Mathematical Modeling Tools Research Articles

Jacobi Spectral Galerkin Method for Distributed-Order Fractional Rayleigh–Stokes Problem for a Generalized Second Grade Fluid

Distributed-order fractional differential operators provide a powerful tool for mathematical modelling of multiscale multiphysics processes, where the differential orders are distributed over a range of values rather than being just a fixed fraction. In this work, we consider the Rayleigh–Stokes problem for a generalized second-grade fluid which involves distributed-order fractional derivative in time. We develop a spectral Galerkin method for this model by employing Jacobi polynomials as temporal and spatial basis/test functions. Numerical results for one- and two-dimensional examples are presented to highlight the convergence rate and the flexibility of this approach. The proposed method yields an exponential rate of convergence when the solution is smooth and allows great flexibility to handle multi-dimensional temporally-distributed order fractional Rayleigh–Stokes problems. Our results confirm that nonlocal numerical methods are best suited to discretize distributed order fractional differential equations as they naturally take the global behavior of the solution into account.

What can we learn from previous pandemics to reduce the frequency of emerging infectious diseases like COVID-19?

The global risks report of 2020 stated, climate-related issues dominate all of the top-five long-term critical global risks burning the planet and according to the report, “as existing health risks resurge and new ones emerge, humanity’s past successes in overcoming health challenges are no guarantee of future results.” Over the last few decades, the world has experienced several pandemic outbreaks of various pathogens and the frequency of the emergence of novel strains of infectious organisms has increased in recent decades. As per expert opinion, rapidly mutating viruses, emergence and re-emergence of epidemics with increasing frequencies, climate-sensitive vector-borne diseases are likely to be increasing over the years and the trends will continue and intensify. Susceptible disease hosts, anthropogenic activities and environmental changes contribute and trigger the ‘adaptive evolution’ of infectious agents to thrive and spread into different ecological niches and to adapt to new hosts. The overarching objective of this paper is to provide insight into the human actions which should be strictly regulated to help to sustain life on earth. To identify and categorize the triggering factors that contribute to disease ecology, especially repeated emergence of disease pandemics, a theory building approach, ‘Total Interpretive Structural Modeling’ (TISM) was used; also the tool, ‘Impact Matrix Cross-Reference Multiplication Applied to a Classification’ analysis (MICMAC) was applied to rank the risk factors based on their impacts on other factors and on the interdependence among them. This mathematical modeling tool clearly explains the strength, position and interconnectedness of each anthropogenic factor that contributes to the evolution of pathogens and to the frequent emergence of pandemics which needs to be addressed with immediate priority. As we are least prepared for another pandemic outbreak, significant policy attention must be focused on the causative factors to limit emerging outbreaks like COVID 19 in the future.

Monitoring and Modelling of Cryptocurrency Trend Resistance by Recurrent and R/S-Analysis

The paper focuses on monitoring and modelling of the cryptocurrency market. The application of the chosen research methods is based on the analysis of existing methods and tools of economic and mathematical modelling of time series research on the example of the cryptocurrency market. It is proved that the use of individual methods is not relevant, as they do not give an adequate assessment of the specified market, so a comprehensive approach is the most acceptable. Therefore, monitoring and modelling of some cryptocurrency pairs with different capitalization degree were implemented by fractal and recurrent methods of the financial markets. The daily values of currency pairs for the period from September 2015 to November 2019 were chosen as information basis for monitoring and modelling. The use of R/S modelling method make it possible to conclude the persistence of time series of the selected cryptocurrencies indicating that the market trends are clearly defined, the currency pair of XRP/USD has the highest level of trend resistance. To compare the obtained results, the comprehensive approach is offered using recurrent diagrams that help to determine the cryptocurrency stability. The results of modelling by the recurrent method show that the most stable cryptocurrencies are the ones with the highest capitalization, namely Bitcoin and Ripple.

