Formulation Of Mathematical Model Research Articles

Is a mathematical model equivalent to its computer implementation?

A recent trend in mathematical modelling is to publish the computer code together with the research findings. Here we explore the formal question, whether and in which sense a computer implementation is distinct from the mathematical model. We argue that, despite the convenience of implemented models, a set of implicit assumptions is perpetuated with the implementation to the extent that even in widely used models the causal link between the (formal) mathematical model and the set of results is no longer certain. Moreover, code publication is often seen as an important contributor to reproducible research, we suggest that in some cases the opposite may be true. A new perspective on this topic stems from the accelerating trend that in some branches of research only implemented models are used, e.g., in artificial intelligence (AI). With the advent of quantum computers, we argue that completely novel challenges arise in the distinction between models and implementations.

Enhancing the treatment efficiency of three-dimensional electro-Fenton system for organic wastewater: An analysis from the comprehensive perspective of H2O2 generation

For optimizing H2O2 generation in three-dimensional electro-Fenton (3D-EF) to enhance efficacy in treating organic wastewater, a comprehensive analysis from various perspectives of H2O2 generation was provided. By quantifying the generation of H2O2 within the reaction system and comparing it with the changing trends in organic wastewater treatment efficiency, a close correlation between H2O2 generation and organic wastewater treatment was revealed. A reliable and accurate kinetic model for H2O2 generation was formulated by building upon the reactions of H2O2 with electrodes and coexisting substances. The mathematical formulation of the kinetic model pinpointed pivotal factors influencing H2O2 generation, including current density, dissolved oxygen concentration, and the Fe catalytic activity substance. The experimental data and fitted results under various conditions indicated that the model could reasonably and accurately describe the relationship between pivotal factors and the quantity of generated H2O2. Crucial strategies were proposed to enhance H2O2 generation in the 3D-EF system by drawing from the impact rules of pivotal factors on H2O2 generation. These strategies primarily focused on improving electrode performance, optimizing reactor conditions, and refining particle electrode preparation processes.

Обобщённая математическая модель основных задач теории упругости для анизотропных тел

Introduction. The assessment of the strength of underground structures is a complex task that requires a comprehensive approach. In many cases empirical methods based on experience are not sufficient. For effective application of analytical methods, it is necessary to use mathematical modelling. This allows to simplify the problem considerably, to consider different variants, to identify cases to obtain a solution in a closed form. Materials and methods. The model is based on a system of singular integral equations with a shift and complex conjugate terms. The solution of the system is the complex elastic potential. Systems of singular equations with a Carleman shift are considered on the space of random functions converging in the mean square to expand the possibility of practical use of the work results. Results. The results of the study are: a mathematical model formulation, the development of an algorithm for reducing a system of singular equations to a system of known Fredholm integral equations of the second kind, a method for determining the solvability conditions and the number of solutions. Discussion. As a result of the study: (1) a general algorithm for finding a solution to a mathematical model is obtained; (2) the methodology for determining the number of solutions and the type of solvability conditions is given; (3) The solution algorithm is extended for the stochastic case; (4) The possibility of wider application of the mathematical apparatus of functions of complex variable for research of strength properties of rocks is proved. Conclusion. The proposed comprehensive approach to assessing the strength characteristics of underground structures, combining a set of analytical methods in conjunction with mathematical modelling, expands the variability of calculation and allows to simplify the problem significantly and obtain a solution in closed form. Resume. The paper develops a mathematical model of the stress state of an elastic body, which allows solving the basic problems of elasticity theory for a variety of media. Suggestions for practical applications and directions for future research. The results of the study make it possible to improve the efficiency of analytical methods in the study of the strength of underground structures. The obtained results are applicable for predicting the strength and safety of underground structures.

Mathematical Formulation of a Co-infection Model and its Analyses for Monkeypox and HIV/AIDS Infections

