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New van der Waals (vdW) heterostructures obtained by stacking monolayers of recently synthesized graphenylene (Gr) and two-dimensional 1H-MoX$_{2}$ (X=S, Te, Se) are proposed and analyzed using ab initio calculations. These heterostructures are stable under normal conditions and have unique crystalline lattices. The study of electronic properties shows that the proposed materials are direct-gap semiconductors with a narrow bandgap, which can be controlled by in-plane tensile strain or transverse electric field. The considered vdW structures demonstrate the transition of band alignments between types I, II and III, when in-plane stress or electric field are applied, which hold great potential for creating multifunctional devices for stretched electronics. Computations based on the non-equilibrium Green functions method indicate a high rectification factor of the order of $10^3$ -- $10^4$ for a diode based on the Gr/MoS$_2$ vdW junction. The studied structures exhibit broad optical absorption across the entire visible range and represent a promising material for optoelectronic applications.
Ruslan M Meftakhutdinov; Renat Timergalievich Sibatov; Dmitry A Evseev; Aleksey Kochaev. First-principles study of graphenylene/MoX2 (X=S, Te,Se) van der Waals heterostructures. Physical Chemistry Chemical Physics 2021, 1 .
AMA StyleRuslan M Meftakhutdinov, Renat Timergalievich Sibatov, Dmitry A Evseev, Aleksey Kochaev. First-principles study of graphenylene/MoX2 (X=S, Te,Se) van der Waals heterostructures. Physical Chemistry Chemical Physics. 2021; ():1.
Chicago/Turabian StyleRuslan M Meftakhutdinov; Renat Timergalievich Sibatov; Dmitry A Evseev; Aleksey Kochaev. 2021. "First-principles study of graphenylene/MoX2 (X=S, Te,Se) van der Waals heterostructures." Physical Chemistry Chemical Physics , no. : 1.
One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.
Vladimir Uchaikin; Renat Sibatov; Dmitry Bezbatko. On a Generalization of One-Dimensional Kinetics. Mathematics 2021, 9, 1264 .
AMA StyleVladimir Uchaikin, Renat Sibatov, Dmitry Bezbatko. On a Generalization of One-Dimensional Kinetics. Mathematics. 2021; 9 (11):1264.
Chicago/Turabian StyleVladimir Uchaikin; Renat Sibatov; Dmitry Bezbatko. 2021. "On a Generalization of One-Dimensional Kinetics." Mathematics 9, no. 11: 1264.
We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined with the use of non-local fractal derivatives. The fractal Hurst exponent is suggested, and its relation with the order of non-local fractal derivatives is established. We relate the Gangal fractal derivative defined on a one-dimensional stochastic fractal to the fractional derivative after an averaging procedure over the ensemble of random realizations. That means the fractal derivative is the progenitor of the fractional derivative, which arises if we deal with a certain stochastic fractal.
Alireza Golmankhaneh; Renat Sibatov. Fractal Stochastic Processes on Thin Cantor-Like Sets. Mathematics 2021, 9, 613 .
AMA StyleAlireza Golmankhaneh, Renat Sibatov. Fractal Stochastic Processes on Thin Cantor-Like Sets. Mathematics. 2021; 9 (6):613.
Chicago/Turabian StyleAlireza Golmankhaneh; Renat Sibatov. 2021. "Fractal Stochastic Processes on Thin Cantor-Like Sets." Mathematics 9, no. 6: 613.
