In this study, the model Riccati equation with variable coefficients as functions, as well as a derivative of a fractional variable order (VO) of the Gerasimov-Caputo type, is used to approximate the data for some physical processes with saturation....
Knowledge of the mathematical models of the fermentation processes is indispensable for their simulation and optimization and for the design and synthesis of the applicable control systems. The paper focuses on determining a dynamic mathematical mode...
The Francis hydro-turbine is a typical nonlinear system with coupled hydraulic, mechanical, and electrical subsystems. It is difficult to understand the reasons for its operational failures, since the main cause of failures is due to the complex inte...
The paper focuses on the experimental investigation and mathematical modeling of the corrosion of steel when a film of water flows over its surface. The experimental monitoring of corrosion dynamics in the flowing film was carried out using a laborat...
In this paper we offer a comprehensive review of Sociophysics, focusing on relevant models as well as selected applications in social trading, behavioral finance and business. We discuss three key aspects of social diffusion dynamics, namely Opinion...
The mathematical modeling of a combination of non-thermal technologies for E. coli inactivation is of great interest for describing the dynamic behavior of microorganisms in food, with the goal of process control, optimization, and prediction. This r...
In hydraulic engineering, some researchers have developed different mathematical and numerical tools for a better understanding of the physical interaction between water flow in pipes with trapped air during emptying processes, where they have made c...
This research work deals with mathematical modeling in complex biological systems in which several types of individuals coexist in various populations. Migratory phenomena among the populations are allowed. We propose a class of mathematical models t...
Mathematical modelling of infection processes in cells is of fundamental interest. It helps to understand the SARS-CoV-2 dynamics in detail and can be useful to define the vulnerability steps targeted by antiviral treatments. We previously developed...
Understanding the emotional dimension of classroom practices benefits sustainable education. However, the dynamic nature of teacher emotions during teaching remains understudied. To acquire an “in-depth” description of the emotional pheno...
This research provides valuable insights into the application of mathematical modeling to real-world scenarios, as exemplified by the COVID-19 pandemic. After data collection, the preparation stage included exploratory analysis, standardization and n...
This study deals with a methodology for increasing the efficiency of dynamic process calculations in elastic elements of complex engineering constructions. We studied the complex dynamic processes in a simple engineering construction, a mechanical sy...
The present work focuses on the problem of steel surface corrosion as a kinetic expression when water droplets are repeatedly deposited and evaporated on/from its surface. This process, together with the rainwater film corrosion process, belongs to t...
Assessing the effects that nonstationary dynamic processes have on the durability of structural elements belongs to an important trend in modern dynamics and technical diagnostics of machines. Normally, fatigue strength calculations are performed tak...
The tumor microenvironment is a highly dynamic and complex system where cellular interactions evolve over time, influencing tumor growth, immune response, and treatment resistance. In this study, we develop a graph-theoretic framework to model the tu...
This research focuses on biological systems with sexual reproduction in which female and male individuals coexist together, forming female–male couples with the purpose of procreation. The couples can originate new females and males according t...
Biosorption has great potential in removing toxic effluents from wastewater, especially heavy metal ions such as cobalt, lead, copper, mercury, cadmium, nickel and other ions. Mathematically modeling of biosorption process is essential for the econom...
Dynamic neural networks (DNNs) are a type of artificial neural network (ANN) designed to work with sequential data where context in time is important. Unlike traditional static neural networks that process data in a fixed order, dynamic neural networ...
This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic...
Mathematical modeling is a powerful tool to study the process of the spread of infectious diseases. Among various mathematical methods for describing the spread of infectious diseases, the cellular automaton makes it possible to explicitly simulate b...
The transformation of long waves—such as tsunamis and storm surges—evolving over a continental shelf is investigated. We approach this problem numerically using a pseudo-spectral method for a higher-order Euler formulation. Solitary waves...
Bubble multiphase systems are crucial in industries such as biotechnology, medicine, oil and gas, and water treatment. Optical data analysis provides critical insights into bubble characteristics, such as the shape and size, complementing physical se...
The COVID-19 pandemic was a profoundly influential global occurrence in recent history, impacting daily life, economics, and healthcare systems for an extended period. The abundance of data has been essential in creating models to simulate and foreca...
This work presents a numerical investigation into broadband radiation effects (with energy flux densities q < 1014 W/cm2) on a magneto–inertial fusion (MIF) target. The calculation results demonstrate the impact of intense energy fluxes on a...
A phenomenological model was developed to describe the dynamic evolution of the batch suspension polymerization of methyl methacrylate in terms of reactor temperature, pressure, concentrations and molecular properties of the final polymer. Then, the...
