We prove that in dimensions three or four, for suitably chosen initial data, the short time smooth solution to the Landau-Lifshitz-Gilbert equation blows up at finite time.

We propose an extension of the Landau-Lifshitz-Gilbert (LLG) equation by explicitly including the role of conduction electrons in magnetization dynamics of conducting ferromagnets. The temporal and spatial dependent magnetization order parameter m(r,t) generates both electrical and spin currents that provide dissipation of the energy and angular momentum of the processing magnet. The resulting ...

We consider a kinetic model of self-propelled particles with alignment interaction and with precession about the alignment direction. We derive a hydrodynamic system for the local density and velocity orientation of the particles. The system consists of the conservative equation for the local density and a non-conservative equation for the orientation. First, we assume that the alignment intera...

We consider a lowest-order finite element scheme for the Landau-Lifshitz-Gilbert equation (LLG) which describes the dynamics of micromagnetism. In contrast to previous works from the mathematics literature, we examine LLG including the total magnetic field induced by physical phenomena described in terms of exchange energy, anisotropy energy, magnetostatic energy, as well as Zeeman energy. Besi...

equation A. Giordano, G. Finocchio, L. Torres, M. Carpentieri, and B. Azzerboni Department of Fisica della Materia e Ingegneria Elettronica, University of Messina, Salita Sperone 31, 98166 Messina, Italy Department of Fı́sica Aplicada, Universidad de Salamanca, Plaza de la Merced, Salamanca 37008, Spain Department of Elettronica, Informatica e Sistemistica, University of Calabria, Via P. Bucci 4...

Methods of numerical integration of ordinary differential equations exploiting the Cayley transform arise in a variety of contexts, ranging from the classical mid-point rule to symplectic and (almost) Poisson integrators, to numerical methods on Lie Groups. In earlier work, the first author investigated the interplay between the Cayley transform and the Jacobi identity in establishing certain e...

In this paper we give an overview of the numerical methods for the solution of the Landau-Lifshitz-Gilbert equation. We discuss advantages of the presented methods and perform numerical experiments to demonstrate their performance. We also discuss the coupling with Maxwell’s equations.

Current-driven magnetization dynamics in ferromagnetic metals is studied in a self-consistent adiabatic local-density approximation in the presence of spin-conserving and spin-dephasing impurity scattering. Based on a quantum kinetic equation, we derive Gilbert damping and spin-transfer torques entering the LandauLifshitz equation to linear order in frequency and wave vector. Gilbert damping an...

Gas-condensate reservoirs contain hydrocarbon fluids with characteristics between oil and gas reservoirs and a high gas-liquid ratio. Due to the large gas-liquid ratio, wellhead choke calculations using the empirical equations such as Gilbert may contain considerable error. In this study, using drill stem test (DST) data of a gas-condensate reservoir, coefficients of Gilbert equation was modifi...