The Scher–Montroll model successfully describes subdiffusive photocurrents in homogeneously disordered semiconductors. The present paper generalizes this model to the case of fractal spatial disorder (self-similar random distribution of localized states) under the conditions of the time-of-flight experiment. Within the fractal model, we calculate charge carrier densities and transient current for different cases, solving the corresponding fractional-order equations of dispersive transport. Photocurrent response after injection of non-equilibrium carriers by the short laser pulse is expressed via fractional stable distributions. For the simplest case of one-sided instantaneous jumps (tunneling) between neighboring localized states, the dispersive transport equation contains fractional Riemann–Liouville derivatives on time and longitudinal coordinate. We discuss the role of back-scattering, spatial correlations induced by quenching of disorder, and spatiotemporal non-locality produced by the fractal trap distribution and the finite velocity of motion between localized states. We derive expressions for the photocurrent and transit time that allow us to determine the fractal dimension of the distribution of traps and the dispersion parameter from the time-of-flight measurements.
Renat T. Sibatov. Fractal Generalization of the Scher–Montroll Model for Anomalous Transit-Time Dispersion in Disordered Solids. Mathematics 2020, 8, 1991 .
AMA StyleRenat T. Sibatov. Fractal Generalization of the Scher–Montroll Model for Anomalous Transit-Time Dispersion in Disordered Solids. Mathematics. 2020; 8 (11):1991.
Chicago/Turabian StyleRenat T. Sibatov. 2020. "Fractal Generalization of the Scher–Montroll Model for Anomalous Transit-Time Dispersion in Disordered Solids." Mathematics 8, no. 11: 1991.
Optical and thermoelectric properties of graphenylene and octagraphene nanotubes (GrNTs and OcNTs) are studied by means of first-principles calculations. The absorption coefficient, optical conductivity, and complex refractive index are calculated using the density functional theory and the Kubo–Greenwood formula. It is shown that the studied structures effectively absorb electromagnetic waves of the visible range, and these nanotubes are promising for the development of electromagnetic radiation sensors. Using the nonequilibrium Green functions method, transport coefficients and thermoelectric figure of merit are estimated and analyzed. The electronic and thermal characteristics of GrNTs and OcNTs are compared with the characteristics of graphene nanotubes.
A.I. Kochaev; R.M. Meftakhutdinov; R.T. Sibatov; D.A. Timkaeva. Optical and thermoelectric properties of graphenylene and octagraphene nanotubes from first-principles calculations. Computational Materials Science 2020, 186, 109999 .
AMA StyleA.I. Kochaev, R.M. Meftakhutdinov, R.T. Sibatov, D.A. Timkaeva. Optical and thermoelectric properties of graphenylene and octagraphene nanotubes from first-principles calculations. Computational Materials Science. 2020; 186 ():109999.
Chicago/Turabian StyleA.I. Kochaev; R.M. Meftakhutdinov; R.T. Sibatov; D.A. Timkaeva. 2020. "Optical and thermoelectric properties of graphenylene and octagraphene nanotubes from first-principles calculations." Computational Materials Science 186, no. : 109999.
The approach based on fractional advection–diffusion equations provides an effective and meaningful tool to describe the dispersive transport of charge carriers in disordered semiconductors. A fractional generalization of Fick’s law containing the Riemann–Liouville fractional derivative is related to the well-known fractional Fokker–Planck equation, and it is consistent with the universal characteristics of dispersive transport observed in the time-of-flight experiment (ToF). In the present paper, we consider the generalized Fick laws containing other forms of fractional time operators with singular and non-singular kernels and find out features of ToF transient currents that can indicate the presence of such fractional dynamics. Solutions of the corresponding fractional Fokker–Planck equations are expressed through solutions of integer-order equation in terms of an integral with the subordinating function. This representation is used to calculate the ToF transient current curves. The physical reasons leading to the considered fractional generalizations are elucidated and discussed.
Renat T. Sibatov; Hongguang Sun. Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators. Fractal and Fractional 2020, 4, 42 .
AMA StyleRenat T. Sibatov, Hongguang Sun. Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators. Fractal and Fractional. 2020; 4 (3):42.
Chicago/Turabian StyleRenat T. Sibatov; Hongguang Sun. 2020. "Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators." Fractal and Fractional 4, no. 3: 42.
