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...... 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...... 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...
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 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…
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
Teaching Mathematical Modelling.
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
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...... 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...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....
Mathematical models of morphogenesis
Directory of Open Access Journals (Sweden)
Dilão Rui
2015-01-01
Full Text Available Morphogenesis is the ensemble of phenomena that generates the form and shape of organisms. Organisms are classified according to some of its structural characteristics, to its metabolism and to its form. In particular, the empirical classification associated with the phylum concept is related with the form and shape of organisms. In the first part of this talk, we introduce the class of mathematical models associated the Turing approach to pattern formation. In the Turing approach, morphogenesis models are described by reaction-diffusion parabolic partial differential equations. Based on this formalism, we present a mathematical model describing the first two hours of development of the fruit fly Drosophila. In the second part of this talk, we present results on Pareto optimality to calibrate and validate mathematical models.
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…
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...
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
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.
Mathematical modeling in psychological researches
Directory of Open Access Journals (Sweden)
Aleksandra Zyolko
2013-04-01
Full Text Available The author considers the nature of mathematical modeling and its significance in psychological researches. The author distinguishes the types of mathematical models: deterministic, stochastic models and synergetic models. The system approach is proposed as an instrument of implementation of mathematical modelling in psychological research.
Examples of Mathematical Modeling
Johnston, Matthew D.; Edwards, Carina M.; Bodmer, Walter F.; Maini, Philip K.; Chapman, S. Jonathan
2008-01-01
Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al.5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters. PMID:17873520
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.
Mathematical Modelling in European Education
Ferri, Rita Borromeo
2013-01-01
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…
Mathematical modeling in chronobiology.
Bordyugov, G; Westermark, P O; Korenčič, A; Bernard, S; Herzel, H
2013-01-01
Circadian clocks are autonomous oscillators entrained by external Zeitgebers such as light-dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell-cell coupling, and (3) optimization of chronotherapy.
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 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...
Mathematical Model for Hit Phenomena
Ishii, Akira; Hayashi, Takefumi; Matsuda, Naoya; Nakagawa, Takeshi; Arakaki, Hisashi; Yoshida, Narihiko
2010-01-01
The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dynamical and non-equilibrium phenomena. The purchase intention for each person is introduced and direct and indirect communications are expressed as two-body and three-body interaction in our model. The mathematical model is expressed as coupled nonlinear differential equations. The important factor in the model is the decay time of rumor for the hit. The calculated results agree very well with revenues of recent 25 movies.
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…
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…
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
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 Models of Biochemical Oscillations
Conrad, Emery David
1999-01-01
The goal of this paper is to explain the mathematics involved in modeling biochemical oscillations. We first discuss several important biochemical concepts fundamental to the construction of descriptive mathematical models. We review the basic theory of differential equations and stability analysis as it relates to two-variable models exhibiting oscillatory behavior. The importance of the Hopf Bifurcation will be discussed in detail for the central role it plays in limit cycle behavior and...
Mathematical Models of Waiting Time.
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)
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...... 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...
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....... It is found that the probability of entering the pore is highest when the largest of the radii in the ellipse is equal to half the radius of the pore, in case of molecules with circular radius less than the pore radius. The results are directly related to the macroscopic distribution coefficient...
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...
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 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...
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.
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.
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…
A Mathematical Model of Mechanotransduction
Roth, Bradley J
2016-01-01
This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between intracellular and extracellular displacements drive mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two dimensions. In several cases the equations are solved analytically, illustrating how displacements divide into two parts: monodomain displacements are identical in both spaces and therefore do not contribute to mechanotransduction, whereas bidomain displacements cause mechanotransduction. A new length constant depends on the intracellular and extracellular shear moduli and the integrin spring constant, and bidomain effects often occur within a few length constants of the tissue edge. Numerical methods for solving the model equations are being developed. Precursors to the model and potential applications are discussed. The bidomain model...
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
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......, thereby implying that interactions between spreading processes are driving forces of attention dynamics. Overall, the thesis contributes to a quantitative understanding of a wide range of different human behaviors by applying mathematical modeling to behavioral data. There can be no doubt......During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...
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 of kidney transport.
Layton, Anita T
2013-01-01
In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.
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.
A mathematical model of inheritance
Institute of Scientific and Technical Information of China (English)
瞿裕忠; 王志坚; 徐家福
1996-01-01
Inheritance is regarded as the hallmark of object-oriented programming languages.A mathematical model of inheritance is presented.In this model,the graph-sorted signature is introduced to represent the algebraic structure of the program,and an extension function on the graph-sorted signatures is used to formally describe the semantics of inheritance.The program’s algebraic structure reflects the syntactic constraints of the language and the corresponding extension function exposes the character of the language’s inheritance.
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 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.
Representations used by mathematics student teachers in mathematical modeling process
Directory of Open Access Journals (Sweden)
Aytuğ Özaltun
2014-02-01
Full Text Available The purpose of this study is to determine representations used by mathematics student teachers in steps of mathematical modeling process based on their solutions of problems formed in the context of different classification of modeling. The study was conducted with fifteen secondary mathematics student teachers given a Mathematical Modeling course. The participants were separated into five collaboration groups of three students. Data were collected with the detailed written papers given by the groups for the problems and GeoGebra solution files. The groups benefited from verbal, algebraic, figural, tabular and dynamic representations while they were solving the problems. Considering all steps of the process, groups at most used verbal and algebraic representations. While they used only verbal representation in analyzing the problem, they benefited from at most verbal representation and then figural representation in establishing the systematic structure. The most used is algebraic and then verbal representations in the steps of mathematization, meta-mathematization, and mathematical analysis. In the steps of interpretation/evaluation and the model verification, the groups mainly benefited from verbal and then algebraic representations. Further researches towards why representations are preferred in the specific steps of the mathematical modeling process are suggested.Key Words: Mathematical modeling, modeling problems, mathematics student teachers, representations.
Mathematical model of induction heating
Rak, Josef
2017-07-01
One of mathematical models of induction heating can be described by a parabolic differential equation with the specific Joule looses in the body. Advantage of this method is that the detailed knowledge of the 3D-magnetic field is not necessary and move of the body or the inductor can be easily implemented. The specific Joule looses can computed by solving the Fredholm integral equation of the second kind for the eddy current of density by the Nyström method with the singularity subtraction.
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…
Mathematical model for bone mineralization
Directory of Open Access Journals (Sweden)
Svetlana V Komarova
2015-08-01
Full Text Available Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly non-linear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.
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...
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
Building fire zone model with symbolic mathematics
Institute of Scientific and Technical Information of China (English)
武红梅; 郜冶; 周允基
2009-01-01
To apply the fire modelling for the fire engineer with symbolic mathematics,the key equations of a zone model were demonstrated. There were thirteen variables with nine constraints,so only four ordinary differential equations (ODEs) were required to solve. A typical fire modelling with two-room structure was studied. Accordingly,the source terms included in the ODEs were simplified and modelled,and the fourth Runge-Kutta method was used to solve the ordinary differential equations (ODEs) with symbolic mathematics. Then a zone model could be used with symbolic mathematics. It is proposed that symbolic mathematics is possible for use by fire engineer.
Mathematical Model for Photovoltaic Cells
Directory of Open Access Journals (Sweden)
Wafaa ABD EL-BASIT
2013-11-01
Full Text Available The study of photovoltaic systems in an efficient manner requires a precise knowledge of the (I-V and (P-V characteristic curves of photovoltaic modules. So, the aim of the present paper is to estimate such characteristics based on different operating conditions. In this concern, a simple one diode mathematical model was implemented using MATLAB script. The output characteristics of PV cell depend on the environmental conditions. For any solar cell, the model parameters are function of the irradiance and the temperature values of the site where the panel is placed. In this paper, the numerical values of the equivalent circuit parameters are generated by the program. As well, the dependence of the cells electrical parameters are analyzed under the influence of different irradiance and temperature levels. The variation of slopes of the (I–V curves of a cell at short-circuit and open-circuit conditions with intensity of illumination in small span of intensity and different temperature levels have been applied to determine the cell parameters, shunt resistance, series resistance. The results show that the efficiency of solar cells has an inverse relationship with temperature, irradiance levels are affected by the change of the photo-generation current and the series resistance in the single diode model.
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...... studies have considered data sets with just one behavioral variable such as email communication. The Social Fabric interdisciplinary research project is an attempt to collect a more complete data set on human behavior by providing 1000 smartphones with pre-installed data collection software to students...... 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...
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.
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...
A Generative Model of Mathematics Learning
Wittrock, M. C.
1974-01-01
The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
2016-01-01
Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.
A Seminar in Mathematical Model-Building.
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
Yilmaz, Suha; Tekin-Dede, Ayse
2016-01-01
Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…
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…
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…
Computacional-representantional model of mathematics (crmmath)
Toro Carvajal, Luis Alberto
2016-01-01
This paper presents the so-called computational representational model of mathematics (MCRMATH), its theoretical importance for mathematics education and its relation with the use of technology tools in mathematics teaching. To do this, from a cognitive point of view, we conduct a research study of representations and we explain the computational-representational model of mind (CRMM).
Applications of mathematical models of road cycling
Dahmen, Thorsten; Saupe, Dietmar; Wolf, Stefan
2012-01-01
This contribution discusses several use cases of mathematical models for road cycling. A mechanical model for the pedaling forces is the basis for an accurate indoor ergometer simulation of road cycling on real-world tracks. Together with a simple physiological model for the exertion of the athlete as a function of his/her accumulated power output, an optimal riding strategy for time trials on mountain ascents is computed. A combination of the two models leads to a mathematical optimization p...
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…
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…
Mathematical Model of Gravitational and Electrostatic Forces
Krouglov, Alexei
2006-01-01
Author presents mathematical model for acting-on-a-distance attractive and repulsive forces based on propagation of energy waves that produces Newton expression for gravitational and Coulomb expression for electrostatic forces. Model uses mathematical observation that difference between two inverse exponential functions of the distance asymptotically converges to function proportional to reciprocal of distance squared.
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…
Mineral potential mapping with mathematical geological models
Porwal, A.K.
2006-01-01
Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based mi
Mathematical Modeling of the Agriculture Crop Technology
Directory of Open Access Journals (Sweden)
D. Drucioc
1999-02-01
Full Text Available The organized structure of computer system for economic and ecological estimation of agriculture crop technologies is described. The system is composed of six interconnected blocks. The linear, non-linear and stochastic mathematical models for machinery sizing and selection in farm-level cropping system is presented in the mathematical model block of computer system.
Mineral potential mapping with mathematical geological models
Porwal, A.K.
2006-01-01
Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based
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.
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 pipeli......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...
The mathematics of cancer: integrating quantitative models.
Altrock, Philipp M; Liu, Lin L; Michor, Franziska
2015-12-01
Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.
Mathematical modelling of cucumber (cucumis sativus) drying
Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.
2014-07-01
This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.
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...... involved. We argue that progress in students’ conceptual learning needs to be conceptualised separately from that of progress in their modelling competency. Findings are that modelling activities open a window to the students’ images of the mathematical concepts involved; that modelling activities can...... 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....
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…
Study of Photovoltaic Cells Engineering Mathematical Model
Zhou, Jun; Yu, Zhengping; Lu, Zhengyi; Li, Chenhui; Zhang, Ruilan
2016-11-01
The characteristic curve of photovoltaic cells is the theoretical basis of PV Power, which simplifies the existing mathematical model, eventually, obtains a mathematical model used in engineering. The characteristic curve of photovoltaic cells contains both exponential and logarithmic calculation. The exponential and logarithmic spread out through Taylor series, which includes only four arithmetic and use single chip microcontroller as the control center. The result shows that: the use of single chip microcontroller for calculating exponential and logarithmic functions, simplifies mathematical model of PV curve, also can meet the specific conditions’ requirement for engineering applications.
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 modeling in biomedical imaging
2012-01-01
This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed mathematical and computational tools. It is particularly suitable for researchers and graduate students in applied mathematics and biomedical engineering.
Mathematical Programming Models in Educational Planning.
McNamara, James F.
This document begins by defining and discussing educational planning. A brief overview of mathematical programing with an explanation of the general linear programing model is then provided. Some recent applications of mathematical programing techniques to educational planning problems are reviewed, and their implications for educational research…
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...
Mathematical modelling of the calcination process | Olayiwola ...
