Role Of Mathematical Models Research Articles

Mathematical Modeling as One of Scientific Research Methods in the Humanities

The article analyzes the terms “model” as a reflection of a real object; “modeling” as one of the most important analytical research methods; and “mathematical modeling” as a powerful interdisciplinary instrument for scientific research. It provides a detailed classification of the concepts analyzed. The role of mathematical modeling in humanitarian studies in general, and in philosophy in particular, is determined. Considerable attention is devoted to the historical preconditions of global use of the mathematical modeling method in the humanities. The main areas of application of this method, such as economics, political science, sociology, psychology, education, etc., are studied. The main types of models to be successfully applied in the humanitarian research, such as fundamental, structural, generative, explicative, and prognostic ones, are outlined. Also, the article determines basic principles of mathematical modeling, which can lead to the most reliable scientific result. Such types of modeling as agent-oriented, theoretical game, simulation, situational, scholastic, and modeling of risks are separately analyzed. The specifics of using the method of mathematical modeling in philosophy are analyzed. The importance of its application to the natural and humanitarian spheres, based on philosophical traditions, is emphasized. The increasing interest of the world scientific community to carrying out humanitarian research with the use of modern technologies is observed. It also turns out that the application of mathematical modeling in various fields of research is gaining considerable popularity among home scientists.

The philosopher in the kitchen: the role of mathematical modelling in explaining drumlin formation

Scientific progress does not take place in a linear fashion, but often occurs through sudden advances following years of stagnation, in the course of which quite heated battles between proponents of different viewpoints can occur. In this paper, we review several instances of such debates, and use them to throw light on a current philosophical tussle between proponents of different explanations for the formation of drumlins, and other subglacial bedforms. We conclude that the differences of opinion which emerge in the literature may be more an issue of semantics rather than a fundamental disagreement about process. In addition, we provide a critical review of some recent theories of drumlin formation, highlighting their merits and demerits, as well as defending them against some of the criticism they have received.

Models, Measurement, and “Universal Patterns”

Development economics in the 1950s and 1960s, as Jan Tinbergen and Irma Adelman saw it, was a “groping in the dark.” Besides the limited knowledge of dynamic mechanisms, the lack of data was a severe problem for any attempt at modeling, whether macroeconomic, input-output, or in the tradition of national income accounting. As concerns the three main figures of this article—the empirical researchers Tinbergen, Hollis Chenery, and Adelman—each developed his or her own approach to modeling: modeling in stages, modeling to capture universal patterns, and factor analysis, respectively. Tinbergen, Chenery, and Adelman shared a common inductive methodology, which might rightly be called “measurement without theory,” in the sense that there was no economic theory that could help them in organizing the available messy and often unreliable data. Chenery saw a role for abstract mathematical models as helping inquirers to rise above such impediments, even if only temporarily, or to gain focus, as was the case with his making technical progress an exogenous variable. Tinbergen’s models of the “first stage” were also intended to make planning for development tractable, but without mixing planning with such focusing devices. Adelman, for her part, preferred to search for and identify factors of development.

M for Models

In this short notice I illustrate the role of mathematical models and their impact on our daily life. In particular I provide a couple of instances of applications: one to the enhancement of sports performances, the others to the improvement of our knowledge of the human cardio-circulatory system.

生態学で, 数理モデルはどのような役割を果たせるのか( 数理生態学の魅力)

生態学で, 数理モデルはどのような役割を果たせるのか( 数理生態学の魅力)

Analytical Equations of State of Natural Gas and Their Role in Mathematical Modeling

Analytical Equations of State of Natural Gas and Their Role in Mathematical Modeling

TASKS STATEMENT FOR MODERN AUTOMATIC CONTROL THEORY OF UNDERWATER COMPLEXES WITH FLEXIBLE TETHERS

The definition of a new class of control objects is proposed. It is an underwater complex with flexible tethers (UCFT) for which there is the need to automate motion control under uncertainty and nonstationarity of own parameters and external disturbances. Classification of marine mobile objects and characteristics of the flexible tethers as UCFT elements is given. The basic UCFTs configurations that are used in the implementation of advanced underwater technologies are revealed. They include single-, double- and three-linked structures with surface or underwater support vessels and self-propelled or towed underwater vehicles. The role of mathematical modeling in tasks of motion control automation is shown. The tasks of UCFT mathematical modeling are formulated for synthesis and study of its automatic control systems. Generalized structures of mathematical models of UCFT basic elements are proposed as the basis for the creation of simulating complex to study the dynamics of its motion. The tasks of UCFT identification as a control object are formulated. Their consistent solution will help to obtain a UCFT mathematical model. The basic requirements for UCFT automatic motion control systems are determined. Their satisfaction will ensure implementation of selected underwater technology. Areas of development of synthesis methods of UCFT automatic control systems are highlighted.

