Conceptual Mathematical Model Research Articles

Aggregating nanoparticle transport with nonlinear attachment: Modeling and experimental validation

A conceptual mathematical model was developed to simulate the transport of migrating nanoparticles in homogeneous, water saturated, 1-dimensional porous media. The model assumes that nanoparticles can collide with each other and aggregate. Nanoparticles can be found attached reversibly and/or irreversibly onto the solid matrix of the aquifer or suspended in aqueous phase. Attached particles may either contribute to the acceleration of subsequent particle deposition or hinder it, leading to the ripening or blocking process, respectively. The aggregation process was simulated based on the Smoluchowski Population Balance Equation (PBE) and was coupled with the advection-dispersion-attachment equation (ADA) to form a family of partial differential equations that govern the migration of nanoparticles in porous media. For the solution of the PBE, an efficient finite volume solver was employed that significantly accelerated computation times, by reducing the number of participating equations, while maintaining the required accuracy. The developed model was applied to nanoparticle transport experimental data available in literature. The model successfully matched the breakthrough concentration curves, and estimated the corresponding nanoparticle diameter, proving its ability to capture the physical processes participating in nanoparticle transport.

Advanced Mathematical Model for the Transport of Aggregating Nanoparticles in Water Saturated Porous Media: Nonlinear Attachment and Particle Size‐Dependent Dispersion

AbstractA conceptual mathematical model was developed to describe the migration of aggregating nanoparticles in water saturated, homogeneous porous media with one‐dimensional uniform flow. Nanoparticles can be found suspended in the aqueous phase or attached reversibly and/or irreversibly onto the solid matrix. The Smoluchowski population balance equation (PBE) was used to model the process of particle aggregation and was coupled with the advection‐dispersion‐attachment equation to form a nonlinear transport model. Furthermore, an efficient and accurate solver for the PBE, and an iterative solver for the linear or nonlinear attachment equations were employed. The new numerical model was applied to nanoparticle transport experimental data available in the literature. Although, conventional transport models can be used to describe nanoparticle migration at low ionic strength conditions, such models might not be applicable for high ionic strength conditions, where aggregation becomes a dominant process. Aggregation is significantly affecting the transport characteristics of nanoparticles. Under high ionic strength conditions, the mass retention in the solid matrix of the porous medium increases, and a nonlinear particle attachment behavior may be observed. The proposed model performed remarkably well, successfully capturing numerous physical processes associated with nanoparticle transport, including particle‐size‐dependent dispersion. Ignoring the aggregation process and using conventional colloidal transport models to model nanoparticle transport may lead to erroneous results.

Holacratic management models in organizational systems

This article presents research results of holacratic models implementation for high-tech sector of Russian and foreign markets. The relevance of conceptual models implementation to organizational systems is caused by a competition of effective business models and continuous costs optimization of high-tech enterprises. The problem of a rapid transition from classical cascade and divisional models to holacratic ones is forced by the needs of management methods and models that will ensure high-quality process and economic changes without a negative impact on the supply chain and the process of creating goods or services with a high added value for modern enterprise economy. This research presents a comparison of classical management methods in organizational systems versus holacratic ones. The problem analysis considers the mathematical features of comparing existing management models. Achieved results presented in this article indicates that the need of the methodology for rapid transition to holacratic management models in organizational systems is beginning to emerge including development of a conceptual mathematical model for an ideal holacratic organization. Functional and process gaps during transition to a new management model including mathematical aspects under given conditions can be considered as the conclusion for research.