African Journals Online (AJOL)
Mathematical modelling of the calcination process. ... High quality lime is an essential raw material for Electric Arc Furnaces and Basic Oxygen Furnaces ... From the numerical simulation, it is observed that the gas temperature increases as 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...... 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......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...
Applied mathematics: Models, Discretizations, and Solvers
Institute of Scientific and Technical Information of China (English)
D.E. Keyes
2007-01-01
@@ Computational plasma physicists inherit decades of developments in mathematical models, numerical algorithms, computer architecture, and software engineering, whose recent coming together marks the beginning of a new era of large-scale simulation.
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
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...... 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...
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)
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…
Mathematical model of cylindrical form tolerance
Institute of Scientific and Technical Information of China (English)
蔡敏; 杨将新; 吴昭同
2004-01-01
Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of toler-ance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.
Mathematical model of cylindrical form tolerance
Institute of Scientific and Technical Information of China (English)
蔡敏; 杨将新; 吴昭同
2004-01-01
Tolerance is essential for integration of CAD and CAM.Unfortunately,the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression,processing and data transferring with computers.How to interpret its semantics is becoming a focus of relevant studies.This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994,established the mathematical model of form tolerance for cylindrical feature.First,each tolerance in the national standard was established by vector equation.Then on the foundation of tolerance's mathematical definition theory,each tolerance zone's mathematical model was established by inequality based on degrees of feature.At last the variance area of each tolerance zone is derived.This model can interpret the semantics of form tolerance exactly and completely.
Mathematical modeling in soil science
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
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 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
About a mathematical model of market
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
Mathematical human modelling for impact loading
Happee, R.; Hoof, J.F.A.M. van; Lange, R. de
2001-01-01
Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models b
Mathematical Modeling of Viral Zoonoses in Wildlife
2011-01-01
Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed.
Mathematical modelling of magnetically targeted drug delivery
Energy Technology Data Exchange (ETDEWEB)
Grief, Andrew D. [Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)]. E-mail: andrew.grief@nottingham.ac.uk; Richardson, Giles [Theoretical Mechanics, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD (United Kingdom)]. E-mail: giles.richardson@nottingham.ac.uk
2005-05-15
A mathematical model for targeted drug delivery using magnetic particles is developed. This includes a diffusive flux of particles arising from interactions between erythrocytes in the microcirculation. The model is used to track particles in a vessel network. Magnetic field design is discussed and we show that it is impossible to specifically target internal regions using an externally applied field.
Mathematical models of cell self-organization
Directory of Open Access Journals (Sweden)
Benoît Perthame
2011-04-01
More recently nonlinear hyperbolic and kinetic models also have been used to describe the phenomena at a smaller scale. We explain here some motivations for ‘microscopic’ descriptions, the mathematical difficulties arising in their analysis and how kinetic models can help in understanding the unity of these descriptions.
Mathematical human modelling for impact loading
Happee, R.; Hoof, J.F.A.M. van; Lange, R. de
2001-01-01
Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models
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 model of electrotaxis in osteoblastic cells
Vanegas-Acosta, J.C.; Garzón-Alvarado, D.A.; Zwamborn, A.P.M.
2012-01-01
Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF stren
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 strengt
Building Mathematical Models Of Solid Objects
Randall, Donald P.; Jones, Kennie H.; Von Ofenheim, William H.; Gates, Raymond L.; Matthews, Christine G.
1989-01-01
Solid Modeling Program (SMP) version 2.0 provides capability to model complex solid objects mathematically through aggregation of geometric primitives (parts). System provides designer with basic set of primitive parts and capability to define new primitives. Six primitives included in present version: boxes, cones, spheres, paraboloids, tori, and trusses. Written in VAX/VMS FORTRAN 77.
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 b
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.
Mathematical modeling of complex noise barriers
Energy Technology Data Exchange (ETDEWEB)
Hayek, S.I.
1982-01-01
Mathematical modeling of the noise reduction efficiency of highway noise barriers depends on the shape and absorptivity of the barrier, the influence of the impedance of the ground under the receiver, the atmospheric conditions as well as traffic details. The mathematical model for a barrier's noise reduction requires the knowledge of point-to-point acoustic diffraction models. In many instances, the shape of the barrier is simple; such as thin wall (edge), sharp wedge, and cylindrically topped berms. However, new designs of more efficient barriers have been investigated recently.
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...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal......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...... 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...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal situation......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...... 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...
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.
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 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...
The (mathematical modelling process in biosciences
Directory of Open Access Journals (Sweden)
Nestor V. Torres
2015-12-01
Full Text Available In this communication we introduce a general framework and discussion on the role of models and the modelling process within the scientific activity in the biosciences realm. The objective is sum up the common procedure during the formalization and analysis of a biological problem under the foundations of Systems Biology, which approach 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 the biology. Then, we present the modelization and analysis process 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 presentation the main features and shortcomings of the process are developed together with a set of rules that could help in the modelling endeavour of any biological system. 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 the modelling are currently posing to the current biology.
Mathematical Modeling of Chemical Stoichiometry
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Mathematical modeling in biomedical imaging
2009-01-01
This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
Mathematical Modeling of Chemical Stoichiometry
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Controllability, Observability, and Stability of Mathematical Models
Iggidr, Abderrahman
2004-01-01
International audience; This article presents an overview of three fundamental concepts in Mathematical System Theory: controllability, stability and observability. These properties play a prominent role in the study of mathematical models and in the understanding of their behavior. They constitute the main research subject in Control Theory. Historically the tools and techniques of Automatic Control have been developed for artificial engineering systems but nowadays they are more and more ap...
Mathematical Modelling of Bridges with SAP2000
Maraž, Miha
2006-01-01
The present work describes a relatively new programme module, which is enhanced in the recently released versions of SAP2000 software. The new module, called Bridge Modeler, is intended for simple, parametric mathematical modelling of bridges. The modelling procedure is explained on a test case through the steps of a user-friendly Bridge Wizard. For each step, we described the basic principles and the application possibilities as well as some limitations. We also explained two types of analys...
Mathematical Modeling of Circadian and Homeostatic Interaction
2011-11-16
Williams and C. Diniz Behn. A Hodgkin- Huxley -type model orexin neuron. SLEEP 32, A25, 2009. 4) C. Diniz Behn, D. Pal, G. Vanini, R. Lydic, G. A. Mashour...Switzerland, September 2009. 11) K. Williams, “A Hodgkin- Huxley -type model orexin neuron”, Associated Professional Sleep Societies Annual Meeting...Seattle, WA, June 2009. 12) K. Williams, “Dynamics in a Hodgkin- Huxley -type model orexin neuron”, Society for Industrial and Applied Mathematics Annual
Mathematical System Theory and System Modeling
1980-01-01
Choosing models related effectively to the questions to be addressed is a central issue in the craft of systems analysis. Since the mathematical description the analyst chooses constrains the types of issues he candeal with, it is important for these models to be selected so as to yield limitations that are acceptable in view of the questions the systems analysis seeks to answer. In this paper, the author gives an overview of the central issues affecting the question of model choice. To ...
Models and structures: mathematical physics
Energy Technology Data Exchange (ETDEWEB)
NONE
2003-07-01
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.
A mathematical model for Neanderthal extinction
Flores, J C
1997-01-01
A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion) is also discussed nevertheless, extinction of Neanderthal seems unavoidable. Numerical analysis of travelling wave solution (fronts) comfirms the extinction. The wave-front-velocity is estimated from linear analysis and numerical simulations confirm this estimation. We conjecture a mathematical formulation for the principle of exclusion between competitive interacting species (Gause).
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.
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 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...
A mathematical model of symmetry based on mathematical definition
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
A mathematical model of symmetry based on mathematical definition
Institute of Scientific and Technical Information of China (English)
刘玉生; 杨将新; 吴昭同; 高曙明
2002-01-01
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disignd/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance beeanse of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: ( 1 ) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements ; after which, the mathematical models of syrmmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
Mathematical Modeling in Continuum Mechanics
Temam, Roger; Miranville, Alain
2005-06-01
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
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 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.
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 ...
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.
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 models for Isoptera (Insecta mound growth
Directory of Open Access Journals (Sweden)
MLT. Buschini
Full Text Available In this research we proposed two mathematical models for Isoptera mound growth derived from the Von Bertalanffy growth curve, one appropriated for Nasutitermes coxipoensis, and a more general formulation. The mean height and the mean diameter of ten small colonies were measured each month for twelve months, from April, 1995 to April, 1996. Through these data, the monthly volumes were calculated for each of them. Then the growth in height and in volume was estimated and the models proposed.
Structured Mathematical Modeling of Industrial Boiler
Abdullah Nur Aziz; Yul Yunazwin Nazaruddin; Parsaulian Siregar; Yazid Bindar
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 modeling of rewarming after cold therapy.
Avet, L M
1978-07-01
Statistical methods are presented for fitting mathematical models to skin temperature data. Three types of regression curves, namely, linear regression (Y = A + BX), second-degree regression (Y = A + BX + CX2), and asymptotic regression (Y = alpha + betapx), are discussed as possible models for the rewarming process following cold therapy. The data for fitting the curves consists of back surface temperature (degrees C) corresponding to various times after cold pack treatment (19 degrees C, administered for 20 minutes) was terminated.
Pedagogical Content Knowledge in Mathematical Modelling Instruction
Tan, Liang Soon; Ang, Keng Cheng
2012-01-01
This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…
Optimization of mathematical models for thematic maps
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The thematic map is a major class of maps designed to demonstrate particular features or concepts,functioning as an indispensable tool in geographical research.The process of thematic mapping is one into which geographical research goes deeply and broadly.The key activity and course of thematic map production is the use of mathematical models to create thematic data layers.Therefore,the selection and optimization of mathematical models is in the forefront of thematic map research.The theoretical foundations,mechanisms and methods of mathematical model optimization are expounded in this paper,including two approaches,the phase by phase mode and the multi-aim scheme balance mode.Case studies in eco-environment mapping and emergency mapping are described and analyzed,with a hierarchical analysis method being used in the model optimization for eco-environment fragility and sensitivity assessment mapping in Beibuwan (Guangxi) District,the dynamic system (DS) method being used in the model optimization for ecological security adjustment mapping in Xishuang Banna,Yunnan province,and the multi-phase mode being used in the models for forest fire and infectious diseases mapping.
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...... attempt to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical...... influence of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...
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...... to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical neuroimaging data...... of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the resulting model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...
Mathematical modelling of leprosy and its control.
Blok, David J; de Vlas, Sake J; Fischer, Egil A J; Richardus, Jan Hendrik
2015-03-01
Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital.
Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
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.
Models of Non-Life Insurance Mathematics
Directory of Open Access Journals (Sweden)
Constanta Nicoleta BODEA
2008-01-01
Full Text Available In this communication we will discuss two regression credibility models from Non Ã¢Â€Â“ Life Insurance Mathematics that can be solved by means of matrix theory. In the first regression credibility model, starting from a well-known representation formula of the inverse for a special class of matrices a risk premium will be calculated for a contract with risk parameter q. In the next regression credibility model, we will obtain a credibility solution in the form of a linear combination of the individual estimate (based on the data of a particular state and the collective estimate (based on aggregate USA data. Mathematics Subject Classification: 62P05.
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
The mathematical modeling revolution in extractive metallurgy
Szekely, Julian
1988-08-01
A brief review is presented of the current state of extractive metallurgy, and it is shown that it is still a significant part of the national economy. Then a definition is given of mathematical models, and the general philosophy of modeling is discussed, together with the cost of models, hardware, and software options. Several illustrative examples are given, drawn from aluminum electrolysis, flash smelting, tundish operations, and plasma systems. The paper is concluded with the future modeling tasks facing us; these include the more widespread applications of models to represent both existing and new processing operations. It is stressed that models can play a major role in developing a holistic approach to metals and materials processing, where the primary extraction and refining operations are combined with the final processing steps.
Mathematical models of human african trypanosomiasis epidemiology.
Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul
2015-03-01
Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.
