arXiv subjects

Lauro Morales

Publications and source records attributed to Lauro Morales.

5 recordsLinked to original sources

arXiv2026

Dynamical stability of planar phase boundaries for hyperelastic materials of Hadamard type

The dynamical stability of laminates or planar phase boundaries for hyperelastic materials of Hadamard type in two space dimensions is studied. For that purpose, the stability function, known as the Lopatinskii determinant, is computed for states of deformation at both sides of the planar interface that account for the generalized Legendre-Hadamard conditions derived by Grabovsky and Truskinovsky (J. Elast. 123 (2016), 225--243). The sufficient conditions for the dynamical stability of such configurations are described in terms of the physical parameters of the model, such as the shear modulus, and computed under kinetic conditions across the interface of both Maxwell (conservation of energy) or Abeyaratne and Knowles (dissipation of energy) types.

math.AP↗

arXiv2026

Time-periodic oscillating Néel walls in ferromagnetic thin films

This paper studies the existence, the structure and the spectral stability of time-periodic oscillating 180-degree Néel walls in ferromagnetic thin films. It is proved that time-periodic coherent structures do exist as solutions to the reduced model for the in-plane magnetization proposed by Capella, Melcher, and Otto (Nonlinearity 20 (2007), no. 11, 2519--2537) when a weak and $T$-periodic external magnetic field is applied in the direction of the easy axes of the film, perturbing in this fashion the well-known static 180-degree Néel wall. The linearization around this time-periodic Néel wall is constituted by a family of linear operators, parametrized by the time variable, which generates an evolution system of generators (or propagator) for the linear problem. Profiting from the stability of the static Néel wall, it is shown that the Floquet spectrum of the monodromy map for the propagator is contained in the complex unit circle, proving stability of the oscillating solution at least at a linear level.

math.AP↗

arXiv2024

Stability of moving Néel walls in ferromagnetic thin films

This paper studies moving 180-degree Néel walls in ferromagnetic thin films under the reduced model for the in-plane magnetization proposed by Capella, Melcher and Otto [5], in the case when a sufficiently weak external magnetic field is applied. It is shown that the linearization around the moving Néel wall's phase determines a spectral problem that is a relatively bounded perturbation of the linearization around the static Néel wall, which is the solution when the external magnetic field is set to zero and which is spectrally stable. Uniform resolvent-type estimates for the linearized operator around the static wall are established in order to prove the spectral stability of the moving wall upon application of perturbation theory for linear operators. The spectral analysis is the basis to prove, in turn, both the decaying properties of the generated semigroup and the nonlinear stability of the moving Néel wall under small perturbations, in the case of a sufficiently weak external magnetic field. The stability of the static Néel wall, which was established in a companion paper [4], plays a key role to obtain the main result.

math.AP↗

arXiv2021

On the quasiconvex hull for a three-well problem in two dimensional linear elasticity

We provide quantitative inner and outer bounds for the symmetric quasiconvex hull $Q^e(\mathcal{U})$ on linear strains generated by three-well sets $\mathcal{U}$ in $\mathbb{R}^{2\times 2}_{sym}$. In our study, we consider all possible compatible configurations for three wells and prove that if there exist two matrices in $\mathcal{U}$ that are rank-one compatible then $Q^e(\mathcal{U})$ coincides with its symmetric lamination convex hull $L^e(\mathcal{U})$. We complete this result by providing an explicit characterization of $L^e(\mathcal{U})$ in terms of the wells in $\mathcal{U}$. Finally, we discuss the optimality of our outer bound and its relationship with quadratic polyconvex functions.

math.AP↗

arXiv2021

On the symmetric lamination convex and quasiconvex hull for the coplanar n-well problem in two dimensions

We study some particular cases of the $n$-well problem in two-dimensional linear elasticity. Assuming that every well in $\mathcal{U}\subset\mathbb{R}^{2\times 2}_\text{sym}$ belong to the same two-dimensional affine subspace, we characterize the symmetric lamination convex hull $L^e(\mathcal{U})$ for any number of wells in terms of the symmetric lamination convex hull of all three-well subsets contained in $\mathcal{U}$. For a family of four-well sets where two pairs of wells are rank-one compatible, we show that the symmetric lamination convex and quasiconvex hulls coincide, but are strictly contained in its convex hull $C(\mathcal{U})$. We extend this result to some particular configurations of $n$ wells. Most of the proofs are constructive, and we also present explicit examples.

math.AP↗