Publications
2023
Tsiberkin K.B. Averaging of the free induction decay from an ensemble of small spin clusters. The European Physical Journal B, 2023, vol. 96, 70. DOI: 10.1140/epjb/s10051-023-00546-7
The current study considers analytical and numerical realization of the averaging procedure modeling the observable magnetization response from the regular diluted spin system. It consists with spin clusters having different sizes and similar geometry. There is a strong effect of the size distribution function on the total magnetization. While the diluted magnetic includes the clusters of close sizes, the transversal magnetization is the typical oscillating Abragam trial function. However, the large dispersion in size of local clusters leads to the monotonous behavior of the signal envelope. It decays exponentially in such a configuration. The analytical estimates and numerical simulation of the spin ensemble match each other.
Tsiberkin K.B., Sosunov A.V., Tselikov G.I. Investigation of absorption spectrum of carbon nanospheres. Optics and Spectroscopy. – Accepted 22.06.2023
Tsiberkin K. B. Verification of continuum-based model of carbon materials. Nanosystems: Physics, Chemistry, Mathematics. – Accepted 08.09.2023
2022
Tsiberkin K.B. Continuum modeling of energy band of carbon sphere. Journal of Experimental and Theoretical Physics, 2022, vol. 135, no. 6, pp. 920-925. DOI: 10.1134/S1063776122120123
The Hubbard model with continuous medium approximation is applied to the functionalized monolayer carbon nanosphere. It permits to evaluate the energy spectrum and frequencies of possible transitions. There is self-similar energy levels structure exist. It the limit of flat carbon sheet it tend to the graphene bands. Carbon functionalization and the Coulomb repulsion of electrons at the carbon sites lead to the band gap is up to few electron-Volts. The transition spectrum includes wide absorption bands in visible light and ultraviolet region. The calcula-tion results match well the established data of fullerenes C_60 and C_70 spectroscopy as well as their theoretical models.
Original Russian Text © K.B. Tsiberkin, 2022, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2022, Vol. 162, No. 6 (12), pp. 968-974. DOI: 10.31857/S0044451022120161
Kovycheva E.I., Tsiberkin K.B. Magnetic resonance of ring spin clusters. Bulletin of Perm University. Physics, 2022, no. 2, pp. 26-35 (In Russian). DOI: 10.17072/1994-3598-2022-2-26-35
Using a quantum-based approach, we modeled the free induction decay signals for ring clusters of finite radius consisting of 6 and 8 particles with spin 1/2. In addition, we modeled a free induction decay signal for a spherical spin cluster by superimposing the ring signals. The current research uses two possible orientations of the spins. The ring plane was assumed to be only parallel or orthogonal to the external magnetic field. The free induction decays curves and their Fourier spectra were calculated both with and without the exchange interaction between the spins. The second and fourth moments of the magnetization response were evaluated by direct theoretical equations. The dependence of relaxation time on the ring radius was found. The exchange interaction was found to cause an increase in the relaxation time of a ring cluster when the exchange is positive, and a decrease in the time when it is negative. At the same time, the results obtained for the spherical cluster model do not show such an effect.
Marychev B.S., Tsiberkin K.B. Continuous medium mechanics: application of tensor calculus. Tutorial. Perm, Perm University Press, 2022. 98 p. In Russian
Keywords: fluid dynamics; Navier-Stokes equations; tensor calculus; vector calculus
2021
Tsiberkin K.B. Low-temperature antiferromagnetism of Ising model with competing interactions. Bulletin of Perm University. Physics, 2021, no. 2, pp. 64-71 (In Russian). DOI: 10.17072/1994-3598-2021-2-64-71
The paper presents a numerical analysis of equilibrium state and spin configuration of square lattice Ising model with competing interaction. The most detailed description is given for case of ferromagnetic interaction of the first-order neighbours and antiferromagnetic coupling of the second-order neighbours. The numerical method is based on Metropolis algorithm. It uses 128×128 lattice with periodic boundary conditions. At first, the simulation results show that the system is in saturation state at low temperatures, and it turns into paramagnetic state at the Curie point. The competing second-order interaction makes possible the domain structure realization. This state is metastable, because its energy is higher than saturation energy. The domains are small at low temperature, and their size increases when temperature is growing until the single domain occupies the whole simulation area. In addition, the antiferromagnetic coupling of the second-order neighbours reduces the Curie temperature of the system. If it is large enough, the lattice has no saturation state. It turns directly from the domain state into paramagnetic phase. There are no extra phases when the system is antiferromagnetic in main order, and only the Neel temperature shift realizes here.
Tsiberkin K.B. Continuum model of free induction decay in diluted magnetic composite. Applied Magnetic Resonance, 2021, vol. 52, pp. 867–877. Special Issue on the 85th Anniversary of Professor Vadim A. Atsarkin. DOI: 10.1007/s00723-021-01343-0
The study presents an analysis of free induction decay (FID) in the diluted magnetic composite using the model of spin waves in continuous media. It takes into account the dipole–dipole interaction of the bulk lattice atoms and between them and ferromagnetic dopant ions, and also the indirect exchange interaction of the dopants. A dispersion relation of the magnetic waves is evaluated from the magnetization evolution equation. There are two spectrum branches of spin waves. Their basic frequencies are determined by the gyromagnetic ratio and interaction parameters of the dopant ions and bulk lattice atoms, and by the dopant concentration. The FID asymptotic behaviour is evaluated.