Mathematical modelling of wood and briquettes torrefaction
Energy Technology Data Exchange (ETDEWEB)
Felfli, Felix Fonseca; Luengo, Carlos Alberto [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Fisica Gleb Wataghin. Grupo Combustiveis Alternativos; Soler, Pedro Beaton [Universidad de Oriente, Santiago de Cuba (Cuba). Fac. de Ingenieria Mecanica. Centro de Estudios de Eficiencia Energetica; Rocha, Jose Dilcio [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Nucleo Interdisciplinar de Planejamento Energetico (NIPE)
2004-07-01
A mathematical model valid for the torrefaction of wood logs and biomass briquettes is presented. The model described both chemical and physical processes, which take place in a moist piece of wood heated at temperatures between 503 and 573 K. Calibration measurements of the temperature profile and mass loss, were performed on dry cylinders of wood samples during torrefaction in an inert atmosphere at 503, 533, and 553 K. The calculated data shows a good agreement with experiments. The model can be a useful tool to estimate projecting and operating parameters for torrefaction furnaces such as minimum time of torrefaction, energy consumption and the mass yield. (author)
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 temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) 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.
Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology.
Lingefjard, Thomas
2002-01-01
Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…
Mathematical analysis of a muscle architecture model.
Navallas, Javier; Malanda, Armando; Gila, Luis; Rodríguez, Javier; Rodríguez, Ignacio
2009-01-01
Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area; and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition, a considerable 'edge effect' is present in the outer zone of the muscle cross-section, making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size.
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 ...
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.
Mathematical Modeling of an Automobile Damper
Directory of Open Access Journals (Sweden)
N. B. Kate, T. A. Jadhav
2013-10-01
Full Text Available - In an automotive industry, to reduce product development time and increase quality of product, it is essential to reduce the number of physical prototypes and rely more on precise & reliable design for the final design of vehicles. This paper presents a mathematical model for the damping force of the hydraulic shock absorber which is implemented to analyse the shock absorbers mounting brackets attached to the vehicle structure. Physical testing results indicate that the considered shock absorber’s mathematical model is reliable and can be used to calculate the durability target life of mounting brackets. Thus this presented methodology can be utilized as an effective way to reduce time and cost in design and development of automotive components.
Mathematical modelling of the lower urinary tract.
Paya, Antonio Soriano; Fernandez, Daniel Ruiz; Gil, David; Garcia Chamizo, Juan Manuel; Perez, Francisco Macia
2013-03-01
The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.
A Mathematical Model for Suppression Subtractive Hybridization
2002-01-01
Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assess...
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)
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 Modelling of Immune Response in Tissues
Directory of Open Access Journals (Sweden)
B. Su
2009-01-01
Full Text Available We have developed a spatial–temporal mathematical model (PDE to capture fundamental aspects of the immune response to antigen. We have considered terms that broadly describe intercellular communication, cell movement, and effector function (activation or inhibition. The PDE model is robust to variation in antigen load and it can account for (1 antigen recognition, (2 an innate immune response, (3 an adaptive immune response, (4 the elimination of antigen and subsequent resolution of the immune response or (5 equilibrium of the immune response to the presence of persistent antigen (chronic infection and the formation of a granuloma.
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
MATHEMATICAL MODEL OF THE MICROBIAL FLOODING
Institute of Scientific and Technical Information of China (English)
Lei Guang-lun; Zhang Zhong-zhi; Chen Yue-ming
2003-01-01
On the basis of growth kinetics of microorganism and the principle of material balance, equations were derived to describe microbial growth, nutrient consumption, metabolites production and their transport in formation. The changes in porosity, permeability, oil viscosity and capillary force were also described as the main facturs of microbial flooding. For reservoirs with black oil properties, three-dimensional three-phase mathematical models with the cosidaration of multi-microbial components were established to depict microbial flooding oil. With this model, calculated results are in good agreement with experimental data.
Mathematical Model of the Processoof Pearlite Austenitization
Directory of Open Access Journals (Sweden)
Olejarczyk-Wożeńska I.
2014-10-01
Full Text Available The paper presents a mathematical model of the pearlite - austenite transformation. The description of this process uses the diffusion mechanism which takes place between the plates of ferrite and cementite (pearlite as well as austenite. The process of austenite growth was described by means of a system of differential equations solved with the use of the finite difference method. The developed model was implemented in the environment of Delphi 4. The proprietary program allows for the calculation of the rate and time of the transformation at an assumed temperature as well as to determine the TTT diagram for the assigned temperature range.
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 of Tyndall Star Initiation
Harvey, Peter; Katz, Richard F; Lacey, Andrew A
2015-01-01
The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid/liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface, and it leads to an interesting class of codimension-2 free boundary problems.
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)
Solar Panel Mathematical Modeling Using Simulink
Directory of Open Access Journals (Sweden)
Chandani Sharma
2014-05-01
Full Text Available For decades, electricity is a key driver of socio-economy development. Nowadays, in the context of competition there is a direct relationship between electricity generation and sustainable development of the country. This paper presents distinct use of a Photovoltaic array offering great potential as source of electricity. The simulation uses One-diode equivalent circuit in order to investigate I-V and P-V characteristics. The GUI model is designed with Simulink block libraries. The goals of proposed model are to perform a systematic analysis, modeling and evaluation of the key subsystems for obtaining Maximum Power Point of a solar cell. Effect of increasing number of cells is described at Standard Test Conditions by mathematical modeling of equations. It is desirable to achieve maximum power output at a minimum cost under various operating conditions. Index Terms—
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…
Study on mathematical model of steam coal blending
Institute of Scientific and Technical Information of China (English)
高洪阁; 李白英; 刘泽常; 尹增德
2002-01-01
It is necessary to set up a new mathematical model of steam coal blending instead of the old model. Indexes such as moisture content, ash content, volatile matter, sulfur content and heating value in the new mathematical model have linear relation. The new mathematical model can also predict ash-fusion temperature precisely by considering coal ash ratio in steam coal blending, therefore it is possible to obtain linear relation of ash-fusion temperature between single coal and steam coal blending. The new mathematical model can improve precision of steam coal blending and perfect the old mathematical model of steam coal blending.
Learning to teach mathematical modelling in secondary and tertiary education
Ferri, Rita Borromeo
2017-07-01
Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.
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.
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...
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.
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.
HEMETβ: improvement of hepatocyte metabolism mathematical model.
Orsi, G; De Maria, C; Guzzardi, M; Vozzi, F; Vozzi, G
2011-10-01
This article describes hepatocyte metabolism mathematical model (HEMETβ), which is an improved version of HEMET, an effective and versatile virtual cell model based on hepatic cell metabolism. HEMET is based on a set of non-linear differential equations, implemented in Simulink®, which describes the biochemical reactions and energetic cell state, and completely mimics the principal metabolic pathways in hepatic cells. The cell energy function and modular structure are the core of this model. HEMETβ as HEMET model describes hepatic cellular metabolism in standard conditions (cell culture in a plastic multi-well placed in an incubator at 37° C with 5% of CO2) and with excess substrates concentration. The main improvements in HEMETβ are the introductions of Michaelis-Menten models for reversible reactions and enzymatic inhibition. In addition, we eliminated hard non-linearities and modelled cell proliferation and every single aminoacid degradation pathway. All these innovations, combined with a user-friendly aspect, allow researchers to create new cell types and validate new experimental protocols just varying 'peripheral' pathways or model inputs.
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.
A MATHEMATICAL MODEL OF RESERVOIR SEDIMENTATION
Institute of Scientific and Technical Information of China (English)
HUANG Jinchi
2001-01-01
Reliable quantitative estimation of bed aggradation or degradation is important for river-training and water management projects. With the development of water resources, sediment problems associated with a dam are becoming more severe. This paper describes some special problems in mathematical model for calculation of degradation and aggradation in a reservoir. The main efforts of this study are on the treatment of some physical processes of fine sediment transport (＜0.05 mm). Problems in a reservoir are obviously different from a natural stream, such as the turbid current flow, orifice sediment flushing;and the initiation and consolidation of cohesive sediment deposition. The case of Liujiaxia Reservoir,which is located in the upper reaches of the Yellow River, is employed to verify the model. The results show that the model is applicable in the evaluation of an engineering planing with plenty of fine sediment movement.
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...
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.
A mathematical model of aortic aneurysm formation
Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai
2017-01-01
Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412
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 modelling of risk reduction in reinsurance
Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.
2017-01-01
The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.
Mathematical modeling of diesel fuel hydrotreating
Tataurshikov, A.; Ivanchina, E.; Krivtcova, N.; Krivtsov, E.; Syskina, A.
2015-11-01
Hydrotreating of the diesel fraction with the high initial sulfur content of 1,4 mass% is carried out in the flow-through laboratory setup with the industrial GKD-202 catalyst at various process temperature. On the basis of the experimental data the regularities of the hydrogenation reactions are revealed, and the formalized scheme of sulfur-containing components (sulfides, benzothiophenes, and dibenzothiophenes) transformations is made. The mathematical model of hydrotreating process is developed, the constant values for the reaction rate of hydrodesulfurization of the specified components are calculated.
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.
Mathematical analysis of epidemiological models with heterogeneity
Energy Technology Data Exchange (ETDEWEB)
Van Ark, J.W.
1992-01-01
For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.
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
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…
A Mathematical Model of Cigarette Smoldering Process
Directory of Open Access Journals (Sweden)
Chen P
2014-12-01
Full Text Available A mathematical model for a smoldering cigarette has been proposed. In the analysis of the cigarette combustion and pyrolysis processes, a receding burning front is defined, which has a constant temperature (~450 °C and divides the cigarette into two zones, the burning zone and the pyrolysis zone. The char combustion processes in the burning zone and the pyrolysis of virgin tobacco and evaporation of water in the pyrolysis zone are included in the model. The hot gases flow from the burning zone, are assumed to go out as sidestream smoke during smoldering. The internal heat transport is characterized by effective thermal conductivities in each zone. Thermal conduction of cigarette paper and convective and radiative heat transfer at the outer surface were also considered. The governing partial differential equations were solved using an integral method. Model predictions of smoldering speed as well as temperature and density profiles in the pyrolysis zone for different kinds of cigarettes were found to agree with the experimental data. The model also predicts the coal length and the maximum coal temperatures during smoldering conditions. The model provides a relatively fast and efficient way to simulate the cigarette burning processes. It offers a practical tool for exploring important parameters for cigarette smoldering processes, such as tobacco components, properties of cigarette paper, and heat generation in the burning zone and its dependence on the mass burn rate.
Knowledge Map: Mathematical Model and Dynamic Behaviors
Institute of Scientific and Technical Information of China (English)
Hai Zhuge; Xiang-Feng Luo
2005-01-01
Knowledge representation and reasoning is a key issue of the Knowledge Grid. This paper proposes a Knowledge Map (KM) model for representing and reasoning causal knowledge as an overlay in the Knowledge Grid. It extends Fuzzy Cognitive Maps (FCMs) to represent and reason not only simple cause-effect relations, but also time-delay causal relations, conditional probabilistic causal relations and sequential relations. The mathematical model and dynamic behaviors of KM are presented. Experiments show that, under certain conditions, the dynamic behaviors of KM can translate between different states. Knowing this condition, experts can control or modify the constructed KM while its dynamic behaviors do not accord with their expectation. Simulations and applications show that KM is more powerful and natural than FCM in emulating real world.
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.
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......, Ontario, Canada), NebuChamber (Astra, Södirtälje, Sweden) and Nebuhaler (Astra) adapted for babies. The dose of fluticasone proportionate delivered by the Babyhaler (Glaxco Wellcome, Oxbridge, Middlesex, UK) was 80% of that predicted, probably because of incomplete priming of this spacer. Of the above...
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.
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.
Building a Two Axes Process Model of Understanding Mathematics
Koyama, Masataka
1993-01-01
The purpose of this study is to make clear what kind of characteristics a model of understanding mathematics should have so as to be useful and effective in mathematics education. The models of understanding presented in preceding papers are classified into two large categories, i. e. "aspect model" and "process model". Focusing on the process of understanding mathematics, reflective thinking plays an important role to develop children's understanding, or to progress children's thinking from ...
