Proposal of a pedagogical model for mathematics teacher education
Directory of Open Access Journals (Sweden)
Alfonso Jiménez Espinosa
2011-01-01
Full Text Available This research-based article reflects on mathematics teacher education, and proposes a pedagogical model for this purpose, called Gradual Research Pedagogical Model (MPGI. This model considers the central curricular elements of any academic education process: student, teacher and contents, with evaluation as transversal element for analysis and feedback. The training of future teachers is constituted by three moments, each with its specific emphasis: the first is “contextualization”, which aims at having the student understand his or her new academic role, and identify and overcome his or her academic weak points, the second is “knowledge foundation”, which offers basic education in the fields of mathematics and pedagogy, as well as sensibilization towards social issues, opening up the student’s possibilities as leader and agent of change, and lastly, “knowledge immersion”, which is centered on research and the identification and study of topics and problems of the mathematical discipline as well as the pedagogical field.
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts
Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep
2016-01-01
The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Mathematical modelling in engineering: A proposal to introduce linear algebra concepts
Directory of Open Access Journals (Sweden)
Andrea Dorila Cárcamo
2016-03-01
Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts: span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
International Nuclear Information System (INIS)
Nawalany, M.
1975-01-01
Mathematical models applied in isotope hydrology are presented in the paper. The most commonly used deterministic models are discussed in the first part of the paper including the piston flow and good mixing models. The model of nonideal mixing is introduced by the author into the hydrological considerations. This model is a generalization of the good mixing model and allows for different processes of mixing of natural isotopes in waters of hydrological systems. The most important stochastic model i.e. the dispersive model is discussed too. The ''three-velocities'' model is proposed the first time by the author. The ''three-velocities'' model differs from the other ones in following properties: it includes finite flow velocity of the tracer particles, it takes into account the presence of stagnant water, it satisfied the law of fluid continuity, it is convergent to the piston-flow model in limit. However the model proposed describes dispersion phenomenon and satisfied the tracer conservation law (i.e. standarization) - the two properties characteristic of all the models. The author's strong belief is that the user (hydrologist) having at his disposal given below review of the models will be able to choose the most adequate model in given hydrological conditions. (author)
Mathematical Modeling Using MATLAB
National Research Council Canada - National Science Library
Phillips, Donovan
1998-01-01
.... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...
Mathematical Modelling Approach in Mathematics Education
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Teaching Mathematical Modeling in Mathematics Education
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
International Nuclear Information System (INIS)
Castillo M, J.A.; Pimentel P, A.E.
2000-01-01
This work presents the results to define the adult egg viability behavior (VHA) of two species, Drosophila melanogaster and D. simulans obtained with the mathematical model proposed, as well as the respective curves. The data are the VHA result of both species coming from the vicinity of the Laguna Verde Nuclear Power plant (CNLV) comprise a 10 years collect period starting from 1987 until 1997. Each collect includes four series of data which are the VHA result obtained after treatment with 0, 4, 6 and 8 Gy of gamma rays. (Author)
MATHEMATICAL MODEL MANIPULATOR ROBOTS
Directory of Open Access Journals (Sweden)
O. N. Krakhmalev
2015-12-01
Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.
Developing mathematical modelling competence
DEFF Research Database (Denmark)
Blomhøj, Morten; Jensen, Tomas Højgaard
2003-01-01
In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....
Mathematical modelling techniques
Aris, Rutherford
1995-01-01
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
A Mathematical Formalization Proposal for Business Growth
Directory of Open Access Journals (Sweden)
Gheorghe BAILESTEANU
2013-01-01
Full Text Available Economic sciences have known a spectacular evolution in the last century; beginning to use axiomatic methods, applying mathematical instruments as a decision-making tool. The quest to formalization needs to be addressed from various different angles, reducing entry and operating formal costs, increasing the incentives for firms to operate formally, reducing obstacles to their growth, and searching for inexpensive approaches through which to enforce compliancy with government regulations. This paper proposes a formalized approach to business growth, based on mathematics and logics, taking into consideration the particularities of the economic sector.
Applied impulsive mathematical models
Stamova, Ivanka
2016-01-01
Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.
Mathematical modelling of metabolism
DEFF Research Database (Denmark)
Gombert, Andreas Karoly; Nielsen, Jens
2000-01-01
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Mathematical models in radiogeochronology
International Nuclear Information System (INIS)
Abril, J.M.; Garcia Leon, M.
1991-01-01
The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)
Concepts of mathematical modeling
Meyer, Walter J
2004-01-01
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec
Directory of Open Access Journals (Sweden)
TURČÁNI, Milan
2013-03-01
Full Text Available Nowadays, quality Mathematical basis - Informatics is an inherent part of study. Mathematical basis is provided by Discrete Mathematics that is taught as a compulsory subject in stated study program in the Department of Mathematics. Authors clarify significance and importance of simple thematic units of subject Discrete Mathematics in teaching technical-system subjects in study programme Applied Informatics. Mentioned subject is being taught in first year of University study and knowledge that students acquire during the study of this course are the "cornerstone" for their further development in technical-system study. Justness and importance of individual topics were analysed based on the evaluation of questionnaires, in which pedagogues teaching professional IT subjects alloted weighted coefficients to individual thematic units. Weighted coefficients were alloted based on the significance of the given topic of the subject Discrete Math, with regard to the IT subject they are teaching. Upon designing the e-course, experience with the creation of linear and branch teaching software were used. For the simulation of the transition of students through individual lessons as well as the whole course, authors employed the method of the teaching process simulation using Petri nets.
Mathematical Modeling: A Structured Process
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
A mathematical model for iodine kinetics
International Nuclear Information System (INIS)
Silva, E.A.T. da.
1976-01-01
A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case [pt
Mathematical models of hysteresis
International Nuclear Information System (INIS)
1998-01-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above
Mathematical models of hysteresis
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-08-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
A Primer for Mathematical Modeling
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
A Proposed Conceptual Model of Military Medical Readiness
National Research Council Canada - National Science Library
Van Hall, Brian M
2007-01-01
.... The basis for the proposed conceptual model builds on common and accepted latent variable and theoretical modeling techniques proposed by healthcare scholars, organizational theorists, mathematical...
Mathematical modeling with multidisciplinary applications
Yang, Xin-She
2013-01-01
Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the
Mathematical models of bipolar disorder
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Mathematical Modelling of Predatory Prokaryotes
Wilkinson, Michael H.F.
2006-01-01
Predator–prey models have a long history in mathematical modelling of ecosystem dynamics and evolution. In this chapter an introduction to the methodology of mathematical modelling is given, with emphasis on microbial predator–prey systems, followed by a description of variants of the basic
Mathematical problems in meteorological modelling
Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella
2016-01-01
This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...
Ivan Kotliarov
2008-01-01
the present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions.
Mathematical Model for the Control of measles 1*PETER, OJ ...
African Journals Online (AJOL)
PROF HORSFALL
2018-04-16
Apr 16, 2018 ... 5Department of Mathematics/Statistics, Federal University of Technology, Minna, Nigeria ... ABSTRACT: We proposed a mathematical model of measles disease dynamics with vaccination by ...... Equation with application.
Mathematical modeling of laser lipolysis
Directory of Open Access Journals (Sweden)
Reynaud Jean
2008-02-01
Full Text Available Abstract Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc. The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s give similar skin surface temperature (max: 41°C. These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction
Mathematical Modeling and Computational Thinking
Sanford, John F.; Naidu, Jaideep T.
2017-01-01
The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Explorations in Elementary Mathematical Modeling
Shahin, Mazen
2010-01-01
In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
Mathematical Modelling Plant Signalling Networks
Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.
2013-01-01
methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more
An introduction to mathematical modeling
Bender, Edward A
2000-01-01
Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The
Mathematical Modeling of Diverse Phenomena
Howard, J. C.
1979-01-01
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
Mathematical modelling of membrane separation
DEFF Research Database (Denmark)
Vinther, Frank
This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
The Spectrum of Mathematical Models.
Karplus, Walter J.
1983-01-01
Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.
1985-06-01
This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics
Wickstrom, Megan H.
2017-01-01
This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Using Covariation Reasoning to Support Mathematical Modeling
Jacobson, Erik
2014-01-01
For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…
The 24-Hour Mathematical Modeling Challenge
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
Mathematical Modeling: A Bridge to STEM Education
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…
Cyclic Concatenated Genetic Encoder: A mathematical proposal for biological inferences.
Duarte-González, M E; Echeverri, O Y; Guevara, J M; Palazzo, R
2018-01-01
The organization of the genetic information and its ability to be conserved and translated to proteins with low error rates have been the subject of study by scientists from different disciplines. Recently, it has been proposed that living organisms display an intra-cellular transmission system of genetic information, similar to a model of digital communication system, in which there is the ability to detect and correct errors. In this work, the concept of Concatenated Genetic Encoder is introduced and applied to the analysis of protein sequences as a tool for exploring evolutionary relationships. For such purposes Error Correcting Codes (ECCs) are used to represent proteins. A methodology for representing or identifying proteins by use of BCH codes over ℤ 20 and F 4 ×ℤ 5 is proposed and cytochrome b6-f complex subunit 6-OS sequences, corresponding to different plants species, are analyzed according to the proposed methodology and results are contrasted to phylogenetic and taxonomic analyses. Through the analyses, it was observed that using BCH codes only some sequences are identified, all of which differ in one amino acid from the original sequence. In addition, mathematical relationships among identified sequences are established by considering minimal polynomials, where such sequences showed a close relationship as revealed in the phylogenetic reconstruction. Results, here shown, point out that communication theory may provide biology of interesting and useful tools to identify biological relationships among proteins, however the proposed methodology needs to be improved and rigorously tested in order to become into an applicable tool for biological analysis. Copyright © 2017 Elsevier B.V. All rights reserved.
Mathematical formalization of theories of motivation proposed by Maslow and Herzberg
Kotliarov,Ivan
2008-01-01
Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of sp...
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.
1985-01-01
This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments
Wind tunnel modeling of roadways: Comparison with mathematical models
International Nuclear Information System (INIS)
Heidorn, K.; Davies, A.E.; Murphy, M.C.
1991-01-01
The assessment of air quality impacts from roadways is a major concern to urban planners. In order to assess future road and building configurations, a number of techniques have been developed including mathematical models, which simulate traffic emissions and atmospheric dispersion through a series of mathematical relationships and physical models. The latter models simulate emissions and dispersion through scaling of these processes in a wind tunnel. Two roadway mathematical models, HIWAY-2 and CALINE-4, were applied to a proposed development in a large urban area. Physical modeling procedures developed by Rowan Williams Davies and Irwin Inc. (RWDI) in the form of line source simulators were also applied, and the resulting carbon monoxide concentrations were compared. The results indicated a factor of two agreement between the mathematical and physical models. The physical model, however, reacted to change in building massing and configuration. The mathematical models did not, since no provision for such changes was included in the mathematical models. In general, the RWDI model resulted in higher concentrations than either HIWAY-2 or CALINE-4. Where there was underprediction, it was often due to shielding of the receptor by surrounding buildings. Comparison of these three models with the CALTRANS Tracer Dispersion Experiment showed good results although concentrations were consistently underpredicted
Mathematical Modeling in the Undergraduate Curriculum
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
Teachers' Conceptions of Mathematical Modeling
Gould, Heather
2013-01-01
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Mathematical modelling in economic processes.
Directory of Open Access Journals (Sweden)
L.V. Kravtsova
2008-06-01
Full Text Available In article are considered a number of methods of mathematical modelling of economic processes and opportunities of use of spreadsheets Excel for reception of the optimum decision of tasks or calculation of financial operations with the help of the built-in functions.
Mathematical modeling of biological processes
Friedman, Avner
2014-01-01
This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
How to Introduce Mathematic Modeling in Industrial Design Education
Langereis, G.R.; Hu, J.; Feijs, L.M.G.; Stillmann, G.A.; Kaiser, G.; Blum, W.B.; Brown, J.P.
2013-01-01
With competency based learning in a project driven environment, we are facing a different perspective of how students perceive mathematical modelling. In this chapter, a model is proposed where conventional education is seen as a process from mathematics to design, while competency driven approaches
Mathematical modelling in solid mechanics
Sofonea, Mircea; Steigmann, David
2017-01-01
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...
Exploring Yellowstone National Park with Mathematical Modeling
Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia
2017-01-01
Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…
Strategies to Support Students' Mathematical Modeling
Jung, Hyunyi
2015-01-01
An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…
Mathematical Modeling in the High School Curriculum
Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary
2016-01-01
In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)
1996-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H Y; Perez-Tello, M; Riihilahti, K M [Utah Univ., Salt Lake City, UT (United States)
1997-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
Mathematical Model of Age Aggression
Golovinski, P. A.
2013-01-01
We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...
Mathematical modeling of cancer metabolism.
Medina, Miguel Ángel
2018-04-01
Systemic approaches are needed and useful for the study of the very complex issue of cancer. Modeling has a central position in these systemic approaches. Metabolic reprogramming is nowadays acknowledged as an essential hallmark of cancer. Mathematical modeling could contribute to a better understanding of cancer metabolic reprogramming and to identify new potential ways of therapeutic intervention. Herein, I review several alternative approaches to metabolic modeling and their current and future impact in oncology. Copyright © 2018 Elsevier B.V. All rights reserved.
Mathematical models of granular matter
Mariano, Paolo; Giovine, Pasquale
2008-01-01
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
Summer Camp of Mathematical Modeling in China
Tian, Xiaoxi; Xie, Jinxing
2013-01-01
The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…
Continuum mechanics the birthplace of mathematical models
Allen, Myron B
2015-01-01
Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer. This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe
Stability Analysis of a Mathematical Model for Onchocerciaisis ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: In this work, we propose a Deterministic Mathematical Model that ... blackflies Center for Disease Control and World ... villages located along fast flowing rivers where the ..... distribution of Blackflies (Simulium Species) in.
International Nuclear Information System (INIS)
Wang Yongqing; Lior, Noam
2011-01-01
Simultaneous production of fresh water and refrigeration are often required, e.g. in warm-climate water-deficient regions, and this study is a proposal and analysis of an efficient way of producing both of them by consuming mainly low-grade heat. After introducing the configuration choice methodology, a combined refrigeration and water system, ARHP-MEE (absorption refrigeration heat pump and multi-effect evaporation desalter), which is the integration of a LiBr-H 2 O refrigeration unit, a LiBr-H 2 O heat pump, and a low-temperature multi-effect evaporation desalination unit, is proposed, and the mathematical model is presented and validated. The model serves for conducting a performance analysis of the combined system, reported in Part 2 of this two-part paper.
Directory of Open Access Journals (Sweden)
Jennifer M. Suh
2017-06-01
Full Text Available This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1 How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2 What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.
Mathematical Modeling in Combustion Science
Takeno, Tadao
1988-01-01
An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.
Proposed reliability cost model
Delionback, L. M.
1973-01-01
The research investigations which were involved in the study include: cost analysis/allocation, reliability and product assurance, forecasting methodology, systems analysis, and model-building. This is a classic example of an interdisciplinary problem, since the model-building requirements include the need for understanding and communication between technical disciplines on one hand, and the financial/accounting skill categories on the other. The systems approach is utilized within this context to establish a clearer and more objective relationship between reliability assurance and the subcategories (or subelements) that provide, or reenforce, the reliability assurance for a system. Subcategories are further subdivided as illustrated by a tree diagram. The reliability assurance elements can be seen to be potential alternative strategies, or approaches, depending on the specific goals/objectives of the trade studies. The scope was limited to the establishment of a proposed reliability cost-model format. The model format/approach is dependent upon the use of a series of subsystem-oriented CER's and sometimes possible CTR's, in devising a suitable cost-effective policy.
mathematical models for estimating radio channels utilization
African Journals Online (AJOL)
2017-08-08
Aug 8, 2017 ... Mathematical models for radio channels utilization assessment by real-time flows transfer in ... data transmission networks application having dynamic topology ..... Journal of Applied Mathematics and Statistics, 56(2): 85–90.
Mathematical models in medicine: Diseases and epidemics
International Nuclear Information System (INIS)
Witten, M.
1987-01-01
This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling
A mathematical model of 'Pride and Prejudice'.
Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro
2014-04-01
A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
Mathematical Modelling Plant Signalling Networks
Muraro, D.
2013-01-01
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.
Mathematical modeling of reciprocating pump
International Nuclear Information System (INIS)
Lee, Jong Kyeom; Jung, Jun Ki; Chai, Jang Bom; Lee, Jin Woo
2015-01-01
A new mathematical model is presented for the analysis and diagnosis of a high-pressure reciprocating pump system with three cylinders. The kinematic and hydrodynamic behaviors of the pump system are represented by the piston displacements, volume flow rates and pressures in its components, which are expressed as functions of the crankshaft angle. The flow interaction among the three cylinders, which was overlooked in the previous models, is considered in this model and its effect on the cylinder pressure profiles is investigated. The tuning parameters in the mathematical model are selected, and their values are adjusted to match the simulated and measured cylinder pressure profiles in each cylinder in a normal state. The damage parameter is selected in an abnormal state, and its value is adjusted to match the simulated and ensured pressure profiles under the condition of leakage in a valve. The value of the damage parameter over 300 cycles is calculated, and its probability density function is obtained for diagnosis and prognosis on the basis of the probabilistic feature of valve leakage.
Explorations in Elementary Mathematical Modeling
Directory of Open Access Journals (Sweden)
Mazen Shahin
2010-06-01
Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.
Mathematical Modeling of Extinction of Inhomogeneous Populations
Karev, G.P.; Kareva, I.
2016-01-01
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117
Reflexion and control mathematical models
Novikov, Dmitry A
2014-01-01
This book is dedicated to modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games that describe the gametheoretical interaction of agents making decisions based on a hierarchy of beliefs regarding (1) essential parameters (informational reflexion), (2) decision principles used by opponents (strategic reflexion), (3) beliefs about beliefs, and so on. Informational and reflexive equilibria in reflexive games generalize a series of well-known equilibrium concepts in noncooperative games and models of collective behavior. These models allow posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, in military applications, etc. (the interested reader will find in the book over 30 examples of possible applications in these fields) and describing uniformly many psychological/sociological phenomena connected with reflexion, viz., implicit control, informational control via the mass media, re...
SOME TRENDS IN MATHEMATICAL MODELING FOR BIOTECHNOLOGY
Directory of Open Access Journals (Sweden)
O. M. Klyuchko
2018-02-01
Full Text Available The purpose of present research is to demonstrate some trends of development of modeling methods for biotechnology according to contemporary achievements in science and technique. At the beginning the general approaches are outlined, some types of classifications of modeling methods are observed. The role of mathematic methods modeling for biotechnology in present époque of information computer technologies intensive development is studied and appropriate scheme of interrelation of all these spheres is proposed. Further case studies are suggested: some mathematic models in three different spaces (1D, 2D, 3D models are described for processes in living objects of different levels of hierarchic organization. In course of this the main attention was paid to some processes modeling in neurons as well as in their aggregates of different forms, including glioma cell masses (1D, 2D, 3D brain processes models. Starting from the models that have only theoretical importance for today, we describe at the end a model which application may be important for the practice. The work was done after the analysis of approximately 250 current publications in fields of biotechnology, including the authors’ original works.
Mathematical formalization of theories of motivation proposed by Maslow and Herzberg
Directory of Open Access Journals (Sweden)
Ivan Kotliarov
2008-12-01
Full Text Available Maslow's theory is by far the most known theory of motivation, and the most common in the business and management practice. Herzberg's theory fits the observations and explains some aspects of human motivation left unexplained by Maslow. However, these theories have never been formalized on a strictly mathematical basis. The present article gives an outline of a mathematical model of theories of motivation proposed by Abraham Maslow and Frederick Herzberg. This model is built on a basis of special non-continuous functions. This description may be a good basis for HR software and may be useful for business and management.
Mathematical models in biological discovery
Walter, Charles
1977-01-01
When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...
Mathematical models of viscous friction
Buttà, Paolo; Marchioro, Carlo
2015-01-01
In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...
Mathematical study of mixing models
International Nuclear Information System (INIS)
Lagoutiere, F.; Despres, B.
1999-01-01
This report presents the construction and the study of a class of models that describe the behavior of compressible and non-reactive Eulerian fluid mixtures. Mixture models can have two different applications. Either they are used to describe physical mixtures, in the case of a true zone of extensive mixing (but then this modelization is incomplete and must be considered only as a point of departure for the elaboration of models of mixtures actually relevant). Either they are used to solve the problem of the numerical mixture. This problem appears during the discretization of an interface which separates fluids having laws of different state: the zone of numerical mixing is the set of meshes which cover the interface. The attention is focused on numerical mixtures, for which the hypothesis of non-miscibility (physics) will bring two equations (the sixth and the eighth of the system). It is important to emphasize that even in the case of the only numerical mixture, the presence in one and same place (same mesh) of several fluids have to be taken into account. This will be formalized by the possibility for mass fractions to take all values between 0 and 1. This is not at odds with the equations that derive from the hypothesis of non-miscibility. One way of looking at things is to consider that there are two scales of observation: the physical scale at which one observes the separation of fluids, and the numerical scale, given by the fineness of the mesh, to which a mixture appears. In this work, mixtures are considered from the mathematical angle (both in the elaboration phase and during their study). In particular, Chapter 5 shows a result of model degeneration for a non-extended mixing zone (case of an interface): this justifies the use of models in the case of numerical mixing. All these models are based on the classical model of non-viscous compressible fluids recalled in Chapter 2. In Chapter 3, the central point of the elaboration of the class of models is
Mathematical modeling courses for Media technology students
DEFF Research Database (Denmark)
Timcenko, Olga
2009-01-01
This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...
Specific Type of Knowledge Map: Mathematical Model
Milan, Houška; Martina, Beránková
2005-01-01
The article deals with relationships between mathematical models and knowledge maps. The goal of the article is to suggest how to use the mathematical model as a knowledge map and/or as a part (esp. the inference mechanism) of the knowledge system. The results are demonstrated on the case study, when the knowledge from a story is expressed by mathematical model. The model is used for both knowledge warehousing and inferencing new artificially derived knowledge.
A Mathematical Model, Implementation and Study of a Swarm System
Varghese, Blesson; McKee, Gerard
2013-01-01
The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to conf...
A mathematical model for transducer working at high temperature
International Nuclear Information System (INIS)
Fabre, J.P.
1974-01-01
A mathematical model is proposed for a lithium niobate piezoelectric transducer working at high temperature in liquid sodium. The model proposed suitably described the operation of the high temperature transducer presented; it allows the optimization of the efficiency and band-pass [fr
a Discrete Mathematical Model to Simulate Malware Spreading
Del Rey, A. Martin; Sánchez, G. Rodriguez
2012-10-01
With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.
Mathematical modeling of drug dissolution.
