Carlos López

Lagrangian-Hamiltonian unified formalism for field theory

The Rusk–Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations.

General critical states in type-II superconductors

The magnetic flux dynamics of type-II superconductors within the critical state regime is posed in a generalized framework, by using a variational theory supported by well established physical principles. The equivalence between the variational statement and more conventional treatments, based on the solution of the differential Maxwell equations together with appropriate conductivity laws is shown. Advantages of the variational method are emphasized, focusing on its numerical performance, that allows to explore new physical scenarios. In particular, we present the extension of the so-called double critical state model to three dimensional configurations in which only flux transport (T-states), cutting (C-states) or both mechanisms (CT-states) occur. The theory is applied to several problems. First, we show the features of the transition from T to CT states. Second, we give a generalized expression for the flux cutting threshold in 3-D and show its relevance in the slab geometry. In addition, several models that allow to treat flux depinning and cutting mechanisms are compared. Finally, the longitudinal transport problem (current is applied parallel to the external magnetic field) is analyzed both under T and CT conditions. The complex interaction between shielding and transport is solved.

Electromagnetics close beyond the critical state: thermodynamic prospect

A theory for the electromagnetic response of type-II superconductors close beyond the critical state is presented. Our formulation relies on general physical principles applied to the superconductor as a thermodynamic system. Metastable equilibrium critical states, externally driven steady solutions, and transient relaxation are all described in terms of free energy and entropy production. This approach allows a consistent macroscopic statement that incorporates the intricate vortex dynamic effects, revealed in non-idealized experimental configurations. Magnetically anisotropic critical currents and flux stirring resistivities are straightforwardly included in three-dimensional scenarios. Starting from a variational form of our postulate, a numerical implementation for practical configurations is shown. In particular, several results are provided for infinite strip geometry: voltage generation in multicomponent experiments, and magnetic relaxation towards the critical state under applied field and transport current. Explicitly, we show that for a given set of external conditions, the well established critical states may be completely obtained as diffusive final profiles.

Magnetic relaxation induced by transverse flux shaking in MgB2 superconductors

We report on measurements and numerical simulations of the behavior of MgB2 superconductors when magnetic field components are applied along mutually perpendicular directions. By closely matching the geometry in simulations and measurements, full quantitative agreement is found. The critical state theory and a single phenomenological law, i.e. the field dependence of the critical current density Jc(B), are sufficient for a full quantitative description of the measurements. These were performed in thick strips of carbon nanotube doped MgB2 samples. Magnetization was measured in two orthogonal directions using a SQUID magnetometer. Magnetic relaxation effects induced by the application of an oscillatory perpendicular field were observed and simulated numerically. The measurements confirm the numerical predictions, that two relaxation regimes appear, depending on the amplitude of the applied magnetic field. The overall agreement constitutes a convincing validation of the critical state model and the numerical procedures used. (Some figures in this article are in colour only in the electronic version)

Geometric treatment of electromagnetic phenomena in conducting materials: variational principles

The dynamical equations of an electromagnetic field coupled with a conducting material are studied. The properties of the interaction are described by a classical field theory with tensorial material laws in spacetime geometry. We show that the main features of superconducting response emerge in a natural way within the covariance, gauge invariance and variational formulation requirements. In particular, the Ginzburg–Landau theory follows straightforwardly from the London equations when fundamental symmetry properties are considered. Unconventional properties, such as the interaction of superconductors with electrostatic fields are naturally introduced in the geometric theory, at a phenomenological level. The BCS background is also suggested by macroscopic fingerprints of the internal symmetries. It is also shown that dissipative conducting behaviour may be approximately treated in a variational framework after breaking covariance for adiabatic processes. Thus, nonconservative laws of interaction are formulated by a purely spatial variational principle, in a quasi-stationary time discretized evolution. This theory justifies a class of nonfunctional phenomenological principles, introduced for dealing with exotic conduction properties of matter (Badia and Lopez 2001 Phys. Rev. Lett. 87 127004).