Modeling of transportation and technological processes in automated systems

The purpose of the study is to create a problem-oriented model of transport and technological processes in automated systems. To achieve this goal, it is necessary to develop methodological aspects of creating an automated modeling system. The content of the basic principles of problem-oriented modeling in the study of an integrated automated system for managing stocks and transport and technological processes is revealed in the paper. At the same time, methodological aspects of creating automated modeling systems, namely, a conceptual mathematical model for the analysis and standardization of technical and economic indicators are considered. The functioning of logistics systems, namely, system modeling (supply — transport) is also considered. The problems of interaction and relationships, optimization of resource flows, and increasing the efficiency of management decisions making have been solved. It is shown that modeling resource flows involves adjustments through iterative redistribution of interregional and intraregional supplies among suppliers and consumers. Combining product items into one delivery leads to savings in stocks formation costs by reducing the number of orders. To create effective automated control systems, it is necessary to study in detail the primary object — the logistics and technical support system itself. The creation of applied mathematical and software is a promising direction for solving this problem and developing it as an automated modeling system. In this regard, when creating such automated control systems, it is most advisable to use a model-oriented approach, which is based on the principles of system analysis, standardization, classification and modularity. Thus, it is shown that the use of the problem-oriented approach to creating an automated modeling system makes it possible to reduce the labor intensity of its development and implementation, to provide the opportunity to unify algorithms for solving a problem, but also to apply standard methods for processing experimental results.

Mitigating non-genetic resistance to checkpoint inhibition based on multiple states of immune exhaustion

Despite the revolutionary impact of immune checkpoint inhibition on cancer therapy, the lack of response in a subset of patients, as well as the emergence of resistance, remain significant challenges. Here we explore the theoretical consequences of the existence of multiple states of immune cell exhaustion on response to checkpoint inhibition therapy. In particular, we consider the emerging understanding that T cells can exist in various states: fully functioning cytotoxic cells, reversibly exhausted cells with minimal cytotoxicity, and terminally exhausted cells. We hypothesize that inflammation augmented by drug activity triggers transitions between these phenotypes, which can lead to non-genetic resistance to checkpoint inhibitors. We introduce a conceptual mathematical model, coupled with a standard 2-compartment pharmacometric (PK) model, that incorporates these mechanisms. Simulations of the model reveal that, within this framework, the emergence of resistance to checkpoint inhibitors can be mitigated through altering the dose and the frequency of administration. Our analysis also reveals that standard PK metrics do not correlate with treatment outcome. However, we do find that levels of inflammation that we assume trigger the transition from the reversibly to terminally exhausted states play a critical role in therapeutic outcome. A simulation of a population that has different values of this transition threshold reveals that while the standard high-dose, low-frequency dosing strategy can be an effective therapeutic design for some, it is likely to fail a significant fraction of the population. Conversely, a metronomic-like strategy that distributes a fixed amount of drug over many doses given close together is predicted to be effective across the entire simulated population, even at a relatively low cumulative drug dose. We also demonstrate that these predictions hold if the transitions between different states of immune cell exhaustion are triggered by prolonged antigen exposure, an alternative mechanism that has been implicated in this process. Our theoretical analyses demonstrate the potential of mitigating resistance to checkpoint inhibitors via dose modulation.

Study to improve the operations of steel ingot reheating furnace using modeling tools

The present investigation obtained a system of mathematical models of operation of the steel ingot heating furnaces. For this, the systems analysis and synthesis methodology were used, from which the conceptual mathematical model was derived, as well as the interrelation of the furnace with the rest of the plant systems. The model was validated under static and dynamic operating conditions by purchasing the values of the variables measured in a Case Study facility with the values obtained by simulation. In addition, objective function optimization tools were applied by exploring a network of variables with a penalty for breach of constraints. The system responded satisfactorily to the disturbances inherent in the production process.

The Creation of Fundamentally New Products as a Factor of Organizations’ Sustainable Economic Development

This study analyzed the sustainable economic development of some organizations for the period of 2020–2022. The authors found that organizations’ sustainable development is influenced by technological superiority based on the creation and production of radical new products that can form new markets or be dominant in existing ones. This study examined effective management based on the application of digital technology and artificial intelligence for the creation and production of radically new products, which creates conditions for the advanced sustainable economic development of the organization. The main drivers of these processes are technological platforms, the formation of which requires significant amounts of different types of resources. To solve the issue of investment in the creation of radically new products in conditions of limited resources, the authors researched and developed tools for the effective use of investment in the creation of radically new products in order to ensure the formation of organizations of advanced, sustainable economic development. In the development of methodological tools for managing the creation and development of radically new products, a conceptual mathematical model for assessing the criteria of economic efficiency of projects is proposed. Thus, the proposed tools for managing the creation of radically new products and advanced sustainable economic development of organizations form the basis for technological superiority and sustainable economic development in modern economic conditions.