Economic Security Threat Modelling of a Commercial Bank in a Globalized Economy

In the paper, one develops a set of models for diagnosing threats to the economic security of a commercial bank, which allows improving the quality of decisions forming and making on managing the safe functioning and development of the bank. The bank's economic security research system has been developed, it includes 3 main blocks: research information space creation; assessment and analysis of the security of a commercial bank; generalization, and formation of decisions on the economic security of a commercial bank. The research made it possible to draw an inference of a theoretical, methodological, and applied nature that reflects the solution of the tasks set following the purpose of the study. A set of models has been built with modern tools of economic and mathematical modelling to improve the quality of decisions made to manage the bank's security and reduce the risks of threats. A model for calculating the bank's economic security indicator has been developed, which includes the following main stages: the construction of a structural scheme taking into account the rules of the theory of banking functioning security, then the terms and their membership functions are set for each input and output variable of the fuzzy inference system under consideration. Results of the response surface for the model are shown in the figure on the graphs of the dependence of the bank's economic security indicator on various input components. The paper requires that it is convenient to diagnose the state of economic security of a bank using fuzzy logic, this allows getting a clear quantitative representation of economic security state of the bank, as the indicators used for diagnostics may be indistinct and approximate and this a priori cannot give an adequate result when accurately calculated.

Visualization of Two-Dimensional Flows of an Ideal Fluid by Computer Technology

The use of application software packages in courses on continuum mechanics is considered as part of the general concept of the use of computer technology in the educational process of engineering specialties at a university. Digital modeling allows you to get an idea of the numerical solution of complex problems of mathematical physics. The powerful capabilities of application programs, combined with a mathematical tool for numerical modeling and graphic post-processing, reproduce the functional relationships between various elements of knowledge. Graphic modeling allows the student in a visual form and in conditions similar to a laboratory experiment to get acquainted with the phenomenon being studied and independently conduct a functional comparison with the corresponding theoretical principles.

Monitoring and modelling of cryptocurrency trend resistance by recurrent and R/S-analysis

The paper focuses on monitoring and modelling of the cryptocurrency market. The application of the chosen research methods is based on the analysis of existing methods and tools of economic and mathematical modelling of time series research on the example of the cryptocurrency market. It is proved that the use of individual methods is not relevant, as they do not give an adequate assessment of the specified market, so a comprehensive approach is the most acceptable. Therefore, monitoring and modelling of some cryptocurrency pairs with different capitalization degree were implemented by fractal and recurrent methods of the financial markets. The daily values of currency pairs for the period from September 2015 to November 2019 were chosen as information basis for monitoring and modelling. The use ofR/S modelling method make it possible to conclude the persistence of time series of the selected cryptocurrencies indicating that the market trends are clearly defined, the currency pair of XRP/USD has the highest level of trend resistance. To compare the obtained results, the comprehensive approach is offered using recurrent diagrams that help to determine the cryptocurrency stability. The results of modelling by the recurrent method show that the most stable cryptocurrencies are the ones with the highest capitalization, namely Bitcoin and Ripple.

Studying the Impact of Vaccination Strategy and Key Parameters on Infectious Disease Models

In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.

Концепция поддержки лазерного аддитивного производства на основе онтологического подхода

A general concept of software and information support for laser-based additive manufacturing of metal parts from powder compositions is proposed. It is based on an ontological two-level approach to the formation of knowledge about the processes of laser additive manufacturing. Under this approach, the ontology is clearly separated from the knowledge base. So subject-matter specialists can create and develop knowledge in the representation that they understand. The conceptual architecture of the decision support software for laser-based additive manufacturing processes is presented. Its information and software components are described. Information components are ontologies, databases of laserbased additive manufacturing system components, databases of materials for additive manufacturing, knowledge base and case database. The knowledge base contains formalized information on the settings of laser-based additive manufacturing modes that ensure compliance of the obtained metal parts with the requirements of the current industry-specific guidelines (regulatory documents for this type of parts). The case database contains a structured description of the protocols for using laser technological equipment for additive manufacturing of metal parts from powder compositions. Software components are editors for creating and maintaining data and knowledge bases (controlled by the corresponding ontologies), decision support system based on both, knowledge and cases, and tool for cases structuring. There are also external tools for mathematical modelling of directed energy deposition physicochemical processes. When making decisions a hybrid approach that combines knowledge engineering methods and case-based search by analogy is proposed. The specialty of the approach is the continuous knowledge base update due to its improvement by experts and due to its verification in the process of accumulating cases.

