Vol. 56 No. 1 Jan-Jun (2010): Revista Mexicana de Física E
Published:
2010-01-01
Artículos
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Quantum confinement particle in a 2D quadrupole potential
Abstract:We analytically solve the Hamiltonian for a quantum particle confined in a cylindrical hard-wall well, subject to the action of a two-dimensional quadrupolar potential at the well center. The angular part of the wavefunction is expressed by Mathieu functions whose angular eigenenergies take negative values when the quadrupolar momentum is above a certain threshold. We show that in this case, the radial part of the eigenfunctions is expressed in terms of Bessel functions of an imaginary order which are imaginary-value functions whose phases are not well defined at the origin. However, the density of probability is well defined everywhere and the wave function satisfies hard-wall boundary conditions for any value of the parameters involved. We discuss an alternative criterion for determining the eigenenergies of the system based on the expected value of the symmetrized radial momentum.⬇️ Scroll down to see the full summary -
A simple inquiry on the critical electric dipole moment in one space dimension
Abstract:The magnitude of an electric dipole moment must be larger or equal to a certain critical value to support bound states. This is not a widely known fact that nevertheless is easy to understand on heuristic terms and relatively easy to calculate. This critical dipole moment, $p_{C}$, has been calculated in 2 and 3 dimensions. It has been ascertained that it does not exist in one dimension or, at least, that it is not computable. In this work, after giving simple arguments on the existence of this critical moment, we compute $p_{C}$ in one dimension.⬇️ Scroll down to see the full summary -
Estudio de casos: conocimientos físicos de los estudiantes cuando terminan la escuela secundaria: una advertencia y algunas alternativas
Abstract:Initial knowledge of mathematics and physics is usually regarded by university physics instructors as a prerequisite for successful estudiante learning. This article describes incoming university estudiantes' understanding of some basic laws of physics at the Universidad de Alcalá, Spain. A 13-item single response multiple choice test has been constructed and used to measure the conceptual knowledge of physics topics normally included in high school physics. It also contains 5 items on mathematics subjects thought to be of relevance for physics instruction. The results show that these student's sample still hold, after high school instruction, major misconceptions of the tested topics. A comparison is made between this measured understanding and the conceptual knowledge adquired by high school estudiantes enrolled in classes that followed active learning methods. The significant differences in learning gains between traditional and active learning instruction strongly indicate that traditional approaches to teaching physics in high schools should be replaced by field-tested, active learning methodologies. It is argue that this study can be considered, in the field of physics, complementary and reaffirmatory of the recently released results of the PISA 2006 survey.⬇️ Scroll down to see the full summary -
On the teaching and learning of physics problem solving
Abstract:This article presents a six-step problem-solving strategy, aimed at addressing three major problems in the learning and teaching of physics: 1) the demand by physics instructors for effective teaching strategies that could help in the teaching of intuitive conceptual and quantitative reasoning in physics, and how to teach both aspects holistically; 2) the students' need for suitable methodology that could help students to fill the gap in textbooks on enhancing their mathematical reasoning abilities, which are essential for reinforcing students' knowledge of conceptual physics; and 3) a deficiency in the teaching of physics leading to students not being taught a coherent physics problem-solving strategy that would enable them to engage in both mathematical and conceptual reasoning. After a review of publications made by the {\em Physics Education Research group} (PER), the importance of a structured, systemic methodology to solve physics problems is considered. Then a structured, systemic methodology for solving physics problems is described by extending the well-known problem-solving steps presented by Polya. The proposed strategy includes the following steps: 1. Understand the problem, 2. Provide a qualitative description of the problem, 3. Plan a solution, 4. Carry out the plan, 5. Verify the internal consistency and coherence of the equations used, and 6. Check and evaluate the obtained solution. Finally, an illustrative example is provided: the calculation of the moment of inertia of a thin hollow right circular cone.⬇️ Scroll down to see the full summary -
Aplicación del sistema 4MAT en la enseñanza de la física a nivel universitario
Abstract:En este trabajo se muestran los resultados de la aplicación del sistema 4MAT de estilos de aprendizaje en la enseñanza de la física a nivel universitario. Se construyeron estrategias de aprendizaje orientadas a atender los cuatro estilos de aprendizaje que propone el Sistema 4MAT. El resultado del análisis hecho muestra que el Sistema 4MAT es adaptable para la enseñanza de la física a nivel universitario, ya que incluye a estudiantes de todos los estilos por medio de actividades dirigidas a los cuatro estilos, dentro de un ciclo de aprendizaje. Los estudiantes muestran un avance en la compresión de los conceptos, y presentan a su vez un grado alto de comodidad en al menos una de las estrategias del ciclo.⬇️ Scroll down to see the full summary -