Assistive Intelligent Transportation Systems: The Need for User Localization and Anonymous Disability Identification

The main goal of Assistive Technology (AT) is to ensure the functional independence of disabled individuals. This paper proposes the definition of a new concept of AT within the context of the ITS, Assistive Intelligent Transportation System (AITS), analyzing its intrinsic requirements and providing a set of examples. We demonstrate that AITS must localize users with disabilities and identify their specific type of impairment in order to provide an efficient response, and we propose a specific procedure to guarantee anonymity while identifying the type of disability. Moreover, this new type of AT is illustrated by means of a new assistive intelligent pedestrian crossing application that is capable of localizing pedestrians with disabilities, identifying the specific type of impairment and providing an adaptive response to enhance functional capabilities of impaired pedestrians while crossing. By combining stereo-based object detection with radio-frequency identification technology (RFID and Bluetooth Low Energy), a specific solution to the problem of user localization and anonymous disability identification is proposed. Our approach has been validated in a real crosswalk scenario and it may be extended to other types of AITS, depending on the localization accuracy requirements and the range of operation of the specific application.

Modelling current voltage characteristics of practical superconductors

Based on recent experimental results, and in the light of fundamental physical properties of the magnetic flux in type-II superconductors, we introduce a practical expression for the material law to be applied in numerical modelling of superconducting applications. Focusing on the computational side, in this paper, previous theory is worked out, so as to take the celebrated form of a power-law-like dependence for the current voltage characteristic. However, contrary to the common approach in numerical studies, this proposal suits the general situation of current density flow with components either parallel or perpendicular to the local magnetic field, and different constraints applying on each component. Mathematically, the theory is generated from an elliptic locus defined in terms of the current density vector components. From the physical side, this contour establishes the boundary for the onset of entropy production related to overcritical current flow in different conditions. The electric field is obtained by partial differentiation and points perpendicular to the ellipse. Some numerical examples, inspired by the geometry of a two-layer helical counter-wound cable are provided. Corrections to the widespread use of the implicit isotropic assumption (physical properties only depend on the modulus of the current density vector) are discussed, and essentially indicate that the current carrying capacity of practical systems may be underestimated by using such simplification.

Material laws and related uncommon phenomena in the electromagnetic response of type-II superconductors in longitudinal geometry

Relying on our theoretical approach for the superconducting critical state problem in 3D magnetic field configurations, we present an exhaustive analysis of the electrodynamic response for the so-called longitudinal transport problem in the slab geometry. A wide set of experimental conditions have been considered, including modulation of the applied magnetic field either perpendicular or parallel (longitudinal) to the transport current density. The main objective of our work was to characterize the role of the macroscopic material law that should properly account for the underlying mechanisms of flux cutting and depinning. The intriguing occurrence of negative current patterns and the enhancement of the transport current flow along the center of the superconducting sample are reproduced as a straightforward consequence of the magnetically induced internal anisotropy. Moreover, we show that, related to a maximal projection of the current density vector onto the local magnetic field, a maximal transport current density occurs somewhere within the sample. The elusive measurement of the flux cutting threshold (critical value of such parallel component ) is suggested on the basis of local measurements of the transport current density. Finally, we show that a high correlation exists between the evolution of the transport current density and the appearance of paramagnetic peak structures in terms of the applied longitudinal magnetic field.

Inversion mechanism for the transport current in type-II superconductors

This work was supported by the Spanish CICyT Project No. MAT2008-05983-C03-01 and the DGA Grant No. PI049/08. H.S.R. acknowledges a grant from the Spanish CSIC (JAE program).

Experimental and numerical study of transverse flux shaking in MgB2 superconductors

Magnetization measurements in the mixed state of thick strips of carbon nanotube doped MgB2 in crossed fields configurations are reported, together with numerical simulations performed with a geometry equivalent to the sample shape. The samples were subjected to magnetic field components along mutually perpendicular directions, an oscillatory field in one direction and a remanent magnetization in the perpendicular direction. The magnetic response along the oscillatory field and the magnetic relaxation perpendicular to it are observed and simulated using the critical state theory. A remarkable quantitative agreement between the experiment and the theory was obtained.