Siepmann, J; Siepmann, F
2013-08-30
The dissolution of a drug administered in the solid state is a pre-requisite for efficient subsequent transport within the human body. This is because only dissolved drug molecules/ions/atoms are able to diffuse, e.g. through living tissue. Thus, generally major barriers, including the mucosa of the gastro intestinal tract, can only be crossed after dissolution. Consequently, the process of dissolution is of fundamental importance for the bioavailability and, hence, therapeutic efficacy of various pharmaco-treatments. Poor aqueous solubility and/or very low dissolution rates potentially lead to insufficient availability at the site of action and, hence, failure of the treatment in vivo, despite a potentially ideal chemical structure of the drug to interact with its target site. Different physical phenomena are involved in the process of drug dissolution in an aqueous body fluid, namely the wetting of the particle's surface, breakdown of solid state bonds, solvation, diffusion through the liquid unstirred boundary layer surrounding the particle as well as convection in the surrounding bulk fluid. Appropriate mathematical equations can be used to quantify these mass transport steps, and more or less complex theories can be developed to describe the resulting drug dissolution kinetics. This article gives an overview on the current state of the art of modeling drug dissolution and points out the assumptions the different theories are based on. Various practical examples are given in order to illustrate the benefits of such models. This review is not restricted to mathematical theories considering drugs exhibiting poor aqueous solubility and/or low dissolution rates, but also addresses models quantifying drug release from controlled release dosage forms, in which the process of drug dissolution plays a major role. Copyright © 2013 Elsevier B.V. All rights reserved.
Mathematical models for plant-herbivore interactions
Feng, Zhilan; DeAngelis, Donald L.
2017-01-01
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.
Common Mathematical Model of Fatigue Characteristics
Directory of Open Access Journals (Sweden)
Z. Maléř
2004-01-01
Full Text Available This paper presents a new common mathematical model which is able to describe fatigue characteristics in the whole necessary range by one equation only:log N = A(R + B(R ∙ log Sawhere A(R = AR2 + BR + C and B(R = DR2 + AR + F.This model was verified by five sets of fatigue data taken from the literature and by our own three additional original fatigue sets. The fatigue data usually described the region of N 104 to 3 x 106 and stress ratio of R = -2 to 0.5. In all these cases the proposed model described fatigue results with small scatter. Studying this model, following knowledge was obtained:– the parameter ”stress ratio R” was a good physical characteristic– the proposed model provided a good description of the eight collections of fatigue test results by one equation only– the scatter of the results through the whole scope is only a little greater than that round the individual S/N curve– using this model while testing may reduce the number of test samples and shorten the test time– as the proposed model represents a common form of the S/N curve, it may be used for processing uniform objective fatigue life results, which may enable mutual comparison of fatigue characteristics.
Surface EXAFS - A mathematical model
International Nuclear Information System (INIS)
Bateman, J.E.
2002-01-01
Extended X-ray absorption fine structure (EXAFS) studies are a powerful technique for studying the chemical environment of specific atoms in a molecular or solid matrix. The study of the surface layers of 'thick' materials introduces special problems due to the different escape depths of the various primary and secondary emission products which follow X-ray absorption. The processes are governed by the properties of the emitted fluorescent photons or electrons and of the material. Their interactions can easily destroy the linear relation between the detected signal and the absorption cross-section. Also affected are the probe depth within the surface and the background superimposed on the detected emission signal. A general mathematical model of the escape processes is developed which permits the optimisation of the detection modality (X-rays or electrons) and the experimental variables to suit the composition of any given surface under study
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
at the Technical University of Denmark. The data set includes face-to-face interaction (Bluetooth), communication (calls and texts), mobility (GPS), social network (Facebook), and general background information including a psychological profile (questionnaire). This thesis presents my work on the Social Fabric...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived....... Evidence is provided, which implies that the asymmetry is caused by a self-enhancement in the initiation dynamics. These results have implications for the formation of social networks and the dynamics of the links. It is shown that the Big Five Inventory (BFI) representing a psychological profile only...
Mathematical model of the Amazon Stirling engine
Energy Technology Data Exchange (ETDEWEB)
Vidal Medina, Juan Ricardo [Universidad Autonoma de Occidente (Colombia)], e-mail: jrvidal@uao.edu.co; Cobasa, Vladimir Melian; Silva, Electo [Universidade Federal de Itajuba, MG (Brazil)], e-mail: vlad@unifei.edu.br
2010-07-01
The Excellency Group in Thermoelectric and Distributed Generation (NEST, for its acronym in Portuguese) at the Federal University of Itajuba, has designed a Stirling engine prototype to provide electricity to isolated regions of Brazil. The engine was designed to operate with residual biomass from timber process. This paper presents mathematical models of heat exchangers (hot, cold and regenerator) integrated into second order adiabatic models. The general model takes into account the pressure drop losses, hysteresis and internal losses. The results of power output, engine efficiency, optimal velocity of the exhaust gases and the influence of dead volume in engine efficiency are presented in this paper. The objective of this modeling is to propose improvements to the manufactured engine design. (author)
Mathematical model on Alzheimer's disease.
Hao, Wenrui; Friedman, Avner
2016-11-18
Alzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. AD is characterized by the presence of two types of neuropathological hallmarks: extracellular plaques consisting of amyloid β-peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins. The disease affects 5 million people in the United States and 44 million world-wide. Currently there is no drug that can cure, stop or even slow the progression of the disease. If no cure is found, by 2050 the number of alzheimer's patients in the U.S. will reach 15 million and the cost of caring for them will exceed $ 1 trillion annually. The present paper develops a mathematical model of AD that includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. The model is represented by a system of partial differential equations. The model is used to simulate the effect of drugs that either failed in clinical trials, or are currently in clinical trials. Based on these simulations it is suggested that combined therapy with TNF- α inhibitor and anti amyloid β could yield significant efficacy in slowing the progression of AD.
Energy Technology Data Exchange (ETDEWEB)
Kahn, Marcio [Petroleo Brasileiro S.A. (PETROBRAS), Rio de Janeiro, RJ (Brazil); Hamacher, Silvio [Pontificia Universidade Catolica do Rio de Janeiro (PUC-Rio), RJ (Brazil)
2012-07-01
A mathematical programming model to support the decision maker how to identify the optimal infrastructure design solution to the Development and Production of an oil field is proposed in this paper. The problem addressed is to maximize the economic return of the additional production of oil in a field with existing production infrastructure installed and as a proposed solution to this problem a model of mixed integer linear programming was developed. This formulation allows identifying the optimal level of exploration and production of a field subject to uncertainties. The variables to be defined are: Floating Production Units installed to be utilized and their oil production, the use of manifolds or not, and the number of wells that will be connected to the Floating Production Units. Finally, the model provides the optimal development plan with the best economic return considering the constraints and uncertainties of the problem. Besides the optimal solution, sensitivity analyzes were performed improving the understanding of the problem and providing useful information to the decision maker. (author)
Leading Undergraduate Research Projects in Mathematical Modeling
Seshaiyer, Padmanabhan
2017-01-01
In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…
Scaffolding Mathematical Modelling with a Solution Plan
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
Modelling and Optimizing Mathematics Learning in Children
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
Mathematical Modelling as a Professional Task
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Modellus: Learning Physics with Mathematical Modelling
Teodoro, Vitor
Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations
Students’ mathematical learning in modelling activities
DEFF Research Database (Denmark)
Kjeldsen, Tinne Hoff; Blomhøj, Morten
2013-01-01
Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts i...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....
Rival approaches to mathematical modelling in immunology
Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.
2007-08-01
In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.
Mathematical modeling of tornadoes and squall storms
Directory of Open Access Journals (Sweden)
Sergey A. Arsen’yev
2011-04-01
Full Text Available Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running perturbation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave (soliton; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.
MATHEMATICAL MODEL OF GRAIN MICRONIZATION
Directory of Open Access Journals (Sweden)
V. A. Afanas’ev
2014-01-01
Full Text Available Summary. During micronisation grain moisture evaporates mainly in decreasing drying rate period. Grain layer located on the surface of the conveyor micronisers will be regarded as horizontal plate. Due to the fact that the micronisation process the surface of the grain evaporates little moisture (within 2-7 % is assumed constant plate thickness. Because in the process of micronization grain structure is changing, in order to achieve an exact solution of the equations necessary to take into account changes thermophysical, optical and others. Equation of heat transfer is necessary to add a term that is responsible for the infrared heating. Because of the small thickness of the grain, neglecting the processes occurring at the edge of the grain, that is actually consider the problem of an infinite plate. To check the adequacy of the mathematical model of the process of micronisation of wheat grain moisture content must be comparable to the function of time, obtained by solving the system of equations with the measured experimental data of experience. Numerical solution of a system of equations for the period of decreasing drying rate is feasible with the help of the Maple 14, substituting the values of the constants in the system. Calculation of the average relative error does not exceed 7- 10 %, and shows a good agreement between the calculated data and the experimental values.
The prediction of epidemics through mathematical modeling.
Schaus, Catherine
2014-01-01
Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.
Mathematical Modeling Applied to Maritime Security
Center for Homeland Defense and Security
2010-01-01
Center for Homeland Defense and Security, OUT OF THE CLASSROOM Download the paper: Layered Defense: Modeling Terrorist Transfer Threat Networks and Optimizing Network Risk Reduction” Students in Ted Lewis’ Critical Infrastructure Protection course are taught how mathematic modeling can provide...
Lowe, James; Carter, Merilyn; Cooper, Tom
2018-01-01
Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…
Mathematical model of highways network optimization
Sakhapov, R. L.; Nikolaeva, R. V.; Gatiyatullin, M. H.; Makhmutov, M. M.
2017-12-01
The article deals with the issue of highways network design. Studies show that the main requirement from road transport for the road network is to ensure the realization of all the transport links served by it, with the least possible cost. The goal of optimizing the network of highways is to increase the efficiency of transport. It is necessary to take into account a large number of factors that make it difficult to quantify and qualify their impact on the road network. In this paper, we propose building an optimal variant for locating the road network on the basis of a mathematical model. The article defines the criteria for optimality and objective functions that reflect the requirements for the road network. The most fully satisfying condition for optimality is the minimization of road and transport costs. We adopted this indicator as a criterion of optimality in the economic-mathematical model of a network of highways. Studies have shown that each offset point in the optimal binding road network is associated with all other corresponding points in the directions providing the least financial costs necessary to move passengers and cargo from this point to the other corresponding points. The article presents general principles for constructing an optimal network of roads.
A Mathematical Model of the Thermo-Anemometric Flowmeter.
Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman
2015-09-11
A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.
Mathematical modeling of swirled flows in industrial applications
Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.
2018-03-01
Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.
Mathematical models in biology bringing mathematics to life
Ferraro, Maria; Guarracino, Mario
2015-01-01
This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...
Mathematical modelling of scour: A review
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2007-01-01
A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...
Mathematical modeling a chemical engineer's perspective
Rutherford, Aris
1999-01-01
Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus
MATHEMATICAL MODEL FOR RIVERBOAT DYNAMICS
Directory of Open Access Journals (Sweden)
Aleksander Grm
2017-01-01
Full Text Available Present work describes a simple dynamical model for riverboat motion based on the square drag law. Air and water interactions with the boat are determined from aerodynamic coefficients. CFX simulations were performed with fully developed turbulent flow to determine boat aerodynamic coefficients for an arbitrary angle of attack for the air and water portions separately. The effect of wave resistance is negligible compared to other forces. Boat movement analysis considers only two-dimensional motion, therefore only six aerodynamics coefficients are required. The proposed model is solved and used to determine the critical environmental parameters (wind and current under which river navigation can be conducted safely. Boat simulator was tested in a single area on the Ljubljanica river and estimated critical wind velocity.
Mathematical modeling of alcohol distillation columns
Directory of Open Access Journals (Sweden)
Ones Osney Pérez
2011-04-01
Full Text Available New evaluation modules are proposed to extend the scope of a modular simulator oriented to the sugar cane industry, called STA 4.0, in a way that it can be used to carry out x calculation and analysis in ethanol distilleries. Calculation modules were developed for the simulation of the columns that are combined in the distillation area. Mathematical models were supported on materials and energy balances, equilibrium relations and thermodynamic properties of the ethanol-water system. Ponchon-Savarit method was used for the evaluation of the theoretical stages in the columns. A comparison between the results using Ponchon- Savarit method and those obtained applying McCabe-Thiele method was done for a distillation column. These calculation modules for ethanol distilleries were applied to a real case for validation.
Mathematical Modeling of the Origins of Life
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Mathematical models for correction of images, obtained at radioisotope scan
International Nuclear Information System (INIS)
Glaz, A.; Lubans, A.
2002-01-01
The images, which obtained at radioisotope scintigraphy, contain distortions. Distortions appear as a result of absorption of radiation by patient's body's tissues. Two mathematical models for reducing of such distortions are proposed. Image obtained by only one gamma camera is used in the first mathematical model. Unfortunately, this model allows processing of the images only in case, when it can be assumed, that the investigated organ has a symmetric form. The images obtained by two gamma cameras are used in the second model. It gives possibility to assume that the investigated organ has non-symmetric form and to acquire more precise results. (authors)
Mathematical Modeling of Hybrid Electrical Engineering Systems
Directory of Open Access Journals (Sweden)
A. A. Lobaty
2016-01-01
Full Text Available A large class of systems that have found application in various industries and households, electrified transportation facilities and energy sector has been classified as electrical engineering systems. Their characteristic feature is a combination of continuous and discontinuous modes of operation, which is reflected in the appearance of a relatively new term “hybrid systems”. A wide class of hybrid systems is pulsed DC converters operating in a pulse width modulation, which are non-linear systems with variable structure. Using various methods for linearization it is possible to obtain linear mathematical models that rather accurately simulate behavior of such systems. However, the presence in the mathematical models of exponential nonlinearities creates considerable difficulties in the implementation of digital hardware. The solution can be found while using an approximation of exponential functions by polynomials of the first order, that, however, violates the rigor accordance of the analytical model with characteristics of a real object. There are two practical approaches to synthesize algorithms for control of hybrid systems. The first approach is based on the representation of the whole system by a discrete model which is described by difference equations that makes it possible to synthesize discrete algorithms. The second approach is based on description of the system by differential equations. The equations describe synthesis of continuous algorithms and their further implementation in a digital computer included in the control loop system. The paper considers modeling of a hybrid electrical engineering system using differential equations. Neglecting the pulse duration, it has been proposed to describe behavior of vector components in phase coordinates of the hybrid system by stochastic differential equations containing generally non-linear differentiable random functions. A stochastic vector-matrix equation describing dynamics of the
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...
Mathematical Modelling of Intraretinal Oxygen Partial Pressure
African Journals Online (AJOL)
Erah
The system of non-linear differential equations was solved numerically using Runge-kutta. Nystroms method. ... artery occlusion. Keywords: Mathematical modeling, Intraretinal oxygen pressure, Retinal capillaries, Oxygen ..... Mass transfer,.
Cooking Potatoes: Experimentation and Mathematical Modeling.
Chen, Xiao Dong
2002-01-01
Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)
А mathematical model study of suspended monorail
Viktor GUTAREVYCH
2012-01-01
The mathematical model of suspended monorail track with allowance for elastic strain which occurs during movement of the monorail carriage was developed. Standard forms for single span and double span of suspended monorail sections were established.
А mathematical model study of suspended monorail
Directory of Open Access Journals (Sweden)
Viktor GUTAREVYCH
2012-01-01
Full Text Available The mathematical model of suspended monorail track with allowance for elastic strain which occurs during movement of the monorail carriage was developed. Standard forms for single span and double span of suspended monorail sections were established.
Mathematical Modeling of Circadian/Performance Countermeasures
National Aeronautics and Space Administration — We developed and refined our current mathematical model of circadian rhythms to incorporate melatonin as a marker rhythm. We used an existing physiologically based...
short communication mathematical modelling for magnetite
African Journals Online (AJOL)
Preferred Customer
The present research focuses to develop mathematical model for the ..... Staler, M.J. The Principle of Ion Exchange Technology, Butterworth-Heinemann: Boston; ... Don, W.G. Perry's Chemical Engineering Hand Book, 7th ed., McGraw-Hill:.
Mathematical Modeling Approaches in Plant Metabolomics.
Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas
2018-01-01
The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
Mathematical modeling of wiped-film evaporators
International Nuclear Information System (INIS)
Sommerfeld, J.T.
1976-05-01
A mathematical model and associated computer program were developed to simulate the steady-state operation of wiped-film evaporators for the concentration of typical waste solutions produced at the Savannah River Plant. In this model, which treats either a horizontal or a vertical wiped-film evaporator as a plug-flow device with no backmixing, three fundamental phenomena are described: sensible heating of the waste solution, vaporization of water, and crystallization of solids from solution. Physical property data were coded into the computer program, which performs the calculations of this model. Physical properties of typical waste solutions and of the heating steam, generally as analytical functions of temperature, were obtained from published data or derived by regression analysis of tabulated or graphical data. Preliminary results from tests of the Savannah River Laboratory semiworks wiped-film evaporators were used to select a correlation for the inside film heat transfer coefficient. This model should be a useful aid in the specification, operation, and control of the full-scale wiped-film evaporators proposed for application under plant conditions. In particular, it should be of value in the development and analysis of feed-forward control schemes for the plant units. Also, this model can be readily adapted, with only minor changes, to simulate the operation of wiped-film evaporators for other conceivable applications, such as the concentration of acid wastes
Mathematical modeling of diphtheria transmission in Thailand.
Sornbundit, Kan; Triampo, Wannapong; Modchang, Charin
2017-08-01
In this work, a mathematical model for describing diphtheria transmission in Thailand is proposed. Based on the course of diphtheria infection, the population is divided into 8 epidemiological classes, namely, susceptible, symptomatic infectious, asymptomatic infectious, carrier with full natural-acquired immunity, carrier with partial natural-acquired immunity, individual with full vaccine-induced immunity, and individual with partial vaccine-induced immunity. Parameter values in the model were either directly obtained from the literature, estimated from available data, or estimated by means of sensitivity analysis. Numerical solutions show that our model can correctly describe the decreasing trend of diphtheria cases in Thailand during the years 1977-2014. Furthermore, despite Thailand having high DTP vaccine coverage, our model predicts that there will be diphtheria outbreaks after the year 2014 due to waning immunity. Our model also suggests that providing booster doses to some susceptible individuals and those with partial immunity every 10 years is a potential way to inhibit future diphtheria outbreaks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.
Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław
2015-07-22
A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.
Modelling Mathematical Reasoning in Physics Education
Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche
2012-04-01
Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.
Mathematical model for spreading dynamics of social network worms
International Nuclear Information System (INIS)
Sun, Xin; Liu, Yan-Heng; Han, Jia-Wei; Liu, Xue-Jie; Li, Bin; Li, Jin
2012-01-01
In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers
Thrasher, Emily Plunkett
2016-01-01
The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
Zbiek, Rose Mary; Conner, Annamarie
2006-01-01
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…
A mathematical model for postirradiation immunity
International Nuclear Information System (INIS)
Smirnova, O.A.
1988-01-01
A mathematical model of autoimmune processes in exposed mammals was developed. In terms of this model a study was made of the dependence of the autoimmunity kinetics on radiation dose and radiosensitivity of autologous tissues. The model simulates the experimentally observed dynamics of autoimmune diseases
Mathematical model of three winding auto transformer
International Nuclear Information System (INIS)
Volcko, V.; Eleschova, Z.; Belan, A.; Janiga, P.
2012-01-01
This article deals with the design of mathematical model of three-winding auto transformer for steady state analyses. The article is focused on model simplicity for the purposes of the use in complex transmission systems and authenticity of the model taking into account different types of step-voltage regulator. (Authors)
Mathematical Modelling of Intraretinal Oxygen Partial Pressure ...
African Journals Online (AJOL)
Purpose: The aim of our present work is to develop a simple steady state model for intraretinal oxygen partial pressure distribution and to investigate the effect of various model parameters on the partial pressure distribution under adapted conditions of light and darkness.. Method: A simple eight-layered mathematical model ...
Potential of mathematical modeling in fruit quality
African Journals Online (AJOL)
ONOS
2010-01-18
Jan 18, 2010 ... successful mathematical model, the modeler needs to chose what .... equations. In the SUCROS models, the rate of CO2 assimilation is .... insect ecology. ... García y García A, Ingram KT, Hatch U, Hoogenboom G, Jones JW,.
Mathematical model of glucose-insulin homeostasis in healthy rats.
Lombarte, Mercedes; Lupo, Maela; Campetelli, German; Basualdo, Marta; Rigalli, Alfredo
2013-10-01
According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat. Copyright © 2013 Elsevier Inc. All rights reserved.
Mathematical models and accuracy of radioisotope gauges
International Nuclear Information System (INIS)
Urbanski, P.
1989-01-01
Mathematical expressions relating the variance and mean value of the intrinsic error with the parameters of one and multi-dimensional mathematical models of radioisotope gauges are given. Variance of the intrinsic error at the model's output is considered as a sum of the variances of the random error which is created in the first stages of the measuring chain and the random error of calibration procedure. The mean value of the intrinsic error (systematic error) appears always for nonlinear models. It was found that the optimal model of calibration procedure not always corresponds to the minimal value of the intrinsic error. The derived expressions are applied for the assessment of the mathematical models of some of the existing gauges (radioisotope belt weigher, XRF analyzer and coating thickness gauge). 7 refs., 5 figs., 1 tab. (author)
Mathematical foundations of the dendritic growth models.
Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos
2007-11-01
At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.
Mathematical Models of Issue Voting
小林, 良彰
2009-01-01
1. Introduction2. An Examination of the Expected Utility Model3. An Examination of the Minimax Regret Model4. An Examination of the Diametros Model5. An Examination of the Revised Diametros Model6. An Examination of the Party Coalition Model7. The Construction and Examination of the Diametros ll Model8. Conclusion
Methodology and Results of Mathematical Modelling of Complex Technological Processes
Mokrova, Nataliya V.
2018-03-01
The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.
Drying of materials in fluidized bed: mathematical modeling
International Nuclear Information System (INIS)
Wildhagen, Gloria Regina S.; Silva, Eder F.; Calcada, Luis A.; Massarani, Giulio
2000-01-01
A three phase mathematical model for drying process in a fluidized bed was established. This model representing a bubble, interstitial gas and solid phase was based on principles of mass and energy conservation and on empirical relations for heat and mass transfer between phases. A fluidized bed dryer was built to test the results of proposed model with those obtained by experiments using alumina particles as a bed charge. A good agreement between the numerical and the experimental results were observed(author)
Mathematical modeling and optimization of complex structures
Repin, Sergey; Tuovinen, Tero
2016-01-01
This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimiz...
Mathematical Models of Tuberculosis Reactivation and Relapse
Directory of Open Access Journals (Sweden)
Robert Steven Wallis
2016-05-01
Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Interfacial Fluid Mechanics A Mathematical Modeling Approach
Ajaev, Vladimir S
2012-01-01
Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail. Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also: Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...
Mathematical models and methods for planet Earth
Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta
2014-01-01
In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.
Mathematical modelling of two-phase flows
International Nuclear Information System (INIS)
Komen, E.M.J.; Stoop, P.M.
1992-11-01
A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs
Mathematical model in economic environmental problems
Energy Technology Data Exchange (ETDEWEB)
Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)
1996-12-31
The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.
