We consider a partial-sum process generated by a sequence of nonidentically distributed independe... more We consider a partial-sum process generated by a sequence of nonidentically distributed independent random variables. Assuming that this process is available for observation along an arbitrary time sequence, we fill the gaps by linear interpolation and prove the functional law of the iterated logarithm (FLIL) for sample paths obtained in this way. Assuming that the V. A. Egorov condition holds, we show that FLIL is valid, while under other conditions sufficient for the usual law of the iterated logarithm FLIL may fail. Bibliography: 16 titles.
We have developed a new specialized version of the fast multipole method (FMM) for dipolar system... more We have developed a new specialized version of the fast multipole method (FMM) for dipolar systems. For this purpose we have derived general expressions of the multipole expansion coefficients (in spherical coordinates) for a system of point dipoles with the potential j dip B1=r 2 : Our version is especially useful for simulations of fine magnetic particle systems (magnetic nanocomposites, ferrofluids), molecular dipolar fluids or electric dipolar glasses.
Using Langevin dynamics simulations, we have calculated the AC-susceptibility " #i of disordered ... more Using Langevin dynamics simulations, we have calculated the AC-susceptibility " #i of disordered "ne magnetic particle systems with the dipolar interparticle interaction. We have shown that the shift of the (¹)-peak with increasing particle concentration depends qualitatively on the single-particle anisotropy and quantitatively on the precession damping.
Numerical simulations of fast remagnetization processes using the stochastic dynamics are widely ... more Numerical simulations of fast remagnetization processes using the stochastic dynamics are widely used to study various magnetic systems. In this paper we first address several crucial methodological problems of such simulations: (i) the influence of the finite-element discretization on the simulated dynamics, (ii) choice between Ito and Stratonovich stochastic calculi by the solution of micromagnetic stochastic equations of motion and (iii) non-trivial correlation properties of the random (thermal) field. Next we discuss several examples to demonstrate the great potential of the Langevin dynamics for studying fast remagnetization processes in technically relevant applications: we present numerical analysis of equilibrium magnon spectra in patterned structures, study thermal noise effects on the magnetization dynamics of nanoelements in pulsed fields and show some results for a remagnetization dynamics induced by a spin-polarized current.
We consider a partial-sum process generated by a sequence of nonidentically distributed independe... more We consider a partial-sum process generated by a sequence of nonidentically distributed independent random variables. Assuming that this process is available for observation along an arbitrary time sequence, we fill the gaps by linear interpolation and prove the functional law of the iterated logarithm (FLIL) for sample paths obtained in this way. Assuming that the V. A. Egorov condition holds, we show that FLIL is valid, while under other conditions sufficient for the usual law of the iterated logarithm FLIL may fail. Bibliography: 16 titles.
We have developed a new specialized version of the fast multipole method (FMM) for dipolar system... more We have developed a new specialized version of the fast multipole method (FMM) for dipolar systems. For this purpose we have derived general expressions of the multipole expansion coefficients (in spherical coordinates) for a system of point dipoles with the potential j dip B1=r 2 : Our version is especially useful for simulations of fine magnetic particle systems (magnetic nanocomposites, ferrofluids), molecular dipolar fluids or electric dipolar glasses.
Using Langevin dynamics simulations, we have calculated the AC-susceptibility " #i of disordered ... more Using Langevin dynamics simulations, we have calculated the AC-susceptibility " #i of disordered "ne magnetic particle systems with the dipolar interparticle interaction. We have shown that the shift of the (¹)-peak with increasing particle concentration depends qualitatively on the single-particle anisotropy and quantitatively on the precession damping.
Numerical simulations of fast remagnetization processes using the stochastic dynamics are widely ... more Numerical simulations of fast remagnetization processes using the stochastic dynamics are widely used to study various magnetic systems. In this paper we first address several crucial methodological problems of such simulations: (i) the influence of the finite-element discretization on the simulated dynamics, (ii) choice between Ito and Stratonovich stochastic calculi by the solution of micromagnetic stochastic equations of motion and (iii) non-trivial correlation properties of the random (thermal) field. Next we discuss several examples to demonstrate the great potential of the Langevin dynamics for studying fast remagnetization processes in technically relevant applications: we present numerical analysis of equilibrium magnon spectra in patterned structures, study thermal noise effects on the magnetization dynamics of nanoelements in pulsed fields and show some results for a remagnetization dynamics induced by a spin-polarized current.
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Papers by Natalia Gorn