Renormalization group approach to nonextensive statistical mechanics

We analyze a simple classical Hamiltonian system within the hypothesis of renormalizability and isotropy that essentially led Maxwell to his ubiquitous Gaussian distribution of velocities. We show that the equilibrium-like power-law energy distribution emerging within nonextensive statistical mechanics satisfies these hypothesis, in spite of not being factorizable. A physically satisfactory renormalization group emerges in the $(q, T_q)$ space, where q and $T_q$ respectively are the entropic index characterizing nonextensivity, and an appropriate temperature. This scenario enables the conjectural formulation of the one to be expected for d-dimensional systems involving long-range interactions (e.g., a classical two-body potential $\propto r^{-\alpha}$ with $0 \le \alpha/d \le 1$). As a corollary, we recover a quite general expression for the classical principle of equipartition of energy for arbitrary q.Comment: 4 pages, 3 ps figure

Medición precisa de temperaturas altas y emisividad espectral normal en metales

Se presentan los detalles de un método experimental para efectuar mediciones precisas de altas temperaturas y de la emisividad espectral normal de metales. Como una aplicación de las técnicas propuestas se estudia la influencia de la temperatura en la emisividad normal espectral de renio en el rango comprendido entre 1.500 y 2.500 K, a intervalos de 100 K. Los experimentos se realizaron utilizando un espécimen en forma de disco de 5 mm de altura y 17 mm de diámetro. Una cavidad circular cilfndrica perforada radia/mente en el espécimen se usó como cuerpo negro para determinar la temperatura real. Los resultados experimentales indican que las temperaturas real y aparente pueden medirse con una incertidumbre relativa igual a O, 19 y 0,06%, respectivamente, cuando se utiliza una cavidad cilíndrica con una relación largodiámetro mayor o igual que JO. Se determina que la emisividad espectral normal (A = 0,535 ¡J.m) disminuye linealmente con aumentos de temperatura y se demuestra que el uso de un pirómetro contador de fotones conduce a la obtención de resultados experimentales muy precisos para la emisividad normal espectral (incertidumbre relativa igual a 2 ,5%)

Photovoltaic module on-orbit assembly for Space Station Freedom

One of the elements of the Space Station Freedom power system is the Photovoltaic (PV) module. These modules will be assembled on-orbit during the assembly phase of the program. These modules will be assembled either from the shuttle orbiter or from the Mobile Servicing Center (MSC). The different types of assembly operations that will be used to assemble PV Modules are described

Preparación de precursores de boroxicarbenos de renio

El trabajo realizado en el Grupo de Investigación Reconocida de Moléculas Inorgánicas y Organometálicas con Metales de Transición (GIR MIOMeT) durante el presente Trabajo Fin de Grado ha perseguido el objetivo de preparar precursores para la síntesis de boroxicarbenos de renio. En primer lugar se obtuvieron los complejos de partida necesarios para producir los precursores y a continuación, se realizó la síntesis del compuesto fac[ReBr(CO)3(pyC(H)=O)]. Una vez obtenido este compuesto, se continuó con la síntesis de fac-[ReBr(CO)3(pyC(H)=NCH2CH=CH2)]. En el transcurso de la producción de los precursores, se encontró de manera fortuita el complejo hemiaminal fac-[ReBr(CO)3(pyC(OH)-NCH2CH=CH2)], el cual es un compuesto intermedio de uno de los complejos deseados (la imina). Este descubrimiento condujo a una minuciosa investigación del mismo, pudiendo conseguir entre otros datos, la estructura de Rayos X. Además, también se consiguió caracterizar el complejo fac[Re(CNXyl)(CO)3(pyC(OH)-NCH2CH=CH2)]. Debido al relativo éxito con el que se estaban consiguiendo estos compuestos, se decidió continuar la investigación en la hidroboración del complejo fac[ReBr(CO)3(pyC(H)=NCH2CH=CH2)] con 9-BBN, lo cual estaba fuera de las pretensiones iniciales del trabajo.Grado en Químic

Scale-adjusted metrics for predicting the evolution of urban indicators and quantifying the performance of cities

More than a half of world population is now living in cities and this number is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific characterization of cities and for the availability of an unprecedented amount of data, academics have recently immersed in this topic and one of the most striking and universal finding was the discovery of robust allometric scaling laws between several urban indicators and the population size. Despite that, most governmental reports and several academic works still ignore these nonlinearities by often analyzing the raw or the per capita value of urban indicators, a practice that actually makes the urban metrics biased towards small or large cities depending on whether we have super or sublinear allometries. By following the ideas of Bettencourt et al., we account for this bias by evaluating the difference between the actual value of an urban indicator and the value expected by the allometry with the population size. We show that this scale-adjusted metric provides a more appropriate/informative summary of the evolution of urban indicators and reveals patterns that do not appear in the evolution of per capita values of indicators obtained from Brazilian cities. We also show that these scale-adjusted metrics are strongly correlated with their past values by a linear correspondence and that they also display crosscorrelations among themselves. Simple linear models account for 31%-97% of the observed variance in data and correctly reproduce the average of the scale-adjusted metric when grouping the cities in above and below the allometric laws. We further employ these models to forecast future values of urban indicators and, by visualizing the predicted changes, we verify the emergence of spatial clusters characterized by regions of the Brazilian territory where we expect an increase or a decrease in the values of urban indicators.Comment: Accepted for publication in PLoS ON

Nonextensive Thermostatistical Investigation of The Blackbody Radiation

Thermodynamical quantities of the blackbody radiation, such as free energy, entropy, total radiation energy, specific heat are calculated within the Tsallis thermostatistics where factorization method is incorparated. It is shown that basic thermodynamical relation of the blackbody radiation is form invariant with respect to nonextensivity entropic index q. Furthermore, the nonextensive thermodynamical quantities related to the blackbody radiation is seperately be obtained in terms of q and the standard thermodynamical quantities of the blackbody radiation .It is indicated that the formulation may give a way to determine the q which determines the degree of the nonextensivity that is the one of the aims of the present study.Comment: 16 pages,No figures,to be appear in Chaos,Solitons&Fractal

Non-extensive study of Rigid and Non-rigid Rotators

The isotropic rigid and non-rigid rotators in the framework of Tsallis statistics are studied in the high and low temperature limits. The generalized partition functions, internal energies and heat capacities are calculated. It has been found that results are in well agreement with the classical Boltzmann-Gibbs statistics in the limiting Tsallis index. It has also been observed that nonextensivity parameter q behaves like a scale parameter in the low temperature regime.Comment: 11 Pages, 3 Figures, Late