Directory of Open Access Journals (Sweden)
Ednilson Sergio Ramalho de Souza
2016-07-01
Full Text Available The pedagogical work with mathematical modeling assumes investigate situations of reality. However, mental models formed from the contact with the experiential world are generally incompatible with the conceptual models. So David Hestenes supports the view that one of the biggest challenges of teaching and learning in science and mathematics is to coordinate conceptual models with mental models, which led to the elaboration of a didactic in mathematical modeling: Modeling Instruction. Our goal is to present a proposal for thematic modeling cycle drawn up in hestenesianos assumptions and discuss possibilities for scientific literacy. The main question was to know how to emerge indicators for scientific literacy for the proposed cycle. This is a bibliographic research in order to identify the available literature contributions on the subject and raise the possibility and challenges for the brazilian teaching science and mathematics. Preliminary results indicate that the proposed modeling cycle can develop indicators for scientific literacy of different natures.
Mathematical modeling of efficient protocols to control glioma growth.
Branco, J R; Ferreira, J A; de Oliveira, Paula
2014-09-01
In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. Copyright © 2014 Elsevier Inc. All rights reserved.
Mathematical Modeling of Column-Base Connections under Monotonic Loading
Directory of Open Access Journals (Sweden)
Gholamreza Abdollahzadeh
2014-12-01
Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.
Mathematical Modeling: Are Prior Experiences Important?
Czocher, Jennifer A.; Moss, Diana L.
2017-01-01
Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…
Uncertainty and Complexity in Mathematical Modeling
Cannon, Susan O.; Sanders, Mark
2017-01-01
Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…
Parallel Boltzmann machines : a mathematical model
Zwietering, P.J.; Aarts, E.H.L.
1991-01-01
A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a
A mathematical model of embodied consciousness
Rudrauf, D.; Bennequin, D.; Granic, I.; Landini, G.; Friston, K.; Williford, K.
2017-01-01
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM
Mathematical model of the reactor coolant pump
International Nuclear Information System (INIS)
Kozuh, M.
1989-01-01
The mathematical model of reactor coolant pump is described in this paper. It is based on correlations for centrifugal reactor coolant pumps. This code is one of the elements needed for the simulation of the whole NPP primary system. In subroutine developed according to this model we tried in every possible detail to incorporate plant specific data for Krsko NPP. (author)
A mathematical model of forgetting and amnesia
Murre, J.M.J.; Chessa, A.G.; Meeter, M.
2013-01-01
We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models
Mathematical finance theory review and exercises from binomial model to risk measures
Gianin, Emanuela Rosazza
2013-01-01
The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...
Mathematical models of human cerebellar development in the fetal period.
Dudek, Krzysztof; Nowakowska-Kotas, Marta; Kędzia, Alicja
2018-04-01
The evaluation of cerebellar growth in the fetal period forms a part of a widely used examination to identify any features of abnormalities in early stages of human development. It is well known that the development of anatomical structures, including the cerebellum, does not always follow a linear model of growth. The aim of the study was to analyse a variety of mathematical models of human cerebellar development in fetal life to determine their adequacy. The study comprised 101 fetuses (48 males and 53 females) between the 15th and 28th weeks of fetal life. The cerebellum was exposed and measurements of the vermis and hemispheres were performed, together with statistical analyses. The mathematical model parameters of fetal growth were assessed for crown-rump length (CRL) increases, transverse cerebellar diameter and ventrodorsal dimensions of the cerebellar vermis in the transverse plane, and rostrocaudal dimensions of the cerebellar vermis and hemispheres in the frontal plane. A variety of mathematical models were applied, including linear and non-linear functions. Taking into consideration the variance between models and measurements, as well as correlation parameters, the exponential and Gompertz models proved to be the most suitable for modelling cerebellar growth in the second and third trimesters of pregnancy. However, the linear model gave a satisfactory approximation of cerebellar growth, especially in older fetuses. The proposed models of fetal cerebellar growth constructed on the basis of anatomical examination and objective mathematical calculations could be useful in the estimation of fetal development. © 2018 Anatomical Society.
Mathematical models of information and stochastic systems
Kornreich, Philipp
2008-01-01
From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t
On the mathematical modeling of memristors
Radwan, Ahmed G.
2012-10-06
Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.
Dynamics of mathematical models in biology bringing mathematics to life
Zazzu, Valeria; Guarracino, Mario
2016-01-01
This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...
Proposed Reliability/Cost Model
Delionback, L. M.
1982-01-01
New technique estimates cost of improvement in reliability for complex system. Model format/approach is dependent upon use of subsystem cost-estimating relationships (CER's) in devising cost-effective policy. Proposed methodology should have application in broad range of engineering management decisions.
FEMME, a flexible environment for mathematically modelling the environment
Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.
2002-01-01
A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model
Mathematical Modelling of Unmanned Aerial Vehicles
Directory of Open Access Journals (Sweden)
Saeed Sarwar
2013-04-01
Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV
Mathematical modelling of unmanned aerial vehicles
International Nuclear Information System (INIS)
Sarwar, S.; Rehman, S.U.
2013-01-01
UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)
MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM
Directory of Open Access Journals (Sweden)
Olha Sushchenko
2017-07-01
Full Text Available Purpose: The paper deals with the mathematical description of the gimballed attitude and heading reference systems, which can be applied in design of strategic precision navigation systems. The main goal is to created mathematical description taking into consideration the necessity to use different navigations operating modes of this class of navigation systems. To provide the high accuracy the indirect control is used when the position of the gimballed platform is controlled by signals of gyroscopic devices, which are corrected using accelerometer’s signals. Methods: To solve the given problem the methods of the classical theoretical mechanics, gyro theory, and inertial navigation are used. Results: The full mathematical model of the gimballed attitude and heading reference system is derived including descriptions of different operating modes. The mathematical models of the system Expressions for control and correction moments in the different modes are represented. The simulation results are given. Conclusions: The represented results prove efficiency of the proposed models. Developed mathematical models can be useful for design of navigation systems of the wide class of moving vehicles.
Applied Mathematics, Modelling and Computational Science
Kotsireas, Ilias; Makarov, Roman; Melnik, Roderick; Shodiev, Hasan
2015-01-01
The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics ...
Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling
Karali, Diren; Durmus, Soner
2015-01-01
The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…
Mathematical modelling a case studies approach
Illner, Reinhard; McCollum, Samantha; Roode, Thea van
2004-01-01
Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; oth...
Mathematical model of compact type evaporator
Borovička, Martin; Hyhlík, Tomáš
2018-06-01
In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.
The (Mathematical) Modeling Process in Biosciences.
Torres, Nestor V; Santos, Guido
2015-01-01
In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.
On the mathematical modeling of aeolian saltation
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Sørensen, Michael
1983-01-01
The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...... on aeolian saltation. This comparison points out the necessity of discriminating between pure and real saltation. -Authors...
Mathematical and physical models and radiobiology
International Nuclear Information System (INIS)
Lokajicek, M.
1980-01-01
The hit theory of the mechanism of biological radiation effects in the cell is discussed with respect to radiotherapy. The mechanisms of biological effects and of intracellular recovery, the cumulative radiation effect and the cumulative biological effect in fractionated irradiation are described. The benefit is shown of consistent application of mathematical and physical models in radiobiology and radiotherapy. (J.P.)
Mathematical Modeling Projects: Success for All Students
Shelton, Therese
2018-01-01
Mathematical modeling allows flexibility for a project-based experience. We share details of our regular capstone course, successful for virtually 100% of our math majors for almost two decades. Our research-like approach in this course accommodates a variety of student backgrounds and interests, and has produced some award-winning student…
ECONOMIC AND MATHEMATICAL MODELING INNOVATION SYSTEMS
Directory of Open Access Journals (Sweden)
D.V. Makarov
2014-06-01
Full Text Available The paper presents one of the mathematical tools for modeling innovation processes. With the help of Kondratieff long waves can define innovation cycles. However, complexity of the innovation system implies a qualitative description. The article describes the problems of this area of research.
Mathematical modeling of optical glazing performance
Nijnatten, van P.A.; Wittwer, V.; Granqvist, C.G.; Lampert, C.M.
1994-01-01
Mathematical modelling can be a powerful tool in the design and optimalization of glazing. By calculation, the specifications of a glazing design and the optimal design parameters can be predicted without building costly prototypes first. Furthermore, properties which are difficult to measure, like
Description of a comprehensive mathematical model
DEFF Research Database (Denmark)
Li, Xiyan; Yin, Chungen
2017-01-01
Biomass gasification is still a promising technology after over 30 years’ research and development and has success only in a few niche markets. In this paper, a comprehensive mathematical model for biomass particle gasification is developed within a generic particle framework, assuming the feed...
Introduction to mathematical models and methods
Energy Technology Data Exchange (ETDEWEB)
Siddiqi, A. H.; Manchanda, P. [Gautam Budha University, Gautam Budh Nagar-201310 (India); Department of Mathematics, Guru Nanak Dev University, Amritsar (India)
2012-07-17
Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.
Mathematical modeling models, analysis and applications
Banerjee, Sandip
2014-01-01
""…the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. … it may be well used as a valuable source of interesting examples as well as complementary reading in a number of courses.""-Svitlana P. Rogovchenko, Zentralblatt MATH 1298
Mathematical Modeling of Loop Heat Pipes
Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.
1998-01-01
The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.
Optimization and mathematical modeling in computer architecture
Sankaralingam, Karu; Nowatzki, Tony
2013-01-01
In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t
Prognosis of Cs 137 dynamics in Pripyat river using mathematical modeling
International Nuclear Information System (INIS)
Ris, T.V.
2010-01-01
The analysis of measured and predicted data of Cs 137 dynamics in the water of Pripyat River are given using mathematical models developed by J. Smith (AQUASCOPE), L. Hakanson, and proposed transport model. (authors)
Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification
Directory of Open Access Journals (Sweden)
Grzegorz Mikułowski
2016-01-01
Full Text Available Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA, which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.
Modeling life the mathematics of biological systems
Garfinkel, Alan; Guo, Yina
2017-01-01
From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Rae, J.; Hodgkinson, D.P.; Robinson, P.C.; Herbert, A.W.
1984-04-01
This progress report contains notes on three aspects of hydrological modelling. Work on hydrodynamic dispersion in fractured media has been extended to transverse dispersion. Further work has been done on diffusion into the rock matrix and its effect on solute transport. The program NAMSOL has been used for the MIRAGE code comparison exercise being organised by Atkins R and D. (author)
Mathematical Models of Breast and Ovarian Cancers
Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron
2016-01-01
Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061
Constraint theory multidimensional mathematical model management
Friedman, George J
2017-01-01
Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...
Mathematical modelling of flooding at Magela Creek
International Nuclear Information System (INIS)
Vardavas, I.
1989-01-01
The extent and frequency of the flooding at Magela Creek can be predicted from a mathematical/computer model describing the hydrological phases of surface runoff. Surface runoff involves complex water transfer processes over very inhomogeneous terrain. A simple mathematical model of these has been developed which includes the interception of rainfall by the plant canopy, evapotranspiration, infiltration of surface water into the soil, the storage of water in surface depressions, and overland and subsurface water flow. The rainfall-runoff model has then been incorporated into a more complex computer model to predict the amount of water that enters and leaves the Magela Creek flood plain, downstream of the mine. 2 figs., ills
Structured Mathematical Modeling of Industrial Boiler
Directory of Open Access Journals (Sweden)
Abdullah Nur Aziz
2014-04-01
Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.
Mathematical modeling and the two-phase constitutive equations
International Nuclear Information System (INIS)
Boure, J.A.
1975-01-01
The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr
Causal Bayes Model of Mathematical Competence in Kindergarten
Directory of Open Access Journals (Sweden)
Božidar Tepeš
2016-06-01
Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.
Directory of Open Access Journals (Sweden)
Dinh An Nguyen
2012-07-01
Full Text Available Many of the Proton Exchange Membrane Fuel Cell (PEMFC models proposed in the literature consist of mathematical equations. However, they are not adequately practical for simulating power systems. The proposed model takes into account phenomena such as activation polarization, ohmic polarization, double layer capacitance and mass transport effects present in a PEM fuel cell. Using electrical analogies and a mathematical modeling of PEMFC, the circuit model is established. To evaluate the effectiveness of the circuit model, its static and dynamic performances under load step changes are simulated and compared to the numerical results obtained by solving the mathematical model. Finally, the applicability of our model is demonstrated by simulating a practical system.
Structured Mathematical Modeling of Industrial Boiler
Aziz, Abdullah Nur; Nazaruddin, Yul Yunazwin; Siregar, Parsaulian; Bindar, Yazid
2014-01-01
As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. T...
Mathematical modelling of the decomposition of explosives
International Nuclear Information System (INIS)
Smirnov, Lev P
2010-01-01
Studies on mathematical modelling of the molecular and supramolecular structures of explosives and the elementary steps and overall processes of their decomposition are analyzed. Investigations on the modelling of combustion and detonation taking into account the decomposition of explosives are also considered. It is shown that solution of problems related to the decomposition kinetics of explosives requires the use of a complex strategy based on the methods and concepts of chemical physics, solid state physics and theoretical chemistry instead of empirical approach.
Models and structures: mathematical physics
International Nuclear Information System (INIS)
2003-01-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems
mathematical modelling of atmospheric dispersion of pollutants
International Nuclear Information System (INIS)
Mohamed, M.E.
2002-01-01
the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established
A novel mathematical model for controllable near-field electrospinning
International Nuclear Information System (INIS)
Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun
2014-01-01
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers
A novel mathematical model for controllable near-field electrospinning
Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun
2014-01-01
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
A novel mathematical model for controllable near-field electrospinning
Energy Technology Data Exchange (ETDEWEB)
Ru, Changhai, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [College of Automation, Harbin Engineering University, Harbin 150001 (China); Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Chen, Jie; Shao, Zhushuai [Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Pang, Ming [College of Automation, Harbin Engineering University, Harbin 150001 (China); Luo, Jun, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072 (China)
2014-01-15
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
Mathematical models of natural gas consumption
International Nuclear Information System (INIS)
Sabo, Kristian; Scitovski, Rudolf; Vazler, Ivan; Zekic-Susac, Marijana
2011-01-01
In this paper we consider the problem of natural gas consumption hourly forecast on the basis of hourly movement of temperature and natural gas consumption in the preceding period. There are various methods and approaches for solving this problem in the literature. Some mathematical models with linear and nonlinear model functions relating to natural gas consumption forecast with the past natural gas consumption data, temperature data and temperature forecast data are mentioned. The methods are tested on concrete examples referring to temperature and natural gas consumption for the area of the city of Osijek (Croatia) from the beginning of the year 2008. The results show that most acceptable forecast is provided by mathematical models in which natural gas consumption and temperature are related explicitly.
Electrorheological fluids modeling and mathematical theory
Růžička, Michael
2000-01-01
This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.
Mathematical modeling of microbial growth in milk
Directory of Open Access Journals (Sweden)
Jhony Tiago Teleken
2011-12-01
Full Text Available A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.
Сontrol systems using mathematical models of technological objects ...
African Journals Online (AJOL)
Сontrol systems using mathematical models of technological objects in the control loop. ... Journal of Fundamental and Applied Sciences ... Such mathematical models make it possible to specify the optimal operating modes of the considered ...
Building Mathematical Models of Simple Harmonic and Damped Motion.
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
Vibratory gyroscopes : identification of mathematical model from test data
CSIR Research Space (South Africa)
Shatalov, MY
2007-05-01
Full Text Available Simple mathematical model of vibratory gyroscopes imperfections is formulated, which includes anisotropic damping and variation of mass-stiffness parameters and their harmonics. The method of identification of parameters of the mathematical model...
Mathematical Modelling of Surfactant Self-assembly at Interfaces
Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.
2015-01-01
© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary
Mathematical models for photovoltaic solar panel simulation
Energy Technology Data Exchange (ETDEWEB)
Santos, Jose Airton A. dos; Gnoatto, Estor; Fischborn, Marcos; Kavanagh, Edward [Universidade Tecnologica Federal do Parana (UTFPR), Medianeira, PR (Brazil)], Emails: airton@utfpr.edu.br, gnoatto@utfpr.edu.br, fisch@utfpr.edu.br, kavanagh@utfpr.edu.br
2008-07-01
A photovoltaic generator is subject to several variations of solar intensity, ambient temperature or load, that change your point of operation. This way, your behavior should be analyzed by such alterations, to optimize your operation. The present work sought to simulate a photovoltaic generator, of polycrystalline silicon, by characteristics supplied by the manufacturer, and to compare the results of two mathematical models with obtained values of field, in the city of Cascavel, for a period of one year. (author)
Selection of productivity improvement techniques via mathematical modeling
Directory of Open Access Journals (Sweden)
Mahassan M. Khater
2011-07-01
Full Text Available This paper presents a new mathematical model to select an optimal combination of productivity improvement techniques. The proposed model of this paper considers four-stage cycle productivity and the productivity is assumed to be a linear function of fifty four improvement techniques. The proposed model of this paper is implemented for a real-world case study of manufacturing plant. The resulted problem is formulated as a mixed integer programming which can be solved for optimality using traditional methods. The preliminary results of the implementation of the proposed model of this paper indicate that the productivity can be improved through a change on equipments and it can be easily applied for both manufacturing and service industries.
Nonconvex Model of Material Growth: Mathematical Theory
Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.
2018-06-01
The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.
Khusna, H.; Heryaningsih, N. Y.
2018-01-01
The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.
A Mathematical Model of Marine Diesel Engine Speed Control System
Sinha, Rajendra Prasad; Balaji, Rajoo
2018-02-01
Diesel engine is inherently an unstable machine and requires a reliable control system to regulate its speed for safe and efficient operation. Also, the diesel engine may operate at fixed or variable speeds depending upon user's needs and accordingly the speed control system should have essential features to fulfil these requirements. This paper proposes a mathematical model of a marine diesel engine speed control system with droop governing function. The mathematical model includes static and dynamic characteristics of the control loop components. Model of static characteristic of the rotating fly weights speed sensing element provides an insight into the speed droop features of the speed controller. Because of big size and large time delay, the turbo charged diesel engine is represented as a first order system or sometimes even simplified to a pure integrator with constant gain which is considered acceptable in control literature. The proposed model is mathematically less complex and quick to use for preliminary analysis of the diesel engine speed controller performance.
The many faces of the mathematical modeling cycle
Perrenet, J.C.; Zwaneveld, B.
2012-01-01
In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been
Simple mathematical models of symmetry breaking. Application to particle physics
International Nuclear Information System (INIS)
Michel, L.
1976-01-01
Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)
Mathematical modelling of steam generator and design of temperature regulator
Energy Technology Data Exchange (ETDEWEB)
Bogdanovic, S.S. [EE Institute Nikola Tesla, Belgrade (Yugoslavia)
1999-07-01
The paper considers mathematical modelling of once-through power station boiler and numerical algorithm for simulation of the model. Fast and numerically stable algorithm based on the linearisation of model equations and on the simultaneous solving of differential and algebraic equations is proposed. The paper also presents the design of steam temperature regulator by using the method of projective controls. Dynamic behaviour of the system closed with optimal linear quadratic regulator is taken as the reference system. The desired proprieties of the reference system are retained and solutions for superheated steam temperature regulator are determined. (author)
Laser filamentation mathematical methods and models
Lorin, Emmanuel; Moloney, Jerome
2016-01-01
This book is focused on the nonlinear theoretical and mathematical problems associated with ultrafast intense laser pulse propagation in gases and in particular, in air. With the aim of understanding the physics of filamentation in gases, solids, the atmosphere, and even biological tissue, specialists in nonlinear optics and filamentation from both physics and mathematics attempt to rigorously derive and analyze relevant non-perturbative models. Modern laser technology allows the generation of ultrafast (few cycle) laser pulses, with intensities exceeding the internal electric field in atoms and molecules (E=5x109 V/cm or intensity I = 3.5 x 1016 Watts/cm2 ). The interaction of such pulses with atoms and molecules leads to new, highly nonlinear nonperturbative regimes, where new physical phenomena, such as High Harmonic Generation (HHG), occur, and from which the shortest (attosecond - the natural time scale of the electron) pulses have been created. One of the major experimental discoveries in this nonlinear...
Thermoregulation in premature infants: A mathematical model.
Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen
2016-12-01
In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright Â© 2016 Elsevier Ltd. All rights reserved.
Mathematical models for atmospheric pollutants. Final report
International Nuclear Information System (INIS)
Drake, R.L.; Barrager, S.M.
1979-08-01
The present and likely future roles of mathematical modeling in air quality decisions are described. The discussion emphasizes models and air pathway processes rather than the chemical and physical behavior of specific anthropogenic emissions. Summarized are the characteristics of various types of models used in the decision-making processes. Specific model subclasses are recommended for use in making air quality decisions that have site-specific, regional, national, or global impacts. The types of exposure and damage models that are currently used to predict the effects of air pollutants on humans, other animals, plants, ecosystems, property, and materials are described. The aesthetic effects of odor and visibility and the impact of pollutants on weather and climate are also addressed. Technical details of air pollution meteorology, chemical and physical properties of air pollutants, solution techniques, and air quality models are discussed in four appendices bound in separate volumes
Mathematical modeling of CANDU-PHWR
Energy Technology Data Exchange (ETDEWEB)
Gaber, F.A.; Aly, R.A.; El-Shal, A.O. [Atomic Energy Authority, Cairo (Egypt)
2003-07-01
The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR). This study involved mathematical modeling of CANDU-PHWR to study its thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique. The reactor model includes the neutronic, reactivity, and fuel channel heat transfer. The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and the reactivity feed back due to the changes in the fuel temperature and coolant temperature. The CANDU-PHWR model was coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative influence...... be carefully selected, so that the model and its visualization enhance our ability to interpret the brain. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular analysis tools within the neuroimaging community. Such methods...... neuroimaging data sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative...... be carefully selected, so that the model and its visualization enhance our ability to interpret brain function. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...
Mathematical methods and models in composites
Mantic, Vladislav
2014-01-01
This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics cover
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London...
Chancroid transmission dynamics: a mathematical modeling approach.
Bhunu, C P; Mushayabasa, S
2011-12-01
Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.
An introduction to mathematical modeling of infectious diseases
Li, Michael Y
2018-01-01
This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.
Fermentation process diagnosis using a mathematical model
Energy Technology Data Exchange (ETDEWEB)
Yerushalmi, L; Volesky, B; Votruba, J
1988-09-01
Intriguing physiology of a solvent-producing strain of Clostridium acetobutylicum led to the synthesis of a mathematical model of the acetone-butanol fermentation process. The model presented is capable of describing the process dynamics and the culture behavior during a standard and a substandard acetone-butanol fermentation. In addition to the process kinetic parameters, the model includes the culture physiological parameters, such as the cellular membrane permeability and the number of membrane sites for active transport of sugar. Computer process simulation studies for different culture conditions used the model, and quantitatively pointed out the importance of selected culture parameters that characterize the cell membrane behaviour and play an important role in the control of solvent synthesis by the cell. The theoretical predictions by the new model were confirmed by experimental determination of the cellular membrane permeability.
