Stanislav I Denisov

• Prof. Dr.
• Professor (Full) at Sumy State University

Using the rigid dipole model, we study the translational and rotational motions of single-domain fer-romagnetic nanoparticles in a dilute suspension induced by the harmonically oscillating gradient magnetic field in the presence of a time-independent uniform magnetic field. Our approach is based on a set of the first-order differential equations th...

We study the deterministic dynamics of ferromagnetic nanoparticles with 'frozen' magnetization induced by the joint action of the oscillating gradient magnetic field and the uniform magnetic field, which has two components, perpendicular and parallel to the gradient one. We derive the corresponding equations for the rotational and translational mot...

We study the nonlinear dynamics of single-domain ferromagnetic nanoparticles in a viscous liquid induced by a harmonically oscillating gradient magnetic field in the absence and presence of a static uniform magnetic field. Under some physically reasonable assumptions, we derive a coupled set of stiff ordinary differential equations for the magnetiz...

We study theoretically the deterministic dynamics of single-domain ferromagnetic nanoparticles in dilute ferrofluids, which is induced by a time-varying gradient magnetic field. Using the force and torque balance equations, we derive a set of the first-order differential equations describing the translational and rotational motions of such particle...

The suspended ferromagnetic particles subjected to the gradient and uniform magnetic fields experience both the translational force generated by the field gradient and the rotational torque generated by the fields strengths. Although the uniform field does not contribute to the force, it nevertheless influences the translational motion of these par...

The suspended ferromagnetic particles subjected to the gradient and uniform magnetic fields experience both the translational force generated by the field gradient and the rotational torque generated by the fields strengths. Although the uniform field does not contribute to the force, it nevertheless influences the translational motion of these par...

We study theoretically the deterministic dynamics of single-domain ferromagnetic nanoparticles in dilute ferrofluids, which is induced by a time-varying gradient magnetic field. Using the force and torque balance equations, we derive a set of the first-order differential equations describing the translational and rotational motions of such particle...

We report the precessional rotation of magnetically isotropic ferromagnetic nanoparticles in a viscous liquid that are subjected to a rotating magnetic field. In contrast to magnetically anisotropic nanoparticles, the rotation of which occurs due to coupling between the magnetic and lattice subsystems through magnetocrystalline anisotropy, the rota...

We report a new phenomenon, the precessional rotation of magnetically isotropic ferromagnetic nanoparticles in a viscous liquid that are subjected to the rotating magnetic field. In contrast to magnetically anisotropic nanoparticles, whose rotation occurs due to coupling between the magnetic and lattice subsystems through magnetocrystalline anisotr...

We present the first detailed analysis of the statistical properties of jump processes bounded by a saturation function and driven by Poisson white noise, being a random sequence of delta pulses. The Kolmogorov–Feller equation for the probability density function (PDF) of such processes is derived and its stationary solutions are found analytically...

We present the first detailed analysis of the statistical properties of jump processes bounded by a saturation function and driven by Poisson white noise, being a random sequence of delta pulses. The Kolmogorov-Feller equation for the probability density function (PDF) of such processes is derived and its stationary solutions are found analytically...

We study the statistical properties of jump processes in a bounded domain that are driven by Poisson white noise. We derive the corresponding Kolmogorov-Feller equation and provide a general representation for its stationary solutions. Exact stationary solutions of this equation are found and analyzed in two particular cases. All our analytical fin...

We study the statistical properties of jump processes in a bounded domain that are driven by Poisson white noise. We derive the corresponding Kolmogorov-Feller equation and provide a general representation for its stationary solutions. Exact stationary solutions of this equation are found and analyzed in two particular cases. All our analytical fin...

We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetiz...

We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetiz...

The phenomenon of drift motion of single-domain ferromagnetic particles induced by the Magnus force in a viscous fluid is studied analytically. We use a minimal set of equations to describe the translational and rotational motions of these particles subjected to a harmonic force and a non-uniformly rotating magnetic field. Assuming that the azimuth...

The phenomenon of drift motion of single-domain ferromagnetic particles induced by the Magnus force in a viscous fluid is studied analytically. We use a minimal set of equations to describe the translational and rotational motions of these particles subjected to a harmonic force and a non-uniformly rotating magnetic field. Assuming that the azimuth...

A minimal system of equations is introduced and applied to study the drift motion of ferromagnetic particles suspended in a viscous fluid and subjected to a time-periodic driving force and a nonuniformly rotating magnetic field. It is demonstrated that the synchronized translational and rotational oscillations of these particles are accompanied by...

