Thermal equilibrium in Einstein's elevator

We report fully relativistic molecular-dynamics simulations that verify the appearance of thermal equilibrium of a classical gas inside a uniformly accelerated container. The numerical experiments confirm that the local momentum distribution in this system is very well approximated by the J\"uttner function -- originally derived for a flat spacetime -- via the Tolman-Ehrenfest effect. Moreover, it is shown that when the acceleration or the container size is large enough, the global momentum distribution can be described by the so-called modified J\"uttner function, which was initially proposed as an alternative to the J\"uttner function

Statistical Thermodynamics of Polymer Quantum Systems

Polymer quantum systems are mechanical models quantized similarly as loop quantum gravity. It is actually in quantizing gravity that the polymer term holds proper as the quantum geometry excitations yield a reminiscent of a polymer material. In such an approach both non-singular cosmological models and a microscopic basis for the entropy of some black holes have arisen. Also important physical questions for these systems involve thermodynamics. With this motivation, in this work, we study the statistical thermodynamics of two one dimensional {\em polymer} quantum systems: an ensemble of oscillators that describe a solid and a bunch of non-interacting particles in a box, which thus form an ideal gas. We first study the spectra of these polymer systems. It turns out useful for the analysis to consider the length scale required by the quantization and which we shall refer to as polymer length. The dynamics of the polymer oscillator can be given the form of that for the standard quantum pendulum. Depending on the dominance of the polymer length we can distinguish two regimes: vibrational and rotational. The first occur for small polymer length and here the standard oscillator in Schr\"odinger quantization is recovered at leading order. The second one, for large polymer length, features dominant polymer effects. In the case of the polymer particles in the box, a bounded and oscillating spectrum that presents a band structure and a Brillouin zone is found. The thermodynamical quantities calculated with these spectra have corrections with respect to standard ones and they depend on the polymer length. For generic polymer length, thermodynamics of both systems present an anomalous peak in their heat capacity $C_V$

Anomalous diffusion of self-propelled particles

The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an arbitrary active motion pattern modelled by a scattering function that defines the dynamics of the change of the self-propulsion direction. The exact probability density of the particle positions at a given time is obtained. From it, the time dependence of the moments, i.e., the mean square displacement and the kurtosis for an arbitrary scattering function, are derived and analysed. Anomalous diffusion is found with a crossover of the scaling exponent from $2\alpha$ in the short-time regime to $\alpha$ in the long-time one, $0<\alpha<1$ being the order of the fractional derivative considered. It is shown that the exact solution found satisfies a fractional diffusion equation that accounts for the non-local and retarded effects of the Laplacian of the probability density function through a coupled temporal and spatial memory function. Such a memory function holds the complete information of the active motion pattern. In the long-time regime, space and time are decoupled in the memory function, and the time fractional telegrapher's equation is recovered. Our results are widely applicable in systems ranging from biological microorganisms to artificially designed self-propelled micrometer particles

Curvature effects on a simplified reaction-diffusion model of biodegradation

The biodegradation process of some types of polymers occurs due to many different factors including their morphology, structure and chemical composition. Although this is a complicated process, most of its important stages like the diffusion of monomers and the hydrolysis reactions have been modeled phenomenologically through reaction-diffusion equations, where the properties of the polymers were encompassed. Using a simplified reaction-diffusion model for the biodegradation of polymers, in this contribution we study the possible effects of the curvature of the system’s geometry in the degradation process, which is characterized by the interaction of the corresponding reaction rate and the diffusion coefficient. To illustrate the problem of diffusion on a curved surface we consider the surface of a cylinder and of the so-called Gaussian bump. We show how the degradation process is affected by the curvature of the system for the simplified model

Eficacia del pronafcap 2010 en la mejora del nivel de desempeño de las docentes de educación inicial de la UGEL 05 - San Juan de Lurigancho - 2011

El propósito de la investigación fue determinar la eficacia que ha tenido el desarrollo del Programa de Formación y Capacitación durante el año 2010, en la mejora del nivel de desempeño docente; para lo cual se analizó el efecto que tuvo en el nivel de desempeño de la población docente del nivel inicial, de las Instituciones Educativas Iniciales de la Jurisdicción de la UGEL Nº 05 del distrito de San Juan de Lurigancho. La investigación básica, de nivel descriptivo y de diseño no experimental, que fue desarrollada mediante un método descriptivo y explicativo, recogió la información del desarrollo del PRONAFCAP 2010 y el desempeño docente de una muestra aleatoria de 140 profesoras y 50 directoras, mediante dos cuestionarios validados por el método de jueces y en los que se estableció que su confiabilidad fue 0.95 y de 0.98 respectivamente, mediante el Coeficiente Alfa de Crombach. El análisis de los datos, permitió llegar a establecer que la eficacia en el desarrollo del PRONAFCAP llegó al 86.5% en las docentes encuestadas; el nivel de desempeño de las docentes que participaron del programa en el 2010, no fue el más adecuado, pues se limitaron a cumplir sus obligaciones sin asumir mayores responsabilidades