Chaos in resonant-tunneling superlattices

Spatio-temporal chaos is predicted to occur in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Under dc voltage bias, undamped time-dependent oscillations of the current (due to the motion and recycling of electric field domain walls) have been observed in recent experiments. Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal.Comment: 3 pages, LaTex, RevTex, 3 uuencoded figures (1.2M) are available upon request from [email protected], to appear in Phys.Rev.

Axisymmetric pulse recycling and motion in bulk semiconductors

The Kroemer model for the Gunn effect in a circular geometry (Corbino disks) has been numerically solved. The results have been interpreted by means of asymptotic calculations. Above a certain onset dc voltage bias, axisymmetric pulses of the electric field are periodically shed by an inner circular cathode. These pulses decay as they move towards the outer anode, which they may not reach. As a pulse advances, the external current increases continuously until a new pulse is generated. Then the current abruptly decreases, in agreement with existing experimental results. Depending on the bias, more complex patterns with multiple pulse shedding are possible.Comment: 8 pages, 15 figure

On the Photorefractive Gunn Effect

We present and numerically solve a model of the photorefractive Gunn effect. We find that high field domains can be triggered by phase-locked interference fringes, as it has been recently predicted on the basis of linear stability considerations. Since the Gunn effect is intrinsically nonlinear, we find that such considerations give at best order-of-magnitude estimations of the parameters critical to the photorefractive Gunn effect. The response of the system is much more complex including multiple wave shedding from the injecting contact, wave suppression and chaos with spatial structure.Comment: Revtex, 8 pag., 4 fig. (jpg), submit to Physical Review

Free boundary problems describing two-dimensional pulse recycling and motion in semiconductors

An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk n-GaAs with circular contacts is presented. A moving pulse far from contacts is approximated by a moving free boundary separating regions where the electric potential solves a Laplace equation with subsidiary boundary conditions. The dynamical condition for the motion of the free boundary is a Hamilton-Jacobi equation. We obtain the exact solution of the free boundary problem (FBP) in simple one-dimensional and axisymmetric geometries. The solution of the FBP is obtained numerically in the general case and compared with the numerical solution of the full system of equations. The agreement is excellent so that the FBP can be adopted as the basis for an asymptotic study of the multi-dimensional Gunn effect.Comment: 19 pages, 9 figures, Revtex. To appear in Phys. Rev.

Exact solution of the Schr\"{o}dinger equation for an hydrogen atom at the interface between the vacuum and a topologically insulating surface

When an hydrogen atom is brought near to the interface between $\theta$-media, the quantum-mechanical motion of the electron will be affected by the electromagnetic interaction between the atomic charges and the $\theta$-interface, which is described by an axionic extension of Maxwell electrodynamics in the presence of a boundary. In this paper we investigate the atom-surface interaction effects upon the energy levels and wave functions of an hydrogen atom placed at the interface between a $\theta$-medium and the vacuum. In the approximation considered, the Schr\"{o}dinger equation can be exactly solved by separation of variables in terms of hypergeometic functions for the angular part and hydrogenic functions for the radial part. In order to make such effects apparent we deal with unrealistic high values of the $\theta$-parameter. We also compute the energy shifts using perturbation theory for a particular small value of $\theta$ and we demonstrate that they are in a very good agreement with the ones obtained from the exact solution.Comment: 20 pages, 17 figures, 6 tables, Accepted for publication in the European Physics Journal

Vacuum stability with spontaneous violation of lepton number

The vacuum of the Standard Model is known to be unstable for the measured values of the top and Higgs masses. Here we show how vacuum stability can be achieved naturally if lepton number is violated spontaneously at the TeV scale. More precise Higgs measurements in the next LHC run should provide a crucial test of our symmetry breaking scenario. In addition, these schemes typically lead to enhanced rates for processes involving lepton flavour violation .Comment: 9 pages, 4+2 figures; some references added, some textual modifications: 2 figures added, appendices added. Results unchanged. Matches published versio

A model for assembly sequence planning in a multirobot environment

2002 IFAC15th Triennial World Congress, Barcelona, SpainThis paper presents a model for the selection of optimal assembly sequences for a product in multirobot systems. The objective of the plan is the minimization of the total assembly time (makespan). To meet this objective, the model takes into account, in addition to the assembly times and resources for each task, the times needed to change tools in the robots, and the delays due to the transportation of intermediate subassemblies between different machines. An A* algorithm that solves the problem is also presented, which starts from the And/Or graph for the product (compressed representation of all feasible assembly plans)

El cuento y la creatividad como preparación a la resolución de problemas matemáticos

La aproximación a la realidad es, hoy en día, una de las estrategias más eficaces para motivar al alumno hacia las matemáticas y más concretamente hacia la resolución de problemas matemáticos (RPM). En el primer ciclo de primaria, las narraciones y los cuentos pertenecen a la realidad del niño y comparten con la RPM fases y estructuras de conocimiento. La manera de aproximarnos a un problema, determina el éxito de su solución y las emociones forman parte de ese proceso. El cuento, a su vez, prepara al niño para el conocimiento y posterior control de las emociones. El arte, la imaginación y el juego son características compartidas entre los cuentos y los problemas matemáticos. La enseñanza basada en el trabajo con los cuentos, durante el primer ciclo de primaria, permitirá abordar la RPM desde una perspectiva reconocible y motivadora en los cursos posteriores. El trabajo previo con los cuentos, pedagógicamente organizados, es un soporte fundamental y una condición necesaria para la “matematización” de la vida real