Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices

Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy principle can be used to close the system of equations for the moments but its accuracy or range of validity are not always clear. In this paper, we compare numerical solutions of balance equations for nonlinear electron transport in semiconductor superlattices. The equations have been obtained from Boltzmann-Poisson kinetic equations very far from equilibrium for strong fields, either by the maximum entropy principle or by a systematic Chapman-Enskog perturbation procedure. Both approaches produce the same current-voltage characteristic curve for uniform fields. When the superlattices are DC voltage biased in a region where there are stable time periodic solutions corresponding to recycling and motion of electric field pulses, the differences between the numerical solutions produced by numerically solving both types of balance equations are smaller than the expansion parameter used in the perturbation procedure. These results and possible new research venues are discussed.This work has been supported by the Ministerio de Economía y Competitividad grant MTM2014-56948-C2-2-P

Entropy-based study of imaging quality in holographic optical elements

A method for obtaining the best image plane for holographic optical elements by the use of the concept of entropy is described. This method is applied to in-line holographic lenses with different values of spherical aberration. Numerical results show that for holograms with large aberrations the best image plane (obtained by the use of the concept of entropy) is different from the minimum-aberration-variance plane.This work was supported by the Direcció General d'Ensenyaments Universitaris i Investigació de la Generalitat Valenciana, Spain, project GV-1165/93

Diagnóstico de reflujo gastro-esofágico mediante impregnación por ácido de férula oclusal

El teflujo gastro-esofágico (RGE) es un trastorno digestivo muy frecuente que se caracteriza por el paso de cantidades patológicas de ácido del estómago hacia el esófago. Esto es debido a una incompetencia de los mecanismos que regulan la retención del contenido gástrico en el estómago por causas primarias o secundarias. Las consecuencias clínicas de este reflujo afectan al tracto aerodigestivo superior, incluyendo la boca. Lo más frecuente es la esofagitis, seguido por la afectación de faringe y laringe y finalmente por alteraciones patológicas en la boca. A éste nivel lo más frecuente es la erosión del esmalte y las lesiones erosivas de la mucosa oral. Presentamos el caso de un paciente en el que el RGE fue diagnosticado de forma indirecta por la impregnación y coloración de una férula oclusal utilizada para el tratamiento de un síndrome miofascial. Partiendo de este caso se discuten las consecuencias del RGE en la cavidad oral y su asociación con el dolor muscular masticatorio.The gastroesophageal reflux (GER) disease is a very frequent digestive disorder, mainly characterised by the reflux of the gastric acidic content to the esophage in abnormal quantities. There are different situations that favour this situation but almost in all of them rely an incompetence of the esophagic sphincter. The clinical consequences are many, including oral manifestations. Among all of them the most frequent is the esophagitis followed by symptoms at the pharynx or larynx and finally, the oral cavity. At this level fundamentally we will find enamel and oral mucosa erosions. We report the case of a patient who was indirectly diagnosed of her esophague disease by the observation of the alterations in the occlusal splint induced by the gastric reflux. We review the literature concerning the above topic and its possible association with the miofascial syndrome

Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis

In this work, we present a numerical study of the influence of matrix degrading enzyme (MDE) dynamics and haptotaxis on the development of vessel networks in tumor-induced angiogenesis. Avascular tumors produce growth factors that induce nearby blood vessels to emit sprouts formed by endothelial cells. These capillary sprouts advance toward the tumor by chemotaxis (gradients of growth factor) and haptotaxis (adhesion to the tissue matrix outside blood vessels). The motion of the capillaries in this constrained space is modelled by stochastic processes (Langevin equations, branching and merging of sprouts) coupled to continuum equations for concentrations of involved substances. There is a complementary deterministic description in terms of the density of actively moving tips of vessel sprouts. The latter forms a stable soliton-like wave whose motion is influenced by the different taxis mechanisms. We show the delaying effect of haptotaxis on the advance of the angiogenic vessel network by direct numerical simulations of the stochastic process and by a study of the soliton motion.We thank Vincenzo Capasso, Bjorn Birnir and Boris Malomed for fruitful discussions. This work has been supported by the Ministerio de Economía y Competitividad grant MTM2014-56948-C2-2-P