A mathematical model on Acquired Immunodeficiency Syndrome
Directory of Open Access Journals (Sweden)
Buddhadeo Mahato
2014-10-01
Full Text Available A mathematical model SEIA (susceptible-exposed-infectious-AIDS infected with vertical transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the world is currently facing. Even with anti-retroviral therapies (ART, many resource-constrained countries are unable to meet the treatment needs of their infected populations. We consider a function of number of AIDS cases in a community with an inverse relation. A stated theorem with proof and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number R0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R0⩽1 and unstable if R0>1. Finally, numerical simulations are presented to illustrate the results.
Assessment of Primary 5 Students' Mathematical Modelling Competencies
Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia
2012-01-01
Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…
Development of a Multidisciplinary Middle School Mathematics Infusion Model
Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura
2011-01-01
The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond
2010-01-01
This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…
Mathematical Modeling in Population Dynamics: The Case of Single ...
African Journals Online (AJOL)
kofimereku
Department of Mathematics, Kwame Nkrumah University of Science and Technology,. Kumasi, Ghana ... The trust of this paper is the application of mathematical models in helping to ..... Statistics and Computing, New York: Wiley. Cox, C.B and ...
Mathematical Modelling and the Learning Trajectory: Tools to Support the Teaching of Linear Algebra
Cárcamo Bahamonde, Andrea Dorila; Fortuny Aymemí, Josep Maria; Gómez i Urgellés, Joan Vicenç
2017-01-01
In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…
A proposed residual stress model for oblique turning
International Nuclear Information System (INIS)
Elkhabeery, M. M.
2001-01-01
A proposed mathematical model is presented for predicting the residual stresses caused by turning. Effects of change in tool free length, cutting speed, feed rate, and the tensile strength of work piece material on the maximum residual stress are investigated. The residual stress distribution in the surface region due to turning under unlubricated condition is determined using a deflection etching technique. To reduce the number of experiments required and build the mathematical model for these variables, Response Surface Methodology (RSM) is used. In addition, variance analysis and an experimental check are conducted to determine the prominent parameters and the adequacy of the model. The results show that the tensile stress of the work piece material, cutting speed, and feed rate have significant effects on the maximum residual stresses. The proposed model, that offering good correlation between the experimental and predicted results, is useful in selecting suitable cutting parameters for the machining of different materials. (author)
Mathematical Modelling of Involute Spur Gears Manufactured by Rack Cutter
Directory of Open Access Journals (Sweden)
Tufan Gürkan YILMAZ
2016-05-01
Full Text Available In this study, mathematical modelling of asymmetric involute spur gears was situated in by Litvin approach. In this context, firstly, mathematical expressions of rack cutter which manufacture asymmetric involute spur gear, then mathematical expression of asymmetric involute spur gear were obtained by using differential geometry, coordinate transformation and gear theory. Mathematical expressions were modelled in MATLAB and output files including points of involute spur gear’s teeth were designed automatically thanks to macros.
A Mathematical Model of Cardiovascular Response to Dynamic Exercise
National Research Council Canada - National Science Library
Magosso, E
2001-01-01
A mathematical model of cardiovascular response to dynamic exercise is presented, The model includes the pulsating heart, the systemic and pulmonary, circulation, a functional description of muscle...
Biological-Mathematical Modeling of Chronic Toxicity.
1981-07-22
34Mathematical Model of Uptake and Distribution," Uptake and Distribution of Anesthetic Agents, E. M. Papper and R. J. Kitz (Editors, McGraw-Hill Book Co., Inc...distribution, In: Papper , E.M. and Kltz, R.J.(eds.) Uptake and distribution of anesthetic agents, McGraw- Hill, New York, p. 72 3. Plpleson, W.W...1963) Quantitative prediction of anesthetic concentrations. In: Papper , E.M. and Kitz, R.J. (eds.) Uptake and distribution of anesthetic agents, McGraw
Mathematical Modeling of Diaphragm Pneumatic Motors
Directory of Open Access Journals (Sweden)
Fojtášek Kamil
2014-03-01
Full Text Available Pneumatic diaphragm motors belong to the group of motors with elastic working parts. This part is usually made of rubber with a textile insert and it is deformed under the pressure of a compressed air or from the external mass load. This is resulting in a final working effect. In this type of motors are in contact two different elastic environments – the compressed air and the esaltic part. These motors are mainly the low-stroke and working with relatively large forces. This paper presents mathematical modeling static properties of diaphragm motors.
A mathematical model of Chagas disease transmission
Hidayat, Dayat; Nugraha, Edwin Setiawan; Nuraini, Nuning
2018-03-01
Chagas disease is a parasitic infection caused by protozoan Trypanosoma cruzi which is transmitted to human by insects of the subfamily Triatominae, including Rhodnius prolixus. This disease is a major problem in several countries of Latin America. A mathematical model of Chagas disease with separate vector reservoir and a neighboring human resident is constructed. The basic reproductive ratio is obtained and stability analysis of the equilibria is shown. We also performed sensitivity populations dynamics of infected humans and infected insects based on migration rate, carrying capacity, and infection rate parameters. Our findings showed that the dynamics of the infected human and insect is mostly affected by carrying capacity insect in the settlement.
Mathematical modeling of infectious disease dynamics
Siettos, Constantinos I.; Russo, Lucia
2013-01-01
Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814
Comparison of Different Mathematical Models of Cavitation
Directory of Open Access Journals (Sweden)
Dorota HOMA
2014-12-01
Full Text Available Cavitation occurs during the flow when local pressure drops to the saturation pressure according to the temperature of the flow. It includes both evaporation and condensation of the vapor bubbles, which occur alternately with high frequency. Cavitation can be very dangerous, especially for pumps, because it leads to break of flow continuity, noise, vibration, erosion of blades and change in pump’s characteristics. Therefore it is very important for pump designers and users to avoid working in cavitation conditions. Simulation of flow can be very useful in that and can indicate if there is risk of cavitating flow occurrence. As this is a multiphase flow and quite complicated phenomena, there are a few mathematical models describing it. The aim of this paper is to make a short review of them and describe their approach to model cavitation. It is desirable to know differences between them to model this phenomenon properly.
Mathematical modeling of the Phoenix Rising pathway.
Directory of Open Access Journals (Sweden)
Chad Liu
2014-02-01
Full Text Available Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2, a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3, caspase 7 (C7, and nuclear factor κB (NFκB. In addition, we simulated the effects of cyclooxygenase-2 (COX2 inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.
Mathematical modeling of CANDU-PHWR
Energy Technology Data Exchange (ETDEWEB)
Gaber, F.A.; Aly, R.A.; El-Shal, A.O. [Atomic Energy Authority, Cairo (Egypt)
2001-07-01
The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR) system. This study involved mathematical modeling of CANDU PHWR major system components and the developments of software to study the thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique.The integrated CANDU-PHWR model includes the neutronic, reactivity, fuel channel heat transfer, piping and the preheater type U-tube steam generator (PUTSG). The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and reactivity feed back due to the changes in fuel temperature and coolant temperature. The complex operation of the preheater type U-tube steam generator (PUTSG) is represented by a non-linear dynamic model using a state variable, moving boundary and lumped parameter techniques. The secondary side of the PUTSG model has six separate lumps including a preheater region, a lower boiling section, a mixing region, a riser, a chimmeny section, and a down-corner. The tube side of PUTSG has three main thermal zones. The PUTSG model is based on conservation of mass, energy and momentum relation-ships. The CANDU-PHWR integrated model are coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)
A mathematical model of microalgae growth in cylindrical photobioreactor
Bakeri, Noorhadila Mohd; Jamaian, Siti Suhana
2017-08-01
Microalgae are unicellular organisms, which exist individually or in chains or groups but can be utilized in many applications. Researchers have done various efforts in order to increase the growth rate of microalgae. Microalgae have a potential as an effective tool for wastewater treatment, besides as a replacement for natural fuel such as coal and biodiesel. The growth of microalgae can be estimated by using Geider model, which this model is based on photosynthesis irradiance curve (PI-curve) and focused on flat panel photobioreactor. Therefore, in this study a mathematical model for microalgae growth in cylindrical photobioreactor is proposed based on the Geider model. The light irradiance is the crucial part that affects the growth rate of microalgae. The absorbed photon flux will be determined by calculating the average light irradiance in a cylindrical system illuminated by unidirectional parallel flux and considering the cylinder as a collection of differential parallelepipeds. Results from this study showed that the specific growth rate of microalgae increases until the constant level is achieved. Therefore, the proposed mathematical model can be used to estimate the rate of microalgae growth in cylindrical photobioreactor.
Dalla Vecchia, Rodrigo
2015-01-01
This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…
Mathematical model of seed germination process
International Nuclear Information System (INIS)
Gładyszewska, B.; Koper, R.; Kornarzyński, K.
1999-01-01
An analytical model of seed germination process was described. The model based on proposed working hypothesis leads - by analogy - to a law corresponding with Verhulst-Pearl's law, known from the theory of population kinetics. The model was applied to describe the germination kinetics of tomato seeds, Promyk field cultivar, biostimulated by laser treatment. Close agreement of experimental and model data was obtained [pl
The mathematical model of thread unrolling from a bobbin
Directory of Open Access Journals (Sweden)
S. M. Tenenbaum
2014-01-01
Full Text Available I. Introduction The subject of research in this work is a process of thread unrolling from a bobbin. The mathematical model of this process considering motion of thread peace on a bobbin and unrolled peace is proposed. The dimension of system of differential equations for this model is constant during deploying.The relevance to simulate this process for design of Heliogyro-like solar sails (Heliogyro [1], BMSTU-Sail [2] is proved. The paper briefly characterizes a blade for such solar sail as a simulation object. It proves the possibility for using a flexible thread model for a long blade because of very small blade thickness (less than 10 μm [3] relative to blade width and the phenomena of Koriolis forces [4] that lead to buckling failure of blade flatness.The major features of the proposed model are:-- simulated as a motion of the thread piece both being on a bobbin and its unrolled peace;-- splitting a thread length into nodes does not depend on the demand to ensure a sufficient number of nodes on a single thread turn on the coil;-- because of avoiding a problem of contact between the thread and bobbin a stable integration of motion equations is provided by the conventional Runge-Kutta method of fourth order with a constant step [5];-- in the course of solution the number of freedom degrees (number of motion equation is constant, thereby simplifying a calculation algorithm.The closest mathematical model is proposed in [6].The scientific novelty of this research is the approach to solving the problem of unrolling thread from a bobbin using a constant number of motion equations while preserving real kinematics coiling process.II. Problem formulationIn this section the problem of unrolling thread with length L from a bobbin of radius r is posed while any kind of forces are acting on the unrolled peace of thread. Moreover, the law of bobbin rotation φ(t assumed to be known with the proviso that the model can be modified if φ(t is the result of
Modelling as a foundation for academic forming in mathematics education
Perrenet, J.C.; Morsche, ter H.G.
2004-01-01
The Bachelor curriculum of Applied Mathematics in Eindhoven includes a series of modelling projects where pairs of students solve mathematical problems posed in non-mathematical language. Communication skills training is integrated with this track. Recently a new course has been added. The students
International Nuclear Information System (INIS)
Begum, N.N.; Ahmed, J.
2006-01-01
A classification of the existing mathematical models of flow-injection (FI) manifolds based on the main principles on which they are built, have been proposed. Numerous mathematical models of FI systems employing ideas from different scientific areas (e.g. mathematical statistics, chemical engineering, chromatography) have been developed so far. The models have been compared with respect to their predictive power, the complexity of their mathematical treatment, and the requirements for computation time when applied to single-line, multi-channel and conjugated two-line FI systems. It is concluded that the axially dispersed plug flow model deserves special attention because it offers an acceptable compromise between the conflicting requirements for maximal possible mathematical simplicity and maximal possible precision. Applicability of these existing flow-injection models to single-line, multi-channel and conjugated two-line systems for environmental monitoring have been discussed. (author)
Directory of Open Access Journals (Sweden)
Melike TURAL SÖNMEZ
2017-12-01
Full Text Available The purpose of this study is to examine the construction of mathematical modelling problems process in the content of financial literacy. It is also aimed to create design proposals for construction of mathematical modelling problems. A design based research method was used in this study. The participants were three seventh grade students, six finance experts and nine mathematics education experts. Data collection tools were transcription of video and tapes group discussions, presentations and worksheets during mathematical modelling activities, and participant experts’ feedback form about mathematical modelling problems. There were three stages in this study. First stage was application of preliminary study. This stage gave information about convenience of problems to grade level, students’ timing for solution of problems, clarity of problems and students’ background about content. In second stage, finance experts commented on convenience of mathematical modelling problems to financial literacy standards. In third stage, mathematics education experts commented on convenience of problems to students’ grade level, mathematical modelling principles and seventh grade mathematics lesson objectives. They also gave suggestion on progress. The frequency value of theme in feedback forms was calculated and experts’ expressions were given as citation. It was given suggestion about stages and application of the design guide
Mathematical models for therapeutic approaches to control HIV disease transmission
Roy, Priti Kumar
2015-01-01
The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...
Mathematical modeling of a thermovoltaic cell
White, Ralph E.; Kawanami, Makoto
1992-01-01
A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.
Description of mathematical models and computer programs
International Nuclear Information System (INIS)
1977-01-01
The paper gives a description of mathematical models and computer programs for analysing possible strategies for spent fuel management, with emphasis on economic analysis. The computer programs developed, describe the material flows, facility construction schedules, capital investment schedules and operating costs for the facilities used in managing the spent fuel. The computer programs use a combination of simulation and optimization procedures for the economic analyses. Many of the fuel cycle steps (such as spent fuel discharges, storage at the reactor, and transport to the RFCC) are described in physical and economic terms through simulation modeling, while others (such as reprocessing plant size and commissioning schedules, interim storage facility commissioning schedules etc.) are subjected to economic optimization procedures to determine the approximate lowest-cost plans from among the available feasible alternatives
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Mathematical Model of Cytomegalovirus (CMV) Disease
Sriningsih, R.; Subhan, M.; Nasution, M. L.
2018-04-01
The article formed the mathematical model of cytomegalovirus (CMV) disease. Cytomegalovirus (CMV) is a type of herpes virus. This virus is actually not dangerous, but if the body's immune weakens the virus can cause serious problems for health and even can cause death. This virus is also susceptible to infect pregnant women. In addition, the baby may also be infected through the placenta. If this is experienced early in pregnancy, it will increase the risk of miscarriage. If the baby is born, it can cause disability in the baby. The model is formed by determining its variables and parameters based on assumptions. The goal is to analyze the dynamics of cytomegalovirus (CMV) disease spread.
Laser interaction with biological material mathematical modeling
Kulikov, Kirill
2014-01-01
This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.
Mathematical Models and Methods for Living Systems
Chaplain, Mark; Pugliese, Andrea
2016-01-01
The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods. Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.
Missing the Promise of Mathematical Modeling
Meyer, Dan
2015-01-01
The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…
Mathematics Teacher Education: A Model from Crimea.
Ferrucci, Beverly J.; Evans, Richard C.
1993-01-01
Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)
A Mathematical Model for Cisplatin Cellular Pharmacodynamics
Directory of Open Access Journals (Sweden)
Ardith W. El-Kareh
2003-03-01
Full Text Available A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours. The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.
Rudolph, Lee
2012-01-01
In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, in
Mathematical modeling of acid-base physiology.
Occhipinti, Rossana; Boron, Walter F
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3(-), [Formula: see text] ) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3(-) influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. Copyright © 2015 Elsevier Ltd. All rights reserved.
APPLICATION OF GIS AND MATHEMATICAL MODELING IN MARITIME CRISIS SITUATIONS
Directory of Open Access Journals (Sweden)
Nenad Mladineo
2010-12-01
Full Text Available This paper aims to propose a decision support system for maritime crisis situation, due to fact that Croatia has decided to implement Directive 2002/59/EC to define places of refuge for ships in need of assistance off their coasts, or to develop techniques for providing assistance to such ships. In order to fulfill this Directive it is necessary to build an effective Decision Support System (DSS based on GIS and mathematical modeling. The basic module of the proposed system is GIS, for all levels of DSS, that comprise information subsystems about spatial and other data and serves the other modules with data and information. Starting points for analysis are shipping corridors, and 380 potential locations for places of refuge designated in the official navigational pilot book. Multicriteria analysis, with GIS-generated input data, has been used to establish "worthiness" of a place of refuge for each ship category, taking into account kinds of accident. Proposed mathematical models facilitate optimal usage of "available intervention resources".
A MATHEMATICAL MODEL OF CHP 2000 TYPE PROGRESSIVE GEAR
Directory of Open Access Journals (Sweden)
Paweł Lonkwic
2016-12-01
Full Text Available The project of CHP2000 type progressive gear has been presented in the article. The offered solution from its construction point of view differs from the existing solutions due to the application of Belleville springs packets supporting the braking roller cam and achieving a flexible range of the gear loading. The standard concept of the gear loading within a mathematical and a geometrical model has been presented in the article. The proposed solution can be used in the friction lifts with the loading capacity from 8500 up to 20000 N.
Teaching Mathematical Modelling for Earth Sciences via Case Studies
Yang, Xin-She
2010-05-01
Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).
Linear models in the mathematics of uncertainty
Mordeson, John N; Clark, Terry D; Pham, Alex; Redmond, Michael A
2013-01-01
The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data is difficult to measure and an assumption of randomness and/or statistical validity is questionable. We apply our methods to real world issues in international relations such as nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and fail...
Mathematical problems in modeling artificial heart
Directory of Open Access Journals (Sweden)
Ahmed N. U.
1995-01-01
Full Text Available In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate. On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.
The use of mathematical models in teaching wastewater treatment engineering
DEFF Research Database (Denmark)
Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.
2002-01-01
Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...... efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available....
Mathematical models for indoor radon prediction
International Nuclear Information System (INIS)
Malanca, A.; Pessina, V.; Dallara, G.
1995-01-01
It is known that the indoor radon (Rn) concentration can be predicted by means of mathematical models. The simplest model relies on two variables only: the Rn source strength and the air exchange rate. In the Lawrence Berkeley Laboratory (LBL) model several environmental parameters are combined into a complex equation; besides, a correlation between the ventilation rate and the Rn entry rate from the soil is admitted. The measurements were carried out using activated carbon canisters. Seventy-five measurements of Rn concentrations were made inside two rooms placed on the second floor of a building block. One of the rooms had a single-glazed window whereas the other room had a double pane window. During three different experimental protocols, the mean Rn concentration was always higher into the room with a double-glazed window. That behavior can be accounted for by the simplest model. A further set of 450 Rn measurements was collected inside a ground-floor room with a grounding well in it. This trend maybe accounted for by the LBL model
Mathematical modeling in mechanics of heterogeneous media
International Nuclear Information System (INIS)
Fedorov, A.V.; Fomin, V.M.
1991-01-01
The paper reviews the work carried out at the Department of Multi-Phase Media Mechanics of the Institute of Theoretical and Applied Mechanics of the Siberian Division of the USSR Academy of Sciences. It deals with mathematical models for the flow of gas mixtures and solid particles that account for phase transitions and chemical reactions. This work is concerned with the problems of construction of laws of conservation, determination of the type of equations of heterogeneous media mechanics, structure of shock waves, and combined discontinuities in mixtures. The theory of ideal and nonideal detonation in suspension of matter in gases is discussed. Self-similar flows of gas mixtures and responding particles, as well as the problem of breakup of discontinuity for suspension of matter in gases, is studied. 42 refs
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.
Ganusov, Vitaly V
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.
Strong inference in mathematical modeling: a method for robust science in the 21st century
Directory of Open Access Journals (Sweden)
Vitaly V. Ganusov
2016-07-01
Full Text Available While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers [1], the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions and data. Following the principle of strong inference for experimental sciences proposed by Platt [2], I suggest ``strong inference in mathematical modeling'' as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are 1 to develop multiple alternative models for the phenomenon in question; 2 to compare the models with available experimental data and to determine which of the models are not consistent with the data; 3 to determine reasons why rejected models failed to explain the data, and 4 to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the 21st century.
Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors
Rash, Agnes M.; Zurbach, E. Peter
2004-01-01
The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…
Akgün, Levent
2015-01-01
The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…
Noise in restaurants: levels and mathematical model.
To, Wai Ming; Chung, Andy
2014-01-01
Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Noise in restaurants: Levels and mathematical model
Directory of Open Access Journals (Sweden)
Wai Ming To
2014-01-01
Full Text Available Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (Leq,1-h was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Mathematical modeling plasma transport in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Quiang, Ji [Univ. of Illinois, Urbana-Champaign, IL (United States)
1997-01-01
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10^{20}/m^{3} with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%.
Mathematical modeling plasma transport in tokamaks
International Nuclear Information System (INIS)
Quiang, Ji
1995-01-01
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10 20 /m 3 with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%
Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2016-01-01
This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century
Ganusov, Vitaly V.
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750
Mathematics in Nature Modeling Patterns in the Natural World
Adam, John A
2011-01-01
From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathem
An introduction to mathematical modeling a course in mechanics
Oden, Tinsley J
2011-01-01
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...
Mathematical model insights into arsenic detoxification
Directory of Open Access Journals (Sweden)
Nijhout H Frederik
2011-08-01
Full Text Available Abstract Background Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs, which then undergoes hepatic methylation to methylarsonic acid (MMAs and a second methylation to dimethylarsinic acid (DMAs. Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation. Methods We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects. Results We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic
The 'model omnitron' proposed experiment
International Nuclear Information System (INIS)
Sestero, A.
1997-05-01
The Model Omitron is a compact tokamak experiment which is designed by the Fusion Engineering Unit of ENEA and CITIF CONSORTIUM. The building of Model Omitron would allow for full testing of Omitron engineering, and partial testing of Omitron physics -at about 1/20 of the cost that has been estimated for the larger parent machine. In particular, due to the unusually large ohmic power densities (up to 100 times the nominal value in the Frascati FTU experiment), in Model Omitron the radial energy flux is reaching values comparable or higher than envisaged of the larger ignition experiments Omitron, Ignitor and Iter. Consequently, conditions are expected to occur at the plasma border in the scrape-off layer of Model Omitron, which are representative of the quoted larger experiments. Moreover, since all this will occur under ohmic heating alone, one will hopefully be able to derive an energy transport model fo the ohmic heating regime that is valid over a range of plasma parameters (in particular, of the temperature parameter) wider than it was possible before. In the Model Omitron experiment, finally - by reducing the plasma current and/or the toroidal field down to, say, 1/3 or 1/4 of the nominal values -additional topics can be tackled, such as: large safety-factor configurations (of interest for improving confinement), large aspect-ratio configurations (of interest for the investigation of advanced concepts in tokamaks), high beta (with RF heating -also of interest for the investigation of advanced concepts in tokamaks), long pulse discharges (of interest for demonstrating stationary conditions in the current profile)
Mathematical model predicts the elastic behavior of composite materials
Directory of Open Access Journals (Sweden)
Zoroastro de Miranda Boari
2005-03-01
Full Text Available Several studies have found that the non-uniform distribution of reinforcing elements in a composite material can markedly influence its characteristics of elastic and plastic deformation and that a composite's overall response is influenced by the physical and geometrical properties of its reinforcing phases. The finite element method, Eshelby's method and dislocation mechanisms are usually employed in formulating a composite's constitutive response. This paper discusses a composite material containing SiC particles in an aluminum matrix. The purpose of this study was to find the correlation between a composite material's particle distribution and its resistance, and to come up with a mathematical model to predict the material's elastic behavior. The proposed formulation was applied to establish the thermal stress field in the aluminum-SiC composite resulting from its fabrication process, whereby the mixture is prepared at 600 °C and the composite material is used at room temperature. The analytical results, which are presented as stress probabilities, were obtained from the mathematical model proposed herein. These results were compared with the numerical ones obtained by the FEM method. A comparison of the results of the two methods, analytical and numerical, reveals very similar average thermal stress values. It is also shown that Maxwell-Boltzmann's distribution law can be applied to identify the correlation between the material's particle distribution and its resistance, using Eshelby's thermal stresses.
