@article{PetreskaPejovSandevetal.2022,
  author    = {Petreska, Irina and Pejov, Ljupco and Sandev, Trifce and Kocarev, Ljupčo and Metzler, Ralf},
  title     = {Tuning of the dielectric relaxation and complex susceptibility in a system of polar molecules: a generalised model based on rotational diffusion with resetting},
  series = {Fractal and fractional},
  volume    = {6},
  journal   = {Fractal and fractional},
  number    = {2},
  publisher = {MDPI AG, Fractal Fract Editorial Office},
  address   = {Basel},
  issn      = {2504-3110},
  doi       = {10.3390/fractalfract6020088},
  pages     = {23},
  year      = {2022},
  abstract  = {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.},
  language  = {en}
}
@phdthesis{Topaj2001,
  author    = {Topaj, Dmitri},
  title     = {Synchronization transitions in complex systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000367},
  school      = {Universit{\"a}t Potsdam},
  year      = {2001},
  abstract  = {Gegenstand dieser Arbeit ist die Untersuchung generischer Synchronisierungsph{\"a}nomene in interagierenden komplexen Systemen. Diese Ph{\"a}nomene werden u.a. in gekoppelten deterministischen chaotischen Systemen beobachtet. Bei sehr schwachen Interaktionen zwischen individuellen Systemen kann ein {\"U}bergang zum schwach koh{\"a}renten Verhalten der Systeme stattfinden. In gekoppelten zeitkontinuierlichen chaotischen Systemen manifestiert sich dieser {\"U}bergang durch den Effekt der Phasensynchronisierung, in gekoppelten chaotischen zeitdiskreten Systemen durch den Effekt eines nichtverschwindenden makroskopischen Feldes. Der {\"U}bergang zur Koh{\"a}renz in einer Kette lokal gekoppelter Oszillatoren, beschrieben durch Phasengleichungen, wird im Bezug auf die Symmetrien des Systems untersucht. Es wird gezeigt, daß die durch die Symmetrien verursachte Reversibilit{\"a}t des Systems nichttriviale topologische Eigenschaften der Trajektorien bedingt, so daß das als dissipativ konstruierte System in einem ganzen Parameterbereich quasi-Hamiltonische Z{\"u}ge aufweist, d.h. das Phasenvolumen ist im Schnitt erhalten, und die Lyapunov-Exponenten sind paarweise symmetrisch. Der {\"U}bergang zur Koh{\"a}renz in einem Ensemble global gekoppelter chaotischer Abbildungen wird durch den Verlust der Stabilit{\"a}t des entkoppelten Zustandes beschrieben. Die entwickelte Methode besteht darin, die Selbstkonsistenz des makroskopischen Feldes aufzuheben, und das Ensemble in Analogie mit einem Verst{\"a}rkerschaltkreis mit R{\"u}ckkopplung durch eine komplexe lineare {\"U}bertragungssfunktion zu charakterisieren. Diese Theorie wird anschließend f{\"u}r einige theoretisch interessanten F{\"a}lle verallgemeinert.},
  language  = {en}
}
@misc{ThielZehbeRoeseretal.2013,
  author    = {Thiel, Kerstin and Zehbe, Rolf and Roeser, Jer{\^o}m{\´e} and Strauch, Peter and Enthaler, Stephan and Thomas, Arne},
  title     = {A polymer analogous reaction for the formation of imidazolium and NHC based porous polymer networks},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-95118},
  pages     = {1848 -- 1856},
  year      = {2013},
  abstract  = {A polymer analogous reaction was carried out to generate a porous polymeric network with N-heterocyclic carbenes (NHC) in the polymer backbone. Using a stepwise approach, first a polyimine network is formed by polymerization of the tetrafunctional amine tetrakis(4-aminophenyl)methane. This polyimine network is converted in the second step into polyimidazolium chloride and finally to a polyNHC network. Furthermore a porous Cu(II)-coordinated polyNHC network can be generated. Supercritical drying generates polymer networks with high permanent surface areas and porosities which can be applied for different catalytic reactions. The catalytic properties were demonstrated for example in the activation of CO2 or in the deoxygenation of sulfoxides to the corresponding sulfides.},
  language  = {en}
}