Experimentos numéricos en el aula sobre fenómenos difusivos: difusión anómala en sistemas físicos y biológicos
Abstract:The diffusion phenomena and the Partial Differential Equations are topics barely reviewed in the undergraduate level of Physics. The main goal of the present work is, precisely, motivate students to study the ubiquitous diffusion phenomena showing the Einstein's model. In the other hand, we propose a very simple numerical experiment that enables us to see the original diffusion equation limitations. The character of the anomalous diffusion showed in the examples appears, in general, in open systems such as foraging walks in animals or inanimated particles moving in a porous media. The proposed numerical experiment shows the superdiffusive and subdiffusive phenomena.⬇️ Scroll down to see the full summary -
Solución de la ecuación de onda como un problema de valores iniciales usando diferencias finitas
Abstract:The solution of the wave equation is presented as the paradigm of the solution of initial value problems with boundary conditions using the finite differences approximation. First, it is developed an elementary solution and a direct discretization in order to introduce the method. Second, the wave equation is solved as a system of first order, the hyperbolicity properties of the resulting system of equations is studied, the characteristic variables and characteristic speeds of the system are calculated and boundary conditions are imposed in terms of the characteristic variables. In this case the method of lines is used as the evolution scheme. Special attention is devoted to the fact that numerical calculations require a criterion to be valid. In the case of the approximation using finite differences of a partial differential equation, the convergence to a correct solution in the continuum limit is presented as such criterion. Finally, it is expected that this manuscript serves as a guide to solve correctly other initial value problems with boundary conditions.⬇️ Scroll down to see the full summary -
Fractional Brownian motion in DNA sequences of bacterial chromosomes: a renormalization group approach
Abstract:A renormalization group (RG) approach shows that the relative dispersion of the distance series of a triplet for each half of most bacterial chromosomes follows an inverse power-law as a function of the window size in a log-log plot. These straight lines indicate that when each half of the bacterial chromosome is analysed a random monofractal is obtained. With this approach, inverse bilateral symmetry of some triplets in the 4 bacterial chromosomes analyzed is also illustrated. Thus, DNA sequences of whole bacterial genomes contain both long-range correlations and random components. In particular the RG approach captures a harmonic modulation of the underlying inverse power-law. The frequency distributions of distances of triplets are also analyzed and they exhibit an oscillatory decaying pattern that displays the well-known 3-base periodicity. It is concluded that the DNA fluctuations of the distance series of triplets are not completely random, like Brownian motion, nor are they the result of processes with short-term correlations. Instead, the inverse power-law reveals that the DNA distance series at any position is influenced by fluctuations that occurred hundreds or thousands of bases apart. This behavior is a consequence of the fractional Brownian nature of the distance series of DNA.⬇️ Scroll down to see the full summary -
Critical strings and analyticity of the $\zeta$ function analyticity
Abstract:In this paper we study a simple analytic continuation of the Riemann $\zeta$ function, using Bernoulli numbers and an analytic continuation of the $\Gamma$ function in the complex plane. We use our results to study the critical condition in bosonic string theory. The approach is simple and gives the student an alternative point of view of the subject. We also show that the mathematical basis needed to understand the critical condition is based on well known properties of the Dirichlet series and the theory of entire functions, and is within reach of the average graduate student.⬇️ Scroll down to see the full summary -
El oscilador repulsivo
Abstract:The repulsive oscillator is characterized for having a potential (-1/2)$x^2$ that acts as a barrier; it is one of the few quantum systems whose solution is explicit. It shows several interesting aspects due to the potential barrier which separates its states into those that classically surmounts the barrier for having positive energy, from those with negative energy, which partially reflect and partially transmit through it. The energy spectrum is double, since the states can move to the right or to the left. Here we analyze this system in quantum phase space through the Wigner function, with the strategy of using $2\times2$ matrices to find the time evolution, factorizing it into a geometric and a dynamical transformation.⬇️ Scroll down to see the full summary -
El modelo BEG con interacciones de largo alcance: propiedades estáticas y dinámicas