The Mathematical Modelling of Heat Transfer in Electrical Cables
Directory of Open Access Journals (Sweden)
Bugajev Andrej
2014-05-01
Full Text Available This paper describes a mathematical modelling approach for heat transfer calculations in underground high voltage and middle voltage electrical power cables. First of the all typical layout of the cable in the sand or soil is described. Then numerical algorithms are targeted to the two-dimensional mathematical models of transient heat transfer. Finite Volume Method is suggested for calculations. Different strategies of nonorthogonality error elimination are considered. Acute triangles meshes were applied in two-dimensional domain to eliminate this error. Adaptive mesh is also tried. For calculations OpenFOAM open source software which uses Finite Volume Method is applied. To generate acute triangles meshes aCute library is used. The efficiency of the proposed approach is analyzed. The results show that the second order of convergence or close to that is achieved (in terms of sizes of finite volumes. Also it is shown that standard strategy, used by OpenFOAM is less efficient than the proposed approach. Finally it is concluded that for solving real problem a spatial adaptive mesh is essential and adaptive time steps also may be needed.
Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe
2016-01-01
Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…
On Mathematical Modeling Of Quantum Systems
International Nuclear Information System (INIS)
Achuthan, P.; Narayanankutty, Karuppath
2009-01-01
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Mathematical Models of Cardiac Pacemaking Function
Li, Pan; Lines, Glenn T.; Maleckar, Mary M.; Tveito, Aslak
2013-10-01
Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.
Manual on mathematical models in isotope hydrogeology
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-10-01
Methodologies based on the use of naturally occurring isotopes are, at present, an integral part of studies being undertaken for water resources assessment and management. Quantitative evaluations based on the temporal and/or spatial distribution of different isotopic species in hydrological systems require conceptual mathematical formulations. Different types of model can be employed depending on the nature of the hydrological system under investigation, the amount and type of data available, and the required accuracy of the parameter to be estimated. This manual provides an overview of the basic concepts of existing modelling approaches, procedures for their application to different hydrological systems, their limitations and data requirements. Guidance in their practical applications, illustrative case studies and information on existing PC software are also included. While the subject matter of isotope transport modelling and improved quantitative evaluations through natural isotopes in water sciences is still at the development stage, this manual summarizes the methodologies available at present, to assist the practitioner in the proper use within the framework of ongoing isotope hydrological field studies. In view of the widespread use of isotope methods in groundwater hydrology, the methodologies covered in the manual are directed towards hydrogeological applications, although most of the conceptual formulations presented would generally be valid. Refs, figs, tabs.
Mathematical Models of Cardiac Pacemaking Function
Directory of Open Access Journals (Sweden)
Pan eLi
2013-10-01
Full Text Available Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.
Manual on mathematical models in isotope hydrogeology
International Nuclear Information System (INIS)
1996-10-01
Methodologies based on the use of naturally occurring isotopes are, at present, an integral part of studies being undertaken for water resources assessment and management. Quantitative evaluations based on the temporal and/or spatial distribution of different isotopic species in hydrological systems require conceptual mathematical formulations. Different types of model can be employed depending on the nature of the hydrological system under investigation, the amount and type of data available, and the required accuracy of the parameter to be estimated. This manual provides an overview of the basic concepts of existing modelling approaches, procedures for their application to different hydrological systems, their limitations and data requirements. Guidance in their practical applications, illustrative case studies and information on existing PC software are also included. While the subject matter of isotope transport modelling and improved quantitative evaluations through natural isotopes in water sciences is still at the development stage, this manual summarizes the methodologies available at present, to assist the practitioner in the proper use within the framework of ongoing isotope hydrological field studies. In view of the widespread use of isotope methods in groundwater hydrology, the methodologies covered in the manual are directed towards hydrogeological applications, although most of the conceptual formulations presented would generally be valid. Refs, figs, tabs
Ocular hemodynamics and glaucoma: the role of mathematical modeling.
Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A
2013-01-01
To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.
Women's Language Model: A Proposal.
Dumas, Bethany K.
It is possible to think of women's language in terms of the model implied by the following statement. Insofar as native speakers of English are concerned, the language of women in America has four sets of components: those shared with the language of men in America; those shared, in varying proportions, with other women living in patriarchies;…
The role of mathematical models in the optimization of radiopharmaceutical therapy
International Nuclear Information System (INIS)
Divgi, C.
2001-01-01
Mathematical models have been used in radiopharmaceutical therapy for over five decades. These have served to determine the amount of radioactivity required to treat disease, as in the therapy of hyperthyroidism with iodine-131, or, more frequently, to determine the largest amount of radioactivity that can be safely administered. Mathematical models are especially useful in the determination of fractionated radiopharmaceutical therapy. This review will briefly outline the historical development and current utility of mathematical models in radiopharmaceutical therapy, including thyroid disorders and radioimmunotherapy; and describe the potential of modeling in fractionated therapy. The extended application of such models to currently used radiopharmaceutical therapy based on indices of body mass or surface area, to alleviate toxicity and increase radiation dose to tumour, will be proposed. Finally, future applications of mathematical models in radiopharmaceutical therapy will be outlined. (author)
Mathematical modeling of a steam generator for sensor fault detection
International Nuclear Information System (INIS)
Prock, J.
1988-01-01
A dynamic model for a nuclear power plant steam generator (vertical, preheated, U-tube recirculation-type) is formulated as a sixth-order nonlinear system. The model integrates nodal mass and energy balances for the primary water, the U-tube metal and the secondary water and steam. The downcomer flow is determined by a static balance of momentum. The mathematical system is solved using transient input data from the Philippsburg 2 (FRG) nuclear power plant. The results of the calculation are compared with actual measured values. The proposed model provides a low-cost tool for the automatic control and simulation of the steam generating process. The ''parity-space'' algorithm is used to demonstrate the applicability of the mathematical model for sensor fault detection and identification purposes. This technique provides a powerful means of generating temporal analytical redundancy between sensor signals. It demonstrates good detection rates of sensor errors using relatively few steps of scanning time and allows the reconfiguration of faulty signals. (author)
Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.
Timalsina, Asim; Tian, Jianjun Paul; Wang, Jin
2017-08-01
We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.
A mathematical model for turbulent incompressible flows through mixing grids
International Nuclear Information System (INIS)
Allaire, G.
1989-01-01
A mathematical model is proposed for the computation of turbulent incompressible flows through mixing grids. This model is obtained as follows: in a three-dimentional-domain we represent a mixing grid by small identical wings of size ε 2 periodically distributed at the nodes of a plane regular mesh of size ε, and we consider incompressible Navier-Stokes equations with a no-slip condition on the wings. Using an appropriate homogenization process we pass to the limit when ε tends to zero and we obtain a Brinkman equation, i.e. a Navier-Stokes equation plus a zero-order term for the velocity, in a homogeneous domain without anymore wings. The interest of this model is that the spatial discretization is simpler in a homogeneous domain, and, moreover, the new term, which expresses the grid's mixing effect, can be evaluated with a local computation around a single wing
Logistics of Mathematical Modeling-Focused Projects
Harwood, R. Corban
2018-01-01
This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical…
Modelling Mathematical Argumentation: The Importance of Qualification
Inglis, Matthew; Mejia-Ramos, Juan; Simpson, Adrian
2007-01-01
In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…
A mathematical model of brain glucose homeostasis
Directory of Open Access Journals (Sweden)
Kimura Hidenori
2009-11-01
Full Text Available Abstract Background The physiological fact that a stable level of brain glucose is more important than that of blood glucose suggests that the ultimate goal of the glucose-insulin-glucagon (GIG regulatory system may be homeostasis of glucose concentration in the brain rather than in the circulation. Methods In order to demonstrate the relationship between brain glucose homeostasis and blood hyperglycemia in diabetes, a brain-oriented mathematical model was developed by considering the brain as the controlled object while the remaining body as the actuator. After approximating the body compartmentally, the concentration dynamics of glucose, as well as those of insulin and glucagon, are described in each compartment. The brain-endocrine crosstalk, which regulates blood glucose level for brain glucose homeostasis together with the peripheral interactions among glucose, insulin and glucagon, is modeled as a proportional feedback control of brain glucose. Correlated to the brain, long-term effects of psychological stress and effects of blood-brain-barrier (BBB adaptation to dysglycemia on the generation of hyperglycemia are also taken into account in the model. Results It is shown that simulation profiles obtained from the model are qualitatively or partially quantitatively consistent with clinical data, concerning the GIG regulatory system responses to bolus glucose, stepwise and continuous glucose infusion. Simulations also revealed that both stress and BBB adaptation contribute to the generation of hyperglycemia. Conclusion Simulations of the model of a healthy person under long-term severe stress demonstrated that feedback control of brain glucose concentration results in elevation of blood glucose level. In this paper, we try to suggest that hyperglycemia in diabetes may be a normal outcome of brain glucose homeostasis.
Kalechofsky, Robert
This research paper proposes several mathematical models which help clarify Piaget's theory of cognition on the concrete and formal operational stages. Some modified lattice models were used for the concrete stage and a combined Boolean Algebra and group theory model was used for the formal stage. The researcher used experiments cited in the…
Hybrid modelling framework by using mathematics-based and information-based methods
International Nuclear Information System (INIS)
Ghaboussi, J; Kim, J; Elnashai, A
2010-01-01
Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.
Mathematical Modeling of Tuberculosis Granuloma Activation
Directory of Open Access Journals (Sweden)
Steve M. Ruggiero
2017-12-01
Full Text Available Tuberculosis (TB is one of the most common infectious diseases worldwide. It is estimated that one-third of the world’s population is infected with TB. Most have the latent stage of the disease that can later transition to active TB disease. TB is spread by aerosol droplets containing Mycobacterium tuberculosis (Mtb. Mtb bacteria enter through the respiratory system and are attacked by the immune system in the lungs. The bacteria are clustered and contained by macrophages into cellular aggregates called granulomas. These granulomas can hold the bacteria dormant for long periods of time in latent TB. The bacteria can be perturbed from latency to active TB disease in a process called granuloma activation when the granulomas are compromised by other immune response events in a host, such as HIV, cancer, or aging. Dysregulation of matrix metalloproteinase 1 (MMP-1 has been recently implicated in granuloma activation through experimental studies, but the mechanism is not well understood. Animal and human studies currently cannot probe the dynamics of activation, so a computational model is developed to fill this gap. This dynamic mathematical model focuses specifically on the latent to active transition after the initial immune response has successfully formed a granuloma. Bacterial leakage from latent granulomas is successfully simulated in response to the MMP-1 dynamics under several scenarios for granuloma activation.
A mathematical model of forgetting and amnesia
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Jaap M. J. Murre
2013-02-01
Full Text Available We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time-scales share two fundamental properties: (1 representations in a store decline in strength (2 while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i the temporal gradient of retrograde amnesia (Ribot's Law, (ii forgetting curves with and without anterograde amnesia, and (iii learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff's Disease, Alzheimer's Dementia, Huntington's Disease, and other disorders.
Simple mathematical models of gene regulatory dynamics
Mackey, Michael C; Tyran-Kamińska, Marta; Zeron, Eduardo S
2016-01-01
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduat...
Mathematical modeling of turbulent stratified flows. Application of liquid metal fast breeders
Energy Technology Data Exchange (ETDEWEB)
Villand, M; Grand, D [CEA-Service des Transferts Thermiques, Grenoble (France)
1983-07-01
Mathematical model of turbulent stratified flow was proposed under the following assumptions: Newtonian fluid; incompressible fluid; coupling between temperature and momentum fields according to Boussinesq approximation; two-dimensional invariance for translation or rotation; coordinates cartesian or curvilinear. Solutions obtained by the proposed method are presented.
Mathematical modeling of the mixing zone for getting bimetallic compound
Energy Technology Data Exchange (ETDEWEB)
Kim, Stanislav L. [Institute of Applied Mechanics, Ural Branch, Izhevsk (Russian Federation)
2011-07-01
A mathematical model of the formation of atomic bonds in metals and alloys, based on the electrostatic interaction between the outer electron shells of atoms of chemical elements. Key words: mathematical model, the interatomic bonds, the electron shell of atoms, the potential, the electron density, bimetallic compound.
iSTEM: Promoting Fifth Graders' Mathematical Modeling
Yanik, H. Bahadir; Karabas, Celil
2014-01-01
Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…
PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE
Directory of Open Access Journals (Sweden)
N. V. Andrianov
2006-01-01
Full Text Available The analysis of the mathematical models which can be used at optimization of the control system of the enterprise organizational structure is presented. The new approach to the mathematical modeling of the enterprise organizational structure, based on using of temporary characteristics of the control blocks working, is formulated
Mathematical Modelling Research in Turkey: A Content Analysis Study
Çelik, H. Coskun
2017-01-01
The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…
An Integrated Approach to Mathematical Modeling: A Classroom Study.
Doerr, Helen M.
Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…
Mathematical modeling of rainwater runoff over catchment surface ...
African Journals Online (AJOL)
The subject of an article is the mathematical modeling of the rainwater runoff along the surface catchment taking account the transport of pollution which permeates into the water flow from a porous media of soil at the certain areas of this surface. The developed mathematical model consists of two types of equations: the ...
Mathematical modeling of dissolved oxygen in fish ponds ...
African Journals Online (AJOL)
Mathematical modeling of dissolved oxygen in fish ponds. WJS Mwegoha, ME Kaseva, SMM Sabai. Abstract. A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide and chemical oxygen demand (COD) on Dissolved Oxygen (DO) in fish ponds. The effects ...
Genetic demographic networks: Mathematical model and applications.
Kimmel, Marek; Wojdyła, Tomasz
2016-10-01
Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise
MATHEMATICAL MODELING OF AC ELECTRIC POINT MOTOR
Directory of Open Access Journals (Sweden)
S. YU. Buryak
2014-03-01
Full Text Available Purpose. In order to ensure reliability, security, and the most important the continuity of the transportation process, it is necessary to develop, implement, and then improve the automated methods of diagnostic mechanisms, devices and rail transport systems. Only systems that operate in real time mode and transmit data on the instantaneous state of the control objects can timely detect any faults and thus provide additional time for their correction by railway employees. Turnouts are one of the most important and responsible components, and therefore require the development and implementation of such diagnostics system.Methodology. Achieving the goal of monitoring and control of railway automation objects in real time is possible only with the use of an automated process of the objects state diagnosing. For this we need to know the diagnostic features of a control object, which determine its state at any given time. The most rational way of remote diagnostics is the shape and current spectrum analysis that flows in the power circuits of railway automatics. Turnouts include electric motors, which are powered by electric circuits, and the shape of the current curve depends on both the condition of the electric motor, and the conditions of the turnout maintenance. Findings. For the research and analysis of AC electric point motor it was developed its mathematical model. The calculation of parameters and interdependencies between the main factors affecting the operation of the asynchronous machine was conducted. The results of the model operation in the form of time dependences of the waveform curves of current on the load on engine shaft were obtained. Originality. During simulation the model of AC electric point motor, which satisfies the conditions of adequacy was built. Practical value. On the basis of the constructed model we can study the AC motor in various mode of operation, record and analyze current curve, as a response to various changes
Mathematical modeling of biomass fuels formation process
International Nuclear Information System (INIS)
Gaska, Krzysztof; Wandrasz, Andrzej J.
2008-01-01
The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task
A mathematical framework for agent based models of complex biological networks.
Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2011-07-01
Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.
Mathematics of epidemics on networks from exact to approximate models
Kiss, István Z; Simon, Péter L
2017-01-01
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...
Mathematical models in marketing a collection of abstracts
Funke, Ursula H
1976-01-01
Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...
International Nuclear Information System (INIS)
Barukčić, M.; Ćorluka, V.; Miklošević, K.
2015-01-01
Highlights: • The temperature and irradiance dependent model for the I–V curve estimation is presented. • The purely mathematical model based on the analysis of the I–V curve shape is presented. • The model includes the Gompertz function with temperature and irradiance dependent parameters. • The input data are extracted from the data sheet I–V curves. - Abstract: The temperature and irradiance dependent mathematical model for photovoltaic panel performances estimation is proposed in the paper. The base of the model is the mathematical function of the photovoltaic panel current–voltage curve. The model of the current–voltage curve is based on the sigmoid function with temperature and irradiance dependent parameters. The temperature and irradiance dependencies of the parameters are proposed in the form of analytic functions. The constant parameters are involved in the analytical functions. The constant parameters need to be estimated to get the temperature and irradiance dependent current–voltage curve. The mathematical model contains 12 constant parameters and they are estimated by using the evolutionary algorithm. The optimization problem is defined for this purpose. The optimization problem objective function is based on estimated and extracted (measured) current and voltage values. The current and voltage values are extracted from current–voltage curves given in datasheet of the photovoltaic panels. The new procedure for estimation of open circuit voltage value at any temperature and irradiance is proposed in the model. The performance of the proposed mathematical model is presented for three different photovoltaic panel technologies. The simulation results indicate that the proposed mathematical model is acceptable for estimation of temperature and irradiance dependent current–voltage curve and photovoltaic panel performances within temperature and irradiance ranges
Mathematical model of radon activity measurements
Energy Technology Data Exchange (ETDEWEB)
Paschuk, Sergei A.; Correa, Janine N.; Kappke, Jaqueline; Zambianchi, Pedro, E-mail: sergei@utfpr.edu.br, E-mail: janine_nicolosi@hotmail.com [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Denyak, Valeriy, E-mail: denyak@gmail.com [Instituto de Pesquisa Pele Pequeno Principe, Curitiba, PR (Brazil)
2015-07-01
Present work describes a mathematical model that quantifies the time dependent amount of {sup 222}Rn and {sup 220}Rn altogether and their activities within an ionization chamber as, for example, AlphaGUARD, which is used to measure activity concentration of Rn in soil gas. The differential equations take into account tree main processes, namely: the injection of Rn into the cavity of detector by the air pump including the effect of the traveling time Rn takes to reach the chamber; Rn release by the air exiting the chamber; and radioactive decay of Rn within the chamber. Developed code quantifies the activity of {sup 222}Rn and {sup 220}Rn isotopes separately. Following the standard methodology to measure Rn activity in soil gas, the air pump usually is turned off over a period of time in order to avoid the influx of Rn into the chamber. Since {sup 220}Rn has a short half-life time, approximately 56s, the model shows that after 7 minutes the activity concentration of this isotope is null. Consequently, the measured activity refers to {sup 222}Rn, only. Furthermore, the model also addresses the activity of {sup 220}Rn and {sup 222}Rn progeny, which being metals represent potential risk of ionization chamber contamination that could increase the background of further measurements. Some preliminary comparison of experimental data and theoretical calculations is presented. Obtained transient and steady-state solutions could be used for planning of Rn in soil gas measurements as well as for accuracy assessment of obtained results together with efficiency evaluation of chosen measurements procedure. (author)
Perspectives on instructor modeling in mathematics teacher education
Brown, Cassondra
2009-01-01
Teachers' instructional practices are greatly shaped by their own learning experiences as students in K-12 and college classrooms, which for most teachers was traditional, teacher-centered instruction. One of the challenges facing mathematics education reform is that, traditional teaching is in contrast to reform student- centered instruction. If teachers learn from their experiences as mathematics students, mathematics teacher educators are encouraged to model practices they would like teach...
On the mathematical modeling of soccer dynamics
Machado, J. A. Tenreiro; Lopes, António M.
2017-12-01
This paper addresses the modeling and dynamical analysis of soccer teams. Two modeling perspectives based on the concepts of fractional calculus are adopted. In the first, the power law behavior and fractional-order integration are explored. In the second, a league season is interpreted in the light of a system where the teams are represented by objects (particles) that evolve in time and interact (collide) at successive rounds with dynamics driven by the outcomes of the matches. The two proposed models embed implicitly details of players and coaches, or strategical and tactical maneuvers during the matches. Therefore, the scale of observation focuses on the teams behavior in the scope of the observed variables. Data characterizing two European soccer leagues in the season 2015-2016 are adopted and processed. The model leads to the emergence of patterns that are analyzed and interpreted.
Application of a Mathematical Model to an Advertisement Reservation Problem
Directory of Open Access Journals (Sweden)
Ozlem COSGUN
2013-01-01
Full Text Available Television networks provide TV programs free of charge to the public. However, they acquire their revenue by telecasting advertisements in the midst of continuing programs or shows. A key problem faced by the TV networks in Turkey is how to accept and televise the advertisements reserved by a client on a specified advertisement break which we called “Advertisement Reservation Problem” (ARP. The problem is complicated by limited time inventory, by different rating points for different target groups, competition avoidance and the relationship between TV networks and clients. In this study we have developed a mathematical model for advertisement reservation problem and extended this model for some cases encountered in real business life. We have also discussed how these cases affect the decisions of a TV network. Mixed integer linear programming approach is proposed to solve these problems. This approach has been implemented to a case taken from one of the biggest TV networks of Turkey.
Mathematical model with autoregressive process for electrocardiogram signals
Evaristo, Ronaldo M.; Batista, Antonio M.; Viana, Ricardo L.; Iarosz, Kelly C.; Szezech, José D., Jr.; Godoy, Moacir F. de
2018-04-01
The cardiovascular system is composed of the heart, blood and blood vessels. Regarding the heart, cardiac conditions are determined by the electrocardiogram, that is a noninvasive medical procedure. In this work, we propose autoregressive process in a mathematical model based on coupled differential equations in order to obtain the tachograms and the electrocardiogram signals of young adults with normal heartbeats. Our results are compared with experimental tachogram by means of Poincaré plot and dentrended fluctuation analysis. We verify that the results from the model with autoregressive process show good agreement with experimental measures from tachogram generated by electrical activity of the heartbeat. With the tachogram we build the electrocardiogram by means of coupled differential equations.
Quantum Gravity Mathematical Models and Experimental Bounds
Fauser, Bertfried; Zeidler, Eberhard
2007-01-01
The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...
Symmetrization of mathematical model of charge transport in semiconductors
Directory of Open Access Journals (Sweden)
Alexander M. Blokhin
2002-11-01
Full Text Available A mathematical model of charge transport in semiconductors is considered. The model is a quasilinear system of differential equations. A problem of finding an additional entropy conservation law and system symmetrization are solved.
