Elaboration Of Mathematical Model Research Articles

Simulation of Thermal Field in Eutectic Microwave Bonding for Electrical Connection of Photovoltaic Cells

Sustainable development requires green energy and low carbon footprint in manufacturing sector of photovoltaic systems. The electrical connections of photovoltaic cells need to have low electrical resistance in order to reduce the electrical losses and therefore to improve the performance of the photovoltaic panels. This paper aims to present researches related to bonding of wires that connect solar cells by using microwave technology. The microwave bonding has the main advantage that offers fast bonding but, in the same time, this technology does not offer stability of the thermal heating. Two different unwanted phenomena like thermal runaway and plasma arc discharge often lead to the damaging of copper and aluminum wires used in electrical connection. The study presented in this paper is focused on simulation of the thermal field developed in copper wires in order to optimize the bonding process and increase the quality of products. The simulation of the thermal field has been done using Fourier equations for conducting heating in copper materials and eutectic alloys. The simulation model has been validated through experimental heating using a 6 kW water-cooled microwave generator controlled by a matching load auto-tuner for best transfer of the power from generator to copper wires. The temperature has been measured in real time using an infrared pyrometer for metals with 2.3 μm spectral range and measurement range between 0o C and 7000 C. The study is finalized with elaboration of mathematical model for microwave-injected power as function for temperature developed in copper wires that can be applied with success in further microwave bonding applications of copper wires. In addition, the electrical resistance of bonded wires was measured in order to collect feedback for improving the microwave bonding process.

Mathematical Model Regarding the Application of the Excitation-Emission Matrix Spectroscopy in Nanofiltration Process Using Humic Acid with a TiO2 Ceramic Membrane

A mathematical model regarding water filtration with a nanofiltration (NF) titanium dioxide ceramic membrane is presented. The experiments aimed to use the excitation-emission matrix (EEM) spectroscopy method to highlight the existence of humic acid (HA) in water, before and after the NF process. Following the established operating conditions, experiments were performed for each quantity of AH separately, leaving the installation to work at the appropriate parameters for 15 minutes. for each quantity of AH. The analyzes for EEM fluorescence were performed using the FP-8300 spectrofluorimeter. The collected samples were analyzed with Spectra Manager II software on fluorescence intensity (au - arbitrary units), with an emission wavelength (nm) between 460 and 640 nm and with an excitation wavelength (nm) between 350 and 600 nm. Following the experiments carried out, mathematical correlations were established between the parameters that influence the filtering process and the studied parameters. It is worth mentioning that as a result of the experiments carried out, a number of 20,450 values were obtained, which were used for the elaboration of mathematical models. These models, for sets of values of the order of tens of thousands, verified both from the point of view of the real values and from the point of view of the regression coefficients (coefficients close to the value 1), demonstrate the quantity and the very good quality of the experimental data, respectively of the measured and calculated sizes. In order to validate the generated equations, they were subjected to checks, the difference being obtained between the value obtained by experimental means and the value obtained within the mathematical model. And the value of the resulting relative error, gives information on the accuracy (truth) of the mathematical model, so that it can be extended to other experiences. It turns out that this method cannot quantitatively determine the value of a parameter, but it can highlight the presence and differences between two samples.

Some properties of solutions to a family of integral equations arising in the models of living systems

We consider the well-posedness problem of nonlinear integral and differential equations with delay which arises in the elaboration of mathematical models of living systems. The questions of existence, uniqueness, and nonnegativity of solutions to these systems on an infinite semiaxis are studied as well as continuous dependence of solutions on the initial data on finite time segments.

Formalized pathogenetic model of diagnostics of dysregulation states for transport operators

Our previous researches have showed that the dysregulation state develops for drivers of motor transport after 10 years of work. We actualized the classification of these states and distinguished 6 classes of dysregulation defects with the aid of the cluster analysis Aim. The formation and verification of precision of discrimination of mathematical model of the dysregulation states for drivers of motor transport Methods. The elaboration of mathematical model is realized by means of the usage of the discriminant analysis that makes it possible to recognize the subjects of a research with the previously known classification. The research showed that the procedure of the class discrimination of the dysregulation states for drivers of motor transport can be actualized by using the mathematical model that consists of 6 - linear discriminant functions and that includes 6 indices of the research: Uric acid in a blood serum, Uric acid in urine, Catecholamine, Index of Tension, VLF and LF. Results. The discriminant model based on the training sample includes 6 indices of the research, the classification matrix showed a good precision of the class discrimination of dysregulation states for drivers of motor transport. Thus, the 1st class recognized into 70.9 %, 2nd class – into 98.0 %, 3rd class – into 88.6 %, the 4th class – into 75.7 %, the 5th class – into 100.0% and the 6th class – in 100.0 % cases. There was only 1st class of dysregulation states distinguished worst of all by discriminant model Conclusions. Generally, the level of distinction of 6 classes of dysregulation states for drivers of motor transport by this discriminant model constituted 89.3 % coincidences that let to recommend it for implantation at work of transport enterprises

Similarity and Comparison of the Electrodynamics Characteristics of Switched Reluctance Motors SRM with Those of Series DC Motors

The switched reluctance motor is appreciated in variable speed drives through his simplicity of design, his low cost, his high reliability and high ability to regulate which allow him to compete with the other common types of electric drives. The mathematical modelling of switched reluctance motors (SRM) allows his study in the areas of research and conception. In this paper, we present the developing of a methodology using the combined model of switched reluctance motor drive bases in standard equations of electrical machines with the field theory analysis of magnetic circuit. Then, the elaboration of mathematical models for switching reluctance motor (SRM) proposes his application based on a similarity with series DC motor to simplify the conception of control of electrical drives systems [1] with Closed Loop Control.

Sortir de l'enfer cantorien

Getting away from the Cantorian hell. Having briefly recalled the paradoxes conveyed by the mathematical continuum and the infinite, inherited from the founding works of Cantor and Dedekind, we show that the various mathematical constructivisms, despite their neo-aristotelian inspiration, prove to be unable to escape actualism and mathematical platonism. This problem actually is, not only, one the key problems in the philosophy of mathematics, but also a problem to the solution of which cognitive science may greatly contribute. The role played by topology in the field of mathematics as well as in the elaboration of mathematical models in cognitive science is typical of this submission to the set-theoretical orthodoxy (punctiform continuum, actual infinite). Locology may be seen as an alternative to topology, a new Analysis situs. Localistic logic, which is based upon the locological substratum, aims at redefining the outline of logical and mathematical constructivism.

Thermal-dynamic analogy method in calorimetry

The paper describes the fundamentals and applications of the thermal-dynamic analogy method to analyze the course of heat effects occurring in calorimeters. The method is based on introduction to the heat effect analysis of the terms, notions and mathematical procedures used in the steering theory. It was pointed out that this method can well be applied for elaboration of mathematical models of various types of calorimeters. These models determine both the heat properties of calorimeters as well as the dynamic ones.