Understanding the impact of disease and vaccine mechanisms on the importance of optimal vaccine allocation.

Vaccination is an important epidemic intervention strategy. However, it is generally unclear how the outcomes of different vaccine strategies change depending on population characteristics, vaccine mechanisms and allocation objective. In this paper we develop a conceptual mathematical model to simulate strategies for pre-epidemic vaccination. We extend the SEIR model to incorporate a range of vaccine mechanisms and disease characteristics. We then compare the outcomes of optimal and suboptimal vaccination strategies for three public health objectives (total infections, total symptomatic infections and total deaths) using numerical optimisation. Our comparison shows that the difference in outcomes between vaccinating optimally and suboptimally depends on vaccine mechanisms, disease characteristics, and objective considered. Our modelling finds vaccines that impact transmission produce better outcomes as transmission is reduced for all strategies. For vaccines that impact the likelihood of symptomatic disease or dying due to infection, the improvement in outcome as we decrease these variables is dependent on the strategy implemented. Through a principled model-based process, this work highlights the importance of designing effective vaccine allocation strategies. We conclude that efficient allocation of resources can be just as crucial to the success of a vaccination strategy as the vaccine effectiveness and/or amount of vaccines available.

Sustainable Water Management in Kalu River Basin of Sri Lanka: Comparison of Watershed Yield Computations for Water Security

Irrigation reservoir design associated with ungauged watersheds requires reliable watershed streamflow estimations. In practice, designs are either based on the empirical model of Irrigation Department guideline or based on recent conceptual mathematical models. Use of empirical models require appropriate design levels for the calculation of design streamflow. Popular mathematical models require adequate guidance for the application of safety factors to the model outputs. The two aspects that need attention are, the reliability of streamflow estimations by models and the incorporation of safety factors when converting model outputs as design streamflow. The main gap in the literature is a critical evaluation of the importance of these two factors with real-life applications. The authors, in a review paper, identified that best available method for yield estimation is the Irrigation Department Guideline Method (IGM) but pointed to the necessity of verification with field observations. Accordingly, the present study compared the most commonly used IGM, HEC HMS and the Unit Hydrograph method (UH) models by carrying out an evaluation of yield estimation in Kalu Ganga watershed at Ellagawa. This study, while focusing on the availability of model parameters for streamflow assessments in ungauged watersheds, aimed at the demonstration of a comparison in a watershed which has data and established model parameters. It is expected that this model demonstration would facilitate the selection of an appropriate yield estimation model not only in wet zone but also the dry zone of Sri Lanka. Spreadsheet models were developed for each method while using literature reported model parameters and incorporating best engineering judgment. Comparison of model estimations with observed data was done for annual and seasonal water balance, and for flow duration curves, while using Mean Ratio of Absolute Error (MRAE) as the numerical indicator. Evaluation of outputs from the three methods showed that the IGM estimates of monthly yield estimations closely matched with the observed data. MRAE for Overall Hydrograph, in-case of IGM, HEC HMS, UH methods were 0.35, 0.58 and 0.4, respectively. The necessity of incorporating yield thresholds for modern hydrological models and updating of available guidelines were highlighted. The study revealed the necessity of establishing design guides for selection of model parameters when computing streamflow in ungauged watersheds. IGM with guidance for parameters was recognized as the best model amongst the selected for monthly yield estimation. HEC and UH results create significant ambiguities when compared with IGM because of the unreliability associated with the selection of processes and parameters. This study pointed to the necessity of considering safety factors, as clearly pointed out in Irrigation Department guidelines. This is vital when using modern mathematical models.