The dynamics of the co-infection of monkeypox and HIV/AIDS is examined from a mathematical perspective via a deterministic 13-compartment model. This consists of the investigation of the equilibrium points, the basic reproduction numbers and the equilibrium points’ stability. The mathematical analysis reveals that the model is epidemiologically well-posed, and that the basic reproduction number for the monkeypox sub-model is a function of the likelihood of getting infected, the rate of effective contact, the infection coefficient of the monkeypox-infectious class, the monkeypox prevention measure, the progression rate from monkeypox-exposed class to monkeypox-infectious class, the natural death rate, the vaccination rate and the waning rate of the vaccine. It also depends on the recovery rate for the monkeypox-exposed class and the monkeypox-induced death rate. The analysis also reveals that the basic reproduction number for the HIV/AIDS sub-model is a function of the likelihood of getting infected, the rate of effective contact, the HIV/AIDS prevention measure, the infection coefficient of the monkeypox-infectious class, the HIV/AIDS-induced death rate, the natural death rate, the infection coefficient of AIDS-only class, and the progression rate of HIV-only class to AIDS-only. The stability analysis reveals that the disease-free equilibrium of the sub-models are globally asymptomatically stable, when the basic reproduction number is less than unity. Numerical simulations of the model reveal the effect of changes in certain parameter values on the population sizes. Increasing or lowering the values of certain parameters can significantly affect the sizes of some classes. The Maple 18 programming software was used to carry out all calculations and numerical simulations.

Analysis of the Spread of Covid-19 via Atangana-Baleanu Fractional Derivatives

We study the spread of the epidemic via Atangana-Baleanu Fractional Derivatives. We present the mathematical analysis and formulation of a fractional model for the epidemic. The existence and uniqueness of the solution for the proposed model are proved. The study also investigates the existence of disease-free equilibrium and analyzes its stability properties. To validate the theoretical results, we provide a numerical scheme for the fractional model and present various simulation results. These results can serve as a valuable resource in developing strategies to mitigate the spread of the epidemic.

Service accessibility strategy for aircraft maintenance routing with interorganizational collaborations on outsourcing maintenance

Airline companies are increasingly outsourcing their fleets’ heavy maintenance to independent maintenance service providers. This paper investigates the aircraft maintenance routing problem (AMRP) under the Maintenance, Repair, and Overhaul (MRO) outsourcing mode. Considering interorganizational maintenance implementation, an airline company’s accessibility to maintenance service is affected by the varying maintenance capabilities of the maintenance service provider, which depends on heterogenous maintenance resource availability (e.g., the accommodation capacity of maintenance hangars and the availability of maintenance technicians and aviation spare parts). To enhance the airline’s service accessibility to maintenance service, we propose an efficient maintenance planning strategy with a collaborative mechanism based on service information sharing and service capability evaluation from the airline’s perspective. Afterward, a time-complexity reduction approach is presented to enhance the discrete-time-stamp-indexed mathematical model formulation. The efficiency and effectiveness of the proposed approach were evaluated through various problem scenarios, based on the operational data from a regional airline. Managerial implications regarding maintenance strategy and the accuracy of maintenance capability evaluation are also discussed.

Efficient bioremediation of indigo-dye contaminated textile wastewater using native microorganisms and combined bioaugmentation-biostimulation techniques

In this work, the bioremediation of wastewater from the textile industry with indigo dye content was carried out using combined bioaugmentation, bioventilation, and biostimulation techniques. Initially, the inoculum was prepared by isolating the microorganisms from the textile wastewater in a 2 L bioreactor. Then, the respirometry technique was implemented to determine the affinity of the microorganisms and the substrate by measuring CO2 and allowed the formulation of an empirical mathematical model for the growth kinetics of the microorganism. Finally, the bioremediation was carried out in a 3 L bioreactor obtaining an indigo dye removal efficiency of 20.7 ± 1.2%, 24.0 ± 1.5%, and 29.7 ± 1.1% for equivalent wavelengths of 436 nm, 525 nm, and 620 nm. The chemical oxygen demand showed an average reduction of 88.9 ± 2.5%, going from 470.7 ± 15.6 to 52.3 ± 10.7 ppm after 30 days under constant agitation and aeration. A negative generalized exponential model was fitted to assess the affinity of the microorganism with the wastewater as a substrate by evaluating the production of CO2 during the bioremediation. Bioremediation techniques improve water discharge parameters compared to chemical treatments implemented in the industry, reducing the use of substances that can generate secondary pollution. Bioaugmentation, biostimulation, and bioventing of the textile wastewater in this study demonstrate the potential of these combined techniques to serve as an efficient alternative for indigo-contaminated wastewater in the textile industry.