A mathematical model of glutathione metabolism
Directory of Open Access Journals (Sweden)
James S Jill
2008-04-01
Full Text Available Abstract Background Glutathione (GSH plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by other tissues. Deficits in glutathione have been implicated in aging and a host of diseases including Alzheimer's disease, Parkinson's disease, cardiovascular disease, cancer, Down syndrome and autism. Approach We explore the properties of glutathione metabolism in the liver by experimenting with a mathematical model of one-carbon metabolism, the transsulfuration pathway, and glutathione synthesis, transport, and breakdown. The model is based on known properties of the enzymes and the regulation of those enzymes by oxidative stress. We explore the half-life of glutathione, the regulation of glutathione synthesis, and its sensitivity to fluctuations in amino acid input. We use the model to simulate the metabolic profiles previously observed in Down syndrome and autism and compare the model results to clinical data. Conclusion We show that the glutathione pools in hepatic cells and in the blood are quite insensitive to fluctuations in amino acid input and offer an explanation based on model predictions. In contrast, we show that hepatic glutathione pools are highly sensitive to the level of oxidative stress. The model shows that overexpression of genes on chromosome 21 and an increase in oxidative stress can explain the metabolic profile of Down syndrome. The model also correctly simulates the metabolic profile of autism when oxidative stress is substantially increased and the adenosine concentration is raised. Finally, we discuss how individual variation arises and its consequences for one-carbon and glutathione metabolism.
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
Mathematical Modeling Social Responsibility for Dynamic Organizations
Directory of Open Access Journals (Sweden)
Farzaneh Chavoshbashi
2012-03-01
Full Text Available Dynamic organizations as accountable organizations, for transparency and accountability to its stakeholders to stakeholders for their toward performance there should express their commitment to social responsibility are through their values and ensure that this commitment throughout the organization are now and thus will have a social responsibility for their mutual benefit, so there is more and more coherent in their ethical approach takes advantage and the community and stakeholders and the organization will have better performance and strengths. Because of interest in social responsibility, in this paper dynamic model is presented for Corporate Social Responsibility of Bionic organization. Model presented a new model is inspired by chaos theory and natural systems theory based on bifurcation in creation to be all natural systems, realizing the value of responsibility as one of the fundamental values of social and institutional development that the relationship between business and work environment in the global market economy and range will be specified. First Social Responsibility factors identified, then experts and scholars determine the weight of the components and technical coefficient for modeling and paired comparison has been done using MATLAB mathematical Software.
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.
Mathematical Model for the Mineralization of Bone
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
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 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.
Bukova-Guzel, Esra
2011-01-01
This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…
Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling
Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan
2012-01-01
The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…
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.
Mathematical modeling of endovenous laser treatment (ELT
Directory of Open Access Journals (Sweden)
Wassmer Benjamin
2006-04-01
Full Text Available Abstract Background and objectives Endovenous laser treatment (ELT has been recently proposed as an alternative in the treatment of reflux of the Great Saphenous Vein (GSV and Small Saphenous Vein (SSV. Successful ELT depends on the selection of optimal parameters required to achieve an optimal vein damage while avoiding side effects. Mathematical modeling of ELT could provide a better understanding of the ELT process and could determine the optimal dosage as a function of vein diameter. Study design/materials and methods The model is based on calculations describing the light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma Inc., Arlington, MA, USA. Damage to the vein wall for CW and single shot energy was calculated for 3 and 5 mm vein diameters. In pulsed mode, the pullback distance (3, 5 and 7 mm was considered. For CW mode simulation, the pullback speed (1, 2, 3 mm/s was the variable. The total dose was expressed as joules per centimeter in order to perform comparison to results already reported in clinical studies. Results In pulsed mode, for a 3 mm vein diameter, irrespective of the pullback distance (2, 5 or 7 mm, a minimum fluence of 15 J/cm is required to obtain a permanent damage of the intima. For a 5 mm vein diameter, 50 J/cm (15W-2s is required. In continuous mode, for a 3 mm and 5 mm vein diameter, respectively 65 J/cm and 100 J/cm are required to obtain a permanent damage of the vessel wall. Finally, the use of different wavelengths (810 nm or 980 nm played only a minor influence on these results. Discussion and conclusion The parameters
Mathematical Simulating Model of Phased-Array Antenna in Multifunction Array Radar
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
A mathematical simulating model of phased-array antenna in multifunction array radar has been approached in this paper, including the mathematical simulating model of plane phased-array pattern, the mathematical simulating model of directionality factor, the mathematical simulating model of array factor, the mathematical simulating model of array element factor and the mathematical simulating model of beam steering.
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 model of electrotaxis in osteoblastic cells.
Vanegas-Acosta, J C; Garzón-Alvarado, D A; Zwamborn, A P M
2012-12-01
Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF strengths and different configurations of both electrical and chemical stimuli. Accordingly, we found that the cell migration speed is described as the combination of an electrical and a chemical term. Cell migration is faster when both stimuli orient cell migration towards the same direction. In contrast, a reduced speed is obtained when the EF vector is opposed to the direction of the chemical stimulus. Numerical relations were obtained to quantify the cell migration speed at each configuration. Additional calculations for the cell colonization of a substrate also show mediation of the EF strength. Therefore, the term electro-osteoconduction is introduced to account the electrically induced cell colonization. Since numerical results compare favorably with experimental evidence, the model is suitable to be extended to other types of cells, and to numerically explore the influence of EF during wound healing. Copyright © 2012 Elsevier B.V. All rights reserved.
The Use of Models in Teaching Proof by Mathematical Induction
Ron, Gila; Dreyfus, Tommy
2004-01-01
Proof by mathematical induction is known to be conceptually difficult for high school students. This paper presents results from interviews with six experienced high school teachers, concerning the use of models in teaching mathematical induction. Along with creative and adequate use of models, we found explanations, models and examples that…
Mathematical Modelling of the Heald Shaft
Directory of Open Access Journals (Sweden)
Bílek Martin
2016-12-01
Full Text Available The manufacturers of weaving equipment recently endeavour to minimise the necessary designing plays in the weaving loom mechanisms. One of the mechanisms most exposed to stress is the shedding motion that defines the held-shaft stroke. Its end part is the heald shaft. The heald shaft constitutes a problematic assembly of the shedding motion. The design employed presently is characterised by dynamic impact loading caused by designing play in the suspension of healds into the heald shaft. During weaving cycle, the healds fly between the main beams of the heald shaft, producing a considerable force pulse. This paper is concerned with the description of dynamic behaviour of the existing design on the basis of mathematical modelling and verification of obtained results by means of experimental analysis.
Mathematical Modeling of Spiral Heat Exchanger
Directory of Open Access Journals (Sweden)
Probal Guha , Vaishnavi Unde
2014-04-01
Full Text Available Compact Heat Exchangers (CHEs are increasingly being used on small and medium scale industries. Due to their compact size and efficient design, they facilitate more efficient heat transfer. Better heat transfer would imply lesser fuel consumption for the operations of the plant, giving improvement to overall efficiency. This reduction in consumption of fuel is a step towards sustainable development. This report exclusively deals with the study the spiral heat exchanger.The design considerations for spiral heat exchanger is that the flow within the spiral has been assumed as flow through a duct and by using Shah London empirical equation for Nusselt number design parameters are further optimized.This is accompanied by a detailed energy balance to generate a concise mathematical model
Mathematical modelling on instability of shear fault
Institute of Scientific and Technical Information of China (English)
范天佑
1996-01-01
A study on mathematical modelling on instability of fault is reported.The fracture mechanics and fracture dynamics as a basis of the discussion,and the method of complex variable function (including the conformal mapping and approximate conformal mapping) are employed,and some analytic solutions of the problem in closed form are found.The fault body concept is emphasized and the characteristic size of fault body is introduced.The effect of finite size of the fault body and the effect of the fault propagating speed (especially the effect of the high speed) and their influence on the fault instability are discussed.These results further explain the low-stress drop phenomena observed in earthquake source.
Some Mathematical Models for ELM Signal
XIE, Hua-sheng
2012-01-01
There is no wide accepted theory for ELM (Edge Localized Mode) yet. Some fusion people feel that we may never get a final theory for ELM and H-mode, since which are too complicated (also related to the unsolved turbulence problem) and with at least three time scales. The only way out is using models. (This is analogous to that we believe quantum mechanics can explain chemistry and biology, but no one can calculate DNA structure from Schrodinger equation directly.) This manuscript gives some possible mathematical approaches to it. I should declare that these are just math toys for me yet. They may inspire to good understandings of ELM and H-mode, may not. Useful or useless, I don't know. One need not take too much care of it. Just for fun and enjoying different interesting ideas.
Mathematical Model for the Continuous Vacuum Drying
Institute of Scientific and Technical Information of China (English)
DAI Hui-liang
2002-01-01
An improved mathematical model for the continuous vacuum drying of highly viscous and heatsensitive foodstuffs was proposed, The process of continuous vacuum drying was presented as a moving boundary problem of moisture evaporation in cylindrical coordinates. Boundary condition of the first kind for the known functional dependence of the drying body surface temperature on time was considered. Finally, the appropriate system of differential equations was solved numerically and the values of drying rate, integral moisture content of the material, moving boundary position as well as temperature in any point of the material and at any moment time were obtained. This procedure was applied to continuous vacuum drying of foods such as natural cheese and fresh meat paste.
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.
The Concept of Model. What is Remarkable in Mathematical Models
Bezruchko, Boris P.; Smirnov, Dmitry A.
Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.
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 Modeling of Photochemical Air Pollution.
McRae, Gregory John
Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations. The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms. Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF(,6)) tracer experiments. Conventional models are employed for neutral and stable conditions. A new formulation for gaseous deposition fluxes
Mathematical modeling of biomass fuels formation process.
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.
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
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Building Mathematics Achievement Models in Four Countries Using TIMSS 2003
Wang, Ze; Osterlind, Steven J.; Bergin, David A.
2012-01-01
Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries…
A mathematical model of embodied consciousness.
Rudrauf, David; Bennequin, Daniel; Granic, Isabela; Landini, Gregory; Friston, Karl; Williford, Kenneth
2017-09-07
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 combines multisensory evidence with prior beliefs in memory and frames them by selecting points of view and perspectives according to preferences. The choice of projective frames governs how expectations are transformed by consciousness. Violations of expectation are encoded as free energy. Free energy minimization drives perspective taking, and controls the switch between perception, imagination and action. In the PCM, consciousness functions as an algorithm for the maximization of resilience, using projective perspective taking and imagination in order to escape local minima of free energy. The PCM can account for a variety of psychological phenomena: the characteristic spatial phenomenology of subjective experience, the distinctions and integral relationships between perception, imagination and action, the role of affective processes in intentionality, but also perceptual phenomena such as the dynamics of bistable figures and body swap illusions in virtual reality. It relates phenomenology to function, showing the computational advantages of consciousness. It suggests that changes of brain states from unconscious to conscious reflect the action of projective transformations and suggests specific neurophenomenological hypotheses about the brain, guidelines for designing artificial systems, and formal principles for psychology. Copyright © 2017 Elsevier Ltd. All rights reserved.
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...
A mathematical model of forgetting and amnesia
Directory of Open Access Journals (Sweden)
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.
Mathematical model I. Electron and quantum mechanics
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical model I. Electron and quantum mechanics
Directory of Open Access Journals (Sweden)
Nitin Ramchandra Gadre
2011-03-01
Full Text Available The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical modeling of Chikungunya fever control
Hincapié-Palacio, Doracelly; Ospina, Juan
2015-05-01
Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.
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...
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...
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).
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)
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...
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.
A basic mathematical and numerical model for gas injection
Molenaar, J.
1996-01-01
In this paper we discuss a mathematical model for gas storage processes. In addition we outline an approach for numerical simulations. The focus is on model assumptions and limitations with respect to the software to be developed.
A basic mathematical and numerical model for gas injection
J. Molenaar (Gijs)
1996-01-01
textabstractIn this paper we discuss a mathematical model for gas storage processes. In addition we outline an approach for numerical simulations. The focus is on model assumptions and limitations with respect to the software to be developed.
Generalized Mathematical Model for Hot Rolling Process of Plate
Institute of Scientific and Technical Information of China (English)
Zhenshan CUI; Bingye XU
2003-01-01
A generalized mathematical model is developed to predict the changes of temperature, rolling pressure, strain,strain rate, and austenite grain size for plate hot rolling and cooling processes. The model is established mainly by incorporating analytical an
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.…
A mathematical model of the Mafia game
Migdal, Piotr
2010-01-01
Mafia (also called Werewolf) is a party game. The participants are divided into two competing groups: citizens and a mafia. The objective is to eliminate the opponent group. The game consists of two consecutive phases (day and night) and a certain set of actions (e.g. lynching during day). The mafia members have additional powers (knowing each other, killing during night) whereas the citizens are more numerous. We propose a simple mathematical model of the game, which is essentially a pure death process with discrete time. We find closed-form formulas for mafia winning chances $w(n,m)$ as well as for evolution of the game. Moreover, we investigate discrete properties of results, as well as its continuous-time approximation. I turns out that a relatively small number of the mafia members $m$ (among $n$ players) give $50:50$ winning chances, i.e. $m\\approx\\sqrt{n}$. Furthermore, the game strongly depends on the parity of the total number of players.