Tsiberkin K. Wave dynamics of magnetization of a ferromagnetic impurity in a paramagnetic matrix. The Physics of Metals and Metallography, 2021, vol. 122, no. 4, pp. 358-361. DOI: 10.1134/S0031918X21040116
Derivation and analysis of equations for magnetization dynamics of a dilute magnetic composite obtained by introducing ferromagnetic ions into a paramagnetic conductive matrix are presented in this work. Impurity ions are bound with each other by indirect exchange interaction and, with the matrix, by dipole interaction. The system is placed in a uniform dc magnetic field. The conditions for the existence of traveling waves of magnetization of the ferromagnetic subsystem are found. The minimum wavelength is determined by the concentration of impurity ions and the average energy of indirect exchange interaction. If its sign is positive, the realization of traveling magnetization waves in a wide range of parameters is possible. If the antiferromagnetic character of the binding of impurity ions is dominant, the wave solutions become unstable.
Tsiberkin K. Traveling magnetization waves in diluted magnetic material. Journal of Physics: Conference Series, 2021, vol. 1809, 012016. Proc. of VII Perm Hydrodynamical Forum (PHD-Forum 2020) 22-24 October 2020, Perm, Russian Federation. DOI: 10.1088/1742-6596/1809/1/012016
The magnetization evolution of the paramagnetic matrix and ferromagnetic admixture ions is considered using the continuous medium model. A dynamical equation system is derived. Two possible solutions are obtained. The first is a travelling wave of finite amplitude, which is stable in the system with a ferromagnetic interaction of admixture ions. The second solution is a soliton; its amplitude and velocity are determined by the exchange energy of the admixture ions and dipole interaction between them and the bulk matrix. The dipolar coupling of the bulk lattice and admixture ions has a significant effect on the solution stability.
Author's note: I expected this conference material should precede the papers in JMMM and Physics of Metal and Metallography. It was really surprising that the JMMM has been published first.
Tsiberkin K., Strunina Ya. Magnetism of dimer ensemble with random exchange energy. European Physical Journal B, 2021, vol. 94, 21. DOI: 10.1140/epjb/s10051-020-00028-0
We present the study of magnetism of dimer ensemble deposited on a non-magnetic conducting substrate. The dimers consist of ions with spin 1/2 and have a random size. The magnetic ions are coupled by RKKY-interaction with random energy value. We consider two interaction models. The first assumes that dimer coupling energy has a Gaussian distribution, and the second model is based on a log-normal distribution of dimer size. The magnetization and susceptibility are evaluated from the exact solution for dimer energy and eigenstates. We show that the average exchange value and its dispersion have a strong effect on the system properties. The magnetic saturation exists under strong magnetic fields. High-temperature leads to the Curie’s law for susceptibility. The saturation magnetization of system with ferromagnetic coupling lowers, while the antiferromagnetic dimer ensemble can have non-zero magnetization under the strong magnetic field. It is determined by the dispersion of exchange energy.
Tsiberkin K. Magnetization wave dynamics within a diluted magnetic semiconductor. Journal of Magnetism and Magnetic Materials, 2021, vol. 523, 167596. DOI: 10.1016/j.jmmm.2020.167596
The paper presents a theoretical analysis of magnetization waves in a diluted magnetic semiconductor. Using the continuous medium approximation, we derived a dynamical equation system that describes the magnetization evolution of the paramagnetic matrix and magnetic admixture ions. Two possible solutions were considered. The first involved a travelling wave of finite amplitude, which was stable in the system with a ferromagnetic coupling with admixture ions. The second solution involved a solitary wave. Here, the soliton amplitude and velocity were determined by the interaction between the admixture ions themselves and between them and the base matrix. The dipolar coupling of the matrix and admixture had significant influence on the wave stability.
2020
Tsiberkin K. Porosity effect on the linear stability of flow overlying a porous medium. European Physical Journal E, 2020, vol 43, 34. DOI: 10.1140/epje/i2020-11959-6
We study how the stability of a homogeneous incompressible fluid flow over a saturated Brinkman porous medium is affected by a change in porosity. We produce neutral curves using the shooting method in the area of bimodality. When the porosity decreases, the topology of these curves changes because of the interplay between two instability modes. The long-wave instability is dominant if the medium is highly porous. In contrast, the short-wave instability is the most significant at low porosity because of high tangential stress at the fluid-medium interface. We identify a stability gap between the neutral curve branches within a narrow range of porosity values. The calculated results show the development and disappearance of this gap when the porosity changes.
Tsiberkin K.B. On the porosity influence on stability of flow over porous medium. Bulletin of Udmurt University. Mathematics, Mechanics, Computer Science, 2020, vol. 30, issue 1, pp. 134-144. DOI: 10.35634/vm100110
The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than 0.7, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin-Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.
Tsiberkin K.B., Kadyrov D.I. Cooperative phenomena in solids: tutorial. Perm, Perm University Press, 2020. 116 p. ISBN 978-5-7944-3541-2 In Russian
Abstract: The introduction into second quantization and field theory methods in condensed matter physics. The main topics: Second quantization operators, electrons in solids, Hubbard model, physical acoustics, phonons, superfluidity, superconductivity, spin waves.
Keywords: quantum field theory, second quantization, condensed matter
2019
Sosunov A.V., Tsiberkin K.B., Henner V.K. The effect of functionalization of carbon nanoshells on their electrical properties. Bulletin of Perm University. Physics, 2019, no. 2, pp. 63–68. DOI: 10.17072/1994-3598-2019-2-63-68
We present an experimental and theoretical study of electronic properties of carbon nanoshells with pore size 3 nm after its functionalization if fluorine radio-frequency plasma. The synthesized samples are CF0.05, CF0.31 and CF0.50 after 5, 15 and 30 hours of functionalization. It is shown that the functionalization time increase changes the electric resistance from 50 to 950 Ohm with stable structure. Theoretical estimate of the band gap with of carbon nanoshells is 0.13 eV. We assume that such small band gap (e.g., fully fluorinated one-layer graphene has ~2–3 eV gap) is a result of incomplete functionalization and influence of additional carbon layers inside the shell.