Gastroesophageal reflux diagnosed by occlusal splint tintion

The gastroesophageal reflux (GER) disease is a very frequent digestive disorder, mainly characterised by the reflux of the gastric acidic content to the esophage in abnormal quantities. There are different situations that favour this situation but almost in all of them rely an incompetence of the esophagic sphincter. The clinical consequences are many, including oral manifestations. Among all of them the most frequent is the esophagitis followed by symptoms at the pharynx or larynx and finally, the oral cavity. At this level fundamentally we will find enamel and oral mucosa erosions. We report the case of a patient who was indirectly diagnosed of her esophague disease by the observation of the alterations in the occlusal splint induced by the gastric reflux. We review the literature concerning the above topic and its possible association with the miofascial syndrome

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.This work has been supported by Ministerio de Economía y Competitividad (Spain) Grant No. MTM2014-56948-C2-2-P

Chaos-based true random number generators

Random number (bit) generators are crucial to secure communications, data transfer and storage, and electronic transactions, to carry out stochastic simulations and to many other applications. As software generated random sequences are not truly random, fast entropy sources such as quantum systems or classically chaotic systems can be viable alternatives provided they generate high-quality random sequences sufficiently fast. The discovery of spontaneous chaos in semiconductor superlattices at room temperature has produced a valuable nanotechnology option. Here we explain a mathematical model to describe spontaneous chaos in semiconductor superlattices at room temperature, solve it numerically to reveal the origin and characteristics of chaotic oscillations, and discuss the limitations of the model in view of known experiments. We also explain how to extract verified random bits from the analog chaotic signal produced by the superlattice.This work has been supported by the Spanish Ministerio de Economía y Competitividad grants FIS2011-28838-C02-01 and MTM2014-56948-C2-2-P

Anomalous angiogenesis in retina

This article belongs to the Special Issue Angiogenesis and Inflammation in Biological Barriers.Age-related macular degeneration (AMD) may cause severe loss of vision or blindness, particularly in elderly people. Exudative AMD is characterized by the angiogenesis of blood vessels growing from underneath the macula, crossing the blood-retina barrier (which comprises Bruch's membrane (BM) and the retinal pigmentation epithelium (RPE)), leaking blood and fluid into the retina and knocking off photoreceptors. Here, we simulate a computational model of angiogenesis from the choroid blood vessels via a cellular Potts model, as well as BM, RPE cells, drusen deposits and photoreceptors. Our results indicate that improving AMD may require fixing the impaired lateral adhesion between RPE cells and with BM, as well as diminishing Vessel Endothelial Growth Factor (VEGF) and Jagged proteins that affect the Notch signaling pathway. Our numerical simulations suggest that anti-VEGF and anti-Jagged therapies could temporarily halt exudative AMD while addressing impaired cellular adhesion, which could be more effective over a longer time-span.This research was funded by FEDER/Ministerio de Ciencia, Innovación y Universidades-Agencia Estatal de Investigación grant number MTM2017-84446-C2-2-R

Periodic Trajectories Obtained With an Active Tractor Beam Using Azimuthal Polarization: Design of Particle Exchanger

We analytically calculate the forces generated on the near field by a focused azimuthally polarized Hermite-Gauss beam after passing a complex mask formed by two annular pupils. The resultant optical tractor beam shows two transport channels that move trapped objects upstream or downstream along the conveyor. From the analysis of the phase diagrams, we theoretically demonstrate that, depending on illumination intensity, the 3-D behavior of nanoparticles in this conveyor shows a limit cycle between transport channels. This limit cycle appears as a consequence of diffraction that produces spatially limited optical forces. We theoretically demonstrate the possibility of using the limit cycle to design a particle exchanger between channels

Helical tractor beam: analytical solution of Rayleigh particle dynamics

We analyze particle dynamics in an optical force field generated by helical tractor beams obtained by the interference of a cylindrical beam with a topological charge and a co-propagating temporally de-phased plane wave. We show that, for standard experimental conditions, it is possible to obtain analytical solutions for the trajectories of particles in such force field by using of some approximations. These solutions show that, in contrast to other tractor beams described before, the intensity becomes a key parameter for the control of particle trajectories. Therefore, by tuning the intensity value the particle can describe helical trajectories upstream and downstream, a circular trajectory in a fixed plane, or a linear displacement in the propagation direction. The approximated analytical solutions show good agreement to the corresponding numerical solutions of the exact dynamical differential equations