Crank-Nicolson and Modified Crank-Nicolson Scheme for One Dimensional Parabolic Equation

Partial differential equations are very important tools for mathematical modeling in some field like; physics, engineering and applied Mathematics. It’s worth knowing that only few of this equation can be solved analytically and numerical method have been proven to perform exceedingly well in solving even difficult partial differential equations. Finite difference method is a popular numerical method which has been applied extensively to solve partial differential equations. A well known type of this method is the Classical Crank-Nicolson scheme which has been used by different researchers. In this work, we present a modified Crank-Nicolson scheme resulting from the modification of the classical Crank-Nicolson scheme to solve one dimensional parabolic equation. We apply both the Classical Crank-Nicolson scheme and the modified Crank-Nicolson scheme to solve one dimensional parabolic partial differential equation and investigate the results of the different schemes. The computation and results of the two schemes converges faster to the exact solution. It is shown that the modified Crank-Nicolson method is more efficient, reliable and better for solving Parabolic Partial differential equations since it requires less computational work. The method is stable and the convergence is fast when the results of the numerical examples where compared with the results from other existing classical scheme, we found that our method have better accuracy than those methods. Some numerical examples were considered to verify our results.

The use of mathematical modeling tools to predict the yield of genetically modified crops

Despite the high-tech innovation level of cultivation and processing, damage by insects - pests, is still high. In this connection, a sense of urgency growing new genetically modified (GM) varieties agricultures containing the gene of the soil bacterium called transgenic or genetically modified. This article explains the importance of mathematical modelling for the cultivation of GM crops.

The use of the model apparatus in solving problems of optimization of multimodal transport

On the basis of retrospective analysis of approaches and principles of modeling of business processes of the company, the main parameters of their modernization in the conditions of globalization of modern economy are allocated. Approaches to the integration of methodological tools of mathematical and simulation modeling of business processes with an emphasis on the need to assess the parameters of the internal and external environment of the transport company in order to optimize its functioning in a competitive market are summarized. The mechanism of formation of the model of multimodal transportation with an emphasis on inland waterway transport, taking into account the resource base of the transport company and the restrictions imposed on the technological parameters of multimodal transportation, is considered.

Planning the forest transport systems based on the principles of sustainable development of territories

The article identifies a new method of dynamic modeling in the design of the transport system in the forest fund (TSFF), which is based on economic and mathematical modeling and fuzzy logic tools. The combination of the indicated methods is designed to reduce the disadvantages of their use and increase the benefits. The article substantiates the choice of assessing the forecast level of the impact of risks on the activities of forestry enterprises (the method of expert assessments), using the methodological tools of fuzzy logic. The indicated method makes it possible to take into account a large variety of risk factors of the internal and external environment. At the same time, methodological aspects of fuzzy logic make it possible to formulate a quantitative assessment of qualitative indicators. The article substantiates the choice of tools for economic and mathematical modeling in order to state the design problem of the planned TSFF. Since the indicated method enables the formalization of the functioning of the timber transport system in the given conditions. The article presents a developed model that correctly takes into account the influence of risk factors when planning a TSFF, through the combination of fuzzy logic methods and economic and mathematical modeling. The advantages of the developed model include: considering the multivariance of material flows, vehicles, points of overload, etc.; automated processing of input parameters and effective data; using the model for forecasting, i.e. the possibility of deriving a fuzzy estimate of the efficiency of the timber transport system by identifying cause-effect relationships between the modeling object and the influence of risk factors on its functioning.

Roasting optimization and kinetics of raw and instant controlled pressure drop pre-treated coffee beans

Introduction: Coffee is one of the most widely consumed beverages in the world. The desired aroma and flavour of coffee are developed duringroasting which is the most important step in coffee processing. Instant Controlled Pressure Drop Process (DIC) technology is controlled hightemperature and short time process which been used successfully to improving the kinetics of drying, extraction, and decontamination of fresh and dried natural products. The main advantages of DIC are that it is a master controlled temperature and time process, the dwell times are short, reducing the chemical degradation, so new products with superior quality attributes may be developed. Materials and Methods: Two coffee beans varieties were investigated by Brazilian and Ethiopian sources. The raw beans were pre-treated using the DIC process under adopted conditions prior to roasting. A two-factor central composite design was used to optimize the settings of roasting time and roasting temperature on response variables of bulk, true and normalized density, and roasting degree. Also, microscopic analysis using Scanning Electron Microscopy (SEM) and kinetics of the roasting processes are included. Results and Discussion: The obtained results confirmed that the roasted DIC treated beans for both varieties have lower densities, higher roasting degree and lower activation energy needed for roasting compared to the raw beans. The physical properties’ magnitude is highly relevant to coffee origin. Roasting time and the temperature seemed to be of significant regarding all the physical characteristics of the beans, however, time was of topmost significance. Besides, treating coffee been by DIC prior to roasting leads to texture modification and conservation of time and energy needed for roasting. Conclusions: The physical properties of the roasted coffee beans are highly affected and changed with the coffee origin, roasting conditions and pre-treatment of coffee beans prior to roasting using the DIC process. The incorporation of the DIC process prior to roasting seemed to achieve more conservation of time and energy needed for roasting compared to the raw untreated beans. The higher degree of roasting and the competitive roasting activation energy of Brazilian coffee beans give aconclusion that more economic roasting process could be achieved with the Brazilian coffee. The pre-treatment by DIC enhances the remarkable reduction in coffee beans density and increasing in the roasting degrees that are in line with the industrial needs of coffee beverages. Response Surface Methodology is an efficient tool for optimization and mathematical modeling of the coffee roasting process.