Tsiberkin K.B., Belozerova T.S., Henner V.K. Simulation of free induction decay at low-temperature with spin waves and classical spins. European Physical Journal B. 2019. Vol. 92, 140. DOI: 10.1140/epjb/e2019-90439-9
Spin system dynamics is analysed with two methods - spin waves approach and classical spins numerical simulations. The methods are applied to free induction decay. The role of dipole interactions is investigated in details.
Tsiberkin K. B. Stability of plane-parallel and two-dimensional flows over porous medium. Bulletin of Perm University. Physics, 2019, no. 1, pp. 52–59. DOI: 10.17072/1994-3598-2019-1-52-59 (In Russian)
The paper presents a comparative study of linear stability problems for the plane-parallel and two-dimensional stationary flow in double layer system of fluid and porous medium. An incom-pressible fluid flows over homogeneous saturated porous layer. The fluid top is a free rigid bound-ary. Porous medium is described by the Brinkman model. Two-dimensional stationary solutions are built numerically by iterative procedure of establishment method. Sets of the neutral curves are obtained by the shooting method; perturbations are assumed to be flat linear waves travelling down the flow. The neutral curves are compared for plane-parallel and two-dimensional station-ary flow for different porosity and thickness of porous layer. The critical Reynolds numbers are almost twice larger than the stability threshold of plane parallel problem while the critical wave numbers close these two cases. If the porous layer is thick, the two-dimensional problem rapidly destabilized. Its stability threshold becomes lower that for plane-parallel flow. The long-wave in-stability realizes. Critical wave numbers are small and tends to zero at high porosities. The neutral curve become bimodal at low porosity.
Stepanov R., Podtaev S., Tsiberkin K. Sample size determination in the laser-Doppler measurements of skin blood flow. Microvascular Research. 2019. Vol. 125, 103883. DOI: 10.1016/j.mvr.2019.103883
Pre-study calculations of the required sample size are vital to a large majority of studies. Using the method based on the Monte-Carlo simulations, we have illustrated how the sample size is related to the statistic power value, the significance level, the variability of observations and the minor magnitude of the effect of interest under study. If the study has been already completed, one should not perform any ‘post hoc’ power calculations. In this case, calculation of confidence intervals is a better choice. We assessed the confidence intervals given in a number of publications where microcirculation is studied by LDF techniques using different protocols. We have found that types I and II errors are frequently encountered in the LDF studies, which is a consequence of an inappropriate sample size.
Rudakov G.A., Tsiberkin K.B., Ponomarev R.S., Henner V.K., Ziolkowska D.A., Jasinski J.B., Sumanasekera Gamini. Magnetic properties of transition metal nanoparticles enclosed in carbon nanocages. Journal of Magnetism and Magnetic Materials. 2019. Vol. 472, pp. 34-39. DOI: 10.1016/j.jmmm.2018.10.016
We have demonstrated a simple, scalable, and low-cost method of producing superparamagnetic nanoparticles (SPNs) encapsulated in carbon nanocages (CNCs). These materials show a very high saturation magnetization and have the potential to find applications in various technologies, including a direct drug delivery, supercapacitors, catalysis, etc. Using a facile method, it was shown that via a simple annealing process of precursors based on a mixture of transition metal (TM) (TM: Ni, Co or Fe) salt (acetate) and citric acid, TM nanoparticles encapsulated in CNCs (TM@CNC) can be readily produced. Our study indicates, that Ni@CNC nanoparticles synthesized at temperatures 500 °C-600 °C are in the 3-4 nm size range and show superparamagnetic behavior while the annealing at 700 °C and higher temperatures leads to the ferromagnetic behavior due to a nanoparticle agglomeration through the Ostwald ripening mechanism. Further, the superparamagnetic Co@CNC nanoparticles synthesized at 600 °C show slightly larger, 4-5 nm, sizes but have much higher saturation magnetization compared to Ni@CNC nanoparticles synthesized at the same temperature making Co@CNC more sensitive to external magnetic field and more useful for direct drug delivery. Finally, for Fe-based precursor, the agglomeration occurs at much lower temperatures. The Fe@CNC nanoparticles synthesized at 600 °C are much larger, in the 10-100 nm size range, show only ferromagnetic behavior, and may be used for magnetic nanoparticle hyperthermia in cancer treatment. The magnetic properties of samples are found to correspond to the theoretical estimates of the critical size of single-domain particles in these TM systems.
2018
Tsiberkin K.B. Non-linear waves and solitons of magnetization in dipolar-coupled paramagnetic. Journal of Experimental and Theoretical Physics, 2018, Vol. 127 (6), pp. 1059–1066. DOI: 10.1134/S1063776118120099
Based on a microscopic approach, we have derived equations for the local magnetization dynamics of a spin system coupled by a dipole–dipole interaction in a uniform magnetic field in the continuum approximation. Using the generalized method of multiple scales, we have found the corrections to the Larmor precession frequency of the magnetic moments due to the interparticle interaction, which lead to a broadening of spectral lines and the formation of satellites far from the Larmor frequency. We have derived nonlinear equations for the magnetization amplitude in higher expansion orders, which admit wave and soliton solutions. We have analyzed the influence of the nonsecular part of the dipole–dipole interaction on the stability of solitons and determined the conditions for their existence.
