arXiv subjects

T. V. Lyutyy

Publications and source records attributed to T. V. Lyutyy.

At least 19 recordsLinked to original sources

arXiv2024

Asymptotic Theory for Directed Transport of Suspended Ferromagnetic Nanoparticles

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 that describe the time dependencies of the particle coordinate and mag-netization angle. We find the asymptotic solutions of this set of equations at small and large times and, by applying the matched asymptotic expansions for discrete times, derive analytical expressions for the aver-age particle coordinate and velocity.

cond-mat.soft↗

arXiv2021

Numerical Analysis of the Nanoparticle Dynamics in a Viscous Liquid: Deterministic Approach

We study the deterministic dynamics of single-domain ferromagnetic nanoparticles in a viscous liquid induced by the joint action of the gradient and uniform magnetic fields. It is assumed that the gradient field depends on time harmonically and the uniform field has two components, perpendicular and parallel to the gradient one. We also assume that the anisotropy magnetic field is so strong that the nanoparticle magnetization lies along the anisotropy axis, i.e., the magnetization vector is "frozen" into the particle body. With these assumptions and neglecting inertial effects we derive the torque and force balance equations that describe the rotational and translational motions of particles. We reduce these equations to a set of two coupled equations for the magnetization angle and particle coordinate, solve them numerically in a wide range of the system parameters and analyze the role of the parallel component of the uniform magnetic field. It is shown, in particular, that nanoparticles perform only periodic rotational and translational motions if the perpendicular component of the uniform magnetic field is absent. In contrast, the nanoparticle dynamics in the presence of this component becomes non-periodic, resulting in the drift motion (directed transport) of nanoparticles. By analyzing the short and long-time dependencies of the magnetization angle and particle coordinate we show that the increase in the parallel component of the uniform magnetic field decreases both the particle displacement for a fixed time and its average drift velocity on each period of the gradient magnetic field.

cond-mat.mes-hall↗

arXiv2021

Drift of suspended single-domain nanoparticles in a harmonically oscillating gradient magnetic field

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 magnetization angle and particle coordinate describing the rotational and translational motions of nanoparticles. Analytical solutions of these equations are determined for nanoparticles near and far from the coordinate origin, and their correctness is confirmed numerically. We show that if a uniform magnetic field is absent, the magnetization angle and particle coordinate of each nanoparticle are periodic functions of time. In contrast, the presence of a uniform magnetic field makes these functions aperiodic. In this case, we perform a detailed analysis of the nanoparticle dynamics and predict the appearance of the drift motion (directed transport) of nanoparticles. We calculate both analytically and numerically the drift velocity, study its dependence on time and model parameters, analyze the physical origin of the drift phenomenon and discuss its potential biomedical applications.

cond-mat.soft↗

arXiv2020

Dynamics of Suspended Nanoparticles in a Time-varying Gradient Magnetic Field: Analytical Results

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 particles characterized by small Reynolds numbers. Since the gradient magnetic field generates both the translations and rotations of particles, these motions are coupled. Based on the derived set of equations, we demonstrate this fact explicitly by expressing the particle position through the particle orientation angle, and vice versa. The obtained expressions are used to show that the solution of the basic set of equations is periodic in time and to determine the intervals, where the particle coordinate and orientation angle oscillate. In addition, this set of equations is solved approximately for the case of small characteristic frequency of the particle oscillations. With this condition, we find that all particles perform small translational oscillations near their initial positions. In contrast, the orientation angle oscillates near the initial angle only if particles are located in the vicinity of zero point of the gradient magnetic field. The possible applications of the obtained results in biomedicine and separation processes are also discussed.

cond-mat.soft↗

arXiv2020

Directed transport of suspended ferromagnetic nanoparticles under both gradient and uniform magnetic fields

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 particles. This occurs because the translational force depends on the direction of the particle magnetization, which in turn depends on the fields strengths. To study this influence, a minimal set of equations describing the coupled translational and rotational motions of nanosized ferromagnetic particles is introduced and solved in the low Reynolds number approximation. Trajectory analysis reveals that, depending on the initial positions of nanoparticles, there exist four regimes of their directed transport. The intervals of initial positions that correspond to different dynamical regimes are determined, their dependence on the uniform magnetic field is established, and strong impact of this field on the directed transport is demonstrated. The ability and efficiency of the uniform magnetic field to control the separation of suspended ferromagnetic nanoparticles is also discussed.