Comparison of specific sediment transport rates obtained from empirical formulae and dam breaching experiments

Sediment transport rate determination plays an essential role in mathematical models of embankment dam breaching. The sediment transport formulae commonly used today were mostly determined under considerably different conditions than those existing during the breaching of embankment dams, i.e. in connection with relatively mild longitudinal slopes. However, due to the scarceness of sediment transport relations for sediment transport rates on steep slopes, these traditional formulae are frequently used in dam breach modelling. This paper contains a description of a physical model of a 0.86 m high sandy dike constructed and breached at an outdoor laboratory operated by the Faculty of Civil Engineering, Brno University of Technology, Czech Republic. The dike shape and material were the same for all experiments. The used material was homogeneous non-cohesive medium-uniform sand. The results of the experimental breaching of the sandy dike were discussed and compared with sediment transport rates obtained from various empirical formulae. The comparison shows differences between experimental and calculated sediment transport rates which in all analysed cases indicate overestimation of the breaching rate calculated by empirical formulae.

The role of mathematical modeling in chemical cybernetics

The role of mathematical modeling in chemical cybernetics

The Role of Mathematical Modeling in Designing and Evaluating Antimicrobial Stewardship Programs

Antimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and suboptimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study cohort size, possible number of replicates, and effective study duration, model simulations can provide valuable information to inform decisions regarding the design of new ASPs, as well as evaluation and improvement of existing ASPs. To date, the potential of mathematical modeling methods in evaluating ASPs is largely untapped and much work remains to be done to leverage this potential.

Fractal analysis and control of the competition model

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

A two-phase model for drug release from microparticles with combined effects of solubilisation and recrystallisation

The present study aims to provide a comprehensive mathematical model for drug release from microparticles to the adjacent tissues. In the elucidation of drug release mechanisms, the role of mathematical modelling has been depicted thereby facilitating the development of new therapeutic drug by a systematic approach, rather than expensive experimental trial-and-error methods. In order to study the whole process, a two-phase mathematical model describing the dynamics of drug transport in two coupled media is presented. Drug release is described taking into consideration both solubilisation dynamics of drug crystallites and diffusion of the solubilised drug through the microparticle. In the coupled media, reversible dissociation/recystallisation processes are taking place. The model has led to a system of partial differential equations that are solved analytically. The model points out the important roles played by the diffusion, mass-transfer and reaction parameters, which are the main architects behind drug kinetics across two layers. The dependence of drug masses on the main parameters is also analysed.

Theoretical Approaches to Nuclear Proliferation

This article analyses discussions between representatives of three schools in the theory of international relations - realism, liberalism and constructivism - on the driving factors of nuclear proliferation. The paper examines major theoretical approaches, outlined in the studies of Russian and foreign scientists, to the causes of nuclear weapons development, while unveiling their advantages and limitations. Much of the article has been devoted to alternative approaches, particularly, the role of mathematical modeling in assessing proliferation risks. The analysis also reveals a variety of different approaches to nuclear weapons acquisition, as well as the absence of a comprehensive proliferation theory. Based on the research results the study uncovers major factors both favoring and impeding nuclear proliferation. The author shows that the lack of consensus between realists, liberals and constructivists on the nature of proliferation led a number of scientists to an attempt to explain nuclear rationale by drawing from the insights of more than one school in the theory of IR. Detailed study of the proliferation puzzle contributes to a greater understating of contemporary international realities, helps to identify mechanisms that are most likely to deter states from obtaining nuclear weapons and is of the outmost importance in predicting short- and long-term security environment. Furthermore, analysis of the existing scientific literature on nuclear proliferation helps to determine future research agenda of the subject at hand.