Original Russian Text © K.B. Tsiberkin, 2018, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2018, Vol. 154, No. 6 (12), pp. 1151-1159.
Tsiberkin K.B. Inertial and Darcy’s terms ratio in boundary layer at fluid–porous medium interface. Transport in Porous Media. 2018. Vol. 125 (2), pp. 259-269. DOI: 10.1007/s11242-018-1117-z
The study considers the forced boundary-layer flow overlying the Darcy–Brinkman porous medium and gives a quantitative analysis of the nonlinear inertial terms in the Brinkman filtration equation. The inertial terms are shown to be larger than the Darcy’s drag near the porous medium interface. The applicability range of boundary-layer approach is determined. It is suitable in high-permeable media with moderate velocities of an external flow. If it is slow enough, the inertial terms can be omitted in spite of interface effect. On the other hand, fast external flow produces the filtration with large pore-scale Reynolds number; therefore, the Forchheimer’s drag should be taken into account. It is shown the Brinkman term as well as inertial terms have a significant role in boundary-layer formation within the porous medium.
Keywords: Interface flow coupling, porous media, inertial terms
Tsiberkin K.B., Belozerova T.S., Henner V.K. Classical models of NMR spectrum. Bulletin of Perm University. Physics. 2018. Issue 2 (40), pp. 13-19. DOI: 10.17072/1994-3598-2018-2-13-19 In Russian
Abstract: NMR dipolar spectrum formation is considered for spin system under strong constant and uniform magnetic field. Numerical simulation of system dynamics uses 125 magnetic moments are in cube 5×5×5. The response on jump of longitudinal external field is simulated. Free induction decay lasts dirung spin-spin relaxation time, while the longitudinal magnetization also jumps. Fourier spectra of magnetization signals include the peaks near zero, Larmor and double-Larmor frequencies. It corresponds well with the quantum theory of magnetic resonance. The Heisenberg equations for spin deviation from saturation state are transformed into continuum magnetization equations. It takes into account the non-secular terms in dipolar Hamiltonian. Final nonlinear system permits the standing monochromatic wave solution. It also reproduces three main peaks in NMR spectrum.
Keywords: dipolar interaction; nuclear magnetic resonanse; continuous medium
Tsiberkin K.B. Effect of inertial terms on fluid-porous medium flow coupling. Transport in Porous Media. 2018. Vol. 121 (1), pp. 109-120. DOI: 10.1007/s11242-017-0951-8
Abstract: The study considers an effect of the nonlinear inertial terms in the Brinkman filtration equation on the characteristics of coupled flows in a pure fluid and porous medium in the frameworks of two independent problems. The first problem is the forced boundary-layer flow overlying the Darcy–Brinkman porous medium. The Prandtl theory is used, and the self-similar equations are built to describe it. It is shown that the inertial terms have a valuable effect on the boundary-layer structure because of the large velocity gradient in the transition zone. The boundary-layer thickness in a porous medium rapidly grows at large Reynolds numbers. The velocity magnitude and gradient at the interface also change. The second independent problem is an analysis of the inertial terms effect on the flow stability. The neutral curves of the full and linearized flow models are built using the shooting method. They have different short-wave asymptotic, but there are no significant changes in the critical Reynolds numbers and corresponding wave numbers.
Keywords: Interface flow coupling, porous media, inertial terms
Tsiberkin K.B., Gaži M. Magnetic response of triangular graphone. Bulletin of Perm University. Physics, 2018, no. 3 (41), pp. 65–72. DOI: 10.17072/1994-3598-2018-3-65-72
We consider triangular graphone structure – a semi-hydrogenated layer of graphene with hydrogen atoms boned to one of its sub-lattices only. The response function of graphone to an external magnetic field is evaluated in general using the Heisenberg Hamiltonian model of the structure with exchange energy coefficient J0 of unknown value (negative due to ferromagnetic behaviour of triangular graphone). The spin wave approach in the limit of near zero temperature is used for the description of the magnetisation. A specific case when the graphone is exposed to a magnetic pulse with a given carrier frequency is examined in greater depth. To obtain the magnetization response, integration over both the frequency space and momentum space is necessary. Due to inapplicability of the isotropic approximation for the given geometry of graphone, integration over momentum space is performed numerically. The calculations show that the resonance of the system occurs at frequencies which correspond to the upper limit of the spin wave energy band and the saddle points of the energy surface. Using these results, further experimental investigation based on THz or far-infrared spectroscopy can be performed, which can determine the as-yet-unknown exchange energy coefficient J0. The coefficient can in turn provide an estimate of a temperature range for which the spin wave approach utilised in our investigation is valid.
Keywords: graphone; magnetization response; spin waves
Henner V.K., Tsiberkin K.B., Krauzin P.V. Quantum theory. One-dimensional problems: tutorial. Perm, Perm University Press, 2018. 124 p. ISBN 978-5-7944-3188-9 In Russian
Abstract: The introduction into quantum mechanics and its basic1D problems: quantum well, scattering on the well or barrier, Kronig-Penney model, hydrogen atom with zero angular momentum. The Schrodinger picture is described.
