scholarly journals RESEARCH AND MATHEMATICAL MODELING OF FRACTIONAL-DIFFERENTIAL RHEOLOGICAL MODELS

2021 ◽  
Vol 3 (1) ◽  
pp. 1-10
Author(s):  
Yaroslav Sokolovskyy ◽  
◽  
Mariana Levkovych ◽  
Yaroslav Kaspryshyn ◽  
◽  
...  
Keyword(s):  
Mass Transfer ◽  
Mathematical Models ◽  
Rheological Properties ◽  
Fractal Structure ◽  
Early Stage ◽  
Mathematical Methods ◽  
Viscoelastic Deformation ◽  
Rheological Models ◽  
Fractal Media ◽  
Fractional Differential

Deformation processes in media with fractal structure have been studied. At present, research on the construction of mathematical methods and models of interconnected deformation-relaxation and heat-mass transfer processes in environments with a fractal structure is at an early stage. There are a number of unsolved problems, in particular, the problem of correct and physically meaningful setting of initial and boundary conditions for nonlocal mathematical models of nonequilibrium processes in environments with fractal structure remains unsolved. To develop adequate mathematical models of heat and mass transfer and viscoelastic deformation in environments with fractal structure, which are characterized by the effects of memory, self-organization and spatial nonlocality, deterministic chaos and variability of rheological properties of the material, it is necessary to use non-traditional approaches. -differential operators. The presence of a fractional derivative in differential equations over time characterizes the effects of memory (eridity) or non-marking of modeling processes. The implementation of mathematical models can be carried out by both analytical and numerical methods. In particular, in this paper the integral form of fractional-differential rheological models is obtained on the basis of using the properties of the non-integer integral-differentiation operator and the Laplace transform method. The obtained analytical solutions of mathematical models of deformation in viscoelastic fractal media made it possible to obtain thermodynamic functions, creep nuclei and fractal-type relaxation. Developed software to study the effect of fractional differentiation parameters on the rheological properties of viscoelastic media.

An Overview: Analysis of Heat and Mass Transfer in Fractal Media by Fractal Geometry and Technique

2010 ◽  
Author(s):  
Boming Yu
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Porous Media ◽  
Heat And Mass Transfer ◽  
Oil Recovery ◽  
Fractal Geometry ◽  
Boiling Heat Transfer ◽  
Nucleate Boiling ◽  
Fractal Media ◽  
Nucleate Boiling Heat Transfer

In the past three decades, fractal geometry and technique have received considerable attention due to its wide applications in sciences and technologies such as in physics, mathematics, geophysics, oil recovery, material science and engineering, flow and heat and mass transfer in porous media etc. The fractal geometry and technique may become particularly powerful when they are applied to deal with random and disordered media such as porous media, nanofluids, nucleate boiling heat transfer. In this paper, a summary of recent advances is presented in the areas of heat and mass transfer in fractal media by fractal geometry technique. The present overview includes a brief summary of the fractal geometry technique applied in the areas of heat and mass transfer; thermal conductivities of porous media and nanofluids; nucleate boiling heat transfer. A few comments are made with respect to the theoretical studies that should be made in the future.

Laboratory Experiments of Mass Transfer in the London Clay

1988 ◽  
Vol 127 ◽  
Author(s):  
P. J. Bourke ◽  
D. Gilling ◽  
N. L. Jefferies ◽  
D. A. Lever ◽  
T. R. Lineham
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Radioactive Waste ◽  
Mass Transport ◽  
Mathematical Models ◽  
Laboratory Experiments ◽  
Naturally Occurring ◽  
Diffusion And Convection ◽  
Waste Repository ◽  
London Clay

ABSTRACTAqueous phase mass transfer through the rocks surrounding a radioactive waste repository will take place by diffusion and convection. This paper presents a comprehensive set of measurements of the mass transfer characteristics for a single, naturally occurring, clay. These data have been compared with the results predicted by mathematical models of mass transport in porous media, in order to build confidence in these models.

