scholarly journals Mathematical Modeling of Layered Nanocomposite of Fractal Structure

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1541
Author(s):  
Sergey Korchagin ◽  
Ekaterina Romanova ◽  
Denis Serdechnyy ◽  
Petr Nikitin ◽  
Vitaliy Dolgov ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Hurst Exponent ◽  
Software Package ◽  
Quantitative Assessment ◽  
Fractal Structure ◽  
Composite Media ◽  
Fractal Properties ◽  
Permissible Range ◽  
Proposed Model ◽  
Fractal Characteristics

A model of a layered hierarchically constructed composite is presented, the structure of which demonstrates the properties of similarity at different scales. For the proposed model of the composite, fractal analysis was carried out, including an assessment of the permissible range of scales, calculation of fractal capacity, Hausdorff and Minkovsky dimensions, calculation of the Hurst exponent. The maximum and minimum sizes at which fractal properties are observed are investigated, and a quantitative assessment of the complexity of the proposed model is carried out. A software package is developed that allows calculating the fractal characteristics of hierarchically constructed composite media. A qualitative analysis of the calculated fractal characteristics is carried out.

A model for transient flow in porous media embedded with randomly distributed tree-shaped fractal networks

2015 ◽  
Vol 29 (19) ◽  
pp. 1550135 ◽  
Author(s):  
Xiao-Hua Tan ◽  
Xiao-Ping Li ◽  
Jian-Yi Liu ◽  
Lie-Hui Zhang ◽  
Jianchao Cai
Keyword(s):  
Porous Media ◽  
Transient Flow ◽  
Heterogeneous Porous Media ◽  
Flow In Porous Media ◽  
Inversion Method ◽  
Type Curves ◽  
Fractal Properties ◽  
Proposed Model ◽  
The Laplace Transform ◽  
Fractal Characteristics

A model for transient flow in porous media embedded with randomly distributed tree-shaped fractal networks was presented based on the fractal properties of tree-shaped capillaries and generalized Darcy's law. The dimensionless expression of flowing pressure was developed using the Laplace transform and Stehfest numerical inversion method. The bilogarithmic type curves were illustrated and the influences of different fractal factors on dimensionless flowing pressure were also discussed. The presented study indicated that the fractal characteristics for the tree-shaped fractal networks should be considered in analysis of transient flow in the heterogeneous porous media. The proposed model may be conducible to a better understanding of the mechanism for transient flow in the multi-porosity porous media.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2106147
Author(s):  
Debkumar Pal ◽  
D Ghosh ◽  
P K Santra ◽  
G S Mahapatra
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Treatment Control ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
The Cost ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

scholarly journals RESEARCH OF INFLUENCE OF AIR TEMPERATURE ON THE LEVEL OF NITROGEN OXIDES IN SMOKE GASES OF BOILER PLANTS

2019 ◽  
Vol 9 (4) ◽  
pp. 27-32
Author(s):  
Olga A. BALANDINA ◽  
Svetlana M. PURING
Keyword(s):  
Mathematical Modeling ◽  
Nitric Oxide ◽  
Nitrogen Oxides ◽  
Flue Gas ◽  
Software Package ◽  
Flame Temperature ◽  
Combustion Process ◽  
Flue Gases ◽  
Oxidizing Agent ◽  
Mixture Formation

The analysis of the values of the concentrations of the formed nitrogen oxides and the temperatures of the jet plume under various conditions of mixture formation is carried out. The plots of the distribution of torch temperatures and concentrations of nitric oxide in the calculated area for oxidizer temperatures of 20, 60, 100, 150, and 200 ° C were obtained and analyzed. Mathematical modeling of the gaseous fuel combustion process was carried out using the FlowVision software package. An analysis of the results showed that a decrease in the temperature of the air supplied as an oxidizing agent leads to a significant decrease in the concentration of nitrogen oxides in flue gases, while not significantly affecting the change in the flame temperature. The research results can be used to solve the problems of optimizing boiler plants, in order to reduce harmful flue gas emissions. Further modeling is planned to determine the dependence of the influence of various factors on the degree of formation of nitrogen oxides in the flue gases of boiler plants.