Keywords: quantum physics, atomic physics, Schrodinger equation
2017
Sosunov A.V., Volyntsev A.B., Tsiberkin K.B., Yuriev V.A., Ponomarev R.S. Features of structure and mechanical properties LiNbO3. Ferroelectrics. 2017. Vol. 506 (1), pp. 24–31. DOI: 10.1080/00150193.2017.1281686
Abstract: This paper reviews the features of the structure, composition and mechanical properties of the subsurface layer of pure lithium niobate. Depth of this layer ranges up to 20 μm, and it's structure and composition vary significantly from the bulk of a material. It is shown that mechanical properties of said layer differ from the bulk material as well, mainly due to a polishing, which increases density of defects, namely dislocations. High density of dislocation leads to drift of various parameters in the optical modulators, making results of their work inconsistent. These results are important in the production of various devices that are created on the basis of lithium niobate.
Keywords: Lithium niobate, subsurface layer, nanoindentation, dislocations, defects, DС-drift, optical modulators
2016
Tsiberkin K.B. Collective spin excitations in 2D paramagnet with dipole interaction. European Physical Journal B. 2016. Vol. 89 (2), 54. DOI: 10.1140/epjb/e2016-60964-2
Abstract: The collective spin excitations in the unbounded 2D paramagnetic system with dipole interactions are studied. The model Hamiltonian includes Zeeman energy and dipole interaction energy, while the exchange vanishes. The system is placed into a constant uniform magnetic field which is orthogonal to the lattice plane. It provides the equilibrium state with spin ordering along the field direction, and the saturation is reached at zero temperature. We consider the deviations of spin magnetic moments from its equilibrium position along the external field. The Holstein--Primakoff representation is applied to spin operators in low-temperature approximation. When the interaction between the spin waves is negligible and only two-magnon terms are taken into account, the Hamiltonian diagonalisation is possible. We obtain the dispersion relation for spin waves in the square and hexagonal honeycomb lattice. Bose--Einstein statistics determine the average number of spin deviations, and total system magnetization. The lattice structure does not influence on magnetization at the long-wavelength limit. The dependencies of the relative magnetization and longitudinal susceptibility on temperature and external field intensity are found. The internal energy and specific heat of the Bose gas of spin waves are calculated. The collective spin excitations play a significant role in the properties of the paramagnetic system at low temperature and strong external magnetic field.
Keywords: spin system, spin waves, paramagnetism, dipolar interaction
Tsiberkin K., Kolchanova E., Lyubimova T. Verification of the boundary condition at the porous medium–fluid interface. European Physical Journal Web of Confereces. 2016. Vol. 114, 02125. Proceedings of "Experimental Fluid Mechanics - 2015", Prague, Czech Republic/ DOI: 10.1051/epjconf/201611402125
Abstract: We study the hydrodynamic stability of liquid flowing down over the inclined layer of uniform porous medium and compare the results obtained in the different frameworks. The flow in porous medium is described by the Brinkman model and by the Darcy model with corresponding boundary conditions at the interface between the homogeneous fluid and porous medium. It is shown the critical Reynolds number is calculated for the Darcy model much lower than in case of the Brinkman model, while the flow velocity is the same in the both models. It is a pure mathematical effect, which can be used to verify the models and to determine the empirical coefficients in the boundary conditions from an experimental study of flow instability.
Keywords: porous media, coupled flows, filtration models, Darcy model, Brinkman model, interface boundary conditions
Lyubimova T.P, Lyubimov D.V., Baydina D.T., Kolchanova E.A., Tsiberkin K.B. Instability of plane-parallel flow of incompressible liquid over a saturated porous medium. Physical Review E. 2016. Vol. 94 (1), 013104. DOI: 10.1103/PhysRevE.94.013104
Abstract: The linear stability of plane-parallel flow of an incompressible viscous fluid over a saturated porous layer is studied to model the instability of water flow in a river over aquatic plants. The saturated porous layer is bounded from below by a rigid plate and the pure fluid layer has a free, undeformable upper boundary. A small inclination of the layers is imposed to simulate the riverbed slope. The layers are inclined at a small angle to the horizon. The problem is studied within two models: the Brinkman model with the boundary conditions by Ochoa-Tapia and Whitaker at the interface, and the Darcy-Forchheimer model with the conditions by Beavers and Joseph. The neutral curves and critical Reynolds numbers are calculated for various porous layer permeabilities and relative thicknesses of the porous layer. The results obtained within the two models are compared and analyzed.
Keywords: porous media, coupled flows, filtration models, Darcy model, Brinkman model, interface boundary conditions
Tsiberkin K. B. On the structure of the steady-state flow velocity field near the interface between a homogeneous liquid and a Brinkman porous medium. Technical Physics. 2016. Vol. 61, pp. 1181-1186. DOI: 10.1134/S1063784216080272
Abstract: The structure of a homogeneous liquid flow at the interface with a porous medium saturated with the same liquid has been studied in the boundary layer approximation. The porous medium is described by the Brinkman model. Self-similar equations of motion in the form of Blasius equation have been found, and their numerical solutions have been presented. An expression for the force exerted by the flow on the porous medium is derived.
Keywords: porous media, coupled flows, Brinkman model, boundary layer theory
Original Russian Text © K.B. Tsiberkin, 2016, published in Zhurnal Tekhnicheskoi Fiziki, 2016, Vol. 86, No. 8, pp. 62–67.
