Analytical Solving a Nonlinear Model of the Glow Discharge

A nonlinear model has been introduced for the positive column of DC glow discharge in apure sealed, or low flow, gas media by including the diffusion, recombination, attachment, detachment,process and having the two-step ionization process of the metastable excited states, too. By thecombination of the system of the nonlinear continuity equations of the system, using some physicalestimations, and degrading the resulted nonlinear PDE in polar and rectangular systems of coordinatethe steady-state nonlinear ODE have been derived. Using a series-based solution, an innovativenonlinear recursion relation has been proposed for calculating the sentence of series. Using the stateof elimination of free charge on the outer boundary of the discharge vessel, the universal equation ofthe characteristic energy of the electrons versus the similarity variable, using the maximum degree ofionization as the parameter, has been derived.

UNIVERSAL METHOD OF CALCULATION OF MULTISPAN BEAMS

The supporting structures of machines and mechanisms of metallurgical equipment, which are characterized by large dimensions, in the calculation scheme can be reduced to multispan beams, which are statically indeterminate. Traditionally, the disclosure of their static uncertainty is based on the graphoanalytical method, which is called "Equation of 3 moments". According to this method, the equations of three points are solved by constructing intermediate epure of bending moments, finding their areas and position of the centers of gravity. These procedures lead to an unreasonable increase in time to solve the problem. It is advisable to have an analytical method for detecting static uncertainty of multispan beams, which would be free from graphical constructions and would significantly reduce the time to solve the problem. At the present stage, the calculation of complex spatial structures is carried out using the calculation and software systems "LIRA", "SCAD" and others. However, this in no way limits the need for the application in engineering practice of simple analytical methods, which include a universal method for detecting static indeterminateness of multispan beams. Additional, to the static equations, the equations of displacement are compiled using the universal equation of the bent axis of the beam, and the number of beams can be any large. Different variants of boundary conditions are considered. The results of the considered examples prove the independence of the values ​of "extra" unknown from the stiffness of the beam. The universal method is quite optimal, as it uses a very simple universal equation of the bent axis of the beam and, with each subsequent additional equation of displacement differs from the previous one only by adding another item with a new load. This approach provides the optimal solution to almost any problem, by revealing the static indeterminateness of multispan beams.

Thermodynamic Discrimination Between Energy Sources for Chemical Reactions

Chemical transformations traverse large energy differences, yet the choice of energy source to drive a chemical reaction is often decided on a case-by-case basis; there is no fundamentally-driven, universal framework with which to analyze and compare the choice of energy source for chemical reactions. In this work, we present a reaction-independent expression for the equilibrium constant as a function of temperature, pressure, and voltage. With a specific set of axes, all reactions can be represented by a single (x,y) point and a quantitative divide between electrochemically and thermochemically driven reactions is visually evident. In addition, we show that our expression has a strong physical basis in work and energy fluxes to the system, although more specific data about reaction operation is necessary to provide a quantitative energy analysis. Overall, this universal equation and facile visualization of chemical reactions enables quick and informed justification for electrochemical versus thermochemical energy sources without knowledge of detailed process parameters.

Thermodynamic Discrimination Between Energy Sources for Chemical Reactions

Chemical transformations traverse large energy differences, yet the choice of energy source to drive a chemical reaction is often decided on a case-by-case basis; there is no fundamentally-driven, universal framework with which to analyze and compare the choice of energy source for chemical reactions. In this work, we present a reaction-independent expression for the equilibrium constant as a function of temperature, pressure, and voltage. With a specific set of axes, all reactions can be represented by a single (x,y) point and a quantitative divide between electrochemically and thermochemically driven reactions is visually evident. In addition, we show that our expression has a strong physical basis in work and energy fluxes to the system, although more specific data about reaction operation is necessary to provide a quantitative energy analysis. Overall, this universal equation and facile visualization of chemical reactions enables quick and informed justification for electrochemical versus thermochemical energy sources without knowledge of detailed process parameters.

Dark Solitons in the Unitary Bose Gas

We study the dilute and ultracold unitary Bose gas, characterized by a universal equation of state due to the diverging s-wave scattering length, under a transverse harmonic confinement. From the hydrodynamic equations of superfluids we derive an effective one-dimensional nonpolynomial Schrödinger equation (1D NPSE) for the axial wavefunction which, however, also takes into account the transverse wavefunction. By solving the 1D NPSE we obtain meaningful analytical formulas for the dark (gray and black) solitons of the bosonic system.

Uso de Técnicas de Geoprocessamento para Estudo da Erosão Hídrica Laminar em Bacia Hidrográfica do Sudoeste do Paraná.

Este trabalho tem como objetivo avaliar a erosão hídrica laminar do solo, por meio da Equação Universal de Perdas de Solos Revisada (RUSLE) na bacia hidrográfica do rio São José, localizada no município de Francisco Beltrão (PR). A perda de solo média anual (A) foi determinada através da RUSLE para os anos 2000, 2005, 2009, 2015 e 2017 utilizando-se técnicas de geoprocessamento com o auxílio do software ArcGis 10.0. O fator erosividade da chuva (R) foi determinado utilizando-se dados pluviométricos correspondentes ao período de 1974 a 2016. O fator erodibilidade do solo (K) foi obtido através da análise de amostras de solo coletadas in loco. O fator topográfico (LS) foi estimado por meio dos dados altimétricos e hidrográficos da bacia. Os fatores de uso e manejo do solo (C) e de práticas conservacionistas do solo (P) foram determinados por meio da caracterização multitemporal do uso e ocupação do solo, através de imagens de satélite. O potencial natural de erosão (PNE) foi determinado pela multiplicação dos fatores R, K e LS.A estimativa de perda de solo (A) foi determinada pela multiplicação do PNE pelos fatores C e P. Use of Geoprocessing Techniques to Study Laminar Water Erosion in Watershed of Southwest Paraná A B S T R A C TThe objective of this work is evaluate the soil erosion by the Universal Equation of Soil Losses Revised (RUSLE) in the São José river basin, located in the municipality of Francisco Beltrão (PR). The average annual soil loss (A) was determined through RUSLE for the years 2000, 2005, 2009, 2015 and 2017 using geoprocessing techniques with ArcGis 10.0 software. Rainfallerosivity (R) was determined using rainfall data from 1974 to 2016, being determined at 11521.26 11521,26 MJ.mm.ha-1.h-1.year-1. The soil erodibility factor (K) was obtained through the analysis of soil samples collected on the spot (0,03018 t.ha.h/ha.MJ.mm, 0,02771 t.ha.h/ha.MJ.mm e 0,02342 t.ha.h/ha.MJ.mm). The topographic factor (LS) was estimated by the altimetric and hydrographic data of the basin. Soil use and management (C) and soil conservation (P) were determined through multitemporal characterization of land use and occupation, using satellite images. The natural erosion potential (NEP) was determined by multiplying the R, K and LS factors, with more than half of the total area of the watershed with very strong PNE. The soil loss estimate (A) was determined by multiplying the NEP by factors C and P with predominance of the class called low (0 to 10 t/ha/year) denoting the reduction of erosion rates through factors C and P, helping to protect the soil from the erosion process.Key words: Soil Erosion; Watershed, Revised Universal Soil Loss Equation, Geoprocessing, Software.