relaxation processes in a medium composed of polar molecules. We give an overview of existing models on non-exponential relaxation and introduce an exponential resetting dynamic in the corresponding process. The autocorrelation function and complex susceptibility are analysed in detail. We show that stochastic resetting leads to a saturation of the autocorrelation function to a constant value, in contrast to the case without resetting, for which it decays to zero. The behaviour of the autocorrelation function, as well as the complex susceptibility in the presence of resetting, confirms that the dielectric relaxation dynamics can be tuned by an appropriate choice of the resetting rate. The presented results are general and flexible, and they will be of interest for the theoretical description of non-trivial relaxation dynamics in heterogeneous systems composed of polar molecules. |
| first_indexed | 2024-03-09T21:55:35Z |
| format | Article |
| id | doaj.art-42fd5716d3fd4f61b810bc96489e3695 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T21:55:35Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-42fd5716d3fd4f61b810bc96489e36952023-11-23T19:59:00ZengMDPI AGFractal and Fractional2504-31102022-02-01628810.3390/fractalfract6020088Tuning of the Dielectric Relaxation and Complex Susceptibility in a System of Polar Molecules: A Generalised Model Based on Rotational Diffusion with ResettingIrina Petreska0Ljupco Pejov1Trifce Sandev2Ljupco Kocarev3Ralf Metzler4Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, 1000 Skopje, MacedoniaInstitute of Chemistry, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, 1000 Skopje, MacedoniaInstitute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, 1000 Skopje, MacedoniaResearch Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, MacedoniaInstitute of Physics & Astronomy, University of Potsdam, D-14776 Potsdam-Golm, GermanyThe application of the fractional calculus in the mathematical modelling of relaxation processes in complex heterogeneous media has attracted a considerable amount of interest lately. The reason for this is the successful implementation of fractional stochastic and kinetic equations in the studies of non-Debye relaxation. In this work, we consider the rotational diffusion equation with a generalised memory kernel in the context of dielectric relaxation processes in a medium composed of polar molecules. We give an overview of existing models on non-exponential relaxation and introduce an exponential resetting dynamic in the corresponding process. The autocorrelation function and complex susceptibility are analysed in detail. We show that stochastic resetting leads to a saturation of the autocorrelation function to a constant value, in contrast to the case without resetting, for which it decays to zero. The behaviour of the autocorrelation function, as well as the complex susceptibility in the presence of resetting, confirms that the dielectric relaxation dynamics can be tuned by an appropriate choice of the resetting rate. The presented results are general and flexible, and they will be of interest for the theoretical description of non-trivial relaxation dynamics in heterogeneous systems composed of polar molecules.https://www.mdpi.com/2504-3110/6/2/88rotational diffusionmemory kernelFokker–Planck equationnon-exponential relaxationautocorrelation functioncomplex susceptibility |
| spellingShingle | Irina Petreska Ljupco Pejov Trifce Sandev Ljupco Kocarev Ralf Metzler Tuning of the Dielectric Relaxation and Complex Susceptibility in a System of Polar Molecules: A Generalised Model Based on Rotational Diffusion with Resetting Fractal and Fractional rotational diffusion memory kernel Fokker–Planck equation non-exponential relaxation autocorrelation function complex susceptibility |
| title | Tuning of the Dielectric Relaxation and Complex Susceptibility in a System of Polar Molecules: A Generalised Model Based on Rotational Diffusion with Resetting |
| title_full | Tuning of the Dielectric Relaxation and Complex Susceptibility in a System of Polar Molecules: A Generalised Model Based on Rotational Diffusion with Resetting |
| title_fullStr | Tuning of the Dielectric Relaxation and Complex Susceptibility in a System of Polar Molecules: A Generalised Model Based on Rotational Diffusion with Resetting |
| title_full_unstemmed | Tuning of the Dielectric Relaxation and Complex Susceptibility in a System of Polar Molecules: A Generalised Model Based on Rotational Diffusion with Resetting |
| title_short | Tuning of the Dielectric Relaxation and Complex Susceptibility in a System of Polar Molecules: A Generalised Model Based on Rotational Diffusion with Resetting |
| title_sort | tuning of the dielectric relaxation and complex susceptibility in a system of polar molecules a generalised model based on rotational diffusion with resetting |
| topic | rotational diffusion memory kernel Fokker–Planck equation non-exponential relaxation autocorrelation function complex susceptibility |
| url | https://www.mdpi.com/2504-3110/6/2/88 |
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