Tsiberkin K.B., Belozerova T.S., Henner V.K. Spin-wave approach to the 2D paramagnetic under the magnetic field. Bulletin of Perm University. Physics. 2016. Issue 2 (33), pp. 35-48. DOI: 10.17072/1994-3598-2016-2-35-48 In Russian
Abstract: We study the possibility of collective spin excitations in 2D paramagnetic crystal with the dipole-dipole interaction and without the exchange interaction. The crystal is under uniform constant magnetic field. All the magnetic moments are oriented along the magnetic field at the saturation. Using the Holstein–Primakoff transformation, we describe the properties of paramagnetic in terms of the spin waves at the low-temperature limit. We obtain the dispersion relations for spin waves at the square and hexagonal flat lattices. It is shown the wavelength of the collective excitations and their bandwidth are determined by the external magnetic field direction. The long-wave per-turbations have the lowest energy when the magnetic field is orthogonal to the lattice plane, and the short-wave perturbations are the most preferable when the field is parallel to the lattice. We provide the direct numerical simulation of the group of interacting magnetic moments under the constant external field with different orientation to the lattice. The total transversal spin and di-pole energy evolution in time and their Fourier-spectrum are considered. The numerical results match the analytical calculation in spin-wave approach
Keywords: paramagnetic; dipolar interaction; spin waves
Antonova N., Tsiberkin K., Podtaev S., Paskova V., Velcheva I., Chaushev N. Comparative study between microvascular tone regulation and rheological properties of blood in patients with type 2 diabetes mellitus. Clinical Hemorheology and Microcirculation. 2016. Vol. 64 (4), pp. 837-844. DOI: 10.3233/CH-168000
Abstract: The aim of the study is to investigate the changes of the skin blood flow responses to cold stress in patients with diabetes mellitus type 2 through wavelet analysis of the peripheral skin temperature oscillations and to estimate their relationship with the blood viscosity values. The amplitudes of the skin temperature pulsations (ASTP) were monitored by “Microtest” device (“FM-Diagnostics”, Russia); the whole blood viscosity and the shear stresses were measured by Contraves LS30 viscometer, (Switzerland) at a steady flow in 9 healthy subjects and in 30 patients with type 2 diabetes mellitus. Power law and Herschel-Bulkley (HB) equations were applied to describe the blood rheology. Both models include consistency (k) and flow index (m), and the HB also gives the yield stress (τ0). The Spearman rank correlations between these parameters and the ASTP in the frequency ranges, corresponding to the myogenic, neurogenic and endothelial mechanisms of the microcirculation tone regulation were calculated. The ASTP values decreased when the blood viscosity increased. The correlation analysis revealed good ASTP–m (r > 0.5) and ASTP–k (r < –0.5) relationships in the endothelial range, while the ASTP–τ0 correlation was weaker (r≈–0.4). These correlations became lower for the ASTP during the cold stress. The results prompt manifestation of endothelial dysfunction in patients with type 2 diabetes.
Keywords: hemorheology; microvascular tone regulation
Tiulkina I.V., Tsiberkin K.B. Structure of coupled flows near the heated interface between liquid and porous medium. Bulletin of Perm University. Physics. 2016. Issue 3 (34), pp. 49-57. DOI: 10.17072/1994-3598-2016-3-49-57. In Russian
Abstract: We consider a structure of laminar convective boundary layer near the heated interface between the homogeneous liquid and Brinkman porous medium is saturated with the same liquid. The interface is heated uniformly. It has the constant temperature. We get the self-similar form of the convection equations in the boundary layer approximation. Also, we assume the power-law dependence of the medium permeability on the longitudinal coordinate. The self-similar profiles of the velocity and temperature in the both media are calculated with the different values of the liquid parameters, heat intensity and porous media properties. The velocity maximum always places in the uniform liquid layer. The self-similar solutions for velocity and temperature have a weak dependence on the heating intensity and porous medium parameters. Therefore, the obtained solution can be considered as universal in the first approximation. The dependencies of flow velocity on the control parameters in characteristic points are obtained. They are maximum velocity position and the interface between media. The flow velocity is almost proportional to the interface temperature. The main control parameter is the Prandtl number. Its’ growth leads to the flow deceleration and viscous boundary layer expansion.
Keywords: convective boundary layer; porous medium; coupled flows
Lyubimov D.V., Maryshev B.S., Tsiberkin K.B. Vector and tensor calculus: tutorial. Perm, Perm University Press, 2016. 92 p. ISBN 978-5-7944-2715-8 In Russian
Abstract: The tutorial considers the main topics of basic vector and tensor calculus are necessary for physicists.
Keywords: vector calculus, tensor calculus, index notation
2015
Podtaev S., Nikolaev V., Samartsev V., Gavrilov V., Tsiberkin K. Frequency and temperature dependence of skin bioimpedance during a contralateral cold test. Physiological Measurement. 2015. Vol. 36, pp. 561-578. DOI: 10.1088/0967-3334/36/3/561
Abstract: A study of the α- and β-dispersion of skin bioimpedance dependence on temperature and micro-hemodynamics is presented. The vascular tone changes during the cold test are verified by the wavelet-analysis of skin temperature signals obtained simultaneously with impedance measurements. Thirty three normal healthy subjects of 28 ± 7 years old were entered into the study. The tetra-polar electrode system was used to record the resistance and reactance; measurements were carried out at 67 frequencies, in a frequency range from 2 Hz to 50 kHz. It has been found that the impedance decreases with vasodilation and increases with vasoconstriction. The high values of correlation among thermal oscillation amplitudes and Nyquist diagram parameters prove the impedance dependence on blood flow in three frequency bands corresponding to the myogenic, neurogenic and endothelial vascular tone regulation mechanisms. Using an equivalent RC circuit, we obtained the changes in the Nyquist diagram matching the experimental data. The proposed descriptive α-dispersion model can be used to study mechanisms responsible for intercellular interaction.