cond-mat.soft↗

arXiv2019

Dissipation-induced rotation of suspended ferromagnetic nanoparticles

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 rotation of isotropic nanoparticles is induced only by magnetic dissipation processes. We propose a theory of this phenomenon based on a set of equations describing the deterministic magnetic and rotational dynamics of such particles. Neglecting inertial effects, we solve these equations analytically, find the magnetization and particle precessions in the steady state, determine the components of the particle angular velocity and analyze their dependence on the model parameters. The possibility of experimental observation of this phenomenon is also discussed.

cond-mat.soft↗

arXiv2018

Uniform and Nonuniform Precession of a Nanoparticle with Finite Anisotropy in a Liquid: Opportunities and Limitations for Magnetic Fluid Hyperthermia

We focus on an in-depth study of the forced dynamics of a ferromagnetic single-domain uniaxial nanoparticle placed in a viscous fluid and driven by an external rotating magnetic field. The process of conversion of magnetic and mechanical energies into heat is a physical basis for magnetic fluid hyperthermia that is very promising for cancer treatment. The dynamical approximation allows us to establish the limits of the heating rate and understand the logic of selection of the system parameters to optimize the therapy. Based on the developed analytical and numerical tools, we analyze from a single viewpoint the synchronous and asynchronous rotation of the nanoparticle or/and its magnetization in the following three cases. For the beginning, we actualize the features of the internal magnetic dynamics, when the nanoparticle body is supposed to be fixed. Then, we study the rotation of the whole nanoparticle, when its magnetization is supposed to be locked to the crystal lattice. And, finally, we realize the analysis of the coupled motion, when the internal magnetic dynamics is performed in the rotated nanoparticle body. In all these cases, we describe analytically the uniform mode, or synchronous rotation along with an external field, while the nonuniform mode, or asynchronous rotation, is investigated numerically.

cond-mat.mes-hall↗

arXiv2018

Dynamics and Energy Dissipation of a Rigid Dipole Driven by the RF-field in a Viscous Fluid: Deterministic Approach

The deterministic rotation of a ferromagnetic nanoparticle in a fluid is considered. The heating arising from viscous friction of a nanoparticle driven by circularly and linearly polarized alternating magnetic fields is investigated. Since the power loss of such fields depends on the character of the induced motion of a nanoparticle, all types of particle trajectories are described in detail. The dependencies of the power loss on the alternating field parameters are determined. The optimal conditions for obtaining the maximum heating efficiency are discussed. The effect of heating enhancement by a static field is analyzed. The results obtained are actual for the description of heating in the magnetic fluid hyperthermia cancer treatment, when the size of the particles used is a few tens of nanometers.

physics.app-ph↗

arXiv2018

Energy dissipation of rigid dipoles in a viscous fluid under the action of a time-periodic field: the influence of thermal bath and dipole interaction

Ferrofluid heating by an external alternating field is studied based on the rigid dipole model, where the magnetization of each particle in a fluid is supposed to be firmly fixed in the crystal lattice. Equations of motion, employing the Newton's second law for rotational motion, the condition of rigid body rotation, and the assumption that the friction torque is proportional to angular velocity, are used. This oversimplification permits us to expand the model easily: to take into account the thermal noise and inter-particle interaction that allows to estimate from unified positions the role of thermal activation and dipole interaction in the heating process. Our studies are conducted in three stages. The exact expressions for the average power loss of a single particle are obtained within the dynamical approximation. Then, in the stochastic case, the power loss of a single particle is estimated analytically using the Fokker-Planck equation and numerically using the effective Langevin equation. Finally, the power loss for the particle ensemble is obtained using the molecular dynamics method. Here, the local dipole fields are calculated approximately based on the Barnes-Hut algorithm. The revealed trends in the behaviour of both a single particle and the particle ensemble suggest the way of choosing the conditions for obtaining the maximum heating efficiency. The competitiveness character of the inter-particle interaction and thermal noise is investigated in details. Two situations, when the thermal noise rectifies the power loss reduction caused by the interaction, are described. The first of them is related to the complete destruction of dense clusters at high noise intensity. The second one is originated from the rare switching of the particles in clusters due to thermal activation, when the noise intensity is relatively weak.

cond-mat.mes-hall↗

arXiv2017

Temperature effects on drift of suspended single-domain particles induced by the Magnus force

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 magnetization is introduced. The Fokker-Planck equation for the probability density of magnetization orientations is solved analytically in the limit of strong thermal fluctuations for both the planar rotor and general models. Using these solutions, we calculate the drift velocity and show that the out-of-plane fluctuations of magnetization, which are not accounted for in the planar rotor model, play an important role. In the general case of arbitrary fluctuations, we investigate the temperature dependence of the drift velocity by numerically simulating a set of effective stochastic differential equations for the magnetization dynamics.