Recently synthesized two-dimensional graphene-like material referred to as graphenylene is a semiconductor with a narrow direct bandgap that holds great promise for nanoelectronic applications. The significant bandgap increase can be provided by the strain applied to graphenylene crystal lattice or by using nanoribbons instead of extended layers. In this paper, we present the systematic study of the electronic, optical and thermoelectric properties of graphenylene nanoribbons using calculations based on the density functional theory. Estimating the binding energies, we substantiate the stability of nanoribbons with zigzag and armchair edges passivated by hydrogen atoms. Electronic spectra indicate that all considered structures could be classified as direct bandgap semiconductors. From the calculated dependence of bandgap on nanoribbon width we observe the identical scaling rule for armchair and zigzag graphenylene ribbons. A family-based classification used for the electronic structure of armchair graphene nanoribbons can not be extended to the case of graphenylene ones. The absorption coefficient, optical conductivity, and complex refractive index are calculated by means of the first-principles methods and the Kubo-Greenwood formula. It has been shown that graphenylene ribbons effectively absorb visible-range electromagnetic waves. Due to this absorption, the conductivity is noticeably increased in this range. The transport coefficients and thermoelectric figure of merit are calculated by the nonequilibrium Green functions method. Summarizing the results, we discuss the possible use of graphenylene films and nanoribbons in nanoelectronic devices.
R M Meftakhutdinov; R T Sibatov; A I Kochaev. Graphenylene nanoribbons: electronic, optical and thermoelectric properties from first-principles calculations. Journal of Physics: Condensed Matter 2020, 32, 345301 .
AMA StyleR M Meftakhutdinov, R T Sibatov, A I Kochaev. Graphenylene nanoribbons: electronic, optical and thermoelectric properties from first-principles calculations. Journal of Physics: Condensed Matter. 2020; 32 (34):345301.
Chicago/Turabian StyleR M Meftakhutdinov; R T Sibatov; A I Kochaev. 2020. "Graphenylene nanoribbons: electronic, optical and thermoelectric properties from first-principles calculations." Journal of Physics: Condensed Matter 32, no. 34: 345301.
The phase-field model based on the Cahn-Hilliard equation is employed to simulate lithium intercalation dynamics in a cathode with particles of distributed size. We start with a simplified phase-field model for a single submicron particle under galvanostatic condition. We observe two stages associated with single-phase and double-phase patterns typical for both charging and discharging processes. The single-phase stage takes approximately 10–15% of the process and plays an important role in the intercalation dynamics. We establish the laws for speed of front propagation and evolution of single-phase concentration valid for different sizes of electrode particles and a wide range of temperatures and C-rates. The universality of these laws allows us to formulate the boundary condition with time-dependent flux density for the Cahn-Hilliard equation and analyze the phase-field intercalation in a heterogeneous cathode characterized by the particle size distribution.
Pavel L’Vov; Renat Sibatov. Effect of the Particle Size Distribution on the Cahn-Hilliard Dynamics in a Cathode of Lithium-Ion Batteries. Batteries 2020, 6, 29 .
AMA StylePavel L’Vov, Renat Sibatov. Effect of the Particle Size Distribution on the Cahn-Hilliard Dynamics in a Cathode of Lithium-Ion Batteries. Batteries. 2020; 6 (2):29.
Chicago/Turabian StylePavel L’Vov; Renat Sibatov. 2020. "Effect of the Particle Size Distribution on the Cahn-Hilliard Dynamics in a Cathode of Lithium-Ion Batteries." Batteries 6, no. 2: 29.