Keywords: thermometers, biophysical techniques (research methods), mechanical and electrical properties of tissues and organs, hemodynamics, muscles, neuroscience
Tsiberkin K.B. Stability of the flow over saturated porous medium containing dissolved admixture. The Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science. 2015. Vol. 25 (1), pp. 107-116. In Russian. DOI: 10.20537/vm150112
Abstract: A two-layer system consisting of a porous layer of finite thickness and a uniform fluid layer on top is considered. A rigid wall bounds the porous layer from below, while the upper fluid surface is assumed to be undeformable. We study the process of admixture extraction from the porous layer and its influence on the stability of the stationary plane-parallel flow above it. We describe a porous layer using a Brinkman model with interface boundary conditions by Ochoa-Tapia-Whitaker. We obtain an exact and an approximate solution for the concentration profile. The quasistationary velocity profile is obtained using "frozen" concentration distribution. We solve a linear stability problem for the plane-parallel stationary flow in a wide range of system parameters. Oscillatory instability evolved in the system at the sufficient flow velocity corresponds to traveling waves near the interface. We show that the convective and diffusion transport practically does not affect the structure of neutral stability curves and Reynolds numbers.
Keywords: flow over porous medium, two-layer system, bimodality, flow instability, admixture transport, Brinkman model
Tsiberkin K.B. On long-range order formation in particle suspension under circular vibrations. Bulletin of Perm University. Series: Physics. 2015. Issue 1 (29), pp. 42-51. In Russian
Abstract: The pattern formation in two-dimensional particles ensemble is suspended in liquid under circular vibrations is studied. Interaction energy of ordered system is calculated. We analyze the hexagonal and square pattern are found in numerical simulation. Lattice constant is calculated using physical parameters from known experiments. The square lattice is shown to be more preferable energetical-ly for high-frequency vibrations. The possible mechanisms of system order control are discussed.
Keywords: vibrations, self-organization, particle-laden flows, long-range order, pattern formation
Kadyrov D.I., Tsiberkin K.B. Physics of nonequilibrium processes: linear response theory: tutorial. Perm, Perm University Press, 2015. 87 p. ISBN 978-5-7944-2488-1. In Russian
Abstract: The tutorial contains the description of linear-response theory. The linear response, response function, correlation and relaxation function, and system susceptibility are considered.
Keywords: linear response theory, Kubo formula, susceptibility, Green's functions method, nonequilibrium thermodynamics
Tsiberkin K.B. Transversal dipole relaxation of nuclear spins in graphene enriched in carbon-13. Bulletin of Perm University. Series: Physics. 2015. Issue 2 (30), pp. 69-75. In Russian
Abstract: We consider a transversal nuclear spin relaxation in graphene enriched with carbon-13 isotope un-der the magnetic field is orthogonal the material plane. Using the momentum method by van Vleck, we calculate the transversal relaxation time, broadening of NMR-peak and free induction decay signal. We shown the dipole interaction plays an important role in relaxation process but it does not give a full description of the transversal relaxation.
Keywords: graphene; nuclear magnetic resonance; spin-spin relaxation
Lyubimova T.P., Lepihin A.P., Parshakova Y.N., Tsiberkin K.B. Numerical modeling of liquid waste infiltration from storage facilities into surrounding groundwater and surface water bodies. Computational Continuum Mechanics. 2015. Vol. 8 (3), pp. 310-318. DOI: 10.7242/1999-6691/2015.8.3.26 In Russian
Abstract: The study focuses on infiltration of saturated brine from liquid waste storage facilities into the surrounding groundwater and surface water bodies. Storage facilities are located at the Verkhnekamsk Potassium and Magnesium Salt Deposit (Perm Region, Russian Federation) and contain highly mineralized brines of potassium, sodium and magnesium chlorides. Using the analytical solution of one-dimensional equation of contaminant transport by homogeneous stationary filtration flow, we have made estimates of the time it takes the contaminant to move from the storage facilities to the nearest surface water body and a settling time for the stationary concentration profile, neglecting and accounting for contaminant adsorption in the porous matrix. The contaminant concentration at the point of brine ingress into the surface reservoir is calculated. The direct 3D numerical modeling of brine infiltration into the surrounding medium is performed using ANSYS Fluent software package. The modeling results indicate different stages of contaminant propagation in the porous medium. It has been found that the contaminant spreads over a wide area with almost uniform concentration close to the saturation value. The contaminant reaches the nearest riverbed 20 days after the start of infiltration. The numerical results agree well with the analytical results obtained in the framework of the one-dimensional mode. The proposed physical models adequately describe hydrodynamic processes associated with the operation of large storage facilities and can be used to predict contamination propagation in groundwater around the storage facilities.
Keywords: liquid wastes storages, contaminant transport in porous media, 1D model, 3D numerical modeling
2014
Tsiberkin K., Lyubimov D.V., Lyubimova T.P., Zikanov O. Evolution of a spherical hydrate-free inclusion in a porous matrix filled with methane hydrate. Physical Review E. 2014. Vol. 89, 023008. DOI: 10.1103/PhysRevE.89.023008
Abstract: The behavior of a small isolated hydrate-free inclusion (a gas bubble) within a porous matrix filled with methane hydrate and either water or methane gas is analyzed. Simplifying assumptions of spherical symmetry, an infinite uniform porous medium, and negligible effects of background temperature and pressure variations focus the investigation on the features of the dynamics of a single bubble determined by a phase transition. Two solutions are presented: an exact solution of the Stefan problem obtained when the effects of gas and water flow are neglected, and a numerical solution of the full problem. The solutions are in good agreement with each other and with known asymptotic dependencies, confirming that the effects of inertia and convection transport can be neglected in the case of small inclusions. It is found that, after an initial adjustment, the radius of any small bubble decreases with time following a self-similar solution of the Stefan problem. The lifetime of a bubble is evaluated as a function of initial radius and the system's physical parameters. Possible effects of such inclusions on the filtration of methane to the surface and other aspects of the dynamics of hydrate-bearing deposits are discussed.
