Propagation Analysis of the Coronavirus Pandemic on the Light of the Percolation Theory

Efforts to combat the Covid-19 pandemic have not been limited to the processes of vaccine production, but they first began to analyze the dynamics of the epidemic’s spread so that they could adopt barrier measures to bypass the spread. To do this, the works of modeling, predicting and analyzing the spread of the virus continue to increase day after day. In this context, the aim of this chapter is to analyze the propagation of the Coronavirus pandemic by using the percolation theory. In fact, an analogy was established between the electrical conductivity of reverse micelles under temperature variation and the spread of the Coronavirus pandemic. So, the percolation theory was used to describe the cumulate infected people versus time by using a modified Sigmoid Boltzman equation (MSBE) and several quantities are introduced such as: the pandemic percolation time, the maximum infected people, the time constant and the characteristic contamination frequency deduced from Arrhenius equation. Scaling laws and critical exponents are introduced to describe the spread nature near the percolation time. The speed of propagation is also proposed and expressed. The novel approach based on the percolation theory was used to study the Coronavirus (Covid-19) spread in five countries: France, Italy, Germany, China and Tunisia, during 6 months of the pandemic spread (the first wave). So, an explicit expression connecting the number of people infected versus time is proposed to analyze the pandemic percolation. The reported MSBE fit results for the studied countries showed high accuracy.

On the Connection of Cascade-Probability Function on the Formation of Primary-Knocked on Atoms for Ions Taking into Account Energy Losses with a Boltzman Equation

The integral-differential equation of the cascade process for ions was solved using the Laplace transform and the method of successive approximations, taking into account the energy loss during the formation of primary-knocked-on atoms (PKA) in a one-dimensional model of an elementary atom. It is shown that the solution includes a cascade-probability function (CPF) for these particles. The main properties of CPF are considered and its graphical dependencies on the depth of registration are presented. It is shown that with the specific ionization loss coefficient k = 0, the FQM turns into the simplest cascade-probability function. When λ0→ 0, λ0→∞ and n→∞, the KV-function is equal to 0. The sum of the probabilities for all possible collisions from 0 to ∞ is 1. As the detection depth h increases, for all values of n, the CRF increases, reaches a maximum and then decreases . With increasing n, the curves shift to the right.

Generation of circular polarization of CMB from the Euler–Heisenberg Lagrangian

It is known that the dominated contribution of primordial anisotropies of cosmic microwave background (CMB) are linearly polarized via Compton scattering. However, circular polarization of this anisotropy has not been observed up to now, but it has not been excluded in observational evidences. Here we show that the Euler–Heisenberg effective Lagrangian can generate circular polarization in CMB. This generation is calculated by using the quantum Boltzman equation for time evolution of the Stokes parameter. Also we estimate Faraday conversion phase on the order of 10−13 due to this Lagrangian, which gives a lower bound on circular polarization of CMB.

Electrical Conductivity Modeling of Polypropylene Composites Filled with Carbon Black and Acetylene Black

Composites of polypropylene filled with carbon black or acetylene black at different concentrations were prepared by melt mixing followed by compression molding. The influences of filler type and filler concentration on the composites conductivity were studied. It was found that the percolation threshold is located at a lower concentration in composites filled with the acetylene black, than that of the composites filled with carbon black. The model of Mamunya gives a fairly good agreement in the evaluation of the conductivity of polymeric composites loaded with carbon black or acetylene black, beyond the percolation threshold. The Boltzman equation was adopted to develop a model that represents more faithfully all results obtained. The expressions of the electrical conductivity, calculated with the model developed, are in good agreement with experimental results for the entire concentration range studied in linear or semilogarithmic scale.

Development of Code, PNFENT, Based on Using Finite Elements for Neutron Transport

A variational treatment of the finite element method for neutron transport is used based on a version of the even parity Boltzman equation for the general case of anisotropic scattering and sources. The theory of maximum principles is based on the Cauchy-Schwartz inequality and the properties of a leakage operator G and a removal operator C. For system with extraneous sources a maximum principle is used in boundary free form to ease finite element computations. The global error of an approximate variational solution is shown. The energy dependence of the angular flux is treated by the multi-group method. In this paper the spatial dependence of the angular flux is given in a finite element representation. The directional dependence of angular flux is represented preferably by a spherical harmonic expansion. The above method has been developed and implemented in the finite element program PNFENT. A homogenous slab of a pure absorber along edge-cell and a two dimensional problems are solved with an accuracy as good as the best problem techniques.