A MATHEMATICAL MODELING OF CAMPUS INFORMATION SYSTEM
Directory of Open Access Journals (Sweden)
S. STALIN KUMAR
2016-07-01
Full Text Available An H-magic labeling in a H-decomposable graph G is a bijection f : V (G ∪ E(G → {1, 2, ..., p + q} such that for every copy H in the decomposition, \\sum\\limits_{v∈V (H}{f(v}+\\sum\\limits_{e∈E(H}{ f(e} is constant. f is said to be H-V -super magic if f(V (G = {1, 2, ..., p}. Suppose that V (G = U(G ∪ W(G with |U(G| = m and |W(G| = n. Then f is said to be H-V -super-strong magic labeling if f(U(G = {1, 2, ..., m} and f(W(G = {m + 1, m + 2, ...,(m + n = p}. A graph that admits a H-V -super-strong magic labeling is called a H-V -super-strong magic decomposable graph. In this paper, we pay our attention to provide a mathematical modeling of campus information system.
Mathematical modelling for nanotube bundle oscillators
Thamwattana, Ngamta; Cox, Barry J.; Hill, James M.
2009-07-01
This paper investigates the mechanics of a gigahertz oscillator comprising a nanotube oscillating within the centre of a uniform concentric ring or bundle of nanotubes. The study is also extended to the oscillation of a fullerene inside a nanotube bundle. In particular, certain fullerene-nanotube bundle oscillators are studied, namely C60-carbon nanotube bundle, C60-boron nitride nanotube bundle, B36N36-carbon nanotube bundle and B36N36-boron nitride nanotube bundle. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the fullerene and the nanotube bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques which provides considerable insight into the underlying mechanisms. The paper presents a synopsis of the major results derived in detail by the present authors in [1, 2].
A mathematical model of a computational problem solving system
Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan
2015-05-01
This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.
Wright, Vince
2014-01-01
Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…
Wright, Vince
2014-01-01
Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…
Typhoid transmission: a historical perspective on mathematical model development.
Bakach, Iurii; Just, Matthew R; Gambhir, Manoj; Fung, Isaac Chun-Hai
2015-11-01
Mathematical models of typhoid transmission were first developed nearly half a century ago. To facilitate a better understanding of the historical development of this field, we reviewed mathematical models of typhoid and summarized their structures and limitations. Eleven models, published in 1971 to 2014, were reviewed. While models of typhoid vaccination are well developed, we highlight the need to better incorporate water, sanitation and hygiene interventions into models of typhoid and other foodborne and waterborne diseases. Mathematical modeling is a powerful tool to test and compare different intervention strategies which is important in the world of limited resources. By working collaboratively, epidemiologists and mathematicians should build better mathematical models of typhoid transmission, including pharmaceutical and non-pharmaceutical interventions, which will be useful in epidemiological and public health practice.
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-
Mathematical Modelling for Micropiles Embedded in Salt Rock
Directory of Open Access Journals (Sweden)
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.
Application of Mathematical Modeling Activities in Costarican High School Education
Directory of Open Access Journals (Sweden)
Karen Porras-Lizano
2015-01-01
Full Text Available This paper describes the experience gained in implementing mathematical modeling activities as a methodological strategy in teaching issues such as proportions, with a group of eighth year of an academic-day-school, located in the province of San Jose, Costa Rica in 2012. Different techniques for gathering information were applied, such as participant observation and questionnaires. Among the relevant results are the cyclical development of mathematical thinking of students in the stages of mathematical modeling (description, manipulation, prediction and validation for solving the problem; developing of teamwork skills; and appreciation of mathematics as a useful and effective discipline. To resolve the activities proposed in this study, social interactions such as sharing information, thoughts and ideas, were generated, stimulating the zone of proximal development of the participating students. Likewise, the mathematical modeling activities allowed students to have a positive role in mathematics classes, stimulating, in turn, a different attitude compared to regular classes.
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.
Retrospective Study on Mathematical Modeling Based on Computer Graphic Processing
Zhang, Kai Li
Graphics & image making is an important field in computer application, in which visualization software has been widely used with the characteristics of convenience and quick. However, it was thought by modeling designers that the software had been limited in it's function and flexibility because mathematics modeling platform was not built. A non-visualization graphics software appearing at this moment enabled the graphics & image design has a very good mathematics modeling platform. In the paper, a polished pyramid is established by multivariate spline function algorithm, and validate the non-visualization software is good in mathematical modeling.
Mathematical Models for Room Air Distribution - Addendum
DEFF Research Database (Denmark)
Nielsen, Peter V.
1982-01-01
A number of different models on the air distribution in rooms are introduced. This includes the throw model, a model on penetration length of a cold wall jet and a model for maximum velocity in the dimensioning of an air distribution system in highly loaded rooms and shows that the amount of heat...
Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration
Warwick, Jon
2015-01-01
This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…
Mathematical Models for Room Air Distribution
DEFF Research Database (Denmark)
Nielsen, Peter V.
1982-01-01
A number of different models on the air distribution in rooms are introduced. This includes the throw model, a model on penetration length of a cold wall jet and a model for maximum velocity in the dimensioning of an air distribution system in highly loaded rooms and shows that the amount of heat...
Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration
Warwick, Jon
2015-01-01
This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…
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…
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
Some Aspects of Mathematical Model of Collaborative Learning
Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu
2012-01-01
There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…
Mathematical Model of Asynchronous Motor with Embedded Combined Braking Device
Directory of Open Access Journals (Sweden)
V. Solencov
2013-01-01
Full Text Available The paper presents a conclusion of a mathematical model pertaining to asynchronous motor with embedded combined braking device on the basis of electromechanical brake and electromagnetic slip coupling. The mathematical model has been obtained in an orthogonal coordinate system a, b, which is fixed with respect to the asymmetric part of the asynchronous motor with embedded combined braking device. The model makes it possible to investigate transient processes in various asynchronous motors with embedded braking devices.
Mathematical Model of Extrinsic Blood Coagulation Cascade Dynamic System
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The blood coagulation system is very important to life. This paper presents a mathematical blood coagulation model for the extrinsic pathway. This model simulates clotting factor VIII, which plays an important role in the coagulation mechanism. The mathematical model is used to study the equilibrium stability, orbit structure, attractors and global stability behavior, with conclusions in accordance with the physiological phenomena. Moreover, the results provide information about blood related illnesses, which can be used for further study of the coagulation mechanism.
The mathematical and computer modeling of the worm tool shaping
Panchuk, K. L.; Lyashkov, A. A.; Ayusheev, T. V.
2017-06-01
Traditionally mathematical profiling of the worm tool is carried out on the first T. Olivier method, known in the theory of gear gearings, with receiving an intermediate surface of the making lath. It complicates process of profiling and its realization by means of computer 3D-modeling. The purpose of the work is the improvement of mathematical model of profiling and its realization based on the methods of 3D-modeling. Research problems are: receiving of the mathematical model of profiling which excludes the presence of the making lath in it; realization of the received model by means of frame and superficial modeling; development and approbation of technology of solid-state modeling for the solution of the problem of profiling. As the basic, the kinematic method of research of the mutually envelope surfaces is accepted. Computer research is executed by means of CAD based on the methods of 3D-modeling. We have developed mathematical model of profiling of the worm tool; frame, superficial and solid-state models of shaping of the mutually enveloping surfaces of the detail and the tool are received. The offered mathematical models and the technologies of 3D-modeling of shaping represent tools for theoretical and experimental profiling of the worm tool. The results of researches can be used at design of metal-cutting tools.
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
influence of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...... parts of brain networks can be overlooked in pursuing maximization of prediction accuracy. This supports the view that the quality of spatial patterns extracted from models cannot be assessed purely by focusing on prediction accuracy. Our results instead suggest that model regularization parameters must...
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.
Mathematical modeling of urea transport in the kidney.
Layton, Anita T
2014-01-01
Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.
Deductive Nomological Model and Mathematics: Making Dissatisfaction more Satisfactory
Directory of Open Access Journals (Sweden)
Daniele Molinini
2014-06-01
Full Text Available The discussion on mathematical explanation has inherited the same sense of dissatisfaction that philosophers of science expressed, in the context of scientific explanation, towards the deductive-nomological model. This model is regarded as unable to cover cases of bona fide mathematical explanations and, furthermore, it is largely ignored in the relevant literature. Surprisingly, the reasons for this ostracism are not sufficiently manifest. In this paper I explore a possible extension of the model to the case of mathematical explanations and I claim that there are at least two reasons to judge the deductive-nomological picture of explanation as inadequate in that context.
Economic-mathematical methods and models under uncertainty
Aliyev, A G
2013-01-01
Brief Information on Finite-Dimensional Vector Space and its Application in EconomicsBases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector SpacePiecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector SpacePiecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a PlaneBases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Comp
A New Activity-Based Cost (ABC) Mathematical Model
Institute of Scientific and Technical Information of China (English)
JIANG Shuo; SONG Lei
2003-01-01
Along with the product price competition growing intensely, it is apparently important for reasonably distributing and counting cost. But, in sharing indirect cost, traditional cost accounting unveils the limitations increasingly, especially in authenticity of cost information. And the accounting theory circles and industry circles begin seeking one kind of new accurate cost calculation method, and the activity-based cost (ABC) method emerges as the times require. In this paper, we will build its mathematical model by the basic principle of ABC, and will improve its mathematical model further. We will establish its comparison mathematical model and make the ABC method go a step further to its practical application.
Mathematics of tsunami: modelling and identification
Krivorotko, Olga; Kabanikhin, Sergey
2015-04-01
Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of
Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors
Directory of Open Access Journals (Sweden)
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 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.
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)
Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent
2017-01-01
Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage…
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…
An Assessment Model for Proof Comprehension in Undergraduate Mathematics
Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron
2012-01-01
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…
Energy Technology Data Exchange (ETDEWEB)
Gorbatov, P.A.; Plyungin, A.V. (Donetskii Politekhnicheskii Institut (USSR))
1990-12-01
Presents calculation methods and mathematical models of dynamic processes that occur in feed systems of cutter loaders with rigid pulling elements. Characteristics of dynamic interactions between driving wheels and the working section of the pulling system are taken into account. Mathematical models are given that describe the dynamic operation of the feed system. A method for calculation of a hydraulic vibration compensating system and its mathematical model is presented. Effectiveness of the vibration compensating system is discussed. 2 refs.
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
Mathematical modeling of a rotary hearth coke calciner
Directory of Open Access Journals (Sweden)
Hilde C. Meisingset
1995-10-01
Full Text Available A mathematical model of a rotary hearth coke calciner is developed. The model is based on first principles including the most important dynamic phenomena. The model is a thermodynamic model involving heat and mass transfer and chemical reactions. Fundamental mass and energy balance equations for the coke phase, the gas phase and the lining are formulated. For the gas phase, a stationary model is used. The equations are solved numerically, and simulated temperature profiles are shown in this paper.
Mathematical modeling of the human knee joint
Energy Technology Data Exchange (ETDEWEB)
Ricafort, Juliet [Univ. of Southern California, Los Angeles, CA (United States). Dept. of Biomedical Engineering
1996-05-01
A model was developed to determine the forces exerted by several flexor and extensor muscles of the human knee under static conditions. The following muscles were studied: the gastrocnemius, biceps femoris, semitendinosus, semimembranosus, and the set of quadricep muscles. The tibia and fibula were each modeled as rigid bodies; muscles were modeled by their functional lines of action in space. Assumptions based on previous data were used to resolve the indeterminacy.