Abstract:We study the static and dynamic properties of the BEG model with long-range interactions. This model is exactly solvable both in the canonical and in the microcanonical ensembles, we obtain the canonical partition function and the phase transition lines. Also, we study the dynamic properties through the master equation within the Glauber dynamics. We have derived and studied the kinetic equation for the magnetization, we observed the critical slowing down phenomenon near the critical point. Thus, this model represents a very interesting example, where it is possible to study all these phenomena, moreover it has a richer phase diagram than the Ising model, so it can be a nice example as part of the courses of statistical physics.⬇️ Scroll down to see the full summary -
Fraccionalización de la transformada discreta de Fourier
Abstract:In this paper we show how to extend the definition of the Finite Fourier Transform (DFT) as we introduce a fractionalization (FrDFT) of them, the FrDFT transform is defined as a real power of the unitary matrix that defines the DFT, of such form that additivity between powers is guaranteed when applying two different FrDFTs, also we describe some of the bases in which it is possible to define the FrDFT, we graphically show how this fractionalization contracts to its continuous equivalent the Fractional Integral Fourier Transform (FrIFT).⬇️ Scroll down to see the full summary -
Elasticidad de las membranas biológicas
Abstract:In this article we review the present knowledge on the elastic properties of membranes of biological origin. Assuming the fluid mosaic hypothesis, we consider the phospholipid bilayer as the structural base of a biological membrane. We expose a model due to Helfrich which can be used to obtain an expression for the membrane elastic energy. The free energy is completely characterized by two local principal curvatures and four parameters that depend on the chemical composition of the membrane and its local environment. In addition we present the theoretical justification of an experimental method (the Micropipette Manipulation technique) that may be used to measure the membrane rigidity (the elastic constant that corresponds to the mean curvature of the membrane). Finally, we describe some physical consequences of these concepts, such as the explanation of the lamellar-sponge phase transition and the emergence of the steric interaction between membranes.⬇️ Scroll down to see the full summary -
Fluido magneto-reológico bajo perturbaciones magnéticas
Abstract:We study a dilute dispersion of magnetic microparticles in mineral oil when it is simultaneously under a static magnetic field and an alternating magnetic field of low amplitude, considered as perturbation, transversal to the static field. We observed the formation of chains of particles that oscillate laterally respect to the direction define by the static field. The induced movement by the perturbation enhance the aggregation particles speed, forming longer chains at a define time in comparison when it is used only the static field. We found the effective viscosity as a function of time is notable effected by the magnetic perturbation. We discuss qualitatively the viscosity measurements in terms of the average length of the chains. We found the system exhibits a critical behavior in the average length and the effective viscosity when varying the frequency. It is proposed an explanation of the critical behavior in terms of the ratio between the drag force and the magnetic force.⬇️ Scroll down to see the full summary -
Evaluación de la incertidumbre en cantidades correlacionadas: aplicación al análisis elemental de aerosoles atmosféricos
Abstract:One of the aspects that are frequently overlooked in the evaluation of uncertainty in experimental data is the possibility that the involved quantities are correlated among them, due to different causes. An example is the elemental analysis of atmospheric aerosols using techniques like X-ray Fluorescence (XRF) or Particle Induced X-ray Emission (PIXE). In these cases, the measured elemental concentrations are highly correlated, and then are used to obtain information about other variables, such as the contributions from emitting sources related to soil, sulfate, non-soil potassium or organic matter. This work describes, as an example, the method required to evaluate the uncertainty in variables determined from correlated quantities from a set of atmospheric aerosol samples collected in the Metropolitan Area of the Mexico Valley and analyzed with PIXE. The work is based on the recommendations of the Guide for the Evaluation of Uncertainty published by the International Organization for Standardization.⬇️ Scroll down to see the full summary -
Separación de variables en la ecuación cinemática $v^2=v_0^2+2\vec{a}\cdot\Delta\vec{r}$ y su importancia
Abstract:Here we show how to separate into variables the scalar kinematic equation $V^{2}=V_{0}^{2}+2\vec{a}\cdot\Delta\vec{r}$ in Cartesian coordinates, a procedure that is little considered in the school texts on general physics, and also the connection between the kinematic expression and the theorem on work and kinetic energy. We also show a generalization of this same kinematic equation.⬇️ Scroll down to see the full summary -
The wavelength of a laser diode and the birefringence of mica. The IPhO40 experimental exam
Abstract:The experiments proposed and the equipment built for the 2009 International Physics Olympiad are described in this article. A list of the items used with details of the constructed elements, as well as an exhaustive discussion of both experiments, including the questions and the step by step solutions, are given.⬇️ Scroll down to see the full summary
