Related papers: Existence results in large-strain magnetoelasticit…
We investigate the properties of minimizers of one-dimensional variational problems when the Lagrangian has no higher smoothness than continuity. An elementary approximation result is proved, but it is shown that this cannot be in general…
We investigate finite-strain elastoplastic evolution in the nonassociative setting. The constitutive material model is formulated in variational terms and coupled with the quasistatic equilibrium system. We introduce measure-valued…
Small-scale turbulence originating from microinstabilities limits the energy confinement time in magnetic confinement fusion. Here we develop a semi-analytical dispersion relation based on lowest-order solutions to the gyrokinetic equations…
This paper is concerned with the rigorous analysis of a recently proposed model of Zheng et. al. for describing nematic liquid crystals within the dense regime, with the orientation distribution function as the variable. A key feature of…
The thermodynamic model of visco-elastic deformable magnetic materials at finite strains is formulated in a fully Eulerian way in rates. The Landau theory applies for ferro-to-para-magnetic phase transition, the gradient theory (leading…
A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappinngs and Cartesian currents. Weak…
We analyze the finite-strain Poynting-Thomson viscoelastic model. In its linearized small-deformation limit, this corresponds to the serial connection of an elastic spring and a Kelvin-Voigt viscoelastic element. In the finite-strain case,…
We study the magnetization dynamics of thin-film magnetic elements with in-plane magnetization subject to a spin-current flowing perpendicular to the film plane. We derive a reduced partial differential equation for the in-plane…
In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…
We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained…
This paper presents the first application of the direct parametrisation method for invariant manifolds to a fully coupled multiphysics problem involving the nonlinear vibrations of deformable structures subjected to an electrostatic field.…
A continuum evolutionary model for micromagnetics is presented that, beside the standard magnetic balance laws, includes thermo-magnetic coupling. To allow conceptually efficient computer implementation, inspired by relaxation method of…
Magnetic emergent crystals are periodic alignment of "particle-like" spin textures that emerge in magnets. Instead of focusing on an individual spin or a macroscopic magnetization field, we analyze the dynamical behaviors of these novel…
We consider the quasi-static magnetic hysteresis model based on a dry-friction like representation of magnetization. The model has a consistent energy interpretation, is intrinsically vectorial, and ensures a direct calculation of the…
A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar $p$-elasticae. It was known that in the non-degenerate regime $p\in(1,2]$, including the classical case of Euler's elastica, there…
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamical accessible frameworks. This is…
This article addresses a problem of micromagnetics: the reversal of magnetic moments in layered spring magnets. A one-dimensional model is used of a film consisting of several atomic layers of a soft material on top of several atomic layers…
We consider periodic homogenization of nonlinearly elastic composite materials. Under suitable assumptions on the stored energy function (frame indifference; minimality, non-degeneracy and smoothness at identity; $p\geq d$-growth from…
To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system of the nonlinear Landau-Lifshitz-Gilbert equation and the conservation of momentum equation. This coupling allows to include magnetostrictive effects…
The full Landau-Lifshitz-Gilbert equation with periodic material coefficients and natural boundary condition is employed to model the magnetization dynamics in composite ferromagnets. In this work, we establish the convergence between the…