Mathematical Modeling of Bird Harvesting in Intensive Poultry System

This work, presents a formulation of mathematical model of bird harvesting in an intensive poultry system, under the assumption that under a favourable environmental atmosphere and good management system, the birds have logistic growth. The model is analysed using methods from dynamical system theory and theory of calculus. It was established that the system has two steady state, the two equilibrium state are both locally asymptotically stable. The first one is stable if there is a bound on the harvest rate of the birds, which is proportional to the growth rate of the birds. The second equilibrium state is locally asymptotically stable (LAS) if k < \(\frac{r(C+y)}{p}\) that is if the carrying capacity is less than the ratio of the sum of and Per unit tax on the bird to that of Per unit price of the birds. Further analysis indicates that the limiting population of bird, that is the maximum population of birds that the available resources in the system can sustain and also ensures harvesting profitability is given as

Formal Languages, Mathematical Models and Bike-Sharing

Abstract Professor Jane Hillston is one of the winners of 2023's Lovelace Medal. She discusses her work with Brian Runciman MBCS.

Applications of Artificial Intelligence in Power Systems

A continuous and reliable supply of electricity is necessary for the functioning of today’s modern and advanced society. Since the early to mid 1980s, most of the effort in power systems analysis has turned away from the methodology of formal mathematical modeling which came from the areas of operations research, control theory and numerical analysis to the less rigorous and less tedious techniques of artificial intelligence (AI). Power systems keep on increasing on the basis of geographical regions, assets additions, and introduction of new technologies in generation, transmission and distribution of electricity. AI techniques have become popular for solving different problems in power systems like control, planning, scheduling, forecast, etc. These techniques can deal with difficult tasks faced by applications in modern large power systems with even more interconnections installed to meet increasing load demand. The application of these techniques has been successful in many areas of power system engineering.

Comparative Assessment of Two Global Sensitivity Approaches Considering Model and Parameter Uncertainty

AbstractGlobal Sensitivity Analysis (GSA) is key to assisting appraisal of the behavior of hydrological systems through model diagnosis considering multiple sources of uncertainty. Uncertainty sources typically comprise incomplete knowledge in (a) conceptual and mathematical formulation of models and (b) parameters embedded in the models. In this context, there is the need for detailed investigations aimed at a robust quantification of the importance of model and parameter uncertainties in a rigorous multi‐model context. This study aims at evaluating and comparing two modern multi‐model GSA methodologies. These are the first GSA approaches embedding both model and parameter uncertainty sources and encompass the variance‐based framework based on Sobol indices (as derived by Dai & Ye, 2015, https://doi.org/10.1016/j.jhydrol.2015.06.034) and the moment‐based approach upon which the formulation of the multi‐model AMA indices (as derived by Dell'Oca et al., 2020, https://doi.org/10.1029/2019wr025754) is based. We provide an assessment of various aspects of sensitivity upon considering a joint analysis of these two approaches in a multi‐model context. Our work relies on well‐established scenarios that comprise (a) a synthetic setting related to reactive transport across a groundwater system and (b) an experimentally‐based study considering heavy metal sorption onto a soil. Our study documents that the joint use of these GSA approaches can provide different while complementary information to assess mutual consistency of approaches and to enrich the information content provided by GSA under model and parameter uncertainty. While being related to groundwater settings, our results can be considered as reference for future GSA studies coping with model and parameter uncertainty.

Sustainable Rail/Road Unimodal Transportation of Bulk Cargo in Zambia: A Review of Algorithm-Based Optimization Techniques

Modern rail/road transportation systems are critical to global travel and commercial transportation. The improvement of transport systems that are needed for efficient cargo movements possesses further challenges. For instance, diesel-powered trucks and goods trains are widely used in long-haul unimodal transportation of heavy cargo in most landlocked and developing countries, a situation that leads to concerns of greenhouse gases (GHGs) such as carbon dioxide coming from diesel fuel combustion. In this context, it is critical to understand aspects such as the use of some parameters, variables and constraints in the formulation of mathematical models, optimization techniques and algorithms that directly contribute to sustainable transportation solutions. In seeking sustainable solutions to the bulk cargo long-haul transportation problems in Zambia, we conduct a systematic review of various transportation modes and related mathematical models, and optimization approaches. In this paper, we provide an updated survey of various transport models for bulk cargo and their associated optimized combinations. We identify key research challenges and notable issues to be considered for further studies in transport system optimization, especially when dealing with long-haul unimodal or single-mode heavy cargo movement in countries that are yet to implement intermodal and multimodal systems.

Performance of a freight platform equipped with automated handling units. Analysis thought an optimization model

Automation should help the freight platforms to be more competitive and sustainable. The automatic handling units (AHUs) allow to speed up the freight handling operations by eliminating time wasters, increasing safety, and also allowing for a reduction in traditional labour; but they require continuous monitoring and intelligent management entrusted to specialized personnel. The use of AHUs is also seen positively from an energy and environmental sustainability point of view.The paper focuses on a smart organizational and functional structure of a freight platform equipped with automated handling vehicles. The study proposes the mathematical formulation of an optimization model that aims to minimize the operating times of handling goods in a logistics platform through the introduction of fully automatic vehicles that replace traditional systems. So, this article concerns the scientific lock of automatic and optimized fleet management of AHU. It is a question of proposing a routing of this kind of smart vehicle fleet without blockages that allow regularly submitted missions to be carried out.

