Scielo RSS <![CDATA[Revista mexicana de física]]> vol. 61 num. 5 lang. en <![CDATA[SciELO Logo]]> <![CDATA[<b>Mathematical differences and physical similarities between Eliezer-Ford-O'connell equation and Landau-Lifshitz equation</b>]]> Recently, for high intensity electromagnetic waves, it has been proven that the solutions for the Eliezer-Ford-O'Connell equation and the Landau-Lifshitz equation coincide within a physically detectable range. For large-scale temporal effects, similar results are obtained for the central force problem. However, in the case of a constant magnetic field, the frequencies which describe the motion in both equations differ. Nonetheless, quantum constraints avoid the measurement of such difference making both equations physically equivalent for all the scale of energies and fields within Classical Mechanics regime. <![CDATA[<b>Luminescent polystyrene films, a novel way to reduce styrofoam residues</b>]]> Polystyrene (PS) films doped with blue, yellow and red organic pigments have been deposited on glass and on commercial LED chips by spray pyrolysis using recycled PS as precursor, at deposition rates between 100 and 200 Å/s. Doped films have roughness between 100 and 2500 Å depending on the kind of pigment used; the surface morphology shows that the organic pigments incorporate into the polystyrene host forming globular particles of about 2 μm in diameter. The organic pigments used have luminescent emissions peaked at 440, 509 and 590 nm. The introduction of the proper combination of pigments on the PS film deposited on the LED chips renders a white light emission with (0.29, 0.37) and (0.30, 0.33) CIE (Commission international de l' eclairage) color coordinates. It was determined that the exposure to violet light degrades the luminescent characteristics, however, blue light is not energetic enough to cause a degradation of the luminescent layer over similar period of time. <![CDATA[<b>Phase map by fringe projection with dammann gratings</b>: <b>an application to measure small objects</b>]]> The phase of a suitable object was obtained with a fringe projection experiment by using phase shifting with Dammann gratings. As the spacing of the Dammann gratings can be manipulated, it is possible to generate projected thin fringes to improve details of the borders of the object. These gratings have the property that their spacing is not constant, can be programmed, encoded and displayed with versatile performance using a monochromatic source light on a liquid crystal display LCD or by means of a DLP (Digital Light Projector) to develop fringe projection experiments easily and at low cost. As result we have found a high-contrast projection fringes, side and rotation displacements can be better adapted to measure an object. Some fringes images can be generated by fifth order Dammann gratings projected on objects ≤ 20 cm of height.<hr/>Empleando la técnica de proyección de franjas se obtiene la fase de objetos, con corrimiento de fase empleando una rejilla binaria Dammann. Debido a que se puede manipular la resolución espacial de las rejillas, podemos modificar el espesor de las franjas que se proyectan y mejorar los detalles de los bordes del objeto. Las rejillas Dammann no tienen un espaciamiento constante, se puede programar y codificar de forma versátil usando luz monocromática a través de una pantalla de cristal líquido LCD, o por medio de un proyector digital de luz DLP para la proyección de franjas, el DLP es una opción de bajo costo y fácil de realizarse. Como resultado, hemos encontrado franjas de alto contraste, los patrones de franjas codificados se pueden girar y desplazar adaptándolas a objetos ≤ 20 cm de altura, En este trabajo se identifica que las rejillas Dammann de orden 5 producen mejores resultados, que se observan en los contrastes de las imágenes obtenidas. <![CDATA[<b>Use of the perfect electric conductor boundary conditions to discretize a diffractor in FDTD/PML environment</b>]]> In this paper we present a computational electromagnetic simulation of a multiform diffractor placed at the center of an antenna array. Our approach is to solve Maxwell's differential equations with a discrete space-time formulation, using the Finite Difference Time Domain (FDTD) method. The Perfectly Matched Layers (PML) method is used as an absorbing boundary condition, to prevent further spread of the electromagnetic wave to the outside of the calculation region. The Perfect Electric Conductor (PEC) boundary conditions are used to represent the periphery of the region and the diffractor. The system consists of an antenna array of 20 elements: a transmission antenna (TX1) which feeds a Gaussian pulse with center frequency of 7.5 GHz, and 19 reception antennas (RX1 to RX19), which serve as sensors. The diffractor is discretized for integration into the environment FDTD, and two case studies are presented according to their geometric shape: square and circular diffractor. In this work, the goal is to determine the Maxwell's equations, analyze all the zones that form the diffractor and plug them in the computational algorithm in Matlab. We show the equations for each case and obtain the electromagnetic parameters of the system: electric fields, magnetic fields, and reflected power, sensed by the RX's.