jorge mahecha

The rankings of all kinds are in vogue. They are supported in the belief
that human activity is likely to be measured, each individual and every
institution must advance continuously to improve its position in the
ranking. Education and research are some of the activities most affected
by the pressure of ranking. MIDE of Ministry of Education Colombia; the
classification of research groups and researchers by Colciencias;
rankings of journals, articles and books; tests Saber, Saber Pro in
Colombia; entrance exams to universities; accreditation of "high
quality", qualified registration, curriculum changes, system Quality
Assurance ... Internationally: The Shanghai rankings of universities
type, those of "Impact" of scientific journals, Test of English as a
Foreign Language (TOEFL), The Graduate Record Examination (GRE), Pisa
Testing, etc. They assume that the intellect can be "measured,"
standardized, branded with basis with a unique number that is obtained
by "Summing Pears and Apples." Then the number is used to classify "by
descending order of quality" whole institutions, academic programs,
research groups and individuals. In this text we discuss the technical
impossibility of such pretension, emphasizing the development of a
ranking to choose people who deserve to enter the University of
Antioquia and discard those who do not deserve it. Seeks to answer the
following questions: (1) The system allows an accurate ranking of the
candidates, based on the scores? (2) Does the system is accomplished by
establishing a solid border between the scores of the admitted and the
unsupported? (3) Do the alleged measurements of the intellectual
abilities are the only measurements that escape protocols of the science
of measurements?

Tools for the numerical study of classical Coulomb three body systems with arbitrary masses and charges in three spatial dimensions. https://github.com/fperez/coulomb-3body The code contained in this repository can solve the electrostatic three body problem (three charged particles) with a numerically stable scheme that uses a regularized form of the equations of motion. The code and manuscript contained in this repository were the senior undergraduate thesis for F. Perez, conducted under the supervision of professor Jorge Mahecha at the physics department of the Universidad de Antioquia, in Medellin, Colombia. This work was completed in 1994 and was part of the following publications: F. Pérez and J. Mahecha. Classical trajectories in Coulomb three body systems. Rev. Mex. Física 42:6, 1070-1086 (1996). (Full text PDF). A. Santander, J. Mahecha and F. Pérez, Rigid Rotator and Fixed shape solutions to the Coulomb Three-Body Problem. Few Body Systems, 22:1, 37-60 (1997).

1  Fundamentos de la mecánica newtoniana
2  Ecuaciones generales de la estática y la dinámica
3  El principio de Hamilton y las ecuaciones de Lagrange
4  La formulación hamiltoniana
5  Movimiento de dos partículas que interactúan por medio de una fuerza central
6  Pequeñas oscilaciones de sistemas de varios grados de libertad
7  Cinemática del cuerpo rígido
8  Dinámica del cuerpo rígido
9  Las transformaciones canónicas
10  La ecuación de Hamilton-Jacobi con variables de acción-ángulo
11  Teoría de perturbaciones
12  Correspondencia con la mecánica cuántica de Heisenberg
13  Correspondencia con la mecánica cuántica de Schrödinger

The Spanish translation of the Declaration of Academic Freedom by D. Rabounski. Translated by Juan Francisco Gonzalez Hernandez, edited by Jorge Mahecha Gomez. This Declaration sets up the basic principles of democracy and tolerance in scientific research. Scientific arguments should stand or fall, in the long term, on their own merits. Disagreement in opinion and tolerance of an opposing opinion are normal elements of the scientific process. According to the Declaration, suppression of the right to adduce scientific argument, disallowing widespread discussion and analysis, manipulation or juggling of the scientific facts in order to obtain a commercial profit from governments or companies, are not scientific, and are intolerable.

A discussion regarding the energy levels spectrum of quantum systems whose classical analogous has states of chaotic motion is presented. The chaotic dynamics of the classical underlying system has its manifestation in the wave functions (in the form of ``scars'') and in the energy levels (in the form of ``statistical repulsion'' of the energy levels). The above mentioned signatures are named ``quantum chaos''. A typical study of quantum chaos requires finding accurate energy eigenvalues of highly excited states, to calculate the nearest neighbors spacing between levels, to perform the ``unfolding'' of the spectrum in order to separate the fluctuations, and finally to find the probability distribution of the unfolded spectrum. This is exemplified by the hydrogen atom under uniform magnetic field and a quadrupole electric field.

Due to the fact that only matter fields have phase, frequently is believed that the gauge principle can induce gauge fields only in quantum systems. But this is not necessary. This paper, of pedagogical scope, presents a classical system constituted by a particle in a classical potential, which is used as a model to illustrate the gauge principle and the spontaneous symmetry breaking. Those concepts appear in the study of second order phase transitions. Ferroelectricity, ferromagnetism, superconductivity, plasmons in a free electron gas, and the mass of vector bosons in the gauge field Yang-Mills theories, are some of the phenomena in which these transitions occur.

© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ... Semi-classical calculation of resonant states of a charged particle interacting with a metallic surface ... John Jairo Zuluaga*, 1, Jorge Mahecha**, 1, and Eugene Chulkov***, 2 1 Institute of Physics, University of Antioquia, ...

In this 607 page book, in Spanish, are described in clear and complete way several problems of statics, mechanics, kinematics, dynamics and analytical dynamics. Includes non conventional subjects like perturbation theory, Kepler problem in parabolic coordinates, and connection with quantum mechanics.