Modeling of polygraphic web-service using colored Petri nets

The use of Petri Networks as a tool for graphical and mathematical modeling of complex systems and processes has recently been widespread. Visual representation techniques and simulations, such as Petri colored networks, are effective at the development stage of complex systems, since they allow formally to describe and model the system at different levels of abstraction and investigate them dynamically. An example of a dynamic system is web-services. Web services and their components can interact with different applications that meet the standards of web services. As a rule, one service does not meet the needs of users, and services are becoming more and more complex. In fact, a modern web service is created by combining different web services and their components to create a component service that offers a set of new functional services. When combining and sharing Web services the most critical is the interaction of Web services and their components among themselves, which requires a detailed study of the functioning of the processes and modeling their behavior to improve their efficiency.Polygraphic web-service is a complex program system that organizes the provision of printing services. It works with the client through the Internet and provides an opportunity to find the necessary service at the printing centers for the best possible means, to make an order, to use various services, to pay for services, to choose a means of payment and delivery of printed products. The complex structure of the web-service requires the study and modeling of the interaction of its components to ensure the effectiveness of the operation.To model the composite web service system, it is necessary to identify the main and auxiliary subsystems by means of structural analysis. The block diagram of a web-service is presented in fig. 1. As a structural analysis tool, we used a data flow diagram (DFD) in the notation of a similar Heine-Sarson notation. A top-level contextual chart contains a set of subsystems connected by data streams.A model of a polygraphic web-service in the form of Petri's network in a hierarchical form was developed and presented for the purpose of analysis of separate networks of the second level. This enables to analyze all parts of the network separately and use the results to formulate conclusions about the correctness of the construction of the entire network. In the presence of links between networks of the second level, it is necessary to add additional criteria for the analysis of networks, which are connected with the addition of the main network of cities and transitions between networks of the second level, the number of which depends on the number of possible states of interaction between networks of the second level.

REVIEW AND ANALYSIS OF LESSONS LEARNED HANDWRITING EXPERTISE AS A WAY TO IDENTIFY PROBLEMS AND WAYS TO SOLVE THEM IN EXISTING METHODS OF HANDWRITING RESEARCH

In today’s environment, information security needs constant improvement. Therefore, biometric technologies are becoming increasingly important as a key area of information protection, contributing to the widespread introduction of biometric systems across firms and organizations. Purpose: in the course of handwriting research, human participation is a prerequisite for handwriting expertise, which entails certain problems in the field of biometric expertise, the emphasis on which is contained in the article. Methodology: tools and methods are considered to reduce the impact of problems on the process of handwriting examination: popular scientific methods of phase and case analysis and synthesis; Mathematical and simulation modeling methods and tools. Results: in order to identify approaches to reducing subjectivity of expert’s conclusions, a review and analysis of existing solutions was carried out, as a result of which a comparative characteristic of approaches to solving the problem of handwriting examination was drawn up. Scope of results: the results of this study will help the organization’s leadership in information security.

Numerical Study of Mass Transport and Electrochemical Kinetics inside Porous Structure Layers of PEMFC Using Direct Simulation Approach