<hr/>En este artículo se describe el uso de las condiciones de Conductor Eléctrico Perfecto (PEC), para modelar un difractor multiforme colocado en el centro de un arreglo de antenas. La estrategia se basa en resolver las ecuaciones diferenciales de Maxwell con una formulación discreta espacio-temporal, mediante el método de Diferencias Finitas en el Dominio del Tiempo (FDTD), el método de Capas Perfectamente Acopladas (PML), se utiliza como condición de frontera absorbente al evitar que la onda electromagnética continÚe propagándose hacia el exterior de la región de cálculo, las condiciones de frontera PEC son utilizadas para representar la periferia de dicha región y el difractor. El sistema consiste en un arreglo de antenas, formado por 20 elementos: una antena de Transmisión (TX1) la cual alimenta un pulso gaussiano a una frecuencia central de 7.5 GHz y 19 antenas Receptoras (RX1 a RX19), que funcionan como sensores. El difractor es discretizado para su integración en el ambiente FDTD, se presentan dos casos de estudio, de acuerdo a su forma geométrica: difractor cuadrado y circular. Se presentan las ecuaciones correspondientes para cada caso, como resultado obtenemos los parámetros electromagnéticos del sistema: campos eléctrico, campos magnéticos, potencia reflejada, sensados por las RX. <![CDATA[<b>Solitones no autónomos en fibras ópticas</b>]]> Soluciones solitónicas de las ecuaciones de Schrödinger no lineales de coeficientes variables que describen muchas situaciones reales de propagación solitónica se pueden obtener usando el mapeo de 'integrabilidad diseñada' a la ecuación estandar de Schrödinger no lineal de coeficientes constantes propuesto por He y Li. En este trabajo se presenta este método para el caso de fibras con ganancia/pérdida y se aplica a los casos de los solitones en fibras (ópticas con amplificadores y los solitones brillantes en fibras no amplificadas.<hr/>Soliton solutions of the non-linear Schrödinger equation of variable coefficients which describe many real cases of solitonic propagation can be obtained by means of the 'designable integrability' mapping to the standard non-linear Schrödinger equation of constant coefficients proposed by He and Li. In this paper, this method of obtaining the non-autonomous soliton solutions is presented for the general case of optical fibers with gain/loss, and applied to fibers with amplifiers, and those allowing the propagation of bright solitons. <![CDATA[<b>Optical and structural properties of PbS:Bi<sup>3</sup>+ nanocrystals</b>]]> We report here the growth of nanocrystalline PbS thin films by chemical bath and the effects of doping on the structural and electronics properties as a function of Bi3+ concentration. Doping of such PbS films with Bi3+ produces considerable optical and structural changes that have an effect on the material properties. The morphological changes of the layers were followed by Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM). X-ray diffraction (XRD) spectra show growth of the zinc blende phase. The grain size for the undoped samples was found to be ~ 32 nm, whereas that for the doped samples was 25-15 nm, thus confirming AFM and SEM results. A conspicuous shift for the forbidden band gap energy was observed by optical absorption from 1.2 eV for the undoped samples to a 1.7-2.0 eV range for the doped films. <![CDATA[<b>Equilibrium profiles of liquids in tilted Taylor-Hauksbee cells</b>]]> In this work we study theoretically and experimentally the equilibrium profiles attained under spontaneous capillary rise of viscous liquids in the wedge-shaped narrow gap between two vertical plates intersecting at a tight angle α<< 1. We contrast the differences among the case with vertical edge and those in which the arista is tilted to the vertical. Our theoretical description agrees well with experimental data for several analyzed inclinations.