A minimal system of equations is introduced and applied to study the drift motion of ferromagnetic particles suspended in a viscous fluid and subjected to a time-periodic driving force and a nonuniformly rotating magnetic field. It is demonstrated that the synchronized translational and rotational oscillations of these particles are accompanied by...

We study the unidirectional motion of spherical ferromagnetic particles suspended in a viscous liquid and subjected to the action of an external periodic force and a non-uniformly rotating magnetic field. In the case when the translational and rotational motions of particles are characterized by small Reynolds numbers, we propose a system of equati...

We study the effect of an elliptically polarized magnetic field on a system of noninteracting, single-domain ferromagnetic nanoparticles characterized by a uniform distribution of easy axis directions. Our main goal is to determine the average magnetization of this system and the power loss in it. In order to calculate these quantities analytically,...

We study the effect of an elliptically polarized magnetic field on a system of non-interacting, single-domain ferromagnetic nanoparticles characterized by a uniform distribution of easy axis directions. Our main goal is to determine the average magnetization of this system and the power loss in it. In order to calculate these quantities analyticall...

We study the effect of an elliptically polarized magnetic field on a system of non-interacting, single-domain ferromagnetic nanoparticles characterized by a uniform distribution of easy axis directions. Our main goal is to determine the average magnetization of this system and the power loss in it. In order to calculate these quantities analyticall...

We study the deterministic and stochastic rotational dynamics of ferromagnetic nanoparticles in a precessing magnetic field. Our approach is based on the system of effective Langevin equations and on the corresponding Fokker-Planck equation. Two key characteristics of the rotational dynamics, the average angular frequency of precession of nanoparti...

We study, both analytically and numerically, the phenomenon of energy dissipation in single-domain ferromagnetic nanoparticles driven by an alternating magnetic field. Our interest is focused on the power loss resulting from the Landau-Lifshitz-Gilbert equation, which describes the precessional motion of the nanoparticle magnetic moment. We determi...

Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function of the waiting times difference and the relaxation law, are of our particular interest. For systems characteri...

We develop an analytical model for describing the magnetization dynamics in ferromagnetic metal nanoparticles, which is based on the coupled system of the Landau-Lifshitz-Gilbert (LLG) and Maxwell equations. By solving Maxwell's equations in the quasi-static approximation and finding the magnetic field of eddy currents, we derive the closed LLG equ...

We derive the Fokker-Planck equation for multivariable Langevin equations with cross-correlated Gaussian white noises for an arbitrary interpretation of the stochastic differential equation. We formulate the conditions when the solution of the Fokker-Planck equation does not depend on which stochastic calculus is adopted. Further, we derive an equi...

We study the role of the magnetic field of eddy currents, which are induced in conducting single-domain particles of spherical form, in the magnetization dynamics. To describe the dynamic behavior of magnetization and electromagnetic field generating by the time-dependent magnetization, we use the coupled system of the Landau-Lifshitz-Gilbert (LLG)...

Using the modified stochastic Landau-Lifshitz equation driven by Poisson white noise, we derive the generalized Fokker-Planck equation for the probability density function of the nanoparticle magnetic moment. In our calculations we employ the Ito interpretation of stochastic equations and take into account the fact that the magnetic moment directio...

We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walks which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed distribution of jump lengths. Both the scaling function and the corresponding limiting probability density are determine...

We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed distribution of jump lengths. Both the scaling function and the corresponding limiting probability density are determined...

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that t...

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that t...

We study the thermal stability of the periodic (P) and quasi-periodic (Q) precessional modes of the nanoparticle magnetic moment induced by a rotating magnetic field. An analytical method for determining the lifetime of the P mode in the case of high anisotropy barrier and small amplitudes of the rotating field is developed within the Fokker-Planck...

We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that, if the random walk is unbiased (biased) and the jump distribution has a finite second moment, then the properly scaled probability density...

We develop a general approach for studying the cumulative probability distribution function of localized objects (particles) whose dynamics is governed by the first-order Langevin equation driven by superheavy-tailed noise. Solving the corresponding Fokker-Planck equation, we show that due to this noise the distribution function can be divided into...

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that t...

Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this behavior of the variance occurs when the complementary cumulative distribution function of waiting times is a...

We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second moments of the particle position as inverse Laplace transforms. By applying to these transforms the ordinary and th...

We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second moments of the particle position as inverse Laplace transforms. By applying to these transforms the ordinary and th...

Using the analytical and numerical solutions of the Landau–Lifshitz equation, we calculate the phase diagrams for the precession states of the nanoparticle magnetization in a rotating magnetic field. We show that there are three different scenarios for the magnetization switching. The bias magnetic field applied antiparallel to the nanoparticle mag...