The development of portable electronic devices has greatly stimulated the need for miniaturized power sources. Planar supercapacitors are micro-scale electrochemical energy storage devices that can be integrated with other microelectronic devices on a chip. In this paper, we study the behavior of microsupercapacitors with in-plane interdigital electrodes of carbon nanotube array under sinusoidal excitation, step voltage input and sawlike voltage input. Considering the anomalous diffusion of ions in the array and interelectrode space, we propose a fractional-order equivalent circuit model that successfully describes the measured impedance spectra. We demonstrate that the response of the investigated micro-supercapacitors is linear and the system is time-invariant. The numerical inversion of the Laplace transforms for electric current response in an equivalent circuit with a given impedance leads to results consistent with potentiostatic measurements and cyclic voltammograms. The use of electrodes based on an ordered array of nanotubes reduces the role of nonlinear effects in the behavior of a supercapacitor. The effect of the disordering of nanotubes with increasing array height on supercapacitor impedance is considered in the framework of a distributed-order subdiffusion model.
Evgeny P. Kitsyuk; Renat T. Sibatov; Vyacheslav V. Svetukhin. Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays. Energies 2020, 13, 213 .
AMA StyleEvgeny P. Kitsyuk, Renat T. Sibatov, Vyacheslav V. Svetukhin. Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays. Energies. 2020; 13 (1):213.
Chicago/Turabian StyleEvgeny P. Kitsyuk; Renat T. Sibatov; Vyacheslav V. Svetukhin. 2020. "Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays." Energies 13, no. 1: 213.
New aspects of electron transport in quantum wires with Lévy-type disorder are described. We study the weak scattering and the incoherent sequential tunneling in one-dimensional quantum systems characterized by a tempered Lévy stable distribution of spacing between scatterers or tunneling barriers. The generalized Dorokhov–Mello–Pereyra–Kumar equation contains the tempered fractional derivative on wire length. The solution describes the evolution from the anomalous conductance distribution to the Dorokhov function for a long wire. For sequential tunneling, average values and relative fluctuations of conductance and resistance are calculated for different parameters of spatial distributions. A tempered Lévy stable distribution of spacing between barriers leads to a transition in conductance scaling.
Renat T. Sibatov; Hongguang Sun. Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder. Fractal and Fractional 2019, 3, 47 .
AMA StyleRenat T. Sibatov, Hongguang Sun. Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder. Fractal and Fractional. 2019; 3 (4):47.
Chicago/Turabian StyleRenat T. Sibatov; Hongguang Sun. 2019. "Tempered Fractional Equations for Quantum Transport in Mesoscopic One-Dimensional Systems with Fractal Disorder." Fractal and Fractional 3, no. 4: 47.
Pavel Kapustin; Mikhail Tikhonchev; Renat T Sibatov. Distribution of niobium atoms in self-interstitial configurations in binary alloys Zr–(0.5–3)%Nb after passing the atomic displacements cascade. Modelling and Simulation in Materials Science and Engineering 2019, 27, 075013 .
AMA StylePavel Kapustin, Mikhail Tikhonchev, Renat T Sibatov. Distribution of niobium atoms in self-interstitial configurations in binary alloys Zr–(0.5–3)%Nb after passing the atomic displacements cascade. Modelling and Simulation in Materials Science and Engineering. 2019; 27 (7):075013.
Chicago/Turabian StylePavel Kapustin; Mikhail Tikhonchev; Renat T Sibatov. 2019. "Distribution of niobium atoms in self-interstitial configurations in binary alloys Zr–(0.5–3)%Nb after passing the atomic displacements cascade." Modelling and Simulation in Materials Science and Engineering 27, no. 7: 075013.
Bed-load transport along widely graded river-beds typically exhibits anomalous dynamics, whose efficient characterization may require parsimonious stochastic models with pre-defined statistics involving the waiting time and hop distance distributions for sediment particles. This study employs a continuous time random walk (CTRW) model to characterize bed-load particle motions on a widely graded gravel-bed with cluster microforms built in our lab. Flume experiments guide the selection of the Mittag-Leffler (M-L) function as the waiting time distribution function, and the Lévy α-stable density for the hop distance distribution function in the CTRW model. Monte Carlo simulations show that the resulting CTRW model can well capture the observed flume experimental data (with either a continuous or an instantaneous source) with coexisting super- and sub-dispersion behaviors in the bed-load transport process. Analyses further discover the dual impact of clusters on the dynamics of fine sediment particles. Some particles are more likely to be blocked or trapped by clusters, while others have a high probability to be accelerated by the flow accelerating belt between the clusters. Therefore, with proper statistical distributions and relevant parameters for sediment waiting times and hop distances, the CTRW model may efficiently capture the complex dynamics in sediment transport.