<hr/>En este trabajo estudiamos teórica y experimentalmente los perfiles de equilibrio alcanzados en virtud de ascenso capilar espontáneo de líquidos viscosos en el pequeño espacio en forma de cuña creado entre dos placas verticales que se unen en un ángulo estrecho α<< 1. Contrastamos las diferencias entre el caso con la arista vertical y aquellos en los que la arista está inclinada respecto a la vertical. Nuestra descripción teórica concuerda bien con los datos experimentales para varias inclinaciones analizadas. <![CDATA[<b>Solution of the Schrödinger equation making use of time-dependent constants of motion</b>]]> It is shown that if a complete set of mutually commuting operators is formed by constants of motion, then, up to a factor that only depends on the time, each common eigenfunction of such operators is a solution of the Schrödinger equation. In particular, the operators representing the initial values of the Cartesian coordinates of a particle are constants of motion that commute with each other and from their common eigenfunction one readily obtains the Green function.<hr/>Se muestra que si un conjunto completo de operadores que conmutan entre sí está formado por constantes de movimiento, entonces, salvo un factor que solo depende del tiempo, cada eigenfunción común de tales operadores es una solución de la ecuación de Schrödinger. En particular, los operadores que representan los valores iniciales de las coordenadas cartesianas de una partícula son constantes de movimiento que conmutan entre sí y de sus eigenfunciones comunes uno obtiene fácilmente la función de Green. <![CDATA[<b>Caracterización eléctrica de un oxido de manganeso laminar tipo birnesita</b>]]> En este trabajo se reporta la caracterización de un (óxido de manganeso sintetizado por rutas de estado sólido, análogo al mineral natural denominado birnesita. Los análisis de difracción de rayos X y el estado promedio de oxidación del manganeso muestran que el material tiene una estructura laminar conteniendo manganeso en estados de oxidación (+4) y (+3). Los resultados de microscopía electrónica, área superficial y tamaño de poro revelan la presencia de micro y mesoporos en el material. La espectroscopía de impedancia sugiere que a altas frecuencias se presenta conducción eléctrica en el volúmen y en la frontera de los agregados, en contraste a bajas frecuencias se presenta conductividad iónica asociada a los iones potasio ubicados en la región interlaminar. Los valores de conductividad AC a bajas frecuencias fue de 1.599 x 10-6 Ω-1 cm-1 ya altas frecuencias fue de 6.416 x 10-5 Ω-1 cm-1 lo que se asoció a un aumento en la probabilidad de salto electrónico a medida que se incrementó la frecuencia. El material estudiado puede tener aplicaciones en el campo de las baterías, supercapacitores y catálisis heterogénea, entre otros, por lo que profundizar en la comprensión de los procesos de conducción eléctrica aporta información importante para establecer sus aplicaciones potenciales.<hr/>This paper records the characterization of a manganese oxide synthesized by solid state routes which is analogous to natural mineral called birnessite. The analysis of X-ray diffraction and average oxidation state of manganese show that the material has a lamellar structure containing manganese in oxidation states (+4) and (+3). The results of electron microscopy along with surface area and pore size measurements reveal the presence of micro and mesopores in the material. Impedance spectroscopy suggests that high frequency electrical conduction occurs in the volume and on the border of the aggregates; in contrast, ionic conductivity at low frequencies was associated with potassium ions located in the interlaminar region. AC conductivity values at low frequencies were 1.599 10-6 Ω-1 cm-1and 6.416 x 10-5 Ω-1 cm-1 at high frequencies. These values are associated with an increased probability of electron jumping as frequency increases. These findings contribute to the understanding of electrical conduction processes and provides important information about its potential applications. As a result, this research will prove relevant in the field of batteries, supercapacitors and heterogeneous catalysis, among others. <![CDATA[<b>Estimation of the space charge limited current with quadratic damping</b>]]> In this paper we analyze the motion of charged particles under the influence of a quadratic velocity dependent frictional force inside a vacuum tube diode. Our study is performed by using the adiabatic approximation that allows for exact analytic solutions for the case of weak damping. The expressions obtained for the space charge limited current reduce to the well known Child-Langmuir law under the adiabatic approximation when the dissipation parameter goes to zero. <![CDATA[<b>The Jacobi elliptic functions and their applications in the advance of mercury's perihelion</b>]]> In this paper we find the exact solution of the nonlinear differential equation describing the trajectory of mercury considering relativistic effects. Instead of the classical perturbation method we use the Jacobi elliptic functions to obtain the exact solution. The deviation of the perihelion of Mercury and other planets is calculated. The results may be of great interest to astronomers and for those interested in the study of nonlinear differential equations.