Personality Systems Interactions (PSI) theory explains differences in personality based on the properties of four cognitive systems—object recognition (OR), intuitive behaviour (IB), intention memory (IM) and extension memory (EM). Each system...
Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread, especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave had subsequent wa...
This work investigates how interpersonal interactions among individuals could affect the dynamics of awareness raising. Even though previous studies on mathematical models of awareness in the decision making context demonstrate how the level of aware...
A mathematical model of the human immunodeficiency virus Type 1 (HIV-1) life cycle in CD4 T cells was constructed and calibrated. It describes the activation of the intracellular Type I interferon (IFN-I) response and the IFN-induced suppression of v...
The COVID-19 infectious disease spread in the world represents, by far, one of the most significant moments in humankind’s recent history, affecting daily activities for a long period of time. The data available now allow important modelling de...
The object of this study is the underground gas storage facilities of Ukraine, with the aim of developing a systematic mathematical model to describe the flow of gas in complex underground gas storage systems. This model will enable to development of...
This research proposes a methodology based on control engineering, transforming the simulation model of system dynamics into a mathematical model expressed as a system transfer function. The differential equations of a time domain present in the Forr...
Multiphase flows in porous media are widespread in nature and various technologies. One of the most common examples of this kind of task is the task of recovering oil from the rock. This article describes a mathematical model of the flow of a two-pha...
Liquefied nature gas (LNG) is a green energy. LNG-fueled vessels are extremely complex engineering systems. In view of the inherent hazardous properties of LNG fuel, LNG fueling is not only an important part, but it is also full of high risks in the...
Aiming at the dynamic penetration process of a shaped-charge jet, we proposed a mathematical model for the penetration of a jet under dynamical conditions based on the theory of virtual origin and the Bernoulli equation taking into account the jet an...
Load shedding processes are widespread in hydropower stations, which has great influence on the safe and stable operation of the hydro–turbine governing system. In order to study the dynamic characteristics of the hydro–turbine governing system durin...
For better small-radius curve negotiation performance, the independently rotating wheelset has the potential to be equipped in urban rail transit. As a crucial part of the running gear, its dynamic characteristics directly affect the railway vehicle&...
The use of digital twins in smart power systems at the stages of the life cycle is promising. The dynamics of such systems (smart energy renewable sources, smart energy hydrogen systems, etc.), are determined mainly by the physical and chemical proce...
The objective of this study is to develop a mathematical model capable of correctly displaying the dynamics of an individual’s cognitive activity under conditions of external information influence of different modalities. The adequacy of the mo...
The main objective of this research is to establish a new formulation and mathematical model based on graph theory to create dynamic equations and provide clarity on the fundamental formulation. We have employed graph theory as a new approach to deve...
This paper presents the mathematical modeling, fluid dynamic analysis, and experimental analysis of a spiral case without guide vanes. Using a specific case of the Archimedes spiral, the model eliminates the need for fixed or moving blades to simplif...
Graph theory is a well-established mathematical concept that is widely used in numerous applications such as in biology, chemistry and network analysis. The advancement in the theory of graph has led to the development of a concept called autocatalyt...
As it results from many research works, the majority of real dynamical objects are fractional-order systems, although in some types of systems the order is very close to integer order. Application of fractional-order models is more adequate for the d...
This work deals with mathematical modeling of dynamical systems. We consider a class of two-sex branching processes with several mating and reproduction strategies. We provide some probabilistic and statistical contributions. We deduce general expres...
Communication, which is information exchange between systems, is one of the basic information processes. To better understand communication and develop more efficient communication tools, it is important to have adequate and concise, static and dynam...
Mineral leaching is the key unit operation in metallurgical processes and corresponds to the dissolution of metals. The study of leaching is carried out in many areas, such as geology, agriculture and metallurgy. This paper provides an introduction t...
Plate structures are the main components of offshore platforms and ships in engineering applications. The vibration control of the low-frequency mode of plate structures has always been a meaningful research object in marine science and engineering....
This paper presents a procedure for the closed-loop stability analysis of a certain variant of the strategy called Fuzzy Model-Based Predictive Control (FMBPC), with a model of the Takagi-Sugeno type, applied to the wastewater treatment process known...
Based on the research results, coefficients in constitutive equations, describing the kinetics of dynamic, meta-dynamic, and static recrystallization in high-carbon bainitic steel during hot deformation were determined. The developed mathematical mod...
The different kinds of knowledge which were connected in Natural Philosophy (NP) have been later separated. The real separation came when Physics took its individuality and developed specific mathematical models, such as dynamic systems. These models...
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