A class of exactly solvable models for the Schrodinger equation

We present a class of confining potentials which allow one to reduce the one-dimensional Schroodinger equation to a named equation of mathematical physics, namely either Bessel's or Whittaker's differential equation. In all cases, we provide closed form expressions for both the symmetric and antisymmetric wavefunction solutions, each along with an associated transcendental equation for allowed eigenvalues. The class of potentials considered contains an example of both cusp-like single wells and a double-well.Comment: 5 pages, 7 figure

Localization of massless Dirac particles via spatial modulations of the Fermi velocity

The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial for determining fundamental properties of the bound states such as the zero-point energy. We discuss the implications for guiding electronic waves in few-mode waveguides formed by Fermi velocity modulation.Comment: 9 pages, 6 figure

One-dimensional Coulomb problem in Dirac materials

We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated Coulomb problems, with the wavefunctions expressed in terms of special functions (namely Whittaker functions), whilst the energy spectrum must be determined via solutions to transcendental equations. Most notably, there are critical bandgaps below which certain low-lying quantum states are missing in a manifestation of atomic collapse.Comment: 7 pages, 5 figure

Charged Particle Radiation Damage in Semiconductors, I- Experimental Proton Irradiation of Solar Cells

Proton irradiation of solar cell

Bielectron vortices in two-dimensional Dirac semimetals

Searching for new states of matter and unusual quasiparticles in emerging materials and especially low-dimensional systems is one of the major trends in contemporary condensed matter physics. Dirac materials, which host quasiparticles which are described by ultrarelativistic Dirac-like equations, are of a significant current interest from both a fundamental and applied physics perspective. Here we show that a pair of two-dimensional massless Dirac-Weyl fermions can form a bound state independently of the sign of the inter-particle interaction potential, as long as this potential decays at large distances faster than Kepler's inverse distance law. This leads to the emergence of a new type of energetically-favourable quasiparticle: bielectron vortices, which are double-charged and reside at zero-energy. Their bosonic nature allows for condensation and may give rise to Majorana physics without invoking a superconductor. These novel quasiparticles arguably explain a range of poorly understood experiments in gated graphene structures at low doping.Comment: 9 pages, 2 figure

Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields

We show how it is possible to trap two-dimensional massless Dirac fermions in spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum dot (or ring) is of a slowly decaying nature. It is found that a modulation of the depth of the magnetic quantum dot leads to successive confinement-deconfinement transitions of vortexlike states with a certain angular momentum, until a regime is reached where only states with one sign of angular momentum are supported. We illustrate these characteristics with both exact solutions and a hitherto unknown quasi-exactly solvable model utilizing confluent Heun functions.Comment: 7 pages, 3 figure

Emerging global role of small lakes and ponds : little things mean a lot

Until recently, small continental waters have been completely ignored in virtually all global processes and cycles. This has resulted from the neglect of these systems and processes by ecologists and the assumption that ecosystems with a small areal extent cannot play a major role in global processes. Recent inventories based on modern geographical and mathematical approaches have shown that continental waters occupy nearly twice as much area as was previously believed. Further, these inventories have shown that small lakes and ponds dominate the areal extent of continental waters, correcting a centurylong misconception that large lakes are most important. The global importance of any ecosystem type in a process or cycle is the product of the areal extent and the intensity of the process in those ecosystems. Several analyses have shown the disproportionately great intensity of many processes in small aquatic ecosystems, indicating that they play an unexpectedly major role in global cycles. Assessments of the global carbon cycle underscore the need for aquatic scientists to view their work on a global scale in order to respond to the Earth's most pressing environmental problems.Hasta muy recientemente, las aguas continentales de pequeño volumen se han ignorado completamente en todos los procesos y ciclos globales. Esto ha sido el resultado de la poca consideración de estos ecosistemas y procesos por los ecólogos y de asumir que los ecosistemas que ocupan un área pequeña no juegan ningún papel importante en los procesos globales. Inventarios recientes basados en aproximaciones geográficas y matemáticas modernas indican que las aguas continentales ocupan casi el doble del área de lo que se creía anteriormente. Además, estos inventarios han mostrado que las charcas y lagunas de pequeñas dimensiones predominan en la extensión superficial de las aguas continentales, corrigiendo la concepción equivocada de todo un siglo de que los grandes lagos eran los más importantes. La importancia global de cualquier tipo de ecosistema en un proceso o ciclo es el producto de su superficie por la intensidad del proceso en el ecosistema. Diversos análisis han mostrado la intensidad desproporcionadamente grande de muchos procesos en los pequeños sistemas acuáticos, indicando su sorprendente papel primordial en los ciclos globales. Evaluaciones del ciclo global del carbono ponen de manifesto la necesidad de que los ecólogos acuáticos tengan una visión de su trabajo a escala global, para poder responder a los problemas ambientales más preocupantes

Development of a sensitivity analysis technique for multiloop flight control systems

This report presents the development and application of a sensitivity analysis technique for multiloop flight control systems. This analysis yields very useful information on the sensitivity of the relative-stability criteria of the control system, with variations or uncertainties in the system and controller elements. The sensitivity analysis technique developed is based on the computation of the singular values and singular-value gradients of a feedback-control system. The method is applicable to single-input/single-output as well as multiloop continuous-control systems. Application to sampled-data systems is also explored. The sensitivity analysis technique was applied to a continuous yaw/roll damper stability augmentation system of a typical business jet, and the results show that the analysis is very useful in determining the system elements which have the largest effect on the relative stability of the closed-loop system. As a secondary product of the research reported here, the relative stability criteria based on the concept of singular values were explored