Akademik Veri Yönetim Sistemi
Hradec Králové International Physics Days 2022, Hradec-Kralove, Çek Cumhuriyeti, 19 - 22 Aralık 2022, ss.65
Transport
dynamics in complex or disordered media namely anomalous transport, as in
amorphous semiconductors and insulators, is represented and derived through the
mathematical instruments of stochastic mechanics and fractional calculus. Anomalous
transport can be described through the drift-diffusion equations that are reformulated
in the fractional form to indicate anomalous diffusion and fractional drift
processes. Random walk in a random environment and continuous-time random walk
(CTRW) are analogical stochastic processes that are used to mimic anomalous
transport in complex media. Fractional dynamics has also a critical role in modeling
anomalous transport in complex media that exhibits non-Markovian (not memoryless)
and non-local properties. There are numerous master equations (MEs) such
Klein-Kramers (KKE), Fokker-Planck (FPE), Telegraph Equation (TE), Diffusion-Advection
(DAE) equations that each express different stochastic processes occurring in
anomalous transport phenomena. The analytical solution of the fractional master
equations for the corresponding transport problems can be obtained using the Fourier-Laplace
(FL) transform that allows changing the space-time domain with the FL domain.
The anomalous transport in complex or disordered media that can be defined in
amorphous semiconductors and insulators is governed through analytically
derived Debye and semi-empirically derived Cole-Cole (CC), Cole Davidson (CD)
and Havriliak-Negami (HN) type conductivity equations. The common contemporary
motivation is to construct the relationship between the semi-empirical
conductivity equations especially HN type and the anomalous transport processes
governed by the approaches of fractional and stochastic dynamics.