Keywords: heat transfer, porous media, multiphase systems, methane hydrates, Stefan problem, solidification
Tsiberkin K. Vector spherical harmonics in convective instability analysis of liquid in spherical cell. Bulletin of Perm University. Series: Physics. 2014. Issue 2-3 (27-28), pp. 5-10. In Russian
Abstract: A convective instability of incompressible liquid in spherical cell heated from below is provided with Galerkin method using expansion of velocity field by vector spherical harmonics is more precise than polynomial bases. Critical Rayleigh numbers and corresponding critical motions are obtained. The efficiency of vector spherical harmonics expansion in convective instability analysis is analyzed.
Keywords: convective instability, spherical cell, vector spherical harmonics, Galerkin method
2013
Lyubimova T.P., Tsiberkin K.B. Simulation of the hydrate grain dissociation within porous matrix. Computational Continuum Mechanics. 2013. Vol. 6 (1), pp. 119-124. DOI: 10.7242/1999-6691/2013.6.1.15 In Russian
Abstract: The results of numerical simulation of the methane hydrate grain dissociation within a water-saturated porous matrix in a linear approximation at small perturbations of thermodynamic equilibrium of phases are presented. The qualitative behavior of the system in this approximation is shown to be reliable. Quantitative estimates of intensity of dissociation and lifetime of methane hydrate grains are obtained.
Keywords: porous medium, filtration, methane hydrates, numerical modeling
2012
Henner V.K., Tsiberkin K.B. Quantum electrodynamics (main reactions): tutorial. Perm, Perm University Press, 2012. 89 p. ISBN 978-5-7944-1960-3 In Russian
Abstract: The tutorial contains examples of cross-section calculation for the scattering and annihilation processes in the lowest orders of a perturbation theory.
Keywords: quantum electrodynamics, Feinman diagrams, cross-section, scattering theory
Podtaev S., Stepanov R., Dumler A., Chugainov S., Tziberkin K. Wavelet analysis of the impedance cardiogram waveforms. Journal of Physics: Conference Series. 2012. Vol. 407 (1), 012003. DOI: 10.1088/1742-6596/407/1/012003
Abstract: Impedance cardiography has been used for diagnosing atrial and ventricular dysfunctions, valve disorders, aortic stenosis, and vascular diseases. Almost all the applications of impedance cardiography require determination of some of the characteristic points of the ICG waveform. The ICG waveform has a set of characteristic points known as A, B, E ((dZ/dt)max) X, Y, O and Z. These points are related to distinct physiological events in the cardiac cycle. Objective of this work is an approbation of a new method of processing and interpretation of the impedance cardiogram waveforms using wavelet analysis. A method of computer thoracic tetrapolar polyrheocardiography is used for hemodynamic registrations. Use of original wavelet differentiation algorithm allows combining filtration and calculation of the derivatives of rheocardiogram. The proposed approach can be used in clinical practice for early diagnostics of cardiovascular system remodelling in the course of different pathologies.
Keywords: impedance cardiography, rheocardiography, wavelet analysis, numerical wavelet differentiation
2010
Podtaev S., Dumler A., Stepanov R., Frick P., Tziberkin K. Wavelet-based correlations of impedance cardiography signals and heart rate variability. Journal of Physics: Conference Series. 2010. Vol. 224 (1), 012107. DOI: 10.1088/1742-6596/224/1/012107
Abstract: The wavelet-based correlation analysis is employed to study impedance cardiography signals (variation in the impedance of the thorax z(t) and time derivative of the thoracic impedance (- dz/dt)) and heart rate variability (HRV). A method of computer thoracic tetrapolar polyrheocardiography is used for hemodynamic registrations. The modulus of wavelet-correlation function shows the level of correlation, and the phase indicates the mean phase shift of oscillations at the given scale (frequency). Significant correlations essentially exceeding the values obtained for noise signals are defined within two spectral ranges, which correspond to respiratory activity (0.14-0.5 Hz), endothelial related metabolic activity and neuroendocrine rhythms (0.0095-0.02 Hz). Probably, the phase shift of oscillations in all frequency ranges is related to the peculiarities of parasympathetic and neuro-humoral regulation of a cardiovascular system.
Keywords: impedance cardiography, hemodynamics, wavelet analysis
Podtaev S., Dumler A., Muravyov N., Myasnikov M., Tsiberkin K. Laser-induced skin temperature oscillation. SPIE Proceedings. 2010. Vol. 7376. Proceedings of LALS 2010. DOI: 10.1117/12.871113
Abstract: Adaptive wavelet analysis algorithms are used to study skin temperature oscillations caused by periodic changes in the blood flow resulting from oscillations in the vasomotor smooth muscle tone. Reduction in the amplitude of temperature fluctuations with frequency arises because the skin, owing to its low thermal diffusivity, has the properties of a lowfrequency filter. In view of their small amplitude, oscillations in the spectral range, reflecting the influence of heartbeat and respiration, cannot be distinguished from the external thermal noise. To analyze changes in oscillations of skin temperature during the laser stimulation (10 mW/cm2, 630 nm) we extract three frequency bands, corresponding to myogenic, neurogenic and endothelial vascular tone regulation mechanisms. Red laser irradiation causes temperature fluctuations changes within spectral ranges corresponding endothelial functioning and neurogenic activity.
Keywords: skin temperature oscillations, skin blood flow, wavelet analysis, laser–tissue interaction