Kirill Tsiberkin- PhD (Candidate of physical and mathematical sciences)
- Professor (Associate) at Perm State University
Kirill Tsiberkin
- PhD (Candidate of physical and mathematical sciences)
- Professor (Associate) at Perm State University
I'm working on theory of the collective effects in weak-coupled magnetics. I'm open for collaboration in this area.
About
61
Publications
19,996
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209
Citations
Introduction
I'm interested in cooperation in the fields: magnetic materials, magnetic resonances, fluid dynamics, flow instability, nonlinear dynamics.
The current topics are the magnetization dynamics of dipolar coupled systems, interaction of atoms adsorbed on carbon sheet, microscopic spin dynamics and nonlinear dynamics of dipole ensembles.
Details about me and my researches you can find here or at my web-page: https://sites.google.com/site/kirilltsiberkin/
Current institution
Additional affiliations
September 2010 - December 2016
Institute of Continuous Media Mechanics, Perm, Russia
Position
- Engineer
October 2013 - December 2016
Position
- Instructor
Description
- Courses: Advanced Numerical Methods; Fluid Dynamics [for geologists]; Partial Differential Equations [for physicists]; Quantum Theory I; Vector and Tensor Calculus [for physicists]; General Relativity.
July 2008 - February 2012
Systemi Kontrolya (Control Systems)
Position
- Technician
Education
December 2012 - June 2015
September 2010 - July 2012
September 2006 - July 2010
Publications
Publications (61)
Carbon nanocages (CNCs) are promising materials for catalysis, filtration and electrochemistry. This work is devoted to the experimental and theoretical study of the magnetic properties of both pure CNCs and those encapsulated by transition metals Ni and Co. This study presents high-resolution transmission electron microscopy (HR-TEM) images of the...
The study presents an analysis of pure dipolar spin waves in a one-dimensional chain under external constant magnetic field. The ‘all-to-all’ interactions are taken into account. The magnetization spectrum of an ensemble of randomly oriented chains are similar to the Pake doublet. The wave dispersion relation is obtained in terms of special Clausen...
The study presents an analysis of free induction decay (FID) in the ensemble of ring spin clusters using the formalism of collective modes similar to the spin waves. A dispersion relation for the waves is obtained. FID from a spin cluster is estimated and averaged over system parameters to simulate the signal given by a spherical structure or by an...
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...
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...
The continuous medium approximation to the description of a carbon material previously used to model the properties of spherical carbon shells of nanometer diameter. This approach is based on the transition from lattice operators to field operators. The present study verifies the given model evaluating the energy spectrum of electrons in a perfect...
Проведен синтез и охарактеризована структура электронно-микроскопическими методами полых углеродных наносфер. Установлено, что наносферы имеют размер 3-5 nm и состоят из нескольких углеродных слоев с примесью кислорода. Экспериментально и теоретически было проведено исследование спектра поглощения наносфер. Предложена простая модель энергетического...
In this paper, we consider the motion of electrons in a constant electric field in a certain temperature range, when the motion can be described by an equation of the Darcy–Brinkman type. We studied the on-set of the stationary current flow in a conductor with and without taking into account the viscosity of elec-trons after switching on a longitud...
An approach to the calculation of the energy spectrum of a monolayer carbon nanoshell (monolayer and multilayer sphere is proposed based on the application of the Hubbard model and the continuous medium approximation with account for the possible deposition of impurity atoms on the carbon surface. A discrete spectrum of energy levels is realized in...
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...
The continuum model of electronic properties of spherical carbon shell or onion is developed. Part of these results is accepted for publication in Journal of Experimental and Theoretical Physics.
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 relati...
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 Metro...
The presentation reports the results of spin waves and / or continuous medium approach to the problems of NMR and magnetization waves in paramagnetic and diluted magnetic materials
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 travel...
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. Th...
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 distributio...
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 travel...
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. Th...
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-...
We study how the stability of 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...
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.
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We present an analysis of 2D flows near the interface between free fluid and porous medium. There are series of problems considered:
- forced flow over the porous medium;
- free convection near heated boundary;
- free convective plume over point heat source at the boundary.
All the problems permit self-similar transform when the permeability change...
We consider the stationary 2D flows in a channel with rigid boundaries is partially filled with a porous medium. The pure fluid is bounded by solid or free rigid boundary, while the channel bottom is solid. The method uses Berman transformation to build the 2D solution. Free flow is described by the Navier–Stokes equations, the filtration flow is d...
The linear stability of non-parallel flow of incompressible viscous fluid over the porous layer is studied. The problem models an instability of water flow in energy storage or cooling systems. Mathematical model of the flow is based on the Navier-Stokes equations for the free flow and the Brinkman equation for the filtration flow. Interface bounda...
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 incompressible fluid flows over homogeneous saturated porous layer. The fluid top is a free rigid boundary. Porous medium is described by the Brinkman model. Two-dimensi...
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 elect...
Описана математическая модель и на её основе проведён анализ стационарных неплоскопараллельных течений в канале, частично заполненном однородной недеформируемой пористой средой. Рассмотрены два варианта условий на верхней границе однородной жидкости: она или твёрдая, или свободная недеформируемая. Модель основывается на преобразовании Бермана для з...
[IN RUSSIAN] 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 magn...
We consider triangular graphone structure – a semi-hydrogenated layer of graphene with hydro-gen 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 d...
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...
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. Us...
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 magn...
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...
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...
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...
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 monito...