Mathematical modeling of electromechanical processes in a brushless DC motor
Directory of Open Access Journals (Sweden)
V.I. Tkachuk
2014-03-01
Full Text Available On the basis of initial assumptions, a mathematical model that describes electromechanical processes in a brushless DC electric motor with a salient-pole stator and permanent-magnet excitation is created.
mathematical model for direct evaporative space cooling systems
African Journals Online (AJOL)
eobe
MATHEMATICAL MODEL FOR DIRECT EVAPORATIVE SPACE COOLING. SYSTEMS ... Water is the working fluid in evaporative cooling thus it is ..... co o lin g efficien cy (%. ) Time (hrs) predicted experimental. 0. 10. 20. 30. 40. 50. 60. 70. 80.
A Local Mathematical Model for EPR-Experiments
Philipp, W.; Hess, K.
2002-01-01
In this paper we give a detailed and simplified version of our original mathematical model published first in the Proceedings of the National Academy of Science. We hope that this will clarify some misinterpretations of our original paper.
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,...
RECENT MATHEMATICAL STUDIES IN THE MODELING OF OPTICS AND ELECTROMAGNETICS
Institute of Scientific and Technical Information of China (English)
Gang Bao
2004-01-01
This work is concerned with mathematical modeling, analysis, and computation of optics and electromagnetics, motivated particularly by optical and microwave applications.The main technical focus is on Maxwell's equations in complex linear and nonlinear media.
The Mathematical Concept of Set and the 'Collection' Model.
Fischbein, Efraim; Baltsan, Madlen
1999-01-01
Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)
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
The mathematical model realization algorithm of high voltage cable
2006-01-01
At mathematical model realization algorithm is very important to know the account order of necessary relations and how it presents. Depending of loads or signal sources connection in selected points of mathematical model its very important to know as to make the equations in this point that it was possible to determine all unknown variables in this point. The number of equations which describe this point must to coincide with number of unknown variables, and matrix which describes factor...
Mathematical Model of Moving Heat-Transfer Agents
Directory of Open Access Journals (Sweden)
R. I. Yesman
2010-01-01
Full Text Available A mathematical model of moving heat-transfer agents which is applied in power systems and plants has been developed in the paper. A paper presents the mathematical model as a closed system of differential convective heat-transfer equations that includes a continuity equation, a motion equation, an energy equation.Various variants of boundary conditions on the surfaces of calculation flow and heat exchange zone are considered in the paper.
Mathematical Modeling for Simulation of Nuclear Reactor Analysis
Salah Ud-Din Khan; Shahab Ud-Din Khan
2013-01-01
In this paper, we have developed a mathematical model for the nuclear reactor analysis to be implemented in the nuclear reactor code. THEATRe is nuclear reactor analysis code which can only work for the cylindrical type fuel reactor and cannot applicable for the plate type fuel nuclear reactor. Therefore, the current studies encompasses on the modification of THEATRe code for the plate type fuel element. This mathematical model is applicable to the thermal analysis of the reactor which is ver...
Mathematical and computational modeling in biology at multiple scales
Tuszynski, Jack A; Winter, Philip; White, Diana; Tseng, Chih-Yuan; Sahu, Kamlesh K.; Gentile, Francesco; Spasevska, Ivana; Omar, Sara Ibrahim; Nayebi, Niloofar; Churchill, Cassandra DM; Klobukowski, Mariusz; El-Magd, Rabab M Abou
2014-01-01
A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields f...
Mathematical modeling of a V-stack piezoelectric aileron actuation
Directory of Open Access Journals (Sweden)
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.
MATHEMATIC MODEL FOR SITY BUS SCHEDULING IN YOGYAKARTA
Directory of Open Access Journals (Sweden)
Sahid Sahid
2016-05-01
Full Text Available Various methods can be used to construct a mathematical model of the transportation problems. One model that can be used is a linear model. Several studies have used a linear model to get the schedule and the optimal route of bus trips. This research will build a mathematical model of a city bus transportation problems in DIY using linear models. Linear model is built to get the condition density city bus passengers on shifts respectively that morning, noon, and evening. After finding a suitable model, applied to the bus passengers data in Yogyakarta. From these results it can be seen the optimum conditions in terms of density, because the condition of the city bus at this time that quiet enthusiasts. Besides, the optimum density at each shift in the morning is 11 passengers, 10 passengers during the day, and evening 9 passengers. Keywords: transportation problems, the linear model, the optimal route, density
Undergraduate Research: Mathematical Modeling of Mortgages
Choi, Youngna; Spero, Steven
2010-01-01
In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current…
A Mathematical Model for Freeze-Drying
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Based on the experiments on freeze-drying carrot and potato slabs, the effects of some parameters, such as heating temperature and pressure on the freeze-drying process are examined. A simple model of freeze-drying is established to predict drying time and the mass variations of materials during the drying. The experimental results agree well with those calculated by the model.
Mathematical modelling of fractional order circuits
Moreles, Miguel Angel
2016-01-01
In this work a classical derivation of fractional order circuits models is presented. Generalized constitutive equations in terms of fractional Riemann-Liouville derivatives are introduced in the Maxwell's equations. Next the Kirchhoff voltage law is applied in a RCL circuit configuration. A fractional differential equation model is obtained with Caputo derivatives. Thus standard initial conditions apply.
A Mathematical model of copper corrosion
Clarelli, Fabrizio; Natalini, Roberto
2012-01-01
A new partial differential model for monitoring and detecting copper corrosion products (mainly brochantite and cuprite) is proposed to provide predictive tools suitable for describing the evolution of damage induced on bronze specimens by sulfur dioxide (SO_2) pollution. This model is characterized by the movement of a double free boundary. Numerical simulations show a nice agreement with experimental result.
Mathematical Modelling of Laser/Material Interactions.
1983-11-25
translated to the model input. Even an experimental mode print can also be digitalised for the model. In trying to describe high order modes matliematically...4. Mazumder J. Steen W.M. "Welding of Ti 6al - 4V by continuous wave CO2 laser". Metal construction Sept. 1980 pp423 - 427. 5. Kogelnik H, Li.T Proc
Mathematical Models of Beam and Rails for the Simulation Programs
Directory of Open Access Journals (Sweden)
V. A. Trudonoshin
2015-01-01
Full Text Available The article considers a mathematical model of the beam adapted for use in general-purpose software systems to analyze dynamic characteristics. The elastic properties of the beam tension, bending and torsion are taken into account. Such a model significantly expands the functional capabilities of the complexes. The mathematical model of the beam designed for the finite element method is taken as a basis. Then its adaptation is carried out taking into account the beam joint to the arbitrary points of a rigid solid, thereby having a model suitable to analyze objects with lumped parameters. Beam parameters are the material parameters, the geometric characteristics, and the coordinates of joint points to the solids.The paper describes in detail the algorithm of computations performed at each step of numerical integration of the systems of ordinary differential equations, and presents an equivalent diagram of the mathematical model of the beam. Mathematical models of elastic rail guides, cylindrical and prismatic, derived from the mathematical model of the beam are more functional compared to the models based on the kinematic equations.The prismatic rail guide (V-guide, unlike the beam, does not counteract the translational motion of solids along it, i.e. only works in torsion and bending, and a deforming part of the rail guide length is variable. The cylindrical rail guide works in bending only. These differences can be easily implemented by modifying the equations of the mathematical model of the beam. Using these models allows us to connect solids by two or more rail guides, and it does not lead to the degeneration of the Jacobi matrix (unlike models based on kinematic equations. The models are implemented in PA8 and PA9 software and methodological support complexes for analysis of dynamic objects developed at the Department of CAD in Bauman MSTU.
The possibilities of a modelling perspective for school mathematics
Directory of Open Access Journals (Sweden)
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.
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 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
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...
EVALUATION OF PLANING CRAFT MANEUVERABILITY USING MATHEMATICAL MODELING
Directory of Open Access Journals (Sweden)
Sajad Hajizadeh
2016-03-01
Full Text Available Ship transportation is increasing globally as is risk of collision especially in congested areas is a main concern. Numerical modeling method is major simulation method to predict ship maneuverability. Ship maneuvering in calm water is an important topic to avoid collisions and leads to safe navigation. Therefore reliable ship maneuvering simulations are required for incident analysis and prevention. In recent time within the research community orientated towards ship hydrodynamics an increasing attention has been paid to simultaneous solution of the maneuvering of planing ship problem. The maneuverability of planing crafts has been the subject of many research projects during the last few decades. To assess the maneuverability of planing crafts at the early design stage, reliable simulation models are required. Traditionally, these tools have used empiric descriptions of the forces and moments on the planing craft’s hull. Ship maneuvering calculations, horizontal plane motion control and development of maneuvering simulators need a mathematical description of ship maneuvering. In the recent years, different mathematical models are suggested for maneuvering of displacement vessels that are capable of estimation of vessel maneuvers with acceptable precision. But simulation of planing craft maneuverability through mathematical model is not common yet and is the subject of future research. Maneuvering of planing crafts is influenced greatly by action of rudder. But research efforts have been to include the rudder action in the mathematical models of planing ship maneuvering. In this paper a mathematical model is developed for planing craft maneuvering that includes the rudder forces and moments. Different maneuvers are executed through the mathematical model. Simulations are validated by model tests. Finally the influence of rudder angle on maneuverability of planing ship is studied. The mathematical model and hydrodynamic coefficients presented
SARS epidemical forecast research in mathematical model
Institute of Scientific and Technical Information of China (English)
DING Guanghong; LIU Chang; GONG Jianqiu; WANG Ling; CHENG Ke; ZHANG Di
2004-01-01
The SIJR model, simplified from the SEIJR model, is adopted to analyze the important parameters of the model of SARS epidemic such as the transmission rate, basic reproductive number. And some important parameters are obtained such as the transmission rate by applying this model to analyzing the situation in Hong Kong, Singapore and Canada at the outbreak of SARS. Then forecast of the transmission of SARS is drawn out here by the adjustment of parameters (such as quarantined rate) in the model. It is obvious that inflexion lies on the crunode of the graph, which indicates the big difference in transmission characteristics between the epidemic under control and not under control. This model can also be used in the comparison of the control effectiveness among different regions. The results from this model match well with the actual data in Hong Kong, Singapore and Canada and as a by-product, the index of the effectiveness of control in the later period can be acquired. It offers some quantitative indexes, which may help the further research in epidemic diseases.
Modelling Mathematical Reasoning in Physics Education
Uhden, Olaf; Karam, Ricardo; Pietrocola, Mauricio; Pospiech, Gesche
2012-01-01
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…
Mathematics Teacher TPACK Standards and Development Model
Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis
2009-01-01
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…
Mathematical models to characterize early epidemic growth: A review
Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile
2016-09-01
There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.
An evaluation of mathematical models for predicting skin permeability.
Lian, Guoping; Chen, Longjian; Han, Lujia
2008-01-01
A number of mathematical models have been proposed for predicting skin permeability, mostly empirical and very few are deterministic. Early empirical models use simple lipophilicity parameters. The recent trend is to use more complicated molecular structure descriptors. There has been much debate on which models best predict skin permeability. This article evaluates various mathematical models using a comprehensive experimental dataset of skin permeability for 124 chemical compounds compiled from various sources. Of the seven models compared, the deterministic model of Mitragotri gives the best prediction. The simple quantitative structure permeability relationships (QSPR) model of Potts and Guy gives the second best prediction. The two models have many features in common. Both assume the lipid matrix as the pathway of transdermal permeation. Both use octanol-water partition coefficient and molecular size. Even the mathematical formulae are similar. All other empirical QSPR models that use more complicated molecular structure descriptors fail to provide satisfactory prediction. The molecular structure descriptors in the more complicated QSPR models are empirically related to skin permeation. The mechanism on how these descriptors affect transdermal permeation is not clear. Mathematically it is an ill-defined approach to use many colinearly related parameters rather than fewer independent parameters in multi-linear regression.
Physical and Mathematical Modeling in Experimental Papers.
Möbius, Wolfram; Laan, Liedewij
2015-12-17
An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations.
Environmental factors in breast cancer invasion: a mathematical modelling review.
Simmons, Alex; Burrage, Pamela M; Nicolau, Dan V; Lakhani, Sunil R; Burrage, Kevin
2017-02-01
This review presents a brief overview of breast cancer, focussing on its heterogeneity and the role of mathematical modelling and simulation in teasing apart the underlying biophysical processes. Following a brief overview of the main known pathophysiological features of ductal carcinoma, attention is paid to differential equation-based models (both deterministic and stochastic), agent-based modelling, multi-scale modelling, lattice-based models and image-driven modelling. A number of vignettes are presented where these modelling approaches have elucidated novel aspects of breast cancer dynamics, and we conclude by offering some perspectives on the role mathematical modelling can play in understanding breast cancer development, invasion and treatment therapies. Copyright © 2016 Royal College of Pathologists of Australasia. Published by Elsevier B.V. All rights reserved.