scholarly journals Descriptions of Entropy with Fractal Dynamics and Their Applications to the Flow Pressure of Centrifugal Compressor

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 266 ◽  
Author(s):  
Yan Liu ◽  
Dongxiao Ding ◽  
Kai Ma ◽  
Kuan Gao
Keyword(s):  
Autocorrelation Function ◽  
Centrifugal Compressor ◽  
Hurst Exponent ◽  
Flow Instability ◽  
Dynamic Pressure ◽  
Stable State ◽  
Nonlinear Dynamic System ◽  
Original Data ◽  
Fractal Spectrum ◽  
Fractal Characteristics

In this study, some important intrinsic dynamics have been captured after analyzing the relationships between the dynamic pressure at an outlet of centrifugal compressor and fractal characteristics, which is one of powerful descriptions in entropy to measure the disorder or complexity in the nonlinear dynamic system. In particular, the fractal dynamics of dynamic pressure of the flow is studied, as the centrifugal compressor is in surge state, resulting in the dynamic pressure of flow and becoming a serious disorder and complex. First, the dynamic pressure at outlet of a centrifugal compressor with 800 kW is tested and then obtained by controlling the opening of the anti-surge valve at the outlet, and both the stable state and surge are initially tested and analyzed. Subsequently, the fractal dynamics is introduced to study the intrinsic dynamics of dynamic pressure under various working conditions, in order to identify surge, which is one typical flow instability in centrifugal compressor. Following fractal dynamics, the Hurst exponent, autocorrelation functions, and variance in measure theories of entropy are studied to obtain the mono-fractal characteristics of the centrifugal compressor. Further, the multi-fractal spectrums are investigated in some detail, and their physical meanings are consequently explained. At last, the statistical reliability of multi-fractal spectrum by modifying the original data has been studied. The results show that a distinct relationship between the dynamic pressure and fractal characteristics exists, including mono-fractal and multi-fractal, and such fractal dynamics are intrinsic. As the centrifugal compressor is working under normal condition, its autocorrelation function curve demonstrates apparent stochastic characteristics, and its Hurst exponent and variance are lower. However, its autocorrelation function curve demonstrates an apparent heavy tail distribution, and its Hurst exponent and variance are higher, as it is working in an unstable condition, namely, surge. In addition, the results show that the multi-fractal spectrum parameters are closely related to the dynamic pressure. With the state of centrifugal compressor being changed from stable to unstable states, some multi-fractal spectrum parameters Δα, Δf(α), αmax, and f(αmin) become larger, but αmin in the multi-fractal spectrum show the opposite trend, and consistent properties are graphically shown for the randomly shuffled data. As a conclusion, the proposed method, as one measure method for entropy, can be used to feasibly identify the incipient surge of a centrifugal compressor and design its surge controller.

Visualizing Coherent and Fractal Structures in Numerical Experiments on Chaotic Advection in Fluids

2005 ◽  
Author(s):  
M. V. Budyansky ◽  
S. V. Prants
Keyword(s):  
Numerical Experiments ◽  
Fractal Structure ◽  
Point Vortex ◽  
Chaotic Advection ◽  
Mixing Zone ◽  
Background Current ◽  
Fractal Structures ◽  
Chaotic Scattering ◽  
And Topology ◽  
Fractal Properties

We investigate typical mixing and fractal properties of chaotic scattering of passive particles in open hydrodynamic flows taking as an example a model two-dimensional incompressible flow composed of a fixed point vortex and a background current with a periodic component, the model inspired by the phenomenon of topographic eddies over mountains in the ocean and atmosphere. We have found, described and visualized a non-attracting invariant chaotic set defining chaotic scattering, fractality, and trapping of incoming particles. Geometry and topology of chaotic scattering have been studied and visualized. Scattering functions in the mixing zone have been found to have a fractal structure with a complicated hierarchy that has been described in terms of strophes and epistrophes. Mixing, trapping, and fractal properties of passive particles have been studied under the influence of a white noise with different amplitudes and frequency ranges. A new effect of clustering the particles in a noised flow has been demonstrated in numerical experiments.