Interaction between crowding and growth in tumours with stem cells: Conceptual mathematical modelling

This research paper proposes and discusses a conceptual modelling of both growth of tumours in presence of immortal multipotent cancer stem cells (CSCs) and of several lineages of differentiated tumour cells (CCs). The replication of CSCs is assumed symmetric or asymmetric with a prescribed mean ratio and mitosis and apoptosis are taken into account for the CCs aging. Replication can be hindered by the local crowding of the cells in the vicinity of the mother cell. The model is implemented in the framework of 3D cellular automata (CA) whose dynamics is governed by stochastic rules. Some simulations are displayed showing the growth of a tumour and the fractions of different lineages and age classes of CCs. Then, an approach that considers the same dynamics of aging, replication, and apoptosis, but with the aim to study the time evolution of the fractions of the different lineages and age classes of cells averaged over the total volume is presented. The dynamics is governed by a system of ordinary differential equations (ODEs), hence by deterministic rules. Numerical simulations of the solution of this system show qualitative similarity with the CA results, although the crowding effect is no longer a local effect, but also averaged over the total volume. The Appendix provides the proof of the mathematical well-poscdness of this model in a general framework.

Mathematical Model of Protection of Critical Infrastructure Object from Trojan Programs

The article proposes a conceptual mathematical model for protecting critical infrastructure objects from Trojan programs. The model is based on a game-theoretic approach where the defender and the attacker have conflicting goals. When applying the model, a vulnerability analysis of critical infrastructure objects is performed to identify potential weak points that can be exploited by Trojan programs. Then a game model is formulated to capture the strategic interaction between the defender and the attacker. An optimal security investment for the defender is introduced, which balances the cost of security against the expected loss from a successful attack. Also, the effectiveness of the proposed protection strategies is evaluated using testing and evaluation methods. The research results show that the model is effective in protecting critical infrastructure objects from Trojans and can help allocate security resources to maximize protection while minimizing costs.

Верификация и валидация компьютерных моделей

The paper considers the steps involved in building modern digital simulations, from a conceptual mathematical model to specific simulation settings, for example, meshing parameters. The paper presents a generalised approach to verification and validation of computer simulations and describes its main stages. The approach proposed is based on the assumption that the complex physical phenomena and objects to be simulated have a hierarchical structure that allows them to be split into constituent components (according to their design purpose, such as assemblies or parts, or according to the field of study, such as gas dynamics, combustion, heat transfer, etc.). Each element uses its own mathematical (or digital) model that will have undergone verification and validation. A complex computer simulation is verified and validated from the bottom up, that is, in the following order: individual parts, then assemblies, and finally the physical phenomenon or object under consideration. We consider a case study of verification and validation as pertaining to a comprehensive calculation of axial turbine parameters for a gas turbine engine. We also address issues concerning verification and certification of software used to develop digital simulations, as well as issues concerning verification and validation of digital product twins.

Nonlinear elite generation change model

The purpose of the presented article was to build a concise conceptual mathematical model of the competitive dynamics of alternative types of social activity. The model was developed in the form of a discrete two-dimensional non-linear mapping. The proposed mapping is new and has not been previously studied either in the field of mathematical social dynamics (sociophysics), or in the section of discrete models of nonlinear dynamics. The approach we used corresponds to the ideas of the theory of social time put forward by F. Braudel. Nonlinear two-dimensional mapping, in a paradoxical way, given the general socio-economic ideas about the relationship between generations, as it turned out, has a Hamiltonian structure. The analysis showed that both formally and in terms of qualitative behavior it is close to the standard model describing a rotator under the action of impacts. It was found that, depending not only on the parameters of the problem, but also on the initial conditions, in this case, periodic, quasiperiodic, and chaotic dynamics are simultaneously possible. Within the framework of the model, this means a great variety of intergenerational relationships. Thus, the data in the system will not be “forgotten”. The influence on the dynamics of the model of “dissipative additions” describing the degradation of the elite, the desire of society to “eliminate the best” is demonstrated. The dynamics of the system and its dependence on parameters become much simpler; nevertheless, cyclicity and multistability do not disappear in it. In this approximation, history turns out to be “local” — the details and peculiarities of society’s behavior will be “forgotten” after several generations. The study of the constructed model opens up great prospects for the analysis of various types of cyclical processes in mathematical history.