Zhipeng Li; Hongguang Sun; Yong Zhang; Dong Chen; Renat T. Sibatov. Continuous time random walk model for non-uniform bed-load transport with heavy-tailed hop distances and waiting times. Journal of Hydrology 2019, 578, 124057 .
AMA StyleZhipeng Li, Hongguang Sun, Yong Zhang, Dong Chen, Renat T. Sibatov. Continuous time random walk model for non-uniform bed-load transport with heavy-tailed hop distances and waiting times. Journal of Hydrology. 2019; 578 ():124057.
Chicago/Turabian StyleZhipeng Li; Hongguang Sun; Yong Zhang; Dong Chen; Renat T. Sibatov. 2019. "Continuous time random walk model for non-uniform bed-load transport with heavy-tailed hop distances and waiting times." Journal of Hydrology 578, no. : 124057.
The effect of anomalous diffusion of lithium on the discharge curves and impedance spectra of lithium-ion batteries (LIB) is studied within the fractional differential generalization of the single-particle model. The distribution of lithium ions in electrolyte and electrode particles is expressed through the Mittag–Leffler function and the Lévy stable density. Using the new model, we generalize the equivalent circuit of LIB. The slope of the low-frequency rectilinear part of the Nyquist diagram does not always unambiguously determine the subdiffusion index and can be either larger or smaller than the slope corresponding to normal diffusion. The new aspect of capacity degradation related to a change in the type of ion diffusion in LIB components is discussed.
Renat T. Sibatov; Vyacheslav V. Svetukhin; Evgeny P. Kitsyuk; Alexander A. Pavlov. Fractional Differential Generalization of the Single Particle Model of a Lithium-Ion Cell. Electronics 2019, 8, 650 .
AMA StyleRenat T. Sibatov, Vyacheslav V. Svetukhin, Evgeny P. Kitsyuk, Alexander A. Pavlov. Fractional Differential Generalization of the Single Particle Model of a Lithium-Ion Cell. Electronics. 2019; 8 (6):650.
Chicago/Turabian StyleRenat T. Sibatov; Vyacheslav V. Svetukhin; Evgeny P. Kitsyuk; Alexander A. Pavlov. 2019. "Fractional Differential Generalization of the Single Particle Model of a Lithium-Ion Cell." Electronics 8, no. 6: 650.
Grain boundary (GB) diffusion in engineering materials at elevated temperatures often determines the evolution of microstructure, phase transformations, and certain regimes of plastic deformation and fracture. Interpreting experimental data with the use of the classical Fisher model sometimes encounters contradictions that can be related to violation of Fick’s law. Here, we generalize the Fisher model to the case of non-Fickian (anomalous) diffusion ubiquitous in disordered materials. The process is formulated in terms of the subdiffusion equations with time-fractional derivatives of order α∈(0,1] and β∈(0,1] for grain volume and GB, respectively. It is shown that propagation along GB for the case of a localized instantaneous source and weak localization in GB (β>α/2) is approximately described by distributed-order subdiffusion with exponents α/2 and β. The mean square displacement is calculated with the use of the alternating renewal process model. The tail of the impurity concentration profiles along the z axis is approximately described by the dependence ∝exp(-Az6/5) for all 0<α≤1, as in the case of normal GB diffusion, so the 6/5-law itself can serve as an identifier of a more general phenomenon, namely, anomalous GB diffusion.