scholarly journals Fractional Dynamics in Soccer Leagues

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 356 ◽  
Author(s):  
António M. Lopes ◽  
Jose A. Tenreiro Machado
Keyword(s):  
Mathematical Modeling ◽  
Fractional Calculus ◽  
Real World ◽  
Complex Dynamics ◽  
Statistical Information ◽  
Fractional Dynamics ◽  
Entropy Analysis ◽  
Real World Data ◽  
Proposed Model ◽  
Soccer Teams

This paper addresses the dynamics of four European soccer teams over the season 2018–2019. The modeling perspective adopts the concepts of fractional calculus and power law. The proposed model embeds implicitly details such as the behavior of players and coaches, strategical and tactical maneuvers during the matches, errors of referees and a multitude of other effects. The scale of observation focuses the teams’ behavior at each round. Two approaches are considered, namely the evaluation of the team progress along the league by a variety of heuristic models fitting real-world data, and the analysis of statistical information by means of entropy. The best models are also adopted for predicting the future results and their performance compared with the real outcome. The computational and mathematical modeling lead to results that are analyzed and interpreted in the light of fractional dynamics. The emergence of patterns both with the heuristic modeling and the entropy analysis highlight similarities in different national leagues and point towards some underlying complex dynamics.

scholarly journals Impact of Awareness to Control Malaria Disease: A Mathematical Modeling Approach

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Malik Muhammad Ibrahim ◽  
Muhammad Ahmad Kamran ◽  
Malik Muhammad Naeem Mannan ◽  
Sangil Kim ◽  
Il Hyo Jung
Keyword(s):  
Mathematical Modeling ◽  
Numerical Technique ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Awareness Campaign ◽  
Runge Kutta Method ◽  
Proposed Model ◽  
Awareness Programs ◽  
Disease Free ◽  
Differential Process

The mathematical modeling of malaria disease has a crucial role in understanding the insights of the transmission dynamics and corresponding appropriate prevention strategies. In this study, a novel nonlinear mathematical model for malaria disease has been proposed. To prevent the disease, we divided the infected population into two groups, unaware and aware infected individuals. The growth rate of awareness programs impacting the population is assumed to be proportional to the unaware infected individuals. It is further assumed that, due to the effect of awareness campaign, the aware infected individuals avoid contact with mosquitoes. The positivity and the boundedness of solutions have been derived through the completing differential process. Local and global stability analysis of disease-free equilibrium has been investigated via basic reproductive number R0, if R0 < 1, the system is stable otherwise unstable. The existence of the unique endemic equilibrium has been also determined under certain conditions. The solution to the proposed model is derived through an iterative numerical technique, the Runge–Kutta method. The proposed model is simulated for different numeric values of the population of humans and anopheles in each class. The results show that a significant increase in the population of susceptible humans is achieved in addition to the decrease in the population of the infected mosquitoes.

scholarly journals Use of fractal analysis to evaluate the surface quality of agricultural machinery parts

2020 ◽  
Vol 17 ◽  
pp. 00189
Author(s):  
Oleg Bavykin ◽  
Tatyana Levina ◽  
Vladlena Matrosova ◽  
Anatoly Klochkov ◽  
Vitaliy Enin
Keyword(s):  
Time Series ◽  
Computer Program ◽  
Surface Quality ◽  
Fractal Analysis ◽  
Hurst Exponent ◽  
High Accuracy ◽  
Agricultural Machinery ◽  
Fractal Characteristics

The research of the determination of the fractal characteristics of the surface of a material proposes the use of a stationary profilograph and a computer program for calculating the Hurst exponent. The low accuracy of fractal analysis using the well-known computer program Fractan is revealed. A computer program developed in VBA for the fractal analysis of the time series is described. The high accuracy of the algorithms for calculating the Hurst exponent incorporated in this program is shown.

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