Generalized Kinetic Theory of Electrons and Phonons

A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium solutions and their stability are investigated.Comment: Proceedings of the International School and Workshop on Nonextensive Thermodynamics and Physical Applications, NEXT 2001, 23-30 May 2001, Cagliari (Italy) (To appear in Physica A

Generalized Kinetic Equations for a System of Interacting Atoms and Photons: Theory and Simulations

In the present paper we introduce generalized kinetic equations describing the dynamics of a system of interacting gas and photons obeying to a very general statistics. In the space homogeneous case we study the equilibrium state of the system and investigate its stability by means of Lyapounov's theory. Two physically relevant situations are discussed in details: photons in a background gas and atoms in a background radiation. After having dropped the statistics generalization for atoms but keeping the statistics generalization for photons, in the zero order Chapmann-Enskog approximation, we present two numerical simulations where the system, initially at equilibrium, is perturbed by an external isotropic Dirac's delta and by a constant source of photons.Comment: 24 pages, 4 figures, IOP macro style, accepted on J. Phys. A: Math. Ge

Generalized Kinetic Theory of Electrons and Phonons: Models, Equilibrium, Stability

In the present paper our aim is to introduce some models for the generalization of the kinetic theory of electrons and phonons (KTEP), as well as to study equilibrium solutions and their stability for the generalized KTEP (GKTEP) equations. We consider a couple of models, relevant to non standard quantum statistics, which give rise to inverse power law decays of the distribution function with respect to energy. In the case of electrons in a phonon background, equilibrium and stability are investigated by means of Lyapounov theory. Connections with thermodynamics are pointed out.Comment: 10 pages, 2 figures, (RevTeX4), to appear in Physica B (2003

Travelling waves in a mixture of gases with bimolecular reversible reactions

Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by means of the relevant Boltzmann-like equation. Conservation laws are considered. Fluid dynamic approximations are used at the Euler level to obtain a close set of PDEs for six unknown macroscopic fields. The dispersion relation of the mixture of reacting gases is explicitly derived in the homogeneous equilibrium state. A set of ODE that governs the propagation of a plane travelling wave is obtained using the Galilei invariance. After numerical integration some solutions, including the well-known Maxwellian and the hard spheres cases, are found for various meaningful interaction laws. The main macroscopic observables for the gas mixture such as the drift velocity, temperature, total density, pressure and its chemical composition are shown.Comment: 13 pages, 2 figures, accepted on Physica

Generalized Pearson distributions for charged particles interacting with an electric and/or a magnetic field

The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meaningful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed.Comment: 24 pages, version accepted on Physica

COVID-19: Revisión de la literatura y su impacto en la realidad sanitaria peruana: COVID-19: Literature review and its impact on the Peruvian health reality

Introduction: The disease called COVID-19 is a pandemic caused by the SARS-CoV-2 virus (severe acute respiratory syndrome 2). In Peru, patient zero or first case with COVID-19 was detected on March 6 and since then the virus has continued to spread. The national government fights against this disease on several fronts, but the health situation differs greatly from developed countries. Objective: To review the current state of the disease and analyze its possible impact on the Peruvian health system. Methods: A bibliographic search of various studies was carried out since the appearance of the disease (December 2019) in the different databases (PUBMED, MEDLINE, PLOs, SciELO) and in Google Scholar. Results: It was found that the virus is transmitted mainly by the respiratory route; the average incubation period is 14 days; most patients have mild disease or are asymptomatic but 5% of these will require hospitalization, some will even require intensive therapy with mechanical ventilation; the current treatment is basically symptomatic, but antibiotics, antivirals and antiparasitics have also been used. Conclusions: The quarantine with strict measures of isolation and social distancing is accurate given the Peruvian health reality and the imminent contagion of the population.Introducción: La enfermedad denominada COVID-19 es una pandemia causada por el virus SARS-CoV-2 (síndrome agudo respiratorio severo 2). En el Perú, el paciente cero o primer caso con COVID-19 fue detectado el último 6 de marzo y desde entonces el virus continúa su propagación. El gobierno nacional lucha contra esta enfermedad desde varios frentes, pero la situación sanitaria difiere mucho con la de países desarrollados. Objetivo: Revisar el estado actual de la enfermedad y analizar su posible impacto en el sistema de salud peruano. Métodos: Se realizó una búsqueda bibliográfica de diversos estudios desde la aparición de la enfermedad (diciembre 2019) en las diferentes bases de datos (PUBMED, MEDLINE, PLOs, SciELO) y también en Google Académico. Resultados: Se encontró que el virus se trasmite principalmente por vía respiratoria; el periodo de incubación promedio es 14 días; la mayoría de los pacientes tienen una enfermedad leve o son asintomáticos pero un 5% de estos requerirá hospitalización, algunos incluso requerirán terapia intensiva con ventilación mecánica; el tratamiento actual es básicamente sintomático, pero también antibióticos, antivirales y antiparasitarios. Conclusiones: La cuarentena con medidas estrictas de aislamiento y distanciamiento social es precisa, dada la realidad sanitaria peruana y el inminente contagio de la población

Relativistic kinetics and power-law tailed distributions

The present paper is devoted to the relativistic statistical theory, introduced in Phys. Rev. E {\bf 66} (2002) 056125 and Phys. Rev. E {\bf 72} (2005) 036108, predicting the particle distribution function $p(E)= \exp_{\kappa} (-\beta[E-\mu])$ with $\exp_{\kappa}(x)=(\sqrt{1+ \kappa^2 x^2}+\kappa x)^{1/\kappa}$, and $\kappa^2<1$. This, experimentally observed, relativistic distribution, at low energies behaves as the exponential, Maxwell-Boltzmann classical distribution, while at high energies presents power law tails. Here, we obtain the evolution equation, conducting asymptotically to the above distribution, by using a new deductive procedure, starting from the relativistic BBGKY hierarchy and by employing the relativistic molecular chaos hypothesis.Comment: 5 two-column page

On modified simple reacting spheres kinetic model for chemically reactive gases

Versão dos autores para esta publicação.We consider the modiffed simple reacting spheres (MSRS) kinetic model that, in addition to the conservation of energy and momentum, also preserves the angular momentum in the collisional processes. In contrast to the line-of-center models or chemical reactive models considered in [1], in the MSRS (SRS) kinetic models, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justi ed. In the MSRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard spheres-like. We consider a four component mixture A, B, A*, B*, in which the chemical reactions are of the type A + B = A* + B*, with A* and B* being distinct species from A and B. We provide fundamental physical and mathematical properties of the MSRS model, concerning the consistency of the model, the entropy inequality for the reactive system, the characterization of the equilibrium solutions, the macroscopic setting of the model and the spatially homogeneous evolution. Moreover, we show that the MSRS kinetic model reduces to the previously considered SRS model (e.g., [2], [3]) if the reduced masses of the reacting pairs are the same before and after collisions, and state in the Appendix the more important properties of the SRS system.Fundação para a Ciência e a Tecnologi

Generalized balance equations for anelectron-phonon system

A new model, based on an asymptotic procedure for solving the generalized kinetic equations of electrons and phonons, is proposed, which gives naturally the displaced Maxwellian at the leading order. The balance equations for the electron number, total energy density and total momentum for the whole system constitute now, together with Poisson equation, a system of four equations for the electron chemical potential, the temperature of the system, the drift velocity and the electric potential. In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered

Polysoliton solutions for plane discrete velocity models of a gas with chemical reactions

Exact polysoliton solutions are given for plane discrete velocity models of a gas with chemical reactions. A technique due to Osland and Wu is systematically applied [3]