cond-mat.soft↗

arXiv2017

Power Loss for a Periodically Driven Ferromagnetic Nanoparticle in a Viscous Fluid: the Finite Anisotropy Aspects

The joint magnetic and mechanical motion of a ferromagnetic nanoparticle in a viscous fluid is considered within the dynamical approach. The equation based on the total momentum conservation law is used for the description of the mechanical rotation, while the modified Landau-Lifshitz-Gilbert equation is utilized for the description of the internal magnetic dynamics. The exact expressions for the particles trajectories and the power loss are obtained in the linear approximation. The comparison with the results of other widespread approaches, such as the model of fixed particle and the model of frozen magnetic moment, is performed. It is established that in the small oscillations mode the damping precession of the nanopartile magnetic moment is the main channel of energy dissipation, but the motion of the nanoparticle easy axis can significantly influence the value of the resulting power loss.

cond-mat.other↗

arXiv2016

Induced magnetization and power loss for a periodically driven system of ferromagnetic nanoparticles with randomly oriented easy axes

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 analytically, we develop a general perturbation theory for the Landau-Lifshitz-Gilbert (LLG) equation and find its steady-state solution for small magnetic field amplitudes. On this basis, we derive the second-order expressions for the average magnetization and power loss, investigate their dependence on the magnetic field frequency, and analyze the role of subharmonic resonances resulting from the nonlinear nature of the LLG equation. For arbitrary amplitudes, the frequency dependence of these quantities is obtained from the numerical solution of this equation. The impact of transitions between different regimes of regular and chaotic dynamics of magnetization, which can be induced in nanoparticles by changing the magnetic field frequency, is examined in detail.

cond-mat.mes-hall↗

arXiv2015

Rotational properties of ferromagnetic nanoparticles driven by a precessing magnetic field in a viscous fluid

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 nanoparticles and their average magnetization, are of our interest. Using the Langevin and Fokker-Planck equations, we calculate both analytically and numerically these characteristics in the deterministic and stochastic cases, determine their dependence on the model parameters, and analyze in detail the role of thermal fluctuations.

cond-mat.mes-hall↗

arXiv2015

Energy dissipation in single-domain ferromagnetic nanoparticles: Dynamical approach

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 determine the power loss as a function of the field amplitude and frequency and analyze its dependence on different regimes of forced precession induced by circularly and linearly polarized magnetic fields. The conditions to maximize the nanoparticle heating are also analyzed.

cond-mat.mes-hall↗

arXiv2014

Eddy current effects in the magnetization dynamics of ferromagnetic metal nanoparticles

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 equation for the magnetization that fully accounts for the effects of conductivity. We analyze the difference between the LLG equations in metallic and dielectric nanoparticles and show that these effects can strongly influence the magnetization dynamics. As an example illustrating the importance of eddy currents, the phenomenon of precessional switching of magnetization is considered.

cond-mat.mes-hall↗

arXiv2013

Large-scale Ferrofluid Simulations on Graphics Processing Units

We present an approach to molecular-dynamics simulations of ferrofluids on graphics processing units (GPUs). Our numerical scheme is based on a GPU-oriented modification of the Barnes-Hut (BH) algorithm designed to increase the parallelism of computations. For an ensemble consisting of one million of ferromagnetic particles, the performance of the proposed algorithm on a Tesla M2050 GPU demonstrated a computational-time speed-up of four order of magnitude compared to the performance of the sequential All-Pairs (AP) algorithm on a single-core CPU, and two order of magnitude compared to the performance of the optimized AP algorithm on the GPU. The accuracy of the scheme is corroborated by comparing the results of numerical simulations with theoretical predictions.

physics.comp-ph↗

arXiv2011

Resonant suppression of thermal stability of the nanoparticle magnetization by a rotating magnetic field

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 formalism. In general case, the thermal stability of both P and Q modes is investigated by numerical simulation of the stochastic Landau-Lifshitz equation. We show analytically and numerically that the lifetime is a nonmonotonic function of the rotating field frequency which, depending on the direction of field rotation, has either a pronounced maximum or a deep minimum near the Larmor frequency.

cond-mat.stat-mech↗

arXiv2009

Directed transport in periodically rocked random sawtooth potentials

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 numerically in terms of a random sawtooth potential and a periodically varying driving force. Precise conditions for the occurrence of transition between these two transport regimes are derived and analyzed in detail.

cond-mat.dis-nn↗