Георізноманіття: виміри, конотації, асоціації

The paper aims to outline the main characteristics of the term ‘geological diversity’ in its three most clear and interrelated aspects: legal, worldview, and natural historic. The legal aspect of geodiversity now seems to be the most clearly comprehended and the most efficient in regard to its primary tasks. The experience of regulation in the international law of various objects of geodiversity is considered in relation to the concept of world her-itage. Based on the convention of biological diversity, which is also part of world heritage, we attempt by anal-ogy to compare biodiversity and geodiversity as an object of legal regulation. The system of Kant’s philosophy is analysed as a worldview basis, which can be used to clarify the meaning of the term ‘geodiversity’ and which is based on the priority of the researcher’s self-reflection in theoretical or practical judgments: being ‘in-tersubjective’ it finds realization in principles of postmodernism and other worldview novelties. The natural his-toric aspects of geodiversity are considered as one of the variants of systematization of the factual materials amassed in the earth sciences, based on the needs of the related scientific, economic, and conservational activ-ities of humans in the geological space. Analysing the demands to science in general and to geology in particu-lar, we suggest that despite the importance of systematizing paradigms, the systematic unity of geology—at least at the current stage of its development—is based on the specifics of geological thinking able to fully comprehend the diversity of geological phenomena and on the basic principles of systematization of the fac-tual material neutral in regard to dominating paradigms. In this sense, geology—as a multi-level dynamic sys-tem of reflection of the results of geological studies—embodies the ‘oncoming movement’ of empirical gener-alizations of the factual material and the conceptual-mathematical models of the more adequate reflection of the diversity of geological phenomena, among which models of fractal geometry appear to be the most pro-spective.

Mathematical Modelling of Vertical Looped Water Slide Using Matlab

Abstract: A conceptual mathematical model of a water slide with vertical loops is developed. The principle used is the conservation of energy. The thrill experienced by a rider on a water slide is mainly due to the variation of G-force acting on the rider through the course of the ride. The geometry of the slide is developed by plotting G-force variation with the arc length of the loop. The G-force exposure limits should meet with the standards set by the F24 committee on amusement parks and rides. The coordinates of the slide geometry are determined by using Euler’s method of discretized equations. Keywords: G-Force, Centripetal acceleration, Clothoid curve, Weightlessness, Potential Energy, Kinetic Energy

AHP-TOPSIS METHOD AS A COMPONENT OF INFORMATION TECHNOLOGY FOR DUAL EDUCATION SYSTEM

Conceptual mathematical model of human resource management (HRM) in the field of personnel training is developed in this paper. The developed model is the basis of information technology of dual education - a component evaluating the students training in the company. The information technology of dual education, which is being developed by us, will integrate education and work in the system of dual education, will solve the problem of cooperation between the company and the educational institution. By the methods of multicriteria analysis the proposed mathematical model of HRM describes the subsystems of dual education: companies, students' academic achievements, criteria for assessing the achievement of competencies by academic courses learning. Intuitionistic fuzzy sets for the determination of the subjectivity of assigning estimates by fuzzy trapezoidal numbers are modified, method of adjusting assigned ratings by experts, taking into account subjectivity is developed in this paper. The method for adjusting the subjectivity of final estimates of the multicriteria problem ranking depending on the aims of the integrating system of ranking alternatives subsystems is proposed. Numerical example of the TOPSIS method application taking into account the subjectivity of experts and without it is presented.Key words: fuzzy logic, analytic hierarchy process, dual education, information technology, TOPSIS, Intuitionistic fuzzy sets

The Impact of Urban Sprawl on Environmental Pollution: Empirical Analysis from Large and Medium-Sized Cities of China.

