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 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.publishedVersio

A mononuclear iron(III) complex with unusual changes of color and magneto-structural properties with temperature: synthesis, structure, magnetization, multi-frequency ESR and DFT study

From the reaction of 2-hydroxy-6-methylpyridine (L) with iron(II) tetrafluoroborate, a new mononuclear iron(III) octahedral complex [FeL6](BF4)3 has been isolated. The color of the complex reversibly changed from red at room temperature to yellow-orange at the liquid nitrogen temperature. Magnetization measurements indicate that iron(III) in [FeL6](BF4)3 is in a high-spin state S = 5/2, from room temperature to 1.8 K. The high-spin ground state of iron(III) is also confirmed by DFT calculations. Although the spin-crossover of the complex is not observed, X-band and multifrequency high-field/high-frequency electron spin resonance (ESR) spectroscopy shows rather uncommon iron(III) spectra at room temperature and an unusual change with cooling. Spectral simulations reveal that the S = 5/2 ground state multiplet of the complex can be characterized by the temperature independent axial zero-field splitting parameter of |D| = +2 GHz (0.067 cm−1) while the value of the rhombic parameter E of the order of some tenths MHz increases on lowering the temperature. Single crystal X-ray diffraction (SCXRD) shows that the iron(III) coordination geometry does not change with temperature while supramolecular interactions are temperature dependent, influencing the iron(III) rhombicity. Additionally, the DFT calculations show temperature variation of the HOMO–LUMO gap, in agreement with the changes of color and ESR-spectra of the iron(III) complex with temperature

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 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

A modal analysis based approach in studying robustness and vulnerability of complex networks

In this paper we propose an alternative way to study robustness and vulnerability of complex networks, applying a modal analysis. The modal weights of the network nodes are considered as a measure of their busyness, which is further used for preferential removal of nodes and attack simulation. Analyses of the attack vulnerability are carried out for several generic graphs, generated according to ER and BA algorithms, as well as for some examples of manmade networks. The results are compared to those obtained by deletion of nodes according to some standard measures and it was found that a modal weight based attack causes significant disintegration of manmade networks by removing a small fraction of the busiest nodes.JRC.DG.G.5-European laboratory for structural assessmen

Application of modal analysis in assessing attack vulnerability of complex networks

In this paper we propose an alternative way to study robustness and vulnerability of complex networks, applying a modal analysis. The modal weights of the network nodes are considered as a measure for their busyness, which is further used for preferential removal of nodes and attack simulation. Analyses of the attack vulnerability are carried out for several generic graphs, generated according to ER and BA algorithms, as well as for some examples of manmade networks. It was found that a modal weight based attack causes significant disintegration of manmade networks by removing a small fraction of the busiest nodes, comparable to the one based on the node degree and betweenness centrality.JRC.DG.G.5-European laboratory for structural assessmen

Application of modal analysis in assessing attack vulnerability of complex networks

In this paper we propose an alternative way to study robustness and vulnerability of complex networks, applying a modal analysis. The modal weights of the network nodes are considered as a measure for their busyness, which is further used for preferential removal of nodes and attack simulation. Analyses of the attack vulnerability are carried out for several generic graphs, generated according to ER and BA algorithms, as well as for some examples of manmade networks. It was found that a modal weight based attack causes signi¯cant disintegration of manmade networks by removing a small fraction of the busiest nodes, comparable to the one based on the node degree and betweenness centralityJRC.DG.G.5-European laboratory for structural assessmen