Papers by Keyword: Mathematical Model

Abstract: The computational studies of a predictive mathematical model for the extraction of interstitial (ISF) for transdermal and non-invasive diagnosis using biodegradable and hollow microneedle patch is presented in this paper. Rapid Diagnostic Tests diagnosis, which is non-invasive, affordable, straightforward, and provides results promptly and reliably, has increased access to parasite-based analysis on a global scale. Microneedle arrays are a rapidly evolving and promising technology for transdermal interstitial fluid extraction, which is used for many clinical diagnostic procedures. Hence, a developed mathematical predictive model used to optimize the design of microneedle patch for transdermal ISF extraction and subsequent diagnosis using dissolvable microneedle arrays was applied in this study. The model's solutions were obtained using the Differential Transform Method. The numerical Runge-Kutta method of fourth order was used to validate it. An experimental test result was also used to further validate the analytical results in the absence of the extracted velocity parameter. And there was a good agreement among them. Influence of dissolution rate constant, microneedle height, diffusion coefficient, velocity of ISF, microneedle ISF drug load, and density of the microneedle; were investigated. Increase in diffusion coefficient and density led to an increase in concentration of ISF extracted over time, an increase in dissolution rate led to a decrease in concentration extracted, while decrease in drug load and height, led to increase in ISF concentration extracted. A negligible effect was observed by varying the velocity of ISF extracted. The approximate analytical approach utilized in the current work has given us a more precise strategy for creating a mathematical model that predicts how ISF will be extracted from skin for use in transdermal and non-invasive rapid diagnostic tests.

Abstract: The article analyzes the state of the global problem of the fuel and energy crisis and environmental pollution by the combustion products of hydrocarbon fuels of industrial and transport power plants. To ensure the energy security of the state, the Cabinet of Ministers of Ukraine developed and adopted the «Energy Strategy of Energy Saving of Ukraine for the period until 2030», which was updated in 2008, to protect the country from energy risks. In addition, the Cabinet of Ministers of Ukraine approved the «Concept of a targeted scientific and technical program for the development of the production and use of biological fuels». To increase the efficiency of using alternative motor fuels, as one of the aspects of solving the problem, an original method and results of calculating the thermophysical properties of a wide class of such motor fuels (hydrogen, natural gas, biogas, mine gas, coke, blast furnace and synthesis gas, etc.) are proposed. A description of the developed mathematical model for determining parameters of phase equilibria and thermophysical properties of dense molecular systems (dense gases and liquids) is given. Calculation procedures are based on the thermodynamic theory of disturbances without the involvement of empirical parameters. Features of the proposed method are: limitation of initial information, high accuracy, the possibility of application in any practically important ranges of states. Calculation errors are at the level of traditional experimental errors.

Abstract: The CNC milling process is one of the most valuable traditional machining processes for machining hardened material by using various coated end mill tools. The attention of the current study has been done on end milling of hardened AISI D2 tool steel which is a commonly used tool steel grade in a press machine. The material removal rate is an essential aspect of improving productivity and reducing lead time and production costs. MRR has been considered as a response in this experimental work. A number of experiments were conducted using the design of the experiment via response surface methodology (RSM). MRR was calculated for each machining performance. A mathematical model of MRR was found using response surface methodology.

Abstract: The research objective is to simplify the method for estimating the density of straight-run hydrotreated winter diesel fuel (HTDFWs). The density of straight-run hydrotreated winter diesel fuel is one of the quality indicators ultimately determining the density of winter diesel fuel and therefore, the quality of winter diesel fuel in terms of density. Problems: to describe the current methodology for estimating the HTDFWs’ density, isolate the cycles, and express the cycles by formulas. Research methods – analysis, synthesis, comparison, mathematical analysis. As a result, simplified density calculation with expressing cycles by formulas has been proposed. A mathematical model has been obtained to estimate the density of straight-run hydrotreated winter diesel fuel.

Abstract: In order to expand the possibilities of practical application of polymeric materials we studied syndiotactic 1,2-polybutadiene (1,2-SPB). The experimental procedure and the MV-002 device for determining the breakdown voltage and electrical breakdown of a polymer are described in detail. Mathematical models of the dependence of the breakdown voltage of the polymer on the frequency and magnitude of the electrical breakdown of the polymer on the thickness of the sample have been built and studied. Regression analysis was used for mathematical data processing. The reliability of the results obtained is proved by the methods of test statistics.