Renat T. Sibatov. Anomalous Grain Boundary Diffusion: Fractional Calculus Approach. Advances in Mathematical Physics 2019, 2019, 1 -9.
AMA StyleRenat T. Sibatov. Anomalous Grain Boundary Diffusion: Fractional Calculus Approach. Advances in Mathematical Physics. 2019; 2019 ():1-9.
Chicago/Turabian StyleRenat T. Sibatov. 2019. "Anomalous Grain Boundary Diffusion: Fractional Calculus Approach." Advances in Mathematical Physics 2019, no. : 1-9.
The evolution of atomic displacements cascades near the spherical binary precipitate Nb-20%Zr with the bcc lattice in the hcp α-Zr matrix was simulated using the method of molecular dynamics. The cascade is initiated by a 10 keV primary-knocked Zr atom at a distance ∼10 Å from the surface of spherical binary precipitate of radius ∼50 Å. The simulation results show that at the stage of the primary radiation damage, a change in the composition of the binary precipitate takes place. After passage of the cascade process, a considerable concentration of niobium in interstitial sites outside the precipitate is observed near the surface. The precipitate mitigates the propagation of atomic displacements cascade. In most cases, we observed cascade flow around the sphere accompanied by weak penetration into the precipitate structure.
P.E. Kapustin; M.Yu. Tikhonchev; R.T. Sibatov; V.V. Svetukhin. Simulation of atomic displacements cascades in α-zirconium near β-Nb-20%Zr precipitate. Results in Physics 2018, 12, 175 -177.
AMA StyleP.E. Kapustin, M.Yu. Tikhonchev, R.T. Sibatov, V.V. Svetukhin. Simulation of atomic displacements cascades in α-zirconium near β-Nb-20%Zr precipitate. Results in Physics. 2018; 12 ():175-177.
Chicago/Turabian StyleP.E. Kapustin; M.Yu. Tikhonchev; R.T. Sibatov; V.V. Svetukhin. 2018. "Simulation of atomic displacements cascades in α-zirconium near β-Nb-20%Zr precipitate." Results in Physics 12, no. : 175-177.
This report discusses a new model of cosmic ray propagation in the Galaxy. In contrast to the known models based on the principles of Brownian motion, the proposed model agrees with the relativistic principle of speed limitation and takes into account the large-scale turbulence of the interstellar medium, justifying introduction of fractional differential operators.
V. V. Uchaikin; R. T. Sibatov. On propagators of nonlocal relativistic diffusion of galactic cosmic rays. Physics of Particles and Nuclei 2018, 49, 120 -124.
AMA StyleV. V. Uchaikin, R. T. Sibatov. On propagators of nonlocal relativistic diffusion of galactic cosmic rays. Physics of Particles and Nuclei. 2018; 49 (1):120-124.
Chicago/Turabian StyleV. V. Uchaikin; R. T. Sibatov. 2018. "On propagators of nonlocal relativistic diffusion of galactic cosmic rays." Physics of Particles and Nuclei 49, no. 1: 120-124.
We present the results of experimental investigations of supercapacitors produced by Panasonic using several methods, namely, measurements of temporal dependences of charging–discharging currents, cyclic dc charging, and cyclic voltammetry. The values of the internal resistance, static and dynamic capacitance, as well as their dependences on the bias voltage of the capacitors, have been determined. Measurements have shown that the initial stage of relaxation of current is well approximated by the exponential time dependence, and then transition to a powerlike dependence occurs. This well-known effect is explained on the basis of the allowance for specific transport properties of a porous fractal-type medium. These processes are adequately described by the fractional-differential model of anomalous diffusion. A weak dependence of relaxation curves on the voltage at low values of the latter (3 V) is explained by the appearance of new percolation paths blocked at low charging voltages due to the presence of high-potential barriers. The internal resistance and the static capacitance have been determined by measuring the voltage across the supercapacitor in the mode of dc charging. These parameters have been shown to depend on the voltage applied to the capacitor. The dependence of the dynamic capacitance on the voltage has been determined using cyclic voltammetry. It has been shown that the capacitance depends not only on the voltage, but also on the prehistory of charging and discharging of the capacitor. Comparison of the experimental results and the published data on the models and equivalent circuits with passive R, L, and C elements allows one to conclude that such models and equivalent circuits can be applied only when explaining a limited number of phenomena, in particular, behavior at small relaxation times.
