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This paper examines the consistency of the exact scaling laws for isotropic MHD turbulence in numerical simulations with large magnetic Prandtl numbers Pm and with Pm=1. The exact laws are used to elucidate the structure of the magnetic and…
The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…
A new methodology for micromagnetic simulations of magnetic nanocomposites is presented. The methodology is especially suitable for simulations of two-phase composites consisting of magnetically hard inclusions in a soft magnetic matrix…
A model is introduced for the theoretical description of nanoscale magnetic films with high perpendicular anisotropy. In the model the magnetic film is described in terms of single domain magnetic grains, interacting via exchange as well as…
We consider a multiscale strategy addressing the disparate scales in the Landau-Lifschitz equations in micro-magnetism. At the microscopic scale, the dynamics of magnetic moments are driven by a high frequency field. On the macroscopic…
We propose and implement a third-order accurate numerical scheme for the Landau-Lifshitz-Gilbert equation, which describes magnetization dynamics in ferromagnetic materials under large damping parameters. This method offers two key…
Magneto-resistance is a physical effect of great fundamental and industrial interest since it is the basis for the magnetic field sensors used in computer read-heads and Magnetic Random Access Memories. As device dimensions are reduced,…
A simple, general and practically exact method is developed for the equilibrium properties of the macroscopic physical systems with translational symmetry. Applied to the Ising model in two and three dimension, a modest calculation gives…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
The magnetic force theorem provides convenient ways to study exchange interactions in magnetic systems. However, it is well known that short range interactions in itinerant magnetic systems are poorly described with the conventional use of…
This work deals with shape optimization of electric machines using isogeometric analysis. Isogeometric analysis is particularly well suited for shape optimization as it allows to easily modify the geometry without remeshing the domain. A…
We consider the numerical approximation of the inertial Landau-Lifshitz-Gilbert equation (iLLG), which describes the dynamics of the magnetization in ferromagnetic materials at subpicosecond time scales. We propose and analyze two fully…
Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of…
The mechanism of appearance of exponentially large number of metastable states in magnetic phases of disordered Ising magnets with short-range random exchange is suggested. It is based on the assumption that transitions into inhomogeneous…
We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be…
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually…
The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…
This chapter provides an introduction to the fundamental physical ideas and models relevant to the phenomenon of magnetic hysteresis in nanoparticle assemblies. The concepts of single-domain particles and superparamagnetism are discussed.…
We examine different models and methods for studying finite-temperature magnetic hysteresis in nanoparticles and ultrathin films. This includes micromagnetic results for the hysteresis of a single magnetic nanoparticle which is misaligned…
Dipole magnetic moments of several long isotopic chains are analyzed within the self-consistent Finite Fermi System theory based on the Generalized Energy Density Functional method with exact account for the pairing and quasi-particle…