This research sought to uncover the environmental effects that urban sprawl brings about by using panel data of 35 large and medium-sized cities over the timespan 1998–2019. A nonlinear relationship between urban sprawl and environmental pollution might exist and be shown by constructing the conceptual mathematical model. The panel unit root test indicated that there exists a long-run equilibrium relationship between urban sprawl and environmental pollution. Regression results showed that there is a U-shaped curve relationship between the two core variables for the full sample. The impacts of urban sprawl on environmental conditions have regional heterogeneity. A significant U-shaped curve was discovered for eastern and western regions, while an insignificant inverted U-shaped curve was discovered for the central region. Furthermore, we found a significant U-shaped curve for cities with high and low degree of sprawl. By contrast, we found a significant inverted U-shaped curve for cities with a middle degree of sprawl, which indicated that moderate urban sprawl is beneficial for environmental conditions. We additionally discovered a significant U-shaped curve and inverted U-shaped curve for cities with low and middle pollution, respectively. Fixed-asset investments and foreign direct investments exacerbate urban environmental pollution. Market freedom and industrial structure adjustment are conducive to pollution reduction. The conclusions were consistent when we subdivided the sample by time periods and substituted with a systematic GMM (Generalized Method of Moments) estimation method in the robustness check. Policy recommendations were put forward according to the research findings.

Web-based tool for the decision making in photovoltaic/wind farms planning with multiple objectives

Decision-making in energy planning implies a compromise between several criteria. Technical, economic and environmental criteria, have been the most adopted. The lack of a system that, taking into account technical, economic and environmental criteria, proposes to the decision makers detailed and efficient solutions that satisfy their preferences system, in energy planning, based on the projection of photovoltaic/wind farms at national level, motivated the present study. Conceptual mathematical model and detailed mathematical model of the task were elaborated. The criteria taken into account by the model determined four objective functions: the maximization of the generated energy, the minimization of costs, the minimization of the impacted area by photovoltaic farms and the minimization of the impacted area by wind farms. NSGA-II algorithm was selected to serve as a solution method to the multi-objective problem obtained. A web-based tool was developed, which constitutes a decision-making support system in the planning of photovoltaic/wind farms at national level. The integration with geographic information systems allowed the estimation of the energy parameters of the model and led to the complete automation of the tool.

Exploring the dynamics of a tumor-immune interplay with time delay

With the effect of discrete time delay in deliberation, we propose and analyze a conceptual mathematical model for the tumor-immune interaction. The proposed model is delineated by a system of three coupled non-linear ordinary differential equations (ODEs), namely tumor cells, effector cells and cytokine Interleukin-2 (IL-2). Though simple, the model can have complicated dynamical behaviors. We have discussed the qualitative properties of the mathematical model including existence and positivity of the solutions. We find out tumor-free singular point and interior steady states in our mathematical model. We have studied the local stability analysis of the biological feasible steady states in both of the delayed and non-delayed system. By using transversality condition, we have analyzed Hopf bifurcation by using time delay τ as a bifurcation parameter. We have estimated the length of time delay parameter applying Laplace transformation for preserving the stability of period-1 limit cycle that provides the idea about the mode of action in controlling oscillations in the growth of tumor cells. We performed numerical simulations and explored their biological implications to validate our theoretical analysis. We have also drawn bifurcation diagram of delayed model with reference to the intrinsic growth rate α of tumor cell, deactivation rate d1 of tumor cell, activation rate c2 of effector cell and death rate d2 of effector cell. Theoretical and numerical analysis show that in presence of IL-2 the effector cells can cause the tumor cell population to regress.

A mathematical model of COVID-19 transmission between frontliners and the general public.

The number of COVID-19 cases is continuously increasing in different countries including the Philippines. It is estimated that the basic reproduction number of COVID-19 is around 1.5–4 (as of May 2020). The basic reproduction number characterizes the average number of persons that a primary case can directly infect in a population full of susceptible individuals. However, there can be superspreaders that can infect more than this estimated basic reproduction number. In this study, we formulate a conceptual mathematical model on the transmission dynamics of COVID-19 between the frontliners and the general public. We assume that the general public has a reproduction number between 1.5 and 4, and frontliners (e.g. healthcare workers, customer service and retail personnel, food service crews, and transport or delivery workers) have a higher reproduction number. Our simulations show that both the frontliners and the general public should be protected against the disease. Protecting only the frontliners will not result in flattening the epidemic curve. Protecting only the general public may flatten the epidemic curve but the infection risk faced by the frontliners is still high, which may eventually affect their work. The insights from our model remind us of the importance of community effort in controlling the transmission of the disease.