The mathematics of models for climatology and environment. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Ildefonso Diaz, J. [ed.] [Universidad Complutense de Madrid (Spain). Facultad de Ciencas Matematicas
1997-12-31
This book presents a coherent survey of modelling in climatology and the environment and the mathematical treatment of those problems. It is divided into 4 parts containing a total of 16 chapters. Parts I, II and III are devoted to general models and part IV to models related to some local problems. Most of the mathematical models considered here involve systems of nonlinear partial differential equations.
Handayani, I.; Januar, R. L.; Purwanto, S. E.
2018-01-01
This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.
Methods and models in mathematical biology deterministic and stochastic approaches
Müller, Johannes
2015-01-01
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
Mathematical and Numerical Modeling in Maritime Geomechanics
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Miguel Martín Stickle
2012-04-01
Full Text Available A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,... combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the overning equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism.
Mathematical modeling and computational intelligence in engineering applications
Silva Neto, Antônio José da; Silva, Geraldo Nunes
2016-01-01
This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.
Mathematical Model of Nicholson’s Experiment
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Sergey D. Glyzin
2017-01-01
Full Text Available Considered is a mathematical model of insects population dynamics, and an attempt is made to explain classical experimental results of Nicholson with its help. In the first section of the paper Nicholson’s experiment is described and dynamic equations for its modeling are chosen. A priori estimates for model parameters can be made more precise by means of local analysis of the dynamical system, that is carried out in the second section. For parameter values found there the stability loss of the problem equilibrium of the leads to the bifurcation of a stable two-dimensional torus. Numerical simulations based on the estimates from the second section allows to explain the classical Nicholson’s experiment, whose detailed theoretical substantiation is given in the last section. There for an atrractor of the system the largest Lyapunov exponent is computed. The nature of this exponent change allows to additionally narrow the area of model parameters search. Justification of this experiment was made possible only due to the combination of analytical and numerical methods in studying equations of insects population dynamics. At the same time, the analytical approach made it possible to perform numerical analysis in a rather narrow region of the parameter space. It is not possible to get into this area, based only on general considerations.
Mathematical manipulative models: in defense of "beanbag biology".
Jungck, John R; Gaff, Holly; Weisstein, Anton E
2010-01-01
Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.
Technological geological and mathematical models of petroleum stratum
International Nuclear Information System (INIS)
Zhumagulov, B.T.; Monakhov, V.N.
1997-01-01
The comparative analysis of different mathematical methods of petroleum stratum, the limit of their applicability and hydrodynamical analysis of numerical calculation's results is carried out. The problem of adaptation of the mathematical models and the identification of petroleum stratum parameters are considered. (author)
Mathematical Modeling, Sense Making, and the Common Core State Standards
Schoenfeld, Alan H.
2013-01-01
On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…
Teaching Writing and Communication in a Mathematical Modeling Course
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
Mathematical modelling of fluidized bed reactors
Energy Technology Data Exchange (ETDEWEB)
Werther, J [BASF A.G., Ludwigshafen am Rhein (Germany, F.R.)
1978-11-01
Among the many fluidized bed models to be found in the literature, the two-phase model originally proposed by May has proved most suitable for accomodation of recent advances in flow mechanics: this model resolves the gas/solids fluidized bed into a bubble phase and a suspension phase surrounding the bubbles. Its limitation to slow reactions is a disadvantage. On the basis of the analogy between fluidized beds and gas/liquid systems, a general two-phase model that is valid for fast reactions has therefore been developed and its validity is confirmed by comparison with the experimental results obtained by others. The model describes mass transfer across the phase interface with the aid of the film theory known from gas/liquid reactor technology, and the reaction occurring in the suspension phase as a pseudo-homogeneous reaction. Since the dependence of the performance of fluidized bed reactors upon geometry is accounted for, the model can also be used for scale-up calculations. Its use is illustrated with the aid of design diagrams.
The role of mathematics and modeling in a competency centered learning system
Langereis, G.R.; Hu, J.; Feijs, L.M.G.
2011-01-01
With competency based learning in a project driven environment, we are facing a different perspective of how students perceive mathematical modelling. In this paper, a model is proposed where conventional education is seen as a process from math to design, while competency driven approaches tend to
Mathematical model of melt flow channel granulator
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A. A. Kiselev
2016-01-01
Full Text Available Granulation of carbohydrate-vitamin-mineral supplements based on molasses is performed at a high humidity (26 %, so for a stable operation of granulator it is necessary to reveal its melt flow pattern. To describe melt non-isothermal flow in the granulator a mathematical model with following initial equations: continuity equation, motion equation and rheological equation – was developed. The following assumptions were adopted: the melt flow in the granulator is a steady laminar flow; inertial and gravity forces can be ignored; melt is an incompressible fluid; velocity gradient in the flow direction is much smaller than in the transverse direction; the pressure gradient over the cross section of the channel is constant; the flow is hydrodynamically fully developed; effects impact on the channel inlet and outlet may be neglected. Due to the assumptions adopted, it can be considered that in this granulator only velocity components in the x-direction are significant and all the members of the equation with the components and their derivatives with respect to the coordinates y and z can be neglected. The resulting solutions were obtained: the equation for the mean velocity, the equation for determining the volume flow, the formula for calculating of mean time of the melt being in the granulator, the equation for determining the shear stress, the equation for determining the shear rate and the equation for determining the pressure loss. The results of calculations of the equations obtained are in complete agreement with the experimental data; deviation range is 16–19 %. The findings about the melt movement pattern in granulator allowed developing a methodology for calculating a rational design of the granulator molding unit.
Mathematical modeling in wound healing, bone regeneration and tissue engineering.
Geris, Liesbet; Gerisch, Alf; Schugart, Richard C
2010-12-01
The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.
[Mathematical models of decision making and learning].
Ito, Makoto; Doya, Kenji
2008-07-01
Computational models of reinforcement learning have recently been applied to analysis of brain imaging and neural recording data to identity neural correlates of specific processes of decision making, such as valuation of action candidates and parameters of value learning. However, for such model-based analysis paradigms, selecting an appropriate model is crucial. In this study we analyze the process of choice learning in rats using stochastic rewards. We show that "Q-learning," which is a standard reinforcement learning algorithm, does not adequately reflect the features of choice behaviors. Thus, we propose a generalized reinforcement learning (GRL) algorithm that incorporates the negative reward effect of reward loss and forgetting of values of actions not chosen. Using the Bayesian estimation method for time-varying parameters, we demonstrated that the GRL algorithm can predict an animal's choice behaviors as efficiently as the best Markov model. The results suggest the usefulness of the GRL for the model-based analysis of neural processes involved in decision making.
Mathematical model of gluconic acid fermentation by Aspergillus niger
Energy Technology Data Exchange (ETDEWEB)
Takamatsu, T.; Shioya, S.; Furuya, T.
1981-11-01
A mathematical model for the study of gluconic acid fermentation by Aspergillus niger has been developed. The model has been deduced from the basic biological concept of multicellular filamentous microorganisms, i.e. cell population balance. It can be used to explain the behaviour of both batch and continuous cultures, even when in a lag phase. A new characteristic, involving the existence of dual equilibrium stages during fermentation, has been predicted using this mathematical model. (Refs. 6).
The possibilities of a modelling perspective for school mathematics
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Dirk Wessels
2009-09-01
complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has deﬁnitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to ﬁnding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full beneﬁt of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future.
Directory of Open Access Journals (Sweden)
Hemant PATHAK
2013-06-01
Full Text Available This paper presents the application of the mathematical modeling to such a specific area as environ-economical interaction in prospect of big countries like India. A model of mutual interaction of dirty drinking water resulting water borne diseases, badly affected economy is proposed. For the description of some of these models illustrates drinking water resources, incapable municipal water treatment consequently expansion of diseases, World Bank loan, affected biggest labour forces (mankind and ultimate results in the form of decrease in GDP. These mathematical models may be used in the solving of similar type problems exist in south and eastern Asian economies.
Key Concept Mathematics and Management Science Models
Macbeth, Thomas G.; Dery, George C.
1973-01-01
The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)
Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors
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Zoran Benić
2016-01-01
Full Text Available Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton’s second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.
Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity
Stohlmann, Micah S.
2017-01-01
Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…
Mathematical Modelling for Micropiles Embedded in Salt Rock
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Rădan (Toader Georgiana
2016-03-01
Full Text Available This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.
Mathematical modelling with case studies using Maple and Matlab
Barnes, B
2014-01-01
Introduction to Mathematical ModelingMathematical models An overview of the book Some modeling approaches Modeling for decision makingCompartmental Models Introduction Exponential decay and radioactivity Case study: detecting art forgeries Case study: Pacific rats colonize New Zealand Lake pollution models Case study: Lake Burley Griffin Drug assimilation into the blood Case study: dull, dizzy, or dead? Cascades of compartments First-order linear DEs Equilibrium points and stability Case study: money, money, money makes the world go aroundModels of Single PopulationsExponential growth Density-
Mechanical-mathematical modeling for landslide process
Svalova, V.
2009-04-01
500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.
Schwerdtfeger, Sara
2017-01-01
This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…
Mathematical rainfall model for hydrographic demarcation of Manabi ...
African Journals Online (AJOL)
PROMOTING ACCESS TO AFRICAN RESEARCH ... To achieve this objective, the basins of the Hydrographic Demarcation of Manabí ... Keywords: multiple regression; mathematical model; GIS; Hydrology; rainfall. ... HOW TO USE AJOL.
Mathematical models of thermohydraulic disturbance sources in the NPP circuits
International Nuclear Information System (INIS)
Proskuryakov, K.N.
1999-01-01
Methods and means of diagnostics of equipment and processes at NPPs allowing one to substantially increase safety and economic efficiency of nuclear power plant operation are considered. Development of mathematical models, describing the occurrence and propagation of violations is conducted
Mathematical modelling of a farm enterprise value on the ...
African Journals Online (AJOL)
Mathematical modelling of a farm enterprise value on the agricultural market with the ... Subsidies in the EU countries reached 45-50% of the value of commodity output ... This financing gap entailed a number of negative consequences.
Improved Mathematical Models for Particle-Size Distribution Data
African Journals Online (AJOL)
BirukEdimon
School of Civil & Environmental Engineering, Addis Ababa Institute of Technology,. 3. Murray Rix ... two improved mathematical models to describe ... demand further improvement to handle the PSD ... statistics and the range of the optimized.
MATHEMATICAL MODELING OF HEATING AND COOLING OF SAUSAGES
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A. V. Zhuchkov
2013-01-01
Full Text Available In the article the mathematical modeling of the processes of heating and cooling of sausage products in order to define reference characteristics of the processes was carried out. Basic regularities of the processes are graphically shown.
Mathematical and numerical foundations of turbulence models and applications
Chacón Rebollo, Tomás
2014-01-01
With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering, and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation, and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics,...
A mathematical look at a physical power prediction model
DEFF Research Database (Denmark)
Landberg, L.
1998-01-01
This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...
2nd Tbilisi-Salerno Workshop on Modeling in Mathematics
Ricci, Paolo; Tavkhelidze, Ilia
2017-01-01
This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling in March 2015. The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such topics as multimodal logic, fractional calculus, special functions, Fourier-like solutions for PDE’s, Rvachev-functions and linear dynamical systems. Special chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula. The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.
A Mathematical Approach to Establishing Constitutive Models for Geomaterials
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Guang-hua Yang
2013-01-01
Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.
A practical course in differential equations and mathematical modeling
Ibragimov , Nail H
2009-01-01
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame
Mathematical modeling of a process the rolling delivery
Stepanov, Mikhail A.; Korolev, Andrey A.
2018-03-01
An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.
A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes
Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.
2018-04-01
Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.
Mathematical model of polyethylene pipe bending stress state
Serebrennikov, Anatoly; Serebrennikov, Daniil
2018-03-01
Introduction of new machines and new technologies of polyethylene pipeline installation is usually based on the polyethylene pipe flexibility. It is necessary that existing bending stresses do not lead to an irreversible polyethylene pipe deformation and to violation of its strength characteristics. Derivation of the mathematical model which allows calculating analytically the bending stress level of polyethylene pipes with consideration of nonlinear characteristics is presented below. All analytical calculations made with the mathematical model are experimentally proved and confirmed.
MATHEMATICAL MODELLING OF AIRCRAFT PILOTING PROSSESS UNDER SPECIFIED FLIGHT PATH
Directory of Open Access Journals (Sweden)
И. Кузнецов
2012-04-01
Full Text Available The author suggests mathematical model of pilot’s activity as follow up system and mathematical methods of pilot’s activity description. The main idea of the model is flight path forming and aircraft stabilization on it during instrument flight. Input of given follow up system is offered to be aircraft deflection from given path observed by pilot by means of sight and output is offered to be pilot’s regulating actions for aircraft stabilization on flight path.
Mathematical modeling of a V-stack piezoelectric aileron actuation
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Ioan URSU
2016-12-01
Full Text Available The article presents a mathematical modeling of aileron actuation that uses piezo V-shaped stacks. The aim of the actuation is the increasing of flutter speed in the context of a control law, in order to widen the flight envelope. In this way the main advantage of such a piezo actuator, the bandwidth is exploited. The mathematical model is obtained based on free body diagrams, and the numerical simulations allow a preliminary sizing of the actuator.
Classical and Weak Solutions for Two Models in Mathematical Finance
Gyulov, Tihomir B.; Valkov, Radoslav L.
2011-12-01
We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.
A mathematical model of cancer cells with phenotypic plasticity
Directory of Open Access Journals (Sweden)
Da Zhou
2015-12-01
Full Text Available Purpose: The phenotypic plasticity of cancer cells is recently becoming a cutting-edge research area in cancer, which challenges the cellular hierarchy proposed by the conventional cancer stem cell theory. In this study, we establish a mathematical model for describing the phenotypic plasticity of cancer cells, based on which we try to find some salient features that can characterize the dynamic behavior of the phenotypic plasticity especially in comparison to the hierarchical model of cancer cells. Methods: We model cancer as population dynamics composed of different phenotypes of cancer cells. In this model, not only can cancer cells divide (symmetrically and asymmetrically and die, but they can also convert into other cellular phenotypes. According to the Law of Mass Action, the cellular processes can be captured by a system of ordinary differential equations (ODEs. On one hand, we can analyze the long-term stability of the model by applying qualitative method of ODEs. On the other hand, we are also concerned about the short-term behavior of the model by studying its transient dynamics. Meanwhile, we validate our model to the cell-state dynamics in published experimental data.Results: Our results show that the phenotypic plasticity plays important roles in both stabilizing the distribution of different phenotypic mixture and maintaining the cancer stem cells proportion. In particular, the phenotypic plasticity model shows decided advantages over the hierarchical model in predicting the phenotypic equilibrium and cancer stem cells’ overshoot reported in previous biological experiments in cancer cell lines.Conclusion: Since the validity of the phenotypic plasticity paradigm and the conventional cancer stem cell theory is still debated in experimental biology, it is worthy of theoretically searching for good indicators to distinguish the two models through quantitative methods. According to our study, the phenotypic equilibrium and overshoot
Mathematical modelling and numerical simulation of oil pollution problems
2015-01-01
Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics, together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems. The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...
The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.
Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin
2016-07-01
Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data.
Innovative mathematical modeling in environmental remediation
International Nuclear Information System (INIS)
Yeh, Gour T.; Gwo, Jin Ping; Siegel, Malcolm D.; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steven B.
2013-01-01
There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g.,Ni, Cr, Co). The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport models
Innovative mathematical modeling in environmental remediation
Energy Technology Data Exchange (ETDEWEB)
Yeh, Gour T. [Taiwan Typhoon and Flood Research Institute (Taiwan); National Central Univ. (Taiwan); Univ. of Central Florida (United States); Gwo, Jin Ping [Nuclear Regulatory Commission (NRC), Rockville, MD (United States); Siegel, Malcolm D. [Sandia National Laboratories, Albuquerque, NM (United States); Li, Ming-Hsu [National Central Univ. (Taiwan); ; Fang, Yilin [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Zhang, Fan [Inst. of Tibetan Plateau Research, Chinese Academy of Sciences (China); Luo, Wensui [Inst. of Tibetan Plateau Research, Chinese Academy of Sciences (China); Yabusaki, Steven B. [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
2013-05-01
There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g.,Ni, Cr, Co).The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport models
On a Mathematical Model of Brain Activities
International Nuclear Information System (INIS)
Fichtner, K.-H.; Fichtner, L.; Freudenberg, W.; Ohya, M.
2007-01-01
The procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an 'expexted view of the world'. Then the brain compares a signal arising from our senses with the signal chosen from the memory leading to a change of the state of both signals. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from 'excited' to 'nonexcited'. For that reason a statistical model of the recognition process should reflect both--the change of the signals and the loss of excited neurons. A first attempt to explain the process of recognition in terms of quantum statistics was given. In the present note it is not possible to present this approach in detail. In lieu we will sketch roughly a few of the basic ideas and structures of the proposed model of the recognition process (Section). Further, we introduce the basic spaces and justify the choice of spaces used in this approach. A more elaborate presentation including all proofs will be given in a series of some forthcoming papers. In this series also the procedures of creation of signals from the memory, amplification, accumulation and transformation of input signals, and measurements like EEG and MEG will be treated in detail
The human body metabolism process mathematical simulation based on Lotka-Volterra model
Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur
2017-08-01
The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.
A theory of drug tolerance and dependence II: the mathematical model.
Peper, Abraham
2004-08-21
The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.
Application of mathematical modeling in sustained release delivery systems.
Grassi, Mario; Grassi, Gabriele
2014-08-01
This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.
Directory of Open Access Journals (Sweden)
Nita Delima
2017-03-01
Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa. Kata Kunci: Comprehensive
Dzierka, M.; Jurczak, P.
2015-12-01
In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.
Mathematical model for solid fuel combustion in fluidized bed
International Nuclear Information System (INIS)
Kostikj, Zvonimir; Noshpal, Aleksandar
1994-01-01
A mathematical model for computation of the combustion process of solid fuel in fluidized bed is presented in this work. Only the combustor part of the plant (the fluidized bed and the free board) is treated with this model. In that manner, all principal, physical presumption and improvements (upon which this model is based) are given. Finally, the results of the numerical realisation of the mathematical model for combustion of minced straw as well as the results of the experimental investigation of a concrete physical model are presented. (author)
A Long-Term Mathematical Model for Mining Industries
International Nuclear Information System (INIS)
Achdou, Yves; Giraud, Pierre-Noel; Lasry, Jean-Michel; Lions, Pierre-Louis
2016-01-01
A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.
A Long-Term Mathematical Model for Mining Industries
Energy Technology Data Exchange (ETDEWEB)
Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France); Giraud, Pierre-Noel [CERNA, Mines ParisTech (France); Lasry, Jean-Michel [Univ. Paris Dauphine (France); Lions, Pierre-Louis [Collège de France (France)
2016-12-15
A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra
Domínguez-García, S.; García-Planas, M. I.; Taberna, J.
2016-01-01
Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…
Mathematical Practice as Sculpture of Utopia: Models, Ignorance, and the Emancipated Spectator
Appelbaum, Peter
2012-01-01
This article uses Ranciere's notion of the ignorant schoolmaster and McElheny's differentiation of artist's models from those of the architect and scientist to propose the reconceptualization of mathematics education as the support of emancipated spectators and sculptors of utopia.
International Nuclear Information System (INIS)
Gorshtein, A.I.; Matyunin, Yu.I.; Poluehktov, P.P.
2000-01-01
A mathematical model is proposed for preliminary choice of the nuclear safe matrix compositions for fissile material immobilization. The IBM PC computer software for nuclear safe matrix composition calculations is developed. The limiting concentration of fissile materials in the some used and perspective nuclear safe matrix compositions for radioactive waste immobilization is calculated [ru
Mathematical, physical and numerical principles essential for models of turbulent mixing
Energy Technology Data Exchange (ETDEWEB)
Sharp, David Howland [Los Alamos National Laboratory; Lim, Hyunkyung [STONY BROOK UNIV; Yu, Yan [STONY BROOK UNIV; Glimm, James G [STONY BROOK UNIV
2009-01-01
We propose mathematical, physical and numerical principles which are important for the modeling of turbulent mixing, especially the classical and well studied Rayleigh-Taylor and Richtmyer-Meshkov instabilities which involve acceleration driven mixing of a fluid discontinuity layer, by a steady accerleration or an impulsive force.
Boronico, Jess; Murdy, Jim; Kong, Xinlu
2014-01-01
This manuscript proposes a mathematical model to address faculty sufficiency requirements towards assuring overall high quality management education at a global university. Constraining elements include full-time faculty coverage by discipline, location, and program, across multiple campus locations subject to stated service quality standards of…
Mathematical model for temperature change of a journal bearing
Directory of Open Access Journals (Sweden)
Antunović Ranko
2018-01-01
Full Text Available In this work, a representative mathematical model has been developed, which reliably describes the heating and cooling of a journal bearing as a result of its malfunctioning, and the model has been further confirmed on a test bench. The bearing model was validated by using analytical modeling methods, i. e. the experimental results were compared to the data obtained by analytical calculations. The regression and variance analysis techniques were applied to process the recorded data, to test the mathematical model and to define mathematical functions for the heating/cooling of the journal bearing. This investigation shows that a representative model may reliably indicate the change in the thermal field, which may be a consequence of journal bearing damage.
AVIATION SECURITY AS AN OBJECT OF MATHEMATICAL MODELING
Directory of Open Access Journals (Sweden)
N. Elisov Lev
2017-01-01
Full Text Available The paper presents a mathematical formulation of the problem formalization of the subject area related to aviation security in civil aviation. The formalization task is determined by the modern issue of providing aviation security. Aviationsecurity in modern systems is based upon organizational standard of security control. This standard doesn’t require calcu- lating the security level. It allows solving the aviation security task without estimating the solution and evaluating the per- formance of security facilities. The issue of acceptable aviation security level stays unsolved, because its control lies in inspections that determine whether the object security facilities meet the requirements or not. The pending problem is also in whether the requirements are calculable and the evaluation is subjective.Lately, there has been determined quite a certain tendency to consider aviation security issues from the perspective of its level optimal control with the following identification, calculation and evaluation problems solving and decision mak- ing. The obtained results analysis in this direction shows that it’s strongly recommended to move to object formalization problem, which provides a mathematical modeling for aviation security control optimization.In this case, the authors assume to find the answer in the process of object formalization. Therefore aviation secu- rity is presented as some security environment condition, which defines the parameters associated with the object protec-tion system quality that depends on the use of protective equipment in conditions of counteraction to factors of external andinternal threats. It is shown that the proposed model belongs to a class of boundary value problems described by differential equations in partial derivatives. The classification of boundary value problems is presented.
Fasni, N.; Turmudi, T.; Kusnandi, K.
2017-09-01
This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.
Mathematical modeling of physiological systems: an essential tool for discovery.
Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J
2014-08-28
Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.
Identification of Chemical Reactor Plant’s Mathematical Model
Pyakullya, Boris Ivanovich; Kladiev, Sergey Nikolaevich
2015-01-01
This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.
Identification of Chemical Reactor Plant’s Mathematical Model
Directory of Open Access Journals (Sweden)
Pyakillya Boris
2015-01-01
Full Text Available This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.