The enhancement of the mass transports in porous layers of a polymer electrolyte fuel cells (PEFCs) is essential for developing material and design system to improve the PEFC performance and durability. The oxygen transport resistance is a large fraction of the mass-transport overpotential at the cathode. Condensed water in the flow field and porous layers reduces oxygen transport to the oxygen reduction reaction (ORR) region. Experimental investigation of locally saturated porous media in the operating cell is difficult. The Computational Fluid Dynamics (CFD) is mathematical modeling tool, which can be considered the incorporation of theory and experimentation in the field of kinetics, heat, and mass transport of the PEFCs. The purpose of this work is to use direct modeling-based, Lattice Boltzmann Method (LBM) within the detailed structure of porous layers to understand the kinetics and multi-scalar/multi-physics transports in a polymer electrolyte fuel cells (PEFCs). The model geometries consist of gas diffusion layer (GDL), micro porous layer (MPL), and Catalyst layer (CL), as shown in Fig. 1. The studies include the understanding of water evolution, water saturation, breakthrough pressure, heat transfer, species transport, and electrochemical kinetics inside porous layers under different conditions and situations that could occur in fuel cells. This work will show the enhancement of direct CFD simulation with LBM (CFD-LBM) approach [1-4], which incorporates with detailed structure of porous and catalyst layers from both micro- and nano- X-ray CT. This approach will consist of the kinetic model in the catalyst layer, which will involve coupling electrochemical kinetic to investigate the electrical potentials, electrical current, electron transfer, and exchange current in the catalyst layers, as shown in Fig. 2. The output of this work will be used for the optimization of catalyst layer thickness, with durability and water management improvement, for novel porous materials, particularly in the catalyst layer.

Modeling microstructure evolution in shape memory alloy rods via Legendre wavelets collocation method

Microstructures play an important role in the research on shape memory alloys (SMA). By using mathematical modeling tools to study microstructures, it is possible to predict the behaviors of these materials under applied fields. In the current paper, a thermo-mechanical model is proposed to simulate the microstructure of a SMA rod with both fixed and impact boundary conditions via Legendre wavelets collocation method. Because of the good performance of Legendre wavelets basis, this method shows excellent properties in both precision and stability. A detailed numerical algorithm is given, and the backward differentiation formula is employed to perform all the simulations in the current paper. Computational simulations are carried out to study the stress-induced phase transformation. The dynamics of microstructure evolution, presented at different temperatures, is well captured by our developed technique.

Application of the Discrete Element Method for Manufacturing Process Simulation in the Pharmaceutical Industry.

Process simulation using mathematical modeling tools is becoming more common in the pharmaceutical industry. A mechanistic model is a mathematical modeling tool that can enhance process understanding, reduce experimentation cost and improve product quality. A commonly used mechanistic modeling approach for powder is the discrete element method (DEM). Most pharmaceutical materials have powder or granular material. Therefore, DEM might be widely applied in the pharmaceutical industry. This review focused on the basic elements of DEM and its implementations in pharmaceutical manufacturing simulation. Contact models and input parameters are essential elements in DEM simulation. Contact models computed contact forces acting on the particle-particle and particle-geometry interactions. Input parameters were divided into two types—material properties and interaction parameters. Various calibration methods were presented to define the interaction parameters of pharmaceutical materials. Several applications of DEM simulation in pharmaceutical manufacturing processes, such as milling, blending, granulation and coating, were categorized and summarized. Based on this review, DEM simulation might provide a systematic process understanding and process control to ensure the quality of a drug product.

Multiperiod optimization model for oilfield production planning: bicriterion optimization and two-stage stochastic programming model

In this work, we present different tools of mathematical modeling that can be used in oil and gas industry to help improve the decision-making for field development, production optimization and planning. Firstly, we formulate models to compare simultaneous multiperiod optimization and sequential single period optimization for the maximization of net present value and the maximization of total oil production over long term time horizons. This study helps to identify the importance of multiperiod optimization in oil and gas production planning. Further, we formulate a bicriterion optimization model to determine the ideal compromise solution between maximization of the two objective functions, the net present value (NPV) and the total oil production. To account for the importance of hedging against uncertainty in the oil production, we formulate a two-stage stochastic programming model to compute an improved expected value of NPV and total oil production for uncertainties in oil prices and productivity indices.

Estimating the effect of seasonally-operating cooling devices during a safe stop of the oil pipeline

Conducting thermal calculations of "hot" oil pipelines through which high-viscosity and high-sticking oils are transported is one of the main ones. Determining the rate of cooling of oil in a stopped pipeline is of practical importance. According to the cooling rate, the time to safely stop the "hot" pipeline is calculated. This is the time at which the "hot" oil pipeline doesn’t freeze and the station’s pressure is enough to overcome the shear stresses arising during the cooling f high-viscosity and high-sticking oil. Oil cooling in underground stopped pipelines depends on the temperature of the soil around it. Installed heat stabilizers designed to cool the soil can affect the cooling rate of the "hot" pipeline. We have carried out a numerical experiment using modern tools of mathematical modelling. The experiment showed that the installed soil heat stabilizers near the underground "hot" pipeline have an impact on the process of cooling oil. These stabilizers have reduced the time to safely stop the pipeline.