We extend the Langevin approach to a class of driving noises whose generating processes have independent increments with super-heavy-tailed distributions. The time-dependent generalized Fokker-Planck equation that corresponds to the first-order Langevin equation driven by such a noise is derived and solved exactly. This noise generates two probabil...

We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second moments of the particle position as inverse Laplace transforms. By applying to these transforms the ordinary and th...

We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infi...

We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infi...

We study directed transport of overdamped particles in a periodically rocked random sawtooth potential. Two transport regimes can be identified which are characterized by a nonzero value of the average velocity of particles and a zero value, respectively. The properties of directed transport in these regimes are investigated both analytically and n...

We study directed transport of overdamped particles in a periodically rocked random sawtooth potential. Two transport regimes can be identified which are characterized by a nonzero value of the average velocity of particles and a zero value, respectively. The properties of directed transport in these regimes are investigated both analytically and n...

We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, incl...

PACS 05.40.Fb – Random walks and Levy flights Abstract.- We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavytailed increments, and the transition probability density of the noise generating process. Explicit expressions for thes...

We study directed transport of overdamped particles in a periodically rocked random sawtooth potential. Two transport regimes can be identified which are characterized by a nonzero value of the average velocity of particles and a zero value, respectively. The properties of directed transport in these regimes are investigated both analytically and n...

We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavy-tailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite va...

We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise generating process. We explicitly consider this equation for various specific types of noises, incl...

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric Lévy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for Lévy flights is derived and solved analytically in the s...

We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the probability density of the arrival time. We explicitly calculate the path integral for a special case of dicho...

We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the probability density of the arrival time. We explicitly calculate the path integral for a special case of dicho...

We perform a time-dependent study of the driven dynamics of overdamped particles that are placed in a one-dimensional, piecewise linear random potential. This setup of spatially quenched disorder then exerts a dichotomous varying random force on the particles. We derive the path integral representation of the resulting probability density function...

We perform a time-dependent study of the driven dynamics of overdamped particles which are placed in a one-dimensional, piecewise linear random potential. This set-up of spatially quenched disorder then exerts a dichotomous varying random force on the particles. We derive the path integral representation of the resulting probability density functio...

We present an analytical method of calculating the mean first-passage times (MFPTs) for the magnetic moment of a uniaxial nanoparticle which is driven by a rapidly rotating, circularly polarized magnetic field and interacts with a heat bath. The method is based on the solution of the equation for the MFPT derived from the two-dimensional backward F...

The investigation of a sizable thermal enhancement of magnetization is put forward for uniaxial ferromagnetic nanoparticles that are placed in a rotating magnetic field. We elucidate the nature of this phenomenon and evaluate the resonant frequency dependence of the induced magnetization. Moreover, we reveal the role of magnetic dipolar interaction...

The two-dimensional backward Fokker-Planck equation is used to calculate the mean first-passage times (MFPTs) of the magnetic moment of a nanoparticle driven by a rotating magnetic field. It is shown that a magnetic field that is rapidly rotating in the plane {\it perpendicular} to the easy axis of the nanoparticle governs the MFPTs just in the sam...

We study dynamical and thermal effects that are induced in nanoparticle systems by a rotating magnetic field. Using the deterministic Landau-Lifshitz equation and appropriate rotating coordinate systems, we derive the equations that characterize the steady-state precession of the nanoparticle magnetic moments and study a stability criterion for thi...

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments, and find their corresponding long-t...

We study analytically and numerically the overdamped, deterministic dynamics of a chain of {\it charged}, interacting particles driven by a longitudinal alternating electric field and additionally interacting with a smooth ratchet potential. We derive the equations of motion, analyze the general properties of their solutions and find the drift crit...

We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive combinatorics we succeed in obtaining the one-variable probability functions for (i) the number of domain walls,...

The investigation of a sizable thermal enhancement of magnetization is put forward for uniaxial ferromagnetic nanoparticles that are placed in a rotating magnetic field. We elucidate the nature of this phenomenon and evaluate the resonant frequency dependence of the induced magnetization. Moreover, we reveal the role of magnetic dipolar interaction...

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments and find their corresponding long-ti...

We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the probability density of the arrival time. We explicitly calculate the path integral for a special case of dicho...

We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive combinatorics we succeed in obtaining the one-variable probability functions for (i) the number of domain walls,...

We study analytically and numerically the overdamped, deterministic dynamics of a chain of charged, interacting particles driven by a longitudinal alternating electric field and additionally interacting with a smooth ratchet potential. We derive the equations of motion, analyze the general properties of their solutions and find the drift criterion...

