arXiv subjects

Eduardo Martínez

Publications and source records attributed to Eduardo Martínez.

24 records · Page 2Linked to original sources

arXiv2017

Analysis of the current-driven domain wall motion in a ratchet ferromagnetic strip

The current-driven domain wall motion in a ratchet memory due to spin-orbit torques is studied from both full micromagnetic simulations and the one dimensional model. Within the framework of this model, the integration of the anisotropy energy contribution leads to a new term in the well known q-$Φ$ equations, being this contribution responsible for driving the domain wall to an equilibrium position. The comparison between the results drawn by the one dimensional model and full micromagnetic simulations proves the utility of such a model in order to predict the current-driven domain wall motion in the ratchet memory. Additionally, since current pulses are applied, the paper shows how the proper working of such a device requires the adequate balance of excitation and relaxation times, being the latter longer than the former. Finally, the current-driven regime of a ratchet memory is compared to the field-driven regime described elsewhere, then highlighting the advantages of this current-driven regime.

physics.app-ph↗

arXiv2016

Structural aspects of Hamilton-Jacobi theory

In our previous papers [11,13] we showed that the Hamilton-Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a lower-dimensional manifold. We also showed how constants of the motion help to solve the Hamilton-Jacobi equation. Here we want to delve into this interpretation by considering the most general case: a dynamical system on a manifold that is described in terms of a family of dynamics (`slicing vector fields') on lower-dimensional manifolds. We identify the relevant geometric structures that lead from this decomposition of the dynamics to the classical Hamilton-Jacobi theory, by considering special cases like fibred manifolds and Hamiltonian dynamics, in the symplectic framework and the Poisson one. We also show how a set of functions on a tangent bundle can determine a second-order dynamics for which they are constants of the motion.

math-ph↗

arXiv2015

Higher-order Variational Calculus on Lie algebroids

The equations for the critical points of the action functional defined by a Lagrangian depending on higher-order derivatives of admissible curves on a Lie algebroid are found. The relation with Euler-Poincaré and Lagrange Poincaré type equations is studied. Reduction and reconstruction results for such systems are established.

math-ph↗

arXiv2014

Conformal Killing vector fields and a virial theorem

The virial theorem is formulated both intrinsically and in local coordinates for a Lagrangian system of mechanical type on a Riemann manifold. An import case studied in this paper is that of an affine virial function associated to a vector field on the configuration manifold. The special cases of a virial function associated to a Killing, a homothetic and a conformal Killing vector field are considered and the corresponding virial theorems are established for this type of functions.

math-ph↗

arXiv2014

Virial theorem in quasi-coordinates and Lie algebroid formalism

In this paper, the geometric approach to the virial theorem developed in \cite{CFR12} is written in terms of quasi-velocities (see \cite{CNCS07}). A generalization of the virial theorem for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.

math-ph↗

arXiv2013

The local description of discrete Mechanics

In this paper, we introduce local expressions for discrete Mechanics. To apply our results simultaneously to several interesting cases, we derive these local expressions in the framework of Lie groupoids, following the program proposed by Alan Weinstein in [19]. To do this, we will need some results on the geometry of Lie groupoids, as, for instance, the construction of symmetric neighborhoods or the existence of local bisections. These local descriptions will be particular useful for the explicit construction of geometric integrators for mechanical systems (reduced or not), in particular, discrete Euler-Lagrange equations, discrete Euler-Poincaré equations, discrete Lagrange-Poincaré equations... The results contained in this paper can be considered as a local version of the study that we have started in [13], on the geometry of discrete Mechanics on Lie groupoids.

math.NA↗