Abstract: In this work, the objects of research are individual chemical substances and multicomponent mixtures (gaseous and liquid) used in extinguishing fires.The design of automatic gas fire extinguishing installations is associated with the solution of many scientific and technical issues and is based on the calculation and forecasting of such important data as the thermophysical properties of individual substances and mixtures consisting of them. Phase equilibria parameters data are of particular interest. Also, such data are necessary for scientific and practical research in the creation of the latest, more progressive fire extinguishing agents. It is often difficult or simply impossible to obtain experimentally thermophysical characteristics and parameters of phase equilibria for a wide range of states. Moreover, experimental information is expensive and time-consuming.The work is dedicated to the development of theoretical methods for determining the parameters of phase equilibria of both individual chemicals used to extinguish fires and multicomponent fire-extinguishing mixtures. The use of the proposed techniques makes it possible to obtain numerical values of the required characteristics of fire extinguishing agents by calculation with the required accuracy using a minimum of initial data.The method of mathematical modeling makes it possible to obtain a mathematical model of phase equilibria based on thermodynamic perturbation theory in order to determine the basic functions of the state in the absence of empirical parameters.The proposed method for calculating the parameters of phase diagrams for multi component fire-extinguishing mixtures was used to determine the thermodynamic parameters of the ozone-safe fire-extinguishing composition.

Abstract: The influence of the process of fire-retardant coating on textiles on the degree of fire protection of cotton and blended fabrics is investigated. Physical-chemical properties of impregnated samples of textile materials depending on the composition of ethyl silicate hydrolysates, concentration and content of diammonium hydrogen phosphate on fire resistance of impregnated samples, time of onset destruction and area of charring of samples after fire tests are analyzed. The obtained experimental data showed the need to build a mathematical model of the protective action of the gel coating based on the laws of heat and mass transfer, which under conditions of maximum simplicity and minimal artificiality takes into account the main processes from the external heat flow processes of heat transfer, thermal decomposition, evaporation and removal of mass, as well as to develop algorithms and software for computer modeling of the protective action of such a coating in conditions of constant or dynamic thermal exposure. A mathematical model of fire-retardant action of organosilicon coating on cellulose-containing fiber of fabric threads has been developed. It provides predictive estimates of fire safety parameters of textile materials, based on the level of thermal impact on the surface of the protected material.

Abstract: This paper considers the basic methods of physical-mathematical modeling that are used to describe the processes of non-stationary mass transfer of "free calcium hydroxide" in concrete structures placed in a liquid environment with a defined flow rate. The boundary value problem of "free calcium hydroxide" mass conductivity in dimensionless variables is obtained. To demonstrate the possibilities of the obtained solution, we will carry out a numerical experiment: in which the fluctuation in the field of dimensionless concentrations by the different values of the Fourier number, in accordance with the theory of similarity, will be considered as an indicator of the process time. The study indicated the results of calculating the concentration distributions "free calcium hydroxide" over the dimensionless thickness of the concrete structure at Fourier numbers 0.01; 0.1; 0.2; 0.5 and 1. The study also provides an example of determining the time of reaching the coastal structure surface critical concentration "of free calcium hydroxide" leading to the beginning of high-basic cement concrete. Analysis of the solution also makes it possible to determine the duration of the service life of a reinforced concrete structure, which is determined by the processes occurring at the interface: in concrete - mass conductivity (k), and in the liquid phase - mass transfer (β).

Abstract: The article outlines the method of digital simulation of electrochemical processing, which allows calculating the shape of the electrode-tool in conjunction with the mode, taking into account the real conditions of processing. The technique allows you to ensure the maximum possible performance with specified processing accuracy and limitations that exclude critical phenomena in the channel between electrodes during intensification of modes. Mathematically, the task is presented in the form of minimax problem with application of penalty functions.

Abstract: To study the face milling of hardened steel, the paper considers the chemical composition of the processed material, as well as metal-cutting, measuring equipment and tools. A full factorial experiment of face milling was carried out by the method of mathematical planning and matrices of levels of variation and planning of independent variables were compiled. The flatness of the samples was measured and the causes of plastic deformation were determined. To find an adequate mathematical model of flatness, a regression analysis was performed, and the correlation analysis revealed the closeness of the relationship between the variables under one-and two-factor influence on the response function. The hypersurfaces and lines of the function levels are projected, which made it possible to determine the optimal and effective cutting conditions graphically and analytically.