The thermally activated magnetic relaxation in two-dimensional lattices of dipolar interacting nanoparticles with large uniaxial perpendicular anisotropy is studied by a numerical method and within the mean-field approximation for comparison. The role that the correlation effects play in magnetic relaxation and the influence of lattice structure an...

A method to numerically simulate the thermally induced magnetic relaxation in two-dimensional (2D) nanoparticle ensembles is generalized for the case of applied perpendicular magnetic fields. The influence of the correlations of the nanoparticle magnetic moments and of the external field on the relaxation law and on the relaxation rate is studied.

An effective method of numerical simulation of magnetic relaxation is proposed for two-dimensional lattices of uniaxial ferromagnetic nanoparticles with perpendicular anisotropy in the presence of a bias field. Within this method and within the meal-field approximation the law of relaxation of magnetization and the coefficient of magnetic viscosity...

We study the role that the cross-correlation of noises plays in the statistical behavior of systems driven by two multiplicative Gaussian white noises. The temporal evolution of the system is described by a Langevin equation, for which we adopt a general interpretation that includes the Ito as well as the Stratonovich interpretation. We derive the...

We study the equilibrium, oscillatory, and transport properties of a chain of charged particles which interact with each other via the Coulomb and powerlike repulsive interactions. Exact analytical expressions for the energy of the ground state, interparticle distances, and vibration spectrum are derived, and the stability criterion for a chain wit...

We study the slow phase of thermally activated magnetic relaxation in finite two-dimensional ensembles of dipolar interacting ferromagnetic nanoparticles whose easy axes of magnetization are perpendicular to the distribution plane. We develop a method to numerically simulate the magnetic relaxation for the case that the smallest heights of the pote...

We study the temporal evolution of a system that has an absorbing state and that is driven by colored Gaussian noise, whose amplitude depends on the system state x as [x](alpha). Exact, analytical expressions for the probability density functions of the system and of the absorption time are derived. We also calculate numerical characteristics of th...

We derive the time-dependent univariate and bivariate probability distribution function for an overdamped system with a quadratic potential driven by colored Gaussian noise, whose amplitude depends on the system state x as [x](alpha). Particular attention is paid to the effect of the correlation function of the noise on the statistical properties o...

The effect of dipolar interaction on the law of magnetic relaxation in the two-dimensional (2D) ensembles of uniaxial spherical nanoparticles distributed on the sites of a square lattice has been studied within the mean-field approximation. The equation that describes the time evolution of magnetization has been derived, and in the limiting cases o...

The law of magnetic relaxation for two-dimensional ensembles of uniaxial spherical nanoparticles distributed on the sites of a square lattice is studied within the mean-field approximation. It is showed that magnetic relaxation in those ensembles is characterized by the initial and final relaxation times and that their difference determines the dec...

The fluctuation theory of magnetic relaxation has been developed for the two-dimensional ensembles of ferromagnetic nanoparticles. The particles have random locations on a square lattice, interact via dipolar interaction, and their easy axes of magnetization are perpendicular to the lattice plane. The derivation of the equation that describes the t...

Using the Caldirola–Kanai formalism, we study the statistical properties of damped quantum particles driven by an arbitrary stationary noise. We develop a new method to solve the corresponding time-dependent Schrödinger equation and derive exact expressions for the dispersion of the particle coordinate and the particle velocity. These expressions a...

The features of the light rays reflecting by the fractal surface are studied within the framework of geometrical optics.

We study the effect of an arbitrary stationary random force on the motion of damped particles. Using a Langevin description, we derive exact expressions for the dispersion of the particle position, of the particle velocity, and their cross dispersion. The particles can exhibit anomalous diffusion, and the connection between this behavior and the fu...

We derive a rigorous expression for the mean first-passage time of an overdamped particle subject to a constant bias in a force field with quenched disorder. Depending on the statistics of the disorder, the disorder-averaged mean first-passage time can undergo a transition from an infinite value for small bias to a finite value for large bias. This...

The phase diagram and mean local field theory for ensembles of dipolar interacting ellipsoidal nanoparticles randomly distributed over the sites of a tetragonal lattice are constructed. Dipolar ferromagnetism in the ensembles arises from a competition between the ferro- and antiferromagnetic interactions of the nanoparticle magnetic moments. A crit...

The ferromagnetic-like ordering in a system of interacting non-spherical nanoparticles is studied.

The paramagnetic-ferromagnetic phase transition and distinctive characteristics of relaxation of the magnetization in a system of interacting single-domain ferromagnetic particles distributed randomly in a nonmagnetic matrix are investigated in the mean-field approximation.