System and mathematical modeling of quadrotor dynamics
Goodman, Jacob M.; Kim, Jinho; Gadsden, S. Andrew; Wilkerson, Stephen A.
2015-05-01
Unmanned aerial systems (UAS) are becoming increasingly visible in our daily lives; and range in operation from search and rescue, monitoring hazardous environments, and to the delivery of goods. One of the most popular UAS are based on a quad-rotor design. These are typically small devices that rely on four propellers for lift and movement. Quad-rotors are inherently unstable, and rely on advanced control methodologies to keep them operating safely and behaving in a predictable and desirable manner. The control of these devices can be enhanced and improved by making use of an accurate dynamic model. In this paper, we examine a simple quadrotor model, and note some of the additional dynamic considerations that were left out. We then compare simulation results of the simple model with that of another comprehensive model.
Mathematical Model For Engineering Analysis And Optimization
Sobieski, Jaroslaw
1992-01-01
Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.
Mathematical modelling of paper degradation in books
Nimmo, A J
2015-01-01
Paper cannot be prevented from degrading and does not necessarily degrade uniformly across its volume. It has been established that as paper degrades, VOCs (Volatile Organic Compounds) are produced. This body of work studies paper degradation with respect to the role VOCs play. The thesis investigates how a VOC a ecting the paper's acidity can in turn a ect the degradation rate and through modelling the VOC concentration pro le, the degradation pro le is found. To create the model from a chem...
Mathematical Model For Engineering Analysis And Optimization
Sobieski, Jaroslaw
1992-01-01
Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.
Directory of Open Access Journals (Sweden)
Universidade Estadual do Oeste do Paraná
2012-12-01
Full Text Available This paper presents an analysis of scientific communications published in the IV Mathematical Modeling National Conference (CNMEM in the Brazilian abbreviation, which took place in 2005. The analysis consists of a meta-analytical and content qualitative approach, aided by the software Atlas T.i. The data collected was originated in the above mentioned conference which is the first of the three which will be analyzed in the study that aims to unveil the research on Mathematical Modeling in Brazil. The categories established in this paper and which will be interpreted are: a Meta-study on Mathematics Modeling; b Modeling application; c Articulation between Modeling and other theories, and d Modeling and teachers education.
Mathematical modeling of polymer electrolyte fuel cells
Sousa, Ruy; Gonzalez, Ernesto R.
Fuel cells with a polymer electrolyte membrane have been receiving more and more attention. Modeling plays an important role in the development of fuel cells. In this paper, the state-of-the-art regarding modeling of fuel cells with a polymer electrolyte membrane is reviewed. Modeling has allowed detailed studies concerning the development of these cells, e.g. in discussing the electrocatalysis of the reactions and the design of water-management schemes to cope with membrane dehydration. Two-dimensional models have been used to represent reality, but three-dimensional models can cope with some important additional aspects. Consideration of two-phase transport in the air cathode of a proton exchange membrane fuel cell seems to be very appropriate. Most fuel cells use hydrogen as a fuel. Besides safety concerns, there are problems associated with production, storage and distribution of this fuel. Methanol, as a liquid fuel, can be the solution to these problems and direct methanol fuel cells (DMFCs) are attractive for several applications. Mass transport is a factor that may limit the performance of the cell. Adsorption steps may be coupled to Tafel kinetics to describe methanol oxidation and methanol crossover must also be taken into account. Extending the two-phase approach to the DMFC modeling is a recent, important point.
The development of mathematical creativity through model-eliciting activities
Directory of Open Access Journals (Sweden)
Helena M. Wessels
2012-03-01
Full Text Available The ability to think creatively and solve problems is regarded as crucial for economic and personal success. The traditional approach in classrooms is not conducive to mathematical creativity, and prospective teachers should be exposed to alternative problem solving activities through which mathematical knowledge, competencies and creativity can be developed. Research studies have pointed out the possibilities and successes of a modelling approach in which complex, open problems or model-eliciting problems are used to develop meaningful mathematical knowledge and prepare learners for everyday life, as well as for tertiary studies and their occupations. Model-eliciting activities (MEAs do not only develop mathematical knowledge, but also creativity. Five hundred and one preservice Foundation Phase teachers completed different model-eliciting activities (MEAs in a longitudinal project over a period of two years. The purpose was to develop and consolidate their own mathematical knowledge, and at the same time develop creativity and modelling competencies. The ultimate purpose of the project is to prepare preservice teachers to use mathematical modelling to develop creativity in young children aged six to nine. Through solving MEAs learners also build and consolidate their mathematical knowledge and improve their own problem-solving abilities. A framework with four criteria for the identification of creativity was successfully used to evaluate levels of creativity in the solutions offered to the MEAs. Preservice teachers’ final models displayed reasonably consistent levels of creativity regarding the four criteria. Their willingness to solve MEAs and create multiple, original and useful – therefore creative – solutions also increased over the period of their exposure to modelling tasks.
Mathematically modelling proportions of Japanese populations by industry
Hirata, Yoshito
2016-10-01
I propose a mathematical model for temporal changes of proportions for industrial sectors. I prove that the model keeps the proportions for the primary, the secondary, and the tertiary sectors between 0 and 100% and preserves their total as 100%. The model fits the Japanese historical data between 1950 and 2005 for the population proportions by industry very well. The model also predicts that the proportion for the secondary industry becomes negligible and becomes less than 1% at least around 2080.
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.
Murata, Aki; Kattubadi, Sailaja
2012-01-01
In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…
Economic mathematical methods and forecasting models
K. Karpovska-Skoryk
2000-01-01
In the article the questions of the expert system, based on the fuzzy mathematics, are discussed. It is pointed out that usage of such a system for medical insurance in the conditions of the Ukrainian economy is very convenient.
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 ...
[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 and Numerical Modeling in Maritime Geomechanics
Directory of Open Access Journals (Sweden)
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 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.
Invention software support by integrating function and mathematical modeling
Chechurin, L.S.; Wits, Wessel Willems; Bakker, H.M.
2015-01-01
New idea generation is imperative for successful product innovation and technology development. This paper presents the development of a novel type of invention support software. The support tool integrates both function modeling and mathematical modeling, thereby enabling quantitative analyses on a
Invention software support by integrating function and mathematical modeling
Chechurin, L.S.; Wits, W.W.; Bakker, H.M.
2015-01-01
New idea generation is imperative for successful product innovation and technology development. This paper presents the development of a novel type of invention support software. The support tool integrates both function modeling and mathematical modeling, thereby enabling quantitative analyses on a
Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.
Millat, Thomas; Winzer, Klaus
2017-03-01
Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the 'evolution' of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.
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.
Applicability of mathematical modeling to problems of environmental physiology
White, Ronald J.; Lujan, Barbara F.; Leonard, Joel I.; Srinivasan, R. Srini
1988-01-01
The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.
The Singing Wineglass: An Exercise in Mathematical Modelling
Voges, E. L.; Joubert, S. V.
2008-01-01
Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…
Use of mathematical modeling in nuclear measurements projects
Energy Technology Data Exchange (ETDEWEB)
Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A. [AREVA/CANBERRA Nuclear Measurements Business Unit, Saint Quentin-en-Yvelines 78182 (France); Chany, P. [AREVA/BE Nuclear Sites Value Development AREVA NC Marcoule, BP 76170, 30206 Bagnols Sur Ceze (France); Devita, A. [AREVA/BE MELOX, BP 124, 30206 Bagnols Sur Ceze (France)
2011-07-01
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)
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
Analysis of rear end impact using mathematical human modelling
Happee, R.; Meijer, R.; Horst, M.J. van der; Ono, K.; Yamazaki, K.
2000-01-01
At TNO an omni-directional mathematical human body model has been developed. Until now this human model has been validated for frontal and lateral loading using response data of volunteer and post mortem human subject (PMHS) sled tests. For rearward loading it has been validated for high speed impac
Mathematical modelling in blood coagulation : simulation and parameter estimation
W.J.H. Stortelder (Walter); P.W. Hemker (Piet); H.C. Hemker
1997-01-01
textabstractThis paper describes the mathematical modelling of a part of the blood coagulation mechanism. The model includes the activation of factor X by a purified enzyme from Russel's Viper Venom (RVV), factor V and prothrombin, and also comprises the inactivation of the products formed. In this
Metaphors and Models in Translation between College and Workplace Mathematics
Williams, Julian; Wake, Geoff
2007-01-01
We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…
Metaphors and Models in Translation between College and Workplace Mathematics
Williams, Julian; Wake, Geoff
2007-01-01
We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…
Mathematical modeling of steel fiber concrete under dynamic impact
Belov, N. N.; Yugov, N. T.; Kopanitsa, D. G.; Kopanitsa, G. D.; Yugov, A. A.; Shashkov, V. V.
2015-01-01
This paper introduces a continuum mechanics mathematical model that describes the processes of deformation and destruction of steel-fiber-concrete under a shock wave impact. A computer modeling method was applied to study the processes of shock wave impact of a steel cylindrical rod and concrete and steel fiber concrete plates. The impact speeds were within 100-500 m/s.
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...
A Mathematical Model for Comparing Holland's Personality and Environmental Codes.
Kwak, Junkyu Christopher; Pulvino, Charles J.
1982-01-01
Presents a mathematical model utilizing three-letter codes of personality patterns determined from the Self Directed Search. This model compares personality types over time or determines relationships between personality types and person-environment interactions. This approach is consistent with Holland's theory yet more comprehensive than one- or…
Analysis of mathematical model for micromechanical vibratory wheel gyroscope
Institute of Scientific and Technical Information of China (English)
LUO Yue-sheng; FAN Chong-jin; TAN Zhen-fan
2003-01-01
By the sketch of structure of MVWG,the working laws of this kind of gyroscope were explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic working laws of MVWG the model was simplified.Under the conditions of the three axial direction rotations and general rotation,the mathematical model was resolved.And finally by the solutions, the working laws of the gyroscope, the working disparity among all sorts of gyrations and the influences from the gyrations in the axial directions were analysed.
Predictive control applied to an evaporator mathematical model
Directory of Open Access Journals (Sweden)
Daniel Alonso Giraldo Giraldo
2010-07-01
Full Text Available This paper outlines designing a predictive control model (PCM applied to a mathematical model of a falling film evaporator with mechanical steam compression like those used in the dairy industry. The controller was designed using the Connoisseur software package and data gathered from the simulation of a non-linear mathematical model. A control law was obtained from minimising a cost function sublect to dynamic system constraints, using a quadratic programme (QP algorithm. A linear programming (LP algorithm was used for finding a sub-optimal operation point for the process in stationary state.
Dependability breakeven point mathematical model for production - quality strategy support
Vilcu, Adrian; Verzea, Ion; Chaib, Rachid
2016-08-01
This paper connects the field of dependability system with the production-quality strategies through a new mathematical model based on breakeven points. The novelties consist in the identification of the parameters of dependability system which, in safety control, represents the degree to which an item is capable of performing its required function at any randomly chosen time during its specified operating period disregarding non-operation related influences, as well as the analysis of the production-quality strategies, defining a mathematical model based on a new concept - dependability breakeven points, model validation on datasets and shows the practical applicability of this new approach.
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
Mathematical model of layered metallurgical furnaces and units
Shvydkiy, V. S.; Spirin, N. A.; Lavrov, V. V.
2016-09-01
The basic approaches to mathematical modeling of the layered steel furnaces and units are considered. It is noted that the particular importance have the knowledge about the mechanisms and physical nature of processes of the charge column movement and the gas flow in the moving layer, as well as regularities of development of heat- and mass-transfer in them. The statement and mathematical description of the problem solution targeting the potential gas flow in the layered unit of an arbitrary profile are presented. On the basis of the proposed mathematical model the software implementation of information-modeling system of BF gas dynamics is carried out. The results of the computer modeling of BF non-isothermal gas dynamics with regard to the cohesion zone, gas dynamics of the combustion zone and calculation of hot-blast stoves are provided
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.