MATHEMATICAL MODELS OF GEOFILTRRATION AND GEOMIGRATION IN POROUS MEDIA WITH FRACTAL STRUCTURE

2020 ◽  
Vol 6 (3) ◽  
pp. 21-27
Author(s):  
R.A. Yusupov ◽  
◽  
Sh.S. Axrolov ◽  
N.M. Mirzanova ◽  
A.N. Nasiriddinov ◽  
...  
Keyword(s):  
Porous Media ◽  
Mathematical Models ◽  
Linear Models ◽  
Fractal Structure ◽  
Fractal Structures

In this study 2-D linear models are coming from generalised, Boussinesq eqution describing geofiltration in soils with fractal structures are presented. In this study are presented too mathematical models geomigration of contaminations with groundwater in classical way and in soils with fractal structures.

scholarly journals AUTOMATED MODELING AND FORECASTING SYSTEM OF ENTERPRISE ACTIVITIES

2021 ◽  
Vol 23 ◽  
pp. 20-26
Author(s):  
A. Khariv ◽  
A. Lagun
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Models ◽  
Computer Technology ◽  
Rapid Development ◽  
Computing Methods ◽  
Automated System ◽  
Enterprise Management ◽  
Mathematical Methods ◽  
The Future ◽  
Modelling And Forecasting

Introduction. Mathematical methods and models are an effective tool for studying complex economic systems at different levels of enterprise management. Economic mathematical modelling is actively developing not only as a scien-tific field but also as a means of substantiating management decisions in business, in the analysis and forecasting of socio-economic processes and phenomena. In the arsenal of economic and mathematical modelling now are using- modern computing methods and computer technology. Libraries of economic and mathematical models are an integral part of the architecture of decision support systems in specific areas of the economy. The rapid development of computer technology stimulates the emergence and formation of new theoretical volumes and applied areas of modelling.Purpose. Like any large and complex field of knowledge, mathematical modelling is evolving in different direc-tions, acquiring new flexible research methods. Therefore, based on new hardware, technology and software platforms it is necessary to create new information systems using economic and mathematical models in particular for forecasting of enterprise activities.Results. The article analyses the methods of modelling and forecasting the enterprise, considers the principles of software design. Using systems analysis, the design problem was analytically divided into parts. Also were investigated the connections and relationships between these parts, in particular, were implemented the problem tree and the goal tree. Implemented business process modelling performs based on created structural-logical diagrams, namely the IDEF0 dia-gram, which helps to visually display data and information that affect software development, a server part, input data and users. Using the results of research, the authors developed an automated information system for modelling and forecasting the activities of the enterprise, which uses models of Holt, Brown, exponential smoothing and Box-Jenkins for modelling. Part of the developed system is a designed software product that implements the objectives of the research. The obtained program results allow creating a clear forecast of the future activities of the enterprise.Conclusions. Based on the built graphs of modelling and forecasting of the Cisco Systems company financial activity with using of the developed automated system, we established that the Brown model is the best for providing educational sampling and a forecast of activity. The development of the automated system in the future involves the expansion of functionality, improvement and increasing of quality, as well as the creation of powerful analytics for more detailed forecasting.

Math Modeling of Vacuum Conductive Timber Drying

2014 ◽  
Vol 1040 ◽  
pp. 478-483
Author(s):  
M. Goreshnev ◽  
E. Litvishko
Keyword(s):  
Mathematical Modeling ◽  
Mass Transfer ◽  
Mathematical Models ◽  
Heat And Mass Transfer ◽  
Block Diagram ◽  
Calculated Data ◽  
Math Modeling ◽  
Advantages And Disadvantages ◽  
Transfer Problems

The article is devoted to the mathematical modeling of vacuum conductive timber drying. Analysis of known mathematical models allowed revealing their advantages and disadvantages. The modeling block diagram based on the drying periods is proposed. Lykov’s equations have been selected to solve heat and mass transfer problems. The comparison of experimental and calculated data has been conducted.

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