Gamification for Non-Majors Mathematics: An Innovative Assignment Model
Leong, Siow Hoo; Tang, Howe Eng
2017-01-01
The most important ingredient of the pedagogy for teaching non-majors is getting their engagement. This paper proposes to use gamification to engage non-majors. An innovative game termed as Cover the Hungarian's Zeros is designed to tackle the common weakness of non-majors mathematics in solving the assignment problem using the Hungarian Method.…
Potential of mathematical modeling in fruit quality | Vazquez-Cruz ...
African Journals Online (AJOL)
A review of mathematical modeling applied to fruit quality showed that these models ranged inresolution from simple yield equations to complex representations of processes as respiration, photosynthesis and assimilation of nutrients. The latter models take into account complex genotype environment interactions to ...
Mathematical modelling of dextran filtration through hollow fibre membranes
DEFF Research Database (Denmark)
Vinther, Frank; Pinelo, Manuel; Brøns, Morten
2014-01-01
In this paper we present a mathematical model of an ultrafiltration process. The results of the model are produced using standard numerical techniques with Comsol Multiphysics. The model describes the fluid flow and separation in hollow fibre membranes. The flow of solute and solvent within the h...
Díaz, Verónica; Poblete, Alvaro
2017-07-01
This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.
Mathematical model and simulations of radiation fluxes from buried radionuclides
International Nuclear Information System (INIS)
Ahmad Saat
1999-01-01
A mathematical model and a simple Monte Carlo simulations were developed to predict radiation fluxes from buried radionuclides. The model and simulations were applied to measured (experimental) data. The results of the mathematical model showed good acceptable order of magnitude agreement. A good agreement was also obtained between the simple simulations and the experimental results. Thus, knowing the radionuclide distribution profiles in soil from a core sample, it can be applied to the model or simulations to estimate the radiation fluxes emerging from the soil surface. (author)
Outlooks for mathematical modelling of the glass melting process
Energy Technology Data Exchange (ETDEWEB)
Waal, H. de [TNO Institute of Applied Physics, Delft (Netherlands)
1997-12-31
Mathematical modelling is nowadays a standard tool for major producers of float glass, T.V. glass and fiberglass. Also for container glass furnaces, glass tank modelling proves to be a valuable method to optimize process conditions. Mathematical modelling is no longer just a way to visualize the flow patterns and to provide data on heat transfer. It can also predict glass quality in relation to process parameters, because all chemical and physical phenomena are included in the latest generation of models, based on experimental and theoretical research on these phenomena.
Mathematical model comparing of the multi-level economics systems
Brykalov, S. M.; Kryanev, A. V.
2017-12-01
The mathematical model (scheme) of a multi-level comparison of the economic system, characterized by the system of indices, is worked out. In the mathematical model of the multi-level comparison of the economic systems, the indicators of peer review and forecasting of the economic system under consideration can be used. The model can take into account the uncertainty in the estimated values of the parameters or expert estimations. The model uses the multi-criteria approach based on the Pareto solutions.
Mathematical model for hysteresis phenomenon in moisture transport of concrete carbonation process
International Nuclear Information System (INIS)
Aiki, Toyohiko; Kumazaki, Kota
2012-01-01
From civil engineering point of view it is very important to construct and analyze a mathematical model for a mechanism of concrete carbonation process. On this subject there are several mathematical results concerned with a one-dimensional model, in which hysteresis effects are neglected. Our aim is to give a model with hysteresis effects appearing in carbonation process. In this paper, as the first step of this research we focus only on moisture transport in the process and propose an initial boundary value problem for a system of partial differential equations as a mathematical model. Also, we give results on the existence of a solution to the problem, globally in time and the uniqueness in only one-dimensional case without proofs.
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V
2016-01-01
Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
A mathematical model for camera calibration based on straight lines
Directory of Open Access Journals (Sweden)
Antonio M. G. Tommaselli
2005-12-01
Full Text Available In other to facilitate the automation of camera calibration process, a mathematical model using straight lines was developed, which is based on the equivalent planes mathematical model. Parameter estimation of the developed model is achieved by the Least Squares Method with Conditions and Observations. The same method of adjustment was used to implement camera calibration with bundles, which is based on points. Experiments using simulated and real data have shown that the developed model based on straight lines gives results comparable to the conventional method with points. Details concerning the mathematical development of the model and experiments with simulated and real data will be presented and the results with both methods of camera calibration, with straight lines and with points, will be compared.
Mathematical modeling of solute transport in the subsurface
International Nuclear Information System (INIS)
Naymik, T.G.
1987-01-01
A review of key works on solute transport models indicates that solute transport processes with the exception of advection are still poorly understood. Solute transport models generally do a good job when they are used to test scientific concepts and hypotheses, investigate natural processes, systematically store and manage data, and simulate mass balance of solutes under certain natural conditions. Solute transport models generally are not good for predicting future conditions with a high degree of certainty, or for determining concentrations precisely. The mathematical treatment of solute transport far surpasses their understanding of the process. Investigations of the extent of groundwater contamination and methods to remedy existing problems show the along-term nature of the hazard. Industrial organic compounds may be immiscible in water, highly volatile, or complexed with inorganic as well as other organic compounds; many remain stable in nature almost indefinitely. In the worst case, future disposal of hazardous waste may be restricted to deep burial, as is proposed for radioactive wastes. For investigations pertinent to transport of radionuclides from a geologic repository, the process cannot be fully understood without adequate thermodynamic and kinetic data bases
Tsunami evacuation mathematical model for the city of Padang
International Nuclear Information System (INIS)
Kusdiantara, R.; Hadianti, R.; Badri Kusuma, M. S.; Soewono, E.
2012-01-01
Tsunami is a series of wave trains which travels with high speed on the sea surface. This traveling wave is caused by the displacement of a large volume of water after the occurrence of an underwater earthquake or volcano eruptions. The speed of tsunami decreases when it reaches the sea shore along with the increase of its amplitudes. Two large tsunamis had occurred in the last decades in Indonesia with huge casualties and large damages. Indonesian Tsunami Early Warning System has been installed along the west coast of Sumatra. This early warning system will give about 10-15 minutes to evacuate people from high risk regions to the safe areas. Here in this paper, a mathematical model for Tsunami evacuation is presented with the city of Padang as a study case. In the model, the safe areas are chosen from the existing and selected high rise buildings, low risk region with relatively high altitude and (proposed to be built) a flyover ring road. Each gathering points are located in the radius of approximately 1 km from the ring road. The model is formulated as an optimization problem with the total normalized evacuation time as the objective function. The constraints consist of maximum allowable evacuation time in each route, maximum capacity of each safe area, and the number of people to be evacuated. The optimization problem is solved numerically using linear programming method with Matlab. Numerical results are shown for various evacuation scenarios for the city of Padang.
Tsunami evacuation mathematical model for the city of Padang
Energy Technology Data Exchange (ETDEWEB)
Kusdiantara, R.; Hadianti, R.; Badri Kusuma, M. S.; Soewono, E. [Department of Mathematics Institut Teknologi Bandung, Bandung 40132 (Indonesia); Department of Civil Engineering Institut Teknologi Bandung, Bandung 40132 (Indonesia); Department of Mathematics Institut Teknologi Bandung, Bandung 40132 (Indonesia)
2012-05-22
Tsunami is a series of wave trains which travels with high speed on the sea surface. This traveling wave is caused by the displacement of a large volume of water after the occurrence of an underwater earthquake or volcano eruptions. The speed of tsunami decreases when it reaches the sea shore along with the increase of its amplitudes. Two large tsunamis had occurred in the last decades in Indonesia with huge casualties and large damages. Indonesian Tsunami Early Warning System has been installed along the west coast of Sumatra. This early warning system will give about 10-15 minutes to evacuate people from high risk regions to the safe areas. Here in this paper, a mathematical model for Tsunami evacuation is presented with the city of Padang as a study case. In the model, the safe areas are chosen from the existing and selected high rise buildings, low risk region with relatively high altitude and (proposed to be built) a flyover ring road. Each gathering points are located in the radius of approximately 1 km from the ring road. The model is formulated as an optimization problem with the total normalized evacuation time as the objective function. The constraints consist of maximum allowable evacuation time in each route, maximum capacity of each safe area, and the number of people to be evacuated. The optimization problem is solved numerically using linear programming method with Matlab. Numerical results are shown for various evacuation scenarios for the city of Padang.
Proposal for an ecoradiological centre model
International Nuclear Information System (INIS)
Perovic, S.M.; Zunic, Z.; Demajo, M.; Konjevic, N.
1998-01-01
The problem of establishing an optimal Ecoradiological Centre Model is studied in some detail for the town of Kotor which is under the protection of the World Cultural and Natural Heritage. The proposed structure of the Centre is analyzed from the view of Engineering, Education and Scientific parameters. This Model is suitable for implementation as a network Centre Model for the state of Montenegro. Further, the modelling strategy of the ecoradiological condition control of natural, construction, bio and technological systems is elaborated. The proposal includes the ecoradiological monitoring, radioactive and electromagnetic radiation processing and protection for different natural zones as well as their different geostructures, aerial and hydrogeological conditions. The programme also includes all housing objects (hotels, flats, houses, office premises etc.). Here will also be presented the radiation protection and recommendations for the implementation of Title VII of the European Basic Safety Standards Directive (BSS), concerning significant increase in exposure due to natural radiation sources. Also, the proposal of Local Radiation Protection for the town of Kotor is presented. Our proposal for an Ecoradiological Centre Model presented here is in a form of a pilot programme, applicable also for other towns and states. (author)
Mathematical model of vertical mass transport in the mine dumps Western Donbass
Directory of Open Access Journals (Sweden)
Yevhrashkina T.P.
2012-09-01
Full Text Available The multivariate mathematical models of the recultivated, recultivated and dumping with dry system, recultivated in systematically irrigation conditions and free of overgrowth by wild plants are proposed, designed and quantified. The theory of physico-chemical hydrodynamics of pore space using analytical and numerical methods for solving the equations of motion and mass conservation of matter all models are based on. The adequacy of built models and man-maid processes that proceed inside the mine dumps is proved.
Mathematical Models of the Sinusoidal Screen Family
Directory of Open Access Journals (Sweden)
Tajana Koren
2011-06-01
Full Text Available In this paper we will define a family of sinusoidal screening elements and explore the possibilities of their application in graphic arts, securities printing and design solutions in photography and typography editing. For this purpose mathematical expressions of sinusoidal families were converted into a Postscript language. The introduction of a random variable results in a countless number of various mutations which cannot be repeated without knowing the programming code itself. The use of the family of screens in protection of securities is thus of great importance. Other possible application of modulated sinusoidal screens is related to the large format color printing. This paper will test the application of sinusoidal screens in vector graphics, pixel graphics and typography. The development of parameters in the sinusoidal screen element algorithms gives new forms defined within screening cells with strict requirements of coverage implementation. Individual solutions include stochastic algorithms, as well as the autonomy of screening forms in regard to multicolor printing channels.
Effectiveness of discovery learning model on mathematical problem solving
Herdiana, Yunita; Wahyudin, Sispiyati, Ririn
2017-08-01
This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.
Mathematical models to predict rheological parameters of lateritic hydromixtures
Directory of Open Access Journals (Sweden)
Gabriel Hernández-Ramírez
2017-10-01
Full Text Available The present work had as objective to establish mathematical models that allow the prognosis of the rheological parameters of the lateritic pulp at concentrations of solids from 35% to 48%, temperature of the preheated hydromixture superior to 82 ° C and number of mineral between 3 and 16. Four samples of lateritic pulp were used in the study at different process locations. The results allowed defining that the plastic properties of the lateritic pulp in the conditions of this study conform to the Herschel-Bulkley model for real plastics. In addition, they show that for current operating conditions, even for new situations, UPD mathematical models have a greater ability to predict rheological parameters than least squares mathematical models.
Mathematical modelling and numerical simulation of forces in milling process
Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.
2018-04-01
Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Mathematical modeling for novel cancer drug discovery and development.
Zhang, Ping; Brusic, Vladimir
2014-10-01
Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.
MATHEMATICAL MODELLING OF QUAZISTEADY MODE OF BEARING AIR BUFFER FILLING
Directory of Open Access Journals (Sweden)
E. D. Chertov
2014-01-01
Full Text Available Summary. Today the only way to eliminate contact with the product during the manufacturing process is to provide a support surface under its support surface air buffer layer formed due to the expiration of the working environment through holes perforated gas distribution grids forms. There proposed the method of contactless formation of products consisting of composite materials by the means of air buffer in the article. The results of theoretical and experimental investigations of hydro-gas-dynamic processes occurring when casting of organic- mineral composite material onto the bearing air buffer expressed in the form of mathematical description realizing original hypotheses reflected in the choice of transformation algorithm and limiting conditions are presented. On the base of obtained mathematical model the algorithm of calculation of optimum parameters of transporting systems with discretely powered gas buffer is developed. The method of deduction of a semi-finished product on the gas buffer, which allows to level the pressure field under the bearing surface of the deduction object due to the usage of devices of pseudo fluidized granular material in pneumatic chambers is offered. The application of this method allows to eliminate the possibility of contact between the composite material and the working surface of the equipment and also to reduce the cost of production of pneumatic devices, to improve operational characteristics of this equipment. Submitted depending allowed to develop the methodology and implementation of engineering calculation device for non-contact casting composite materials on air buffer, semi-industrial and industrial variants were created and put into production.
Mathematical modeling of renal hemodynamics in physiology and pathophysiology.
Sgouralis, Ioannis; Layton, Anita T
2015-06-01
In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.
Solutions manual to accompany finite mathematics models and applications
Morris, Carla C
2015-01-01
A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr
The Relevance of Using Mathematical Models in Macroeconomic Policies Theory
Directory of Open Access Journals (Sweden)
Nora Mihail
2006-11-01
Full Text Available The article presents a look of the principal’s mathematical models – starting with Theil, Hansen and Tinbergen work – and their results used to analysis and design macroeconomic policies. In modeling field changes are very fast in theoretical aspects of modeling the many problems of macroeconomic policies and in using in practice the different political models elaboration. The article points out the problems of static and dynamic theory used in macro-policies modeling.
The Relevance of Using Mathematical Models in Macroeconomic Policies Theory
Directory of Open Access Journals (Sweden)
Nora Mihail
2006-09-01
Full Text Available The article presents a look of the principal’s mathematical models – starting with Theil, Hansen and Tinbergen work – and their results used to analysis and design macroeconomic policies. In modeling field changes are very fast in theoretical aspects of modeling the many problems of macroeconomic policies and in using in practice the different political models elaboration. The article points out the problems of static and dynamic theory used in macro-policies modeling.
Directory of Open Access Journals (Sweden)
Silvio Henrique Fiscarelli
2016-05-01
Full Text Available The current conditions of the classroom learning tend to be a one-way process based in teacher exposition, this make a negative impact on learning make it a mechanical and not meaningful activity. One possibility to improve the quality of teaching is to innovate methodologies and varying forms of presenting information to students, such as the use of technology in the teaching process. The Interactive Whiteboard (IBW is one of the technologies that are being implemented in Brazilian schools. One of the promising possibilities to add value to the use of LDI in classroom are "learning objects" (LO. However, one problem is that often the LO are not fully suited to the dynamics of IWB, whether functional or pedagogical point of view. The objective of this study is to analyze and propose a set of indicators that evaluate the learning objects for use in conjunction with Interactive Whiteboards. The selection and definition of evaluation indicators was carried from the literature review on the subject and based on LDI experiences of use in Municipal Elementary School. After defining the set of indicators was conducted a evaluation of a sample of 30 OA utilized to teaching mathematics in 3rd grade of elementary school. The results of the evaluation indicate that the proposed indicators are suitable for a pre-analysis of OA and assisting in the process of selection of these.
Eliseev, A. V.; Sitov, I. S.; Eliseev, S. V.
2018-03-01
The methodological basis of constructing mathematical models of vibratory technological machines is developed in the article. An approach is proposed that makes it possible to introduce a vibration table in a specific mode that provides conditions for the dynamic damping of oscillations for the zone of placement of a vibration exciter while providing specified vibration parameters in the working zone of the vibration table. The aim of the work is to develop methods of mathematical modeling, oriented to technological processes with long cycles. The technologies of structural mathematical modeling are used with structural schemes, transfer functions and amplitude-frequency characteristics. The concept of the work is to test the possibilities of combining the conditions for reducing loads with working components of a vibration exciter while simultaneously maintaining sufficiently wide limits in variating the parameters of the vibrational field.
Existence and characterization of optimal control in mathematics model of diabetics population
Permatasari, A. H.; Tjahjana, R. H.; Udjiani, T.
2018-03-01
Diabetes is a chronic disease with a huge burden affecting individuals and the whole society. In this paper, we constructed the optimal control mathematical model by applying a strategy to control the development of diabetic population. The constructed mathematical model considers the dynamics of disabled people due to diabetes. Moreover, an optimal control approach is proposed in order to reduce the burden of pre-diabetes. Implementation of control is done by preventing the pre-diabetes develop into diabetics with and without complications. The existence of optimal control and characterization of optimal control is discussed in this paper. Optimal control is characterized by applying the Pontryagin minimum principle. The results indicate that there is an optimal control in optimization problem in mathematics model of diabetic population. The effect of the optimal control variable (prevention) is strongly affected by the number of healthy people.
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
Mathematical modeling of a three-phase trickle bed reactor
Directory of Open Access Journals (Sweden)
J. D. Silva
2012-09-01
Full Text Available The transient behavior in a three-phase trickle bed reactor system (N2/H2O-KCl/activated carbon, 298 K, 1.01 bar was evaluated using a dynamic tracer method. The system operated with liquid and gas phases flowing downward with constant gas flow Q G = 2.50 x 10-6 m³ s-1 and the liquid phase flow (Q L varying in the range from 4.25x10-6 m³ s-1 to 0.50x10-6 m³ s-1. The evolution of the KCl concentration in the aqueous liquid phase was measured at the outlet of the reactor in response to the concentration increase at reactor inlet. A mathematical model was formulated and the solutions of the equations fitted to the measured tracer concentrations. The order of magnitude of the axial dispersion, liquid-solid mass transfer and partial wetting efficiency coefficients were estimated based on a numerical optimization procedure where the initial values of these coefficients, obtained by empirical correlations, were modified by comparing experimental and calculated tracer concentrations. The final optimized values of the coefficients were calculated by the minimization of a quadratic objective function. Three correlations were proposed to estimate the parameters values under the conditions employed. By comparing experimental and predicted tracer concentration step evolutions under different operating conditions the model was validated.
A mathematical model for the occurrence of historical events
Ohnishi, Teruaki
2017-12-01
A mathematical model was proposed for the frequency distribution of historical inter-event time τ. A basic ingredient was constructed by assuming the significance of a newly occurring historical event depending on the magnitude of a preceding event, the decrease of its significance by oblivion during the successive events, and an independent Poisson process for the occurrence of the event. The frequency distribution of τ was derived by integrating the basic ingredient with respect to all social fields and to all stake holders. The function of such a distribution was revealed as the forms of an exponential type, a power law type or an exponential-with-a-tail type depending on the values of constants appearing in the ingredient. The validity of this model was studied by applying it to the two cases of Modern China and Northern Ireland Troubles, where the τ-distribution varies depending on the different countries interacting with China and on the different stage of history of the Troubles, respectively. This indicates that history is consisted from many components with such different types of τ-distribution, which are the similar situation to the cases of other general human activities.
A proposed general model of information behaviour.
Directory of Open Access Journals (Sweden)
2003-01-01
Full Text Available Presents a critical description of Wilson's (1996 global model of information behaviour and proposes major modification on the basis of research into information behaviour of managers, conducted in Poland. The theoretical analysis and research results suggest that Wilson's model has certain imperfections, both in its conceptual content, and in graphical presentation. The model, for example, cannot be used to describe managers' information behaviour, since managers basically are not the end users of external from organization or computerized information services, and they acquire information mainly through various intermediaries. Therefore, the model cannot be considered as a general model, applicable to every category of information users. The proposed new model encompasses the main concepts of Wilson's model, such as: person-in-context, three categories of intervening variables (individual, social and environmental, activating mechanisms, cyclic character of information behaviours, and the adoption of a multidisciplinary approach to explain them. However, the new model introduces several changes. They include: 1. identification of 'context' with the intervening variables; 2. immersion of the chain of information behaviour in the 'context', to indicate that the context variables influence behaviour at all stages of the process (identification of needs, looking for information, processing and using it; 3. stress is put on the fact that the activating mechanisms also can occur at all stages of the information acquisition process; 4. introduction of two basic strategies of looking for information: personally and/or using various intermediaries.
Mathematical Model for Direct Evaporative Space Cooling Systems ...
African Journals Online (AJOL)
This paper deals with the development of a simple mathematical model for experimental validation of the performance of a small evaporative cooling system in a tropical climate. It also presents the coefficient of convective heat transfer of wide range of temperatures based on existing model. Extensive experiments have ...
Mathematical and computational modeling simulation of solar drying Systems
Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...
Mathematical modelling as basis for efficient enterprise management
Directory of Open Access Journals (Sweden)
Kalmykova Svetlana
2017-01-01
Full Text Available The choice of the most effective HR- management style at the enterprise is based on modeling various socio-economic situations. The article describes the formalization of the managing processes aimed at the interaction between the allocated management subsystems. The mathematical modelling tools are used to determine the time spent on recruiting personnel for key positions in the management hierarchy selection.
Mathematical Analysis of a Model for Human Immunodeficiency ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: The objective of this paper is to present a mathematical model formulated to investigate the dynamics of human immunodeficiency virus (HIV). The disease free equilibrium of the model was found to be locally and globally asymptotically stable. The endemic equilibrium point exists and it was discovered that the ...
Mathematical models of ABE fermentation: review and analysis.
Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S
2013-12-01
Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.
The Interval Market Model in Mathematical Finance : Game Theoretic Methods
Bernhard, P.; Engwerda, J.C.; Roorda, B.; Schumacher, J.M.; Kolokoltsov, V.; Saint-Pierre, P.; Aubin, J.P.
2013-01-01
Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous
Use of mathematical modeling in nuclear measurements projects
International Nuclear Information System (INIS)
Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.
2011-01-01
Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)
Mathematical Model for Prediction of Flexural Strength of Mound ...
African Journals Online (AJOL)
The mound soil-cement blended proportions were mathematically optimized by using scheffe's approach and the optimization model developed. A computer program predicting the mix proportion for the model was written. The optimal proportion by the program was used prepare beam samples measuring 150mm x 150mm ...
Precipitation of metal sulphides using gaseous hydrogen sulphide: mathematical modelling
Al Tarazi, M.Y.M.; Heesink, Albertus B.M.; Versteeg, Geert
2004-01-01
A mathematical model has been developed that describes the precipitation of metal sulffides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use
Precipitation of metal sulphides using gaseous hydrogen sulphide : mathematical modelling
Tarazi, Mousa Al-; Heesink, A. Bert M.; Versteeg, Geert F.
2004-01-01
A mathematical model has been developed that describes the precipitation of metal sulphides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use
A mathematical model of combustion kinetics of municipal solid ...