This study focuses on the infiltration of saturated brine from liquid-waste storage facilities into the surrounding groundwater and surface-water bodies. The storage facilities are situated at the Verkhnekamsk Potassium and Magnesium Salt Deposit (Perm krai, Russian Federation); they store highly mineralized brine of potassium, sodium, and magnesiu...
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 monito...
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 t...
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 presente...
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...
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...
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...
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 chlori...
We consider a transversal nuclear spin relaxation in graphene enriched with carbon-13 isotope under 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...
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 lattic...
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 ente...
[In Russian] 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 st...
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 expans...
Geophysical Research Abstracts, Vol. 16, EGU2014-481-4, 2014
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 t...
Behavior of a small isolated hydrate-free inclusion (a bubble) within hydrate-bearing porous matrix is studied analytically and numerically.
An infinite porous matrix of uniform properties with pores filled by methane hydrates and either water (excessive water situation) or methane gas (excessive gas situation) is considered. A small spherical hy...
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 disso...
Behavior of a small isolated hydrate-free inclusion (a bubble) within
hydrate-bearing porous matrix is studied analytically and numerically.
An infinite porous matrix of uniform properties with pores filled by
methane hydrates and either water (excessive water situation) or methane
gas (excessive gas situation) is considered. A small spherical
hyd...
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
(...
We present results of a broad study of the dynamics of natural deposits
of methane hydrates in response to global warming. Particular attention
is given to the hydrodynamic aspects of the process associated with
instability and deformation of boundaries and filtration of released
methane to the surface. The study is computational and is based on a...
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...
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 wa...
Questions
Questions (10)
During the current project, I'm working on the problem of rarefied system magnetization (e.g., diluted magnetic semiconductor). The main factor here is the RKKY (or something similar) exchange between the ferromagnetic impurities, while the bulk matrix is assumed to be paramagnetic or non-magnetic. There is also the dipolar coupling between the matrix and impurities, but it is significant for magnetization waves in the system. It is something completely different.
So, I think that the nested Bethe lattice can be an effective way at least for the estimates. Why nested? That because any magnetic ion has some number (q1) of the 1st order neighbours at some average distance (average exchange J1), another number (q2) of the 2nd order neighbours (J2), etc. Therefore, we can introduce the Bethe lattice with q1 connections and coupling energy J1, the next lattice with q2 and J2,... All the q2, q3 and higher are connected with q1, of course. And we have some number of nested lattices (or Cayley trees).
Unfortunately, I'm not very strong in the graphs and building the reccurence relations for the Bethe model. Honestly, I'm tried :)
So, the questions:
1. Does this model sounds well and possible? Maybe I don't see any pitfalls.
2. Some nodes seems to be taken into account many times when the total magnetization is evaluated. Can I say that the sum of the nested magnetizations evaluated from any final formula (e.g., from free energy by Muller-Hartmann. Z Physik B, 27:161-168, 1977, or anything more recent) and normalized to the total lattice nodes number is an upper estimate?
3. When the system is under external magnetic field H, how can it be "distributed" between the N nested lattices? Can we estimate that any lattice is under field H/N? Or, we need to introduce some weigth coefficients for any nesting level?
I'm just need to clarify some moment. Assume, we have some energy spectrum, and we calculate the correction to it from the usual stationary perturbation theory. The new spectrum is real in common, but corrections to some levels are pure imaginary.
Thus, can we say that these levels becomes metastable under the perturbation influence, and its life-time is determined from the imaginary part of energy? These levels are higher than the ground state, therefore the transition to ground state is possible (and it is not prohibited by any selection rules).
I'm searching the description of specific heat measurement technique below 1K.
The Schottky anomaly is well-studied, but it exists in ideal systems without interactions. What is the dependence of specific heat on temperature, if the spin-spin interaction is significant? I've found only some fragmented information on it.
There are a lot of theoretical models, and it is necessary to verify them.
I need to make a relatively quick calculation of confluent Heun function (It is HeunC in Maplesoft Maple notation) values with different parameters in different points. I understand that it is possible to solve a Heun equation numerically, but that way seems not to be effective.
Of course, it is possible to use, e.g. Maple, for numerical procedure realization I need this in my study, but applying some series expansion or hypergeometric functions is more preferable.
So, I would appreciate simple (because I'm not a pure mathematician) information about series expansions of the Heun confluent function, its expression by hypergeometrics or any other known functions which are available to realize the numerical calculation.
There are many publications about the flow stability over the Darcy-Brinkman medium with nice and clear results. e.g. Chang M. H., Chen F., Straughan B. "Instability of Poiseuille flow in a fluid overlying a porous layer", J. Fluid Mech. V.564 (2006); Hill A. A. and Straughan B. "Poiseuille flow in a fluid overlying a porous medium", J. Fluid Mech. V.603 (2008); Tilton N., Cortelezzi L. "Linear stability analysis of pressure-driven flows in channels with porous walls" J. Fluid Mech. V.604 (2008); Hill A.A. "Instability of Poiseuille flow in a fluid overlying a glass bead packed porous layer", Acta Mechanica, V.206 (2009); Lyubimova T.P., Baydina D.T. "Stability and nonlinear regimes of flow over a saturated porous medium", Nonlinear Processes in Geophysics V.20 (2013), etc.
All the studies are based on Darcy-Brinkman porous medium model. I'm trying to make a similar research but, due to the project plan, it should be based on pure Darcy and Darcy-Forchheimer model without laplacian in the momentum equation. Are there any publications about the question topic?