A. S. Ambrozevich; S. A. Ambrozevich; R. T. Sibatov; V. V. Uchaikin. Features of Charging–Discharging of Supercapacitors. Russian Electrical Engineering 2018, 89, 64 -70.
AMA StyleA. S. Ambrozevich, S. A. Ambrozevich, R. T. Sibatov, V. V. Uchaikin. Features of Charging–Discharging of Supercapacitors. Russian Electrical Engineering. 2018; 89 (1):64-70.
Chicago/Turabian StyleA. S. Ambrozevich; S. A. Ambrozevich; R. T. Sibatov; V. V. Uchaikin. 2018. "Features of Charging–Discharging of Supercapacitors." Russian Electrical Engineering 89, no. 1: 64-70.
Anomalous advection-diffusion in two-dimensional semiconductor systems with coexisting energetic and structural disorder is described in the framework of a generalized model of multiple trapping on a comb-like structure. The basic equations of the model contain fractional-order derivatives. To validate the model, we compare analytical solutions with results of a Monte Carlo simulation of phonon-assisted tunneling in two-dimensional patterns of a porous nanoparticle agglomerate and a phase-separated bulk heterojunction. To elucidate the role of directed percolation, we calculate transient current curves of the time-of-flight experiment and the evolution of the mean squared displacement averaged over medium realizations. The variations of the anomalous advection-diffusion parameters as functions of electric field intensity, levels of energetic, and structural disorder are presented.
Renat Sibatov; Vadim Shulezhko; Vyacheslav Svetukhin. Fractional Derivative Phenomenology of Percolative Phonon-Assisted Hopping in Two-Dimensional Disordered Systems. Entropy 2017, 19, 463 .
AMA StyleRenat Sibatov, Vadim Shulezhko, Vyacheslav Svetukhin. Fractional Derivative Phenomenology of Percolative Phonon-Assisted Hopping in Two-Dimensional Disordered Systems. Entropy. 2017; 19 (9):463.
Chicago/Turabian StyleRenat Sibatov; Vadim Shulezhko; Vyacheslav Svetukhin. 2017. "Fractional Derivative Phenomenology of Percolative Phonon-Assisted Hopping in Two-Dimensional Disordered Systems." Entropy 19, no. 9: 463.
V.V. Uchaikin; R.T. Sibatov. Fractional derivatives on cosmic scales. Chaos, Solitons & Fractals 2017, 102, 197 -209.
AMA StyleV.V. Uchaikin, R.T. Sibatov. Fractional derivatives on cosmic scales. Chaos, Solitons & Fractals. 2017; 102 ():197-209.
Chicago/Turabian StyleV.V. Uchaikin; R.T. Sibatov. 2017. "Fractional derivatives on cosmic scales." Chaos, Solitons & Fractals 102, no. : 197-209.
R.T. Sibatov; V.V. Svetukhin. Grain boundary diffusion in terms of the tempered fractional calculus. Physics Letters A 2017, 381, 2021 -2027.
AMA StyleR.T. Sibatov, V.V. Svetukhin. Grain boundary diffusion in terms of the tempered fractional calculus. Physics Letters A. 2017; 381 (24):2021-2027.
Chicago/Turabian StyleR.T. Sibatov; V.V. Svetukhin. 2017. "Grain boundary diffusion in terms of the tempered fractional calculus." Physics Letters A 381, no. 24: 2021-2027.