Perforation-mediated modified atmosphere packaging of fresh and minimally processed produce—A review

The overwhelming global demand by consumers for convenience and fresh quality fruit and vegetables, heightens the need for appropriate postharvest technologies. In order to maintain freshness quality attributes, extend the shelf life of fresh/minimally processed produce and reduce postharvest losses. Perforation-mediated modified atmosphere packaging (PM-MAP) offers the benefit of avoiding in-package anaerobiosis, extending the shelf life and maintaining quality fresh or minimally processed produce. This article presents an overview on the role of postharvest hurdle technologies in food packaging, critical evaluation of MAP and PM-MAP dependent parameters and the role of mathematical models. Furthermore, the successful application of PM-MAP on fresh and minimally processed produce was highlighted and future research prospects and challenges were identified.

Review: Bioelectrical mechanisms in spinal cord stimulation.

The aim of this review is to make specialists in a variety of disciplines familiar with basic aspects of spinal cord stimulation and the role of mathematical modeling in understanding its mechanisms of action and the solution of basic problems. The paper is divided into five sections. The content of each section also covers aspects of various disciplines. Most aspects are presented in an unusual way, likely resulting in new viewpoints and further developments in the growing field of neuromodulation. A special, integrating role is the mathematical modeling of spinal cord stimulation and the simulation studies of various aspects, such as the stimulation in axial low-back pain. In particular the conclusions from several computer simulation studies are relevant and of interest to specialists in many disciplines.

Theoretical Basics of Teaching Discrete Mathematics

The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures) plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training.

Current Views on Hydrodynamic Models of Nonideal Flow Anaerobic Reactors

A critical review of the different hydrodynamic mathematical models available for nonideal flow configurations of both low-rate and high-rate anaerobic reactors is presented, including upflow anaerobic sludge blanket reactors, anaerobic fluidized bed reactors, anaerobic biofilters, wet and dry digesters. The review highlights the role of mathematical modeling on design and operational optimization of organic waste and wastewater treatment plants. For each reactor configuration the following approaches, proposed by various authors, are presented and compared: (a) plug flow model, (b) tank in series model, (c) dispersion model, and (d) computational fluid dynamic model. The review gives a general overview on mathematical modeling of anaerobic nonideal plug-flow reactors and compares different models indicating the advantages and disadvantages to apply them for different reactor type.

Role of Mathematical Modelling in Transportation Sciences

A logistics network consists of suppliers, manufacturing centres, warehouses, distribution centres, and retail outlets as well as channels for the flow of raw materials, work-in-process inventory, and finished products between the facilities. In many cases, the problems of each logistics functions are treated as isolated functions. There are network design; information flow; transportation; inventory; and warehousing, material handling, and packaging. Whereas, the basis of performance improvement in integrated logistics network is total cost analysis. That is minimising the total cost of transportation, warehousing, order processing and information, lot quantity, and inventory carrying cost. In this paper, we consider an integrated logistics problem in minimising the total logistics cost and provide model for logistics network optimisation in form of a mathematical programming model. To solve a cost optimisation problem in those problem both production and distribution cost are significant and inter-related. An integrated model of logistics network minimises total physical distribution costs by simultaneously determining optimal plants and warehouse locations, flows in the resulting network, shipment compositions and shipment frequencies in the network using heuristics methodology. The objective is to optimise the production and distribution plan so as to minimise its total logistics cost.

Understanding Experimental LCMV Infection of Mice: The Role of Mathematical Models.

Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations should be tightly linked to a fundamental step called “coordinatization” (Hermann Weyl), that is, the definition of observables, parameters, and structures that enable the link with a biological phenotype. In this review, we analyse the mathematical modelling approaches to LCMV infection in mice that resulted in quantification of some fundamental parameters of the CTL-mediated virus control including the rates of T cell turnover, infected target cell elimination, and precursor frequencies. We show how the modelling approaches can be implemented to address diverse aspects of immune system functioning under normal conditions and in response to LCMV and, importantly, make quantitative predictions of the outcomes of immune system perturbations. This may highlight the notion that data-driven applications of meaningful mathematical models in infection biology remain a challenge.

The role of mathematical modelling in modern criminology: Comment on “Statistical physics of crime: A review” by M.R. D'Orsogna and M. Perc

The role of mathematical modelling in modern criminology: Comment on “Statistical physics of crime: A review” by M.R. D'Orsogna and M. Perc