Formal description model and conditions for detecting linked coupling faults of the memory devices

Objectives. The aim of the work is to develop and analyze a formal model for describing complex linked coupling faults of memory devices and to formulate the necessary and sufficient conditions for their detection. The relevance of these studies lies in the fact that modern memory devices, characterized by a large amount of stored data and manufactured according to the latest technological standards, are distinguished by the manifestation of complex types of faults in them.Methods. The presented results are based on the classical theory and practice of march tests (March tests) of memory devices. In particular, the paper uses formal mathematical models for describing memory faults and shows their limitations for representing complex linked coupling faults. The main idea of the approach proposed by the authors is based on the use of a new formal description of such faults, the key element of which is the introduction of roles performed by the cells involved in the fault.Results. Three main roles are defined that cells of the complex linked coupling faults perform, namely the role of the aggressor (A), the role of the victim (V), as well as the role of both the victim and the aggressor (B), performed by two cells simultaneously in relation to each other. It is shown that the scenario for the implementation of the roles of memory failure cells is determined by the marching test used, and, first of all, by the address sequence used to access the cells. The procedure for setting a formal model of a linked fault is given, the basis of which is the roles performed by the cells included in the fault and the scenario specified by the test. A statement is given that determines, on the basis of a new formal description of linked coupling faults, the necessary and sufficient conditions for the detection of such faults. The presence of undetectable linked coupling faults is shown, and the conditions for their detection are formulated using multiple March tests. The conducted experimental studies have confirmed the validity of the formulated provisions of the article. On the basis of the classical example of a linked coupling fault, the fulfillment of necessary and sufficient conditions for its detection by a single march test is shown.Conclusion. The results of the research confirm that the proposed formal mathematical model for describing linked coupling faults makes it possible to determine their detection by marching tests. Within the framework of the proposed model, the necessary and sufficient conditions for detecting linked coupling faults by marching tests that detect single coupled faults are determined.

Modeling Plant Height and Biomass Production of Cluster Bean and Sesbania across Diverse Irrigation Qualities in Pakistan’s Thar Desert

Plant height (PH) plays a crucial role in determining per-plant growth and biomass production. Various characteristics of PH, along with the formulation of mathematical growth models, can provide a theoretical yield or biomass production based on water quality, fruit quality, and yields. The aim of this study was to investigate the relationship between PH and biomass per-plant production of two fodder crops (Cluster bean and Sesbania) under different water quality irrigation parameters in the Thar desert of Pakistan. Universal models of PH were established in which growing degree days (GDDs) and different water quality irrigation techniques have been applied as independent variables to calculate the maximum plant height of both of these crops. For this purpose, the logistic growth model, Gaussian growth model, modified Gaussian growth model, and Cubic polynomial growth model were used. Furthermore, universal biomass per plant production models have been developed for both crops, between biomass per plant, GDDs, and PH. However, among all these developed models, the modified Gaussian and Cubic polynomial growth models produced the best results. The Cubic polynomial model has meaningless parameters that make the model not very accurate, so the modified Gaussian growth model is the best among all models. Furthermore, the relationship between biomass per plant and different water qualities was established using Michaelis–Menten equations for both crops. It was observed that an increase in salt concentration within the water quality led to a decline in biomass per plant, indicating a negative linear relationship between these factors. The growth of Cluster bean and Sesbania ceased when the electrical conductivity (EC) reached or exceeded 12.34 ds/m and 11.51 ds/m, respectively. Furthermore, the results show that Cluster bean and Sesbania have the maximum plant height under brackish water irrigation when the GDD is at 1500 °C, while in freshwater irrigation, the maximum plant height of Sesbania and Cluster bean was observed when the GDD is at 1444 °C and 1600 °C. It was concluded that these developed mathematical models can provide crucial insights for enhancing production in desert conditions by improving water use efficiency across diverse irrigation water qualities.