African Journals Online (AJOL)
Municipal Solid Waste has become a serious environmental problem troubling many cities. In this paper, a mathematical model of combustion kinetics of municipal solid waste with focus on plastic waste was studied. An analytical solution is obtained for the model. From the numerical simulation, it is observed that the ...
Mathematical model for dissolved oxygen prediction in Cirata ...
African Journals Online (AJOL)
This paper presents the implementation and performance of mathematical model to predict theconcentration of dissolved oxygen in Cirata Reservoir, West Java by using Artificial Neural Network (ANN). The simulation program was created using Visual Studio 2012 C# software with ANN model implemented in it. Prediction ...
A Mathematical Model for Analysis on Ships Collision Avoidance ...
African Journals Online (AJOL)
This study develops a mathematical model for analysis on collision avoidance of ships. The obtained model provides information on the quantitative effect of the ship's engine's response and the applied reversing force on separation distance and stopping abilities of the ships. Appropriate evasive maneuvers require the ...
Mathematical modelling of zirconium salicylate solvent extraction process
International Nuclear Information System (INIS)
Smirnova, N.S.; Evseev, A.M.; Fadeeva, V.I.; Kochetkova, S.K.
1979-01-01
Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built
Mathematical modelling of zirconium salicylate solvent extraction process
Energy Technology Data Exchange (ETDEWEB)
Smirnova, N S; Evseev, A M; Fadeeva, V I; Kochetkova, S K [Moskovskij Gosudarstvennyj Univ. (USSR)
1979-11-01
Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built.
Simple mathematical models for housing allocation to a homeless ...
African Journals Online (AJOL)
We present simple mathematical models for modelling a homeless population and housing allocation. We look at a situation whereby the local authority makes temporary accommodation available for some of the homeless for a while and we examine how this affects the number of families homeless at any given time.
A proposed experiment on ball lightning model
International Nuclear Information System (INIS)
Ignatovich, Vladimir K.; Ignatovich, Filipp V.
2011-01-01
Highlights: → We propose to put a glass sphere inside an excited gas. → Then to put a light ray inside the glass in a whispering gallery mode. → If the light is resonant to gas excitation, it will be amplified at every reflection. → In ms time the light in the glass will be amplified, and will melt the glass. → A liquid shell kept integer by electrostriction forces is the ball lightning model. -- Abstract: We propose an experiment for strong light amplification at multiple total reflections from active gaseous media.
Mathematical model of two-phase flow in accelerator channel
Directory of Open Access Journals (Sweden)
О.Ф. Нікулін
2010-01-01
Full Text Available The problem of two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in counter jet mill accelerator channel design.
Mathematical Modeling of Biofilm Structures Using COMSTAT Data
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Davide Verotta
2017-01-01
Full Text Available Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data in terms of few parameters and the capability to (i compare different experiments and exposures to different agents, (ii test different hypotheses regarding biofilm growth and interaction with different agents, and (iii simulate arbitrary administrations of agents. The mathematical framework is divided to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We demonstrate the application of (some of the models using confocal microscopy data obtained using the computer program COMSTAT.
Mathematical modeling of oxygen transport in solid oxide fuel cells
Energy Technology Data Exchange (ETDEWEB)
Svensson, Ann Mari
1997-12-31
This thesis develops mathematical models to describe the electrochemical performance of a solid oxide fuel cell cathode based on electrochemical kinetics and mass transfer. The individual effects of various coupled processes are investigated. A one-dimensional model is developed based on porous electrode theory. Two different mechanisms are investigated for the charge transfer reaction. One of these assumes that intermediately adsorbed oxygen atoms are reduced at the electrode/electrolyte interface, similar to the models proposed for metal electrodes. Simulated polarization curves exhibit limited currents due to depletion of oxygen adsorbates at high cathodic overvoltages. An empirical correlation is confirmed to exist between the limiting current an the oxygen partial pressure, however, a similar correlation often assumed to exist between the measured polarization resistance and the oxygen partial pressure could not be justified. For the other model, oxygen vacancies are assumed to be exchanged directly at the electrode/electrolyte interface. The electrochemical behaviour is improved by reducing the oxygen partial pressure, due to increased vacancy concentration of the electrode material. Simulated polarization curves exhibit Tafel-like slopes in the cathodic direction, which are due to polarization concentration, and not activation polarization in the conventional sense. Anodic limiting currents are predicted due to lack of available free sites for vacancy exchange at the cathode side. The thesis also presents a theoretical treatment of current and potential distributions in simple two-dimensional cell geometries, and a two-dimensional model for a porous electrode-electrolyte system for investigation of the effect of interfacial diffusion of adsorbates along the electrode/electrolyte interface. 172 refs., 60 figs., 11 tabs.
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS
Directory of Open Access Journals (Sweden)
L. V. Ursulyak
2017-12-01
Full Text Available Purpose. Using scientific publications the paper analyzes the mathematical models developed in Ukraine, CIS countries and abroad for theoretical studies of train dynamics and also shows the urgency of their further improvement. Methodology. Information base of the research was official full-text and abstract databases, scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodological materials of ministries and departments. Analysis of publications on existing mathematical models used to solve a wide range of problems associated with the train dynamics study shows the expediency of their application. Findings. The results of these studies were used in: 1 design of new types of draft gears and air distributors; 2 development of methods for controlling the movement of conventional and connected trains; 3 creation of appropriate process flow diagrams; 4 development of energy-saving methods of train driving; 5 revision of the Construction Codes and Regulations (SNiP ΙΙ-39.76; 6 when selecting the parameters of the autonomous automatic control system, created in DNURT, for an auxiliary locomotive that is part of a connected train; 7 when creating computer simulators for the training of locomotive drivers; 8 assessment of the vehicle dynamic indices characterizing traffic safety. Scientists around the world conduct numerical experiments related to estimation of train dynamics using mathematical models that need to be constantly improved. Originality. The authors presented the main theoretical postulates that allowed them to develop the existing mathematical models for solving problems related to the train dynamics. The analysis of scientific articles published in Ukraine, CIS countries and abroad allows us to determine the most relevant areas of application of mathematical models. Practicalvalue. The practical value of the results obtained lies in the scientific validity
Modeling eBook acceptance: A study on mathematics teachers
Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad
2014-12-01
The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.
Mathematical Modeling of Constrained Hamiltonian Systems
Schaft, A.J. van der; Maschke, B.M.
1995-01-01
Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the
THE FEATURES OF LASER EMISSION ENERGY DISTRIBUTION AT MATHEMATIC MODELING OF WORKING PROCESS
Directory of Open Access Journals (Sweden)
A. M. Avsiyevich
2013-01-01
Full Text Available The space laser emission energy distribution of different continuous operation settings depends from many factors, first on the settings design. For more accurate describing of multimode laser emission energy distribution intensity the experimental and theoretic model, which based on experimental laser emission distribution shift presentation with given accuracy rating in superposition basic function form, is proposed. This model provides the approximation error only 2,2 percent as compared with 24,6 % and 61 % for uniform and Gauss approximation accordingly. The proposed model usage lets more accurate take into consideration the laser emission and working surface interaction peculiarity, increases temperature fields calculation accuracy for mathematic modeling of laser treatment processes. The method of experimental laser emission energy distribution studying for given source and mathematic apparatus for calculation of laser emission energy distribution intensity parameters depended from the distance in radial direction on surface heating zone are shown.
Mathematical model of transmission network static state estimation
Directory of Open Access Journals (Sweden)
Ivanov Aleksandar
2012-01-01
Full Text Available In this paper the characteristics and capabilities of the power transmission network static state estimator are presented. The solving process of the mathematical model containing the measurement errors and their processing is developed. To evaluate difference between the general model of state estimation and the fast decoupled state estimation model, the both models are applied to an example, and so derived results are compared.
Mathematical Model of the Emissions of a selected vehicle
Directory of Open Access Journals (Sweden)
Matušů Radim
2014-10-01
Full Text Available The article addresses the quantification of exhaust emissions from gasoline engines during transient operation. The main targeted emissions are carbon monoxide and carbon dioxide. The result is a mathematical model describing the production of individual emissions components in all modes (static and dynamic. It also describes the procedure for the determination of emissions from the engine’s operating parameters. The result is compared with other possible methods of measuring emissions. The methodology is validated using the data from an on-road measurement. The mathematical model was created on the first route and validated on the second route.
A mathematical look at a physical power prediction model
Energy Technology Data Exchange (ETDEWEB)
Landberg, L. [Riso National Lab., Roskilde (Denmark)
1997-12-31
This paper takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations, and to give guidelines as to where the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.
Mathematical Ship Modeling for Control Applications
DEFF Research Database (Denmark)
Perez, Tristan; Blanke, Mogens
2002-01-01
In this report, we review the models for describing the motion of a ship in four degrees of freedom suitable for control applications. We present the hydrodynamic models of two ships: a container and a multi-role naval vessel. The models are based on experimental results in the four degrees...
One-dimensional chain of quantum molecule motors as a mathematical physics model for muscle fibers
International Nuclear Information System (INIS)
Si Tie-Yan
2015-01-01
A quantum chain model of multiple molecule motors is proposed as a mathematical physics theory for the microscopic modeling of classical force-velocity relation and tension transients in muscle fibers. The proposed model was a quantum many-particle Hamiltonian to predict the force-velocity relation for the slow release of muscle fibers, which has not yet been empirically defined and was much more complicated than the hyperbolic relationships. Using the same Hamiltonian model, a mathematical force-velocity relationship was proposed to explain the tension observed when the muscle was stimulated with an alternative electric current. The discrepancy between input electric frequency and the muscle oscillation frequency could be explained physically by the Doppler effect in this quantum chain model. Further more, quantum physics phenomena were applied to explore the tension time course of cardiac muscle and insect flight muscle. Most of the experimental tension transient curves were found to correspond to the theoretical output of quantum two- and three-level models. Mathematical modeling electric stimulus as photons exciting a quantum three-level particle reproduced most of the tension transient curves of water bug Lethocerus maximus. (special topic)
Incorporating neurophysiological concepts in mathematical thermoregulation models
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
Tracer kinetic modelling of receptor data with mathematical metabolite correction
International Nuclear Information System (INIS)
Burger, C.; Buck, A.
1996-01-01
Quantitation of metabolic processes with dynamic positron emission tomography (PET) and tracer kinetic modelling relies on the time course of authentic ligand in plasma, i.e. the input curve. The determination of the latter often requires the measurement of labelled metabilites, a laborious procedure. In this study we examined the possibility of mathematical metabolite correction, which might obviate the need for actual metabolite measurements. Mathematical metabilite correction was implemented by estimating the input curve together with kinetic tissue parameters. The general feasibility of the approach was evaluated in a Monte Carlo simulation using a two tissue compartment model. The method was then applied to a series of five human carbon-11 iomazenil PET studies. The measured cerebral tissue time-activity curves were fitted with a single tissue compartment model. For mathematical metabolite correction the input curve following the peak was approximated by a sum of three decaying exponentials, the amplitudes and characteristic half-times of which were then estimated by the fitting routine. In the simulation study the parameters used to generate synthetic tissue time-activity curves (K 1 -k 4 ) were refitted with reasonable identifiability when using mathematical metabolite correciton. Absolute quantitation of distribution volumes was found to be possible provided that the metabolite and the kinetic models are adequate. If the kinetic model is oversimplified, the linearity of the correlation between true and estimated distribution volumes is still maintained, although the linear regression becomes dependent on the input curve. These simulation results were confirmed when applying mathematical metabolite correction to the 11 C iomazenil study. Estimates of the distribution volume calculated with a measured input curve were linearly related to the estimates calculated using mathematical metabolite correction with correlation coefficients >0.990. (orig./MG)
Mathematical modeling in municipal solid waste management: case study of Tehran
Akbarpour Shirazi, Mohsen; Samieifard, Reza; Abduli, Mohammad Ali; Omidvar, Babak
2016-01-01
Background Solid Waste Management (SWM) in metropolises with systematic methods and following environmental issues, is one of the most important subjects in the area of urban management. In this regard, it is regarded as a legal entity so that its activities are not overshadowed by other urban activities. In this paper, a linear mathematical programming model has been designed for integrated SWM. Using Lingo software and required data from Tehran, the proposed model has been applied for Tehra...
Mathematical Modeling of Biofilm Structures Using COMSTAT Data
DEFF Research Database (Denmark)
Verotta, Davide; Haagensen, Janus Anders Juul; Spormann, Alfred M.
2017-01-01
Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data...... in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided...... to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We...
International Workshop on Mathematical Modeling of Tumor-Immune Dynamics
Kim, Peter; Mallet, Dann
2014-01-01
This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction betwe...
Use of mathematical modelling to assess the impact of vaccines on antibiotic resistance.
Atkins, Katherine E; Lafferty, Erin I; Deeny, Sarah R; Davies, Nicholas G; Robotham, Julie V; Jit, Mark
2017-11-13
Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
D.M. Kozachenko
2013-06-01
Full Text Available Purpose. The article aims to create a mathematical model of the railway station functioning for the solving of problems of station technology development on the plan-schedule basis. Methodology. The methods of graph theory and object-oriented analysis are used as research methods. The model of the station activity plan-schedule includes a model of technical equipment of the station (plan-schedule net and a model of the station functioning , which are formalized on the basis of parametric graphs. Findings. The presented model is implemented as an application to the graphics package AutoCAD. The software is developed in Visual LISP and Visual Basic. Taking into account that the construction of the plan-schedule is mostly a traditional process of adding, deleting, and modifying of icons, the developed interface is intuitively understandable for a technologist and practically does not require additional training. Originality. A mathematical model was created on the basis of the theory of graphs and object-oriented analysis in order to evaluate the technical and process of railway stations indicators; it is focused on solving problems of technology development of their work. Practical value. The proposed mathematical model is implemented as an application to the graphics package of AutoCAD. The presence of a mathematical model allows carrying out an automatic analysis of the plan-schedule and, thereby, reducing the period of its creation more than twice.
MATHEMATICAL MODELING OF ORANGE SEED DRYING KINETICS
Directory of Open Access Journals (Sweden)
Daniele Penteado Rosa
2015-06-01
Full Text Available Drying of orange seeds representing waste products from juice processing was studied in the temperatures of 40, 50, 60 and 70 °C and drying velocities of 0.6, 1.0 and 1.4 m/s. Experimental drying kinetics of orange seeds were obtained using a convective air forced dryer. Three thin-layer models: Page model, Lewis model, and the Henderson-Pabis model and the diffusive model were used to predict the drying curves. The Henderson-Pabis and the diffusive models show the best fitting performance and statistical evaluations. Moreover, the temperature dependence on the effective diffusivity followed an Arrhenius relationship, and the activation energies ranging from 16.174 to 16.842 kJ/mol
Physical and mathematical models of communication systems
International Nuclear Information System (INIS)
Verkhovskaya, E.P.; Yavorskij, V.V.
2006-01-01
The theoretical parties connecting resources of communication system with characteristics of channels are received. The model of such systems from positions quasi-classical thermodynamics is considered. (author)
Mathematical models for radiation effects on human health
International Nuclear Information System (INIS)
Negi, U.S.; Petwal, K.C.
2015-01-01
In this paper, we are proposing a theoretical approach of basic mathematical models for radiation effect on human health. The largest natural sources of radiation exposure to humans are radon gas. While radon gas has always been in the environment, awareness of its contribution to human radiation exposure has increased in recent years. Radon's primary pathway is through air space in soil and rock. Pressure differences between the soil and the inside of buildings may cause radon gas to move indoors. Radon decays to radon daughters, some of which emit alpha radiation. Alpha-emitting radon daughters are adsorbed on to dust particles which, when inhaled, are trapped in the lungs and may cause gene damage, mutations and finally cancer. Exposure to excess UV radiation increases risk of skin cancer but there is also a dark side. The incidence of all types of skin cancer is related to exposure to UV radiation. Non-melanoma skin cancer, eye melanoma, and lip cancer have also been related to natural UV light
Mathematical model of an integrated circuit cooling through cylindrical rods
Directory of Open Access Journals (Sweden)
Beltrán-Prieto Luis Antonio
2017-01-01
Full Text Available One of the main challenges in integrated circuits development is to propose alternatives to handle the extreme heat generated by high frequency of electrons moving in a reduced space that cause overheating and reduce the lifespan of the device. The use of cooling fins offers an alternative to enhance the heat transfer using combined a conduction-convection systems. Mathematical model of such process is important for parametric design and also to gain information about temperature distribution along the surface of the transistor. In this paper, we aim to obtain the equations for heat transfer along the chip and the fin by performing energy balance and heat transfer by conduction from the chip to the rod, followed by dissipation to the surrounding by convection. Newton's law of cooling and Fourier law were used to obtain the equations that describe the profile temperature in the rod and the surface of the chip. Ordinary differential equations were obtained and the respective analytical solutions were derived after consideration of boundary conditions. The temperature along the rod decreased considerably from the initial temperature (in contatct with the chip surface. This indicates the benefit of using a cilindrical rod to distribute the heat generated in the chip.
Molecular modeling: An open invitation for applied mathematics
Mezey, Paul G.
2013-10-01
Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.
Ordinary Mathematical Models in Calculating the Aviation GTE Parameters
Directory of Open Access Journals (Sweden)
E. A. Khoreva
2017-01-01
Full Text Available The paper presents the analytical review results of the ordinary mathematical models of the operating process used to study aviation GTE parameters and characteristics at all stages of its creation and operation. Considers the mathematical models of the zero and the first level, which are mostly used when solving typical problems in calculating parameters and characteristics of engines.Presents a number of practical problems arising in designing aviation GTE for various applications.The application of mathematical models of the zero-level engine can be quite appropriate when the engine is considered as a component in the aircraft system to estimate its calculated individual flight performance or when modeling the flight cycle of the aircrafts of different purpose.The paper demonstrates that introduction of correction functions into the first-level mathematical models in solving typical problems (influence of the Reynolds number, characteristics deterioration of the units during the overhaul period of engine, as well as influence of the flow inhomogeneity at the inlet because of manufacturing tolerance, etc. enables providing a sufficient engineering estimate accuracy to reflect a realistic operating process in the engine and its elements.
Mathematical modelling of tissue formation in chondrocyte filter cultures.
Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J
2011-12-17
In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.
Mathematical Modeling Of Life-Support Systems
Seshan, Panchalam K.; Ganapathi, Balasubramanian; Jan, Darrell L.; Ferrall, Joseph F.; Rohatgi, Naresh K.
1994-01-01
Generic hierarchical model of life-support system developed to facilitate comparisons of options in design of system. Model represents combinations of interdependent subsystems supporting microbes, plants, fish, and land animals (including humans). Generic model enables rapid configuration of variety of specific life support component models for tradeoff studies culminating in single system design. Enables rapid evaluation of effects of substituting alternate technologies and even entire groups of technologies and subsystems. Used to synthesize and analyze life-support systems ranging from relatively simple, nonregenerative units like aquariums to complex closed-loop systems aboard submarines or spacecraft. Model, called Generic Modular Flow Schematic (GMFS), coded in such chemical-process-simulation languages as Aspen Plus and expressed as three-dimensional spreadsheet.
Development of a revised mathematical model of the gastrointestinal tract
International Nuclear Information System (INIS)
Barker, A.
1991-01-01
The objectives of this research are as follows. First, to incorporate new biological data into a revised mathematical adult gastrointestinal tract model that includes: ingestion in both liquid and solid forms; consideration of absorption in the stomach, small intestine, ascending colon, transverse colon or not at all; gender and age of the adult; and whether the adult is a smoker or not. Next, to create a computer program in basic language for calculating residence times in each anatomical section of the GI tract for commonly used radionuclides. Also, to compare and contrast the new model with the ICRP 30 GI tract model in terms of physiological concepts, mathematical concepts, and revised residence times for several commonly used radionuclides. Finally, to determine whether the new model is sufficiently better than the current model to warrant its use as a replacement for the Eve model
Unlocking the black box: teaching mathematical modeling with popular culture.
Lofgren, Eric T
2016-10-01
Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.
Yates, James W T
2008-07-03
One feature of recent research in pharmacodynamic modelling has been the move towards more mechanistically based model structures. However, in all of these models there are common sub-systems, such as feedback loops and time-delays, whose properties and contribution to the model behaviour merit some mathematical analysis. In this paper a common pharmacodynamic model sub-structure is considered: the linear transit compartment. These models have a number of interesting properties as the length of the cascade chain is increased. In the limiting case a pure time-delay is achieved [Milsum, J.H., 1966. Biological Control Systems Analysis. McGraw-Hill Book Company, New York] and the initial behaviour becoming increasingly sensitive to parameter value perturbation. It is also shown that the modelled drug effect is attenuated, though the duration of action is longer. Through this analysis the range of behaviours that such models are capable of reproducing are characterised. The properties of these models and the experimental requirements are discussed in order to highlight how mathematical analysis prior to experimentation can enhance the utility of mathematical modelling.
Mathematical and physical modeling of rainfall in centrifuge
CAICEDO, Bernardo; THOREL, Luc; TRISTANCHO, Julian
2015-01-01
Rainfall simulation in centrifuge models is important for modelling soil-atmosphere interactions. However, the presence of Coriolis force, drag forces, evaporation and wind within the centrifuge may affect the distribution of rainfall over the model. As a result, development of appropriate centrifuge rain simulators requires a demanding process of experimental trial and error. This paper highlights the key factors involved in controlling rainfall in centrifuge simulations, develops a mathemat...
Mathematical and Computational Aspects Related to Soil Modeling and Simulation
2017-09-26
and simulation challenges at the interface of applied math (homogenization, handling of discontinuous behavior, discrete vs. continuum representations...topics: a) Visco-elasto-plastic continuum models of geo-surface materials b) Discrete models of geo-surface materials (rocks/gravel/sand) c) Mixed...continuum- discrete representations. Coarse-graining and fine-graining mathematical formulations d) Multi-physics aspects related to the modeling of
An upper limb mathematical model of an oil palm harvester
Tumit, N. P.; Rambely, A. S.; BMT, Shamsul; Shahriman A., B.; Ng Y., G.; Deros, B. M.; Zailina, H.; Goh, Y. M.; Arumugam, Manohar; Ismail, I. A.; Abdul Hafiz A., R.
2014-09-01
The main purpose of this article is to develop a mathematical model of human body during harvesting via Kane's method. In this paper, a 2-D closed-kinematic biomechanical model that represents a harvesting movement is developed. The model of six segments consisted of upper right arm, right forearm, harvesting equipment, left forearm, upper left arm, and upper part of trunk. Finally, the inverse dynamic equations are represented in matrix form.
MATHEMATICAL MODEL OF WEAR CHARACTER FAILURE IN AIRCRAFT OPERATION
Радько, Олег Віталійович; Молдован, Володимир Дмитрович
2016-01-01
In this paper the mathematical model of failures associated with wear during aircraft exploitationis developed. Тhe calculations of the distribution function, distribution density and failurerate gamma distribution at low coefficients of variation and the relatively low value of averagewear rate for the current time, which varies quite widely. The results coincide well with thephysical concepts and can be used to build different models of aircraft. Gamma distribution is apretty good model for...