Pre-asymptotic dispersion revisited

We develop a new approach to formulation and solution of mathematical models of one-dimensional advective–dispersive transport that specifies the hydrodynamic dispersion coefficient as a function of time since the solute has entered the flow field, termed ‘age.’ This approach addresses Taylor’s concern about the use of time-dependent dispersion coefficients to model pre-asymptotic dispersion by replacing time-dependence with age-dependence, where age of solute is exposure-time to the flow. We show closed form solutions obtained for transport on the −∞<x<∞ and a numerical solution for transport on the 0<x<∞ domain. We demonstrate how this works by application to an in-silico experiment recently published in a study addressing the same issue in a different manner. Our simple and intuitive approach matches the simulated pre-asymptotic data without additional terms or parameter fitting. The same principle applies to pre-asymptotic dispersion in other important upscaled one-dimensional transports e.g., in river corridor or groundwater flows.

Mathematical Formulation of Memory Model for Magnetization of Magnetic Fluid and its application using Numerical Methods

In this paper we propose memory model for magnetization of magnetic fluid - a colloidal suspension of magnetic nano particles in a liquid carrier.The idea originates from the mathematical formulation of constitutive equations of solids with memory given by Boltzmann.

Mitigation of wave force on a tunnel in the presence of submerged porous plate over trench-type bottom topography

Abstract Thin porous plates serve as an effective model for the construction of breakwater. Thus, the problem involving oblique wave interaction with a tunnel in the presence of a submerged horizontal porous plate over a trench-type bottom is investigated. In this paper, for the mathematical formulation of the physical model, water wave potentials are defined using Havelock's expansions and flow past over porous structure is modelled based on Darcy's law. The advantage of the trench type of bottom and horizontal plate are studied through the numerical results of forces on the tunnel. The study reveals that more energy loss and less force on the tunnel are obtained if the porous effect parameter of the plate or the length of the plate is increased up to a moderated value of these parameters. Compared to the case without porous plate and trench-type bottom topography, there are significant changes in forces due to this porous breakwater and trench-type bottom topography. In addition, from the present results, it may be noted that the load on the submerged tunnel is reduced by adding a submerged horizontal porous plate and asymmetric trench, which is helpful in understanding the role of porous breakwaters and trenches in applications to Ocean and Coastal Engineering.

A New Ridgely-Nevitt Regression-Based Computational Tool for Resistance and Power Predictions for Trawlers

This paper aims to present the architecture and the prediction accuracy of a new computational procedure of the “Ship Power V 1.0” software based on the Ridgely–Nevitt regression, applied to hull resistance predictions for Ridgely-Nevitt series trawlers. The Ridgely-Nevitt series is an important series of trawlers developed by and tested at the Webb Institute. Experimental resistance data have also been presented in the form of a regression model used to develop a new procedure of the “Ship Power V 1.0” software. Furthermore, this new procedure was completely harmonized with other software procedures based on the Holtrop and Van Oortmerssen evaluation methods. Although the mathematical formulation of the Ridgely-Nevitt regression model allows the assessment of the residual resistance coefficient of only nine values from the speed-length ratio, the implementation of an interpolation procedure made possible resistance predictions for any speeds from the acceptable speed-length ratio range. Resistance prediction accuracy improvement introduced by the new procedure was proven by the validation of calculation results not only against experimental data but also against the prediction results of other software procedures for three hulls from the Ridgely-Nevitt fishing vessel series. MAPE (mean absolute percentage error) values calculated against experimental data for the analyzed models were 3.26, 1.71, and 3.36, respectively. Prediction result comparisons of the Ridgely-Nevitt regression-based “Ship Power V 1.0” computational procedure and the experimental data and predictions of other computational procedures performed on three hulls from the Ridgely-Nevitt series have shown a substantial improvement in prediction accuracy.

A finite volume method based multi-group neutron diffusion model for space-time nuclear reactor kinetics problems in RZ geometry

The transient analysis of Fast Breeder Reactor (FBR) requires the development of high fidelity space-time nuclear reactor kinetics codes for the realistic prediction of spatial and temporal behavior of neutron flux and fission power along with the feedback effects. So, a space-time nuclear reactor kinetics model has been developed for solving the coupled time dependent multi-group neutron diffusion equations and the delayed neutron precursor equations in axi-symmetric cylindrical (r-z) geometry. The numerical model employs an orthogonal mesh finite volume method for spatial discretization and implicit method for time discretization. A computer code named MANDIR-KRZ (Multi-group Analysis of Neutron DIffusion in Reactor for Kinetics problems in RZ geometry) has been developed and employed to reconstruct the keff, transient neutron flux and power results of different benchmark problems. Mathematical formulation of the numerical model and results of the code for Dodds and FBR transient benchmark problems are discussed in this paper.