What Is Known about Elementary Grades Mathematical Modelling
Directory of Open Access Journals (Sweden)
Micah S. Stohlmann
2016-01-01
Full Text Available Mathematical modelling has often been emphasized at the secondary level, but more research is needed at the elementary level. This paper serves to summarize what is known about elementary mathematical modelling to guide future research. A targeted and general literature search was conducted and studies were summarized based on five categories: content of mathematical modelling intervention, assessment data collected, unit of analysis studied, population, and effectiveness. It was found that there were three main units of analysis into which the studies could be categorized: representational and conceptual competence, models created, and student beliefs. The main findings from each of these units of analysis are discussed along with future research that is needed.
Sullivan, A L
2007-01-01
In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or ...
Physical and mathematical modelling of extrusion processes
DEFF Research Database (Denmark)
Arentoft, Mogens; Gronostajski, Z.; Niechajowics, A.
2000-01-01
The main objective of the work is to study the extrusion process using physical modelling and to compare the findings of the study with finite element predictions. The possibilities and advantages of the simultaneous application of both of these methods for the analysis of metal forming processes...
A Cognitive Model of College Mathematics Placement
1989-08-01
study focused on the precalculus -- calculus placement decision. The Cognitive model uses novel, or analysis level, placement test items in an attempt to...relative to the requirements of a precalculus course. Placement test scores may be partitioned to give analysis and non-analysis subtest scores which can...67 5.1.1 1989 Intercorrelations ....................................................................... 67 5.1.2 1989 Precalculus -Calculus
MATHEMATICAL MODELING OF INFRARED MILK PASTEURIZATION
Directory of Open Access Journals (Sweden)
S. T. Antipov
2013-01-01
Full Text Available Based on the model representation of the process of pasteurization of milk infrared patterns of change in temperature of the product in the heating zone with the heat flows of different nature were obtained. The changes in the basic performance of the quartz oscillator during operation were also obtained.
Mathematical Models for Camouflage Pattern Assessment
2013-04-01
and NL/MSTV provide superior results to local models by better recovering textures and large missing regions. 5. NL/MSTV reconstructs images best in...Un esempio di gamma-convergenza. Bollettino della Unione Matematica Italiana B, 5-14:285299, 1977. C.5.1 [19] David Mumford and Jayant Shah. Optimal
Mathematical Model of Porous Medium Dynamics
Gerschuk, Peotr; Sapozhnikov, Anatoly
1999-06-01
Semiempirical model describing porous material strains under pulse mechanical and thermal loadings is proposed. Porous medium is considered as continuous one but with special form of pressure dependence upon strain. This model takes into account principal features of porous materials behavior which can be observed when the material is strained in dynamic and static experiments ( non-reversibility of large strains, nonconvexity of loading curve). Elastoplastic properties of porous medium, its damages when it is strained and dynamic fracture are also taken into account. Dispersion of unidirectional motion caused by medium heterogeneity (porousness) is taken into acount by introducing the physical viscosity depending upon pores size. It is supposed that at every moment of time pores are in equilibrium with pressure i.e. kinetic of pores collapse is not taken into account. The model is presented by the system of differential equations connecting pressure and energy of porous medium with its strain. These equations close system of equations of motion and continuity which then is integrated numerically. The proposed model has been tested on carbon materials and porous copper . Results of calculation of these materials shock compressing are in satisfactory agreement with experimental data. Results of calculation of thin plate with porous copper layer collision are given as an illustration.
Mathematical Models Light Up Plant Signaling
Chew, Y.H.; Smith, R.W.; Jones, H.J.; Seaton, D.D.; Grima, R.; Halliday, K.J.
2014-01-01
Plants respond to changes in the environment by triggering a suite of regulatory networks that control and synchronize molecular signaling in different tissues, organs, and the whole plant. Molecular studies through genetic and environmental perturbations, particularly in the model plant Arabidopsis
Potential of mathematical modeling in fruit quality
African Journals Online (AJOL)
ONOS
2010-01-18
Jan 18, 2010 ... estimate seasonal changes in quality traits as fruit size, dry matter, water content and the concentration of sugars and ... The global goodness-of-fit of a model is computed by averaging the ... into account climate variables such as radiation, salinity, .... and on exponential light extinction (Beer-Lambert Law).
Using Archeological Data to Model Mathematics
Yanik, H. Bahadir; Kurz, Terri L.; Memis, Yasin
2014-01-01
The purpose of this investigation is to describe an implementation of a modeling task using mock data from an ancient archeological find. Students discover the relationship between the height of a person and his or her stride length. Qualitative data from student discussions document thinking and reasoning.
Mathematical Models Light Up Plant Signaling
Chew, Y.H.; Smith, R.W.; Jones, H.J.; Seaton, D.D.; Grima, R.; Halliday, K.J.
2014-01-01
Plants respond to changes in the environment by triggering a suite of regulatory networks that control and synchronize molecular signaling in different tissues, organs, and the whole plant. Molecular studies through genetic and environmental perturbations, particularly in the model plant Arabidopsis
Physical and mathematical modelling of extrusion processes
DEFF Research Database (Denmark)
Arentoft, Mogens; Gronostajski, Z.; Niechajowics, A.
2000-01-01
The main objective of the work is to study the extrusion process using physical modelling and to compare the findings of the study with finite element predictions. The possibilities and advantages of the simultaneous application of both of these methods for the analysis of metal forming processes...
Managing mathematical modelling by guiding and monitoring
Scholten, H.; Beulens, A.J.M.
2006-01-01
This case study discusses how a knowledge base can be used to solve complex multi-disciplinary problems through a model based approach in the water management sector. We learn how successful execution and completion of multi-disciplinary complex projects can be supported through a knowledge-based
Modeling Students' Mathematics Using Steffe's Fraction Schemes
Norton, Anderson H.; McCloskey, Andrea V.
2008-01-01
Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…
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
Affinity and Hostility in Divided Communities: a Mathematical Model
Thron, Christopher
2015-01-01
We propose, develop, and analyze a mathematical model of intergroup attitudes in a community that is divided between two distinct social groups (which may be distinguished by religion, ethnicity, or some other socially distinguishing factor). The model is based on very simple premises that are both intuitive and justified by sociological research. We investigate the behavior of the model in various special cases, for various model configurations. We discuss the stability of the model, and the continuous or discontinuous dependence of model behavior on various parameters. Finally, we discuss possible implications for strategies to improve intergroup affinity, and to defuse tension and prevent deterioration of intergroup relationships.
Mathematical Model of Piston Ring Sealing in Combustion Engine
Directory of Open Access Journals (Sweden)
Koszałka Grzegorz
2015-01-01
Full Text Available This paper presents a mathematical model of piston-rings-cylinder sealing (TPC of a combustion engine. The developed model is an itegrated model of gas flow through gaps in TPC unit, displacements and twisting motions of piston rings in ring grooves as well as generation of oil film between ring face surfaces and cylinder liner. Thermal deformations and wear of TPC unit elements as well as heat exchange between flowing gas and surrounding walls, were taken into account in the model. The paper contains descriptions of: assumptions used for developing the model, the model itself, its numerical solution as well as its computer application for carrying out simulation tests.
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...
Three dimensional mathematical model of tooth for finite element analysis
Directory of Open Access Journals (Sweden)
Puškar Tatjana
2010-01-01
Full Text Available Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body into simple geometric bodies (cylinder, cone, pyramid,.... Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
[Three dimensional mathematical model of tooth for finite element analysis].
Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka
2010-01-01
The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
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)
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 Model of Silicon Oxidation in Microelectronics
Directory of Open Access Journals (Sweden)
V. A. Bondarev
2006-01-01
Full Text Available The paper involves analytical solutions and formulae for determination of the oxide film thickness in the silicon oxidation while using nitride mask. Calculations are based on solutions of a three-dimensional diffusion equation and new mathematical functions that are firstly defined by the author. Suitable analytical and numerical solutions based on the diffusion equation have not yet been obtained
Mathematical analysis and numerical simulation of a model of morphogenesis.
Muñoz, Ana I; Tello, José Ignacio
2011-10-01
We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters.
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.
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.
Mathematical Modeling of the Induced Mutation Process in Bacterial Cells
Belov, Oleg V.; Krasavin, Evgeny A.; Parkhomenko, Alexander Yu.
2010-01-01
A mathematical model of the ultraviolet (UV) irradiation-induced mutation process in bacterial cells Escherichia coli is developed. Using mathematical approaches, the whole chain of events is tracked from a cell exposure to the damaging factor to mutation formation in the DNA chain. An account of the key special features of the regulation of this genetic network allows predicting the effects induced by the cell exposure to certain UV energy fluence.
Mathematical Modeling on Open Limestone Channel
Bandstra, Joel; Wu, Naiyi
2014-01-01
Acid mine drainage (AMD) is the outflow of acidic water from metal mines or coal mines. When exposed to air and water, metal sulfides from the deposits of the mines are oxidized and produce acid, metal ions and sulfate, which lower the pH value of the water. An open limestone channel (OLC) is a passive and low cost way to neutralize AMD. The dissolution of calcium into the water increases the pH value of the solution. A differential equation model is numerically solved to predict the variation of concentration of each species in the OLC solution. The diffusion of Calcium due to iron precipitates is modeled by a linear equation. The results give the variation of pH value and the concentration of Calcium.
Novel mathematical neural models for visual attention
DEFF Research Database (Denmark)
Li, Kang
Visual attention has been extensively studied in psychology, but some fundamental questions remain controversial. We focus on two questions in this study. First, we investigate how a neuron in visual cortex responds to multiple stimuli inside the receptive eld, described by either a response...... for the visual attention theories and spiking neuron models for single spike trains. Statistical inference and model selection are performed and various numerical methods are explored. The designed methods also give a framework for neural coding under visual attention theories. We conduct both analysis on real...... system, supported by simulation study. Finally, we present the decoding of multiple temporal stimuli under these visual attention theories, also in a realistic biophysical situation with simulations....
Mathematical models of ecology and evolution
DEFF Research Database (Denmark)
Zhang, Lai
2012-01-01
dynamics but as a trade-o promotes species survival by shortening juvenile delay between birth and the onset of reproduction. Paper II compares the size-spectrum and food-web representations of communities using two traits (body size and habitat location) based unstructured population model of Lotka......) based size-structured population model, that is, interference in foraging, maintenance, survival, and recruitment. Their impacts on the ecology and evolution of size-structured populations and communities are explored. Ecologically, interference aects population demographic properties either negatively...... or positively, depending on the balance between interference induced gain and cost. Evolutionarily, the maturation size is either depressed (interference in foraging and maintenance) or elevated (interference in survival and recruitment) in a monomorphic population environment. Moreover, among the four...
Novel mathematical neural models for visual attention
DEFF Research Database (Denmark)
Li, Kang
Visual attention has been extensively studied in psychology, but some fundamental questions remain controversial. We focus on two questions in this study. First, we investigate how a neuron in visual cortex responds to multiple stimuli inside the receptive eld, described by either a response...... for the visual attention theories and spiking neuron models for single spike trains. Statistical inference and model selection are performed and various numerical methods are explored. The designed methods also give a framework for neural coding under visual attention theories. We conduct both analysis on real...... system, supported by simulation study. Finally, we present the decoding of multiple temporal stimuli under these visual attention theories, also in a realistic biophysical situation with simulations....
Mathematical modelling of triple arterial stenoses.
Ang, K C; Mazumdar, J
1995-06-01
This paper examines the effects of triple stenoses (ie. three stenoses in series) in a reasonably large artery. The model developed is axi-symmetric and blood is assumed to be a Newtonian fluid. The governing equations are the Navier-Stokes equations and the continuity equation. These equations are solved using the Finite Element Method and the FIDAP computational fluid dynamics (C.F.D.) package. Various combinations of differing degrees of stenosis in the triplet are considered. Pressure drop profiles and streamline plots of the solutions to these models show that the effects of milder stenoses are diminished in the presence of more severe ones. Also, a pressure recovery is observed whenever a mild stenosis follows a more severe stenosis in multiply stenosed arteries.
Mathematical modeling and visualization of functional neuroimages
Rasmussen, Peter Mondrup; Hansen, Lars Kai; Madsen, Kristoffer Hougaard
2011-01-01
Denne afhandling præsenterer forskningsresultater omhandlende matematisk modellering indenfor analyse af funktionelle hjernescanningsbilleder. Specifikt fokuserer afhandlingen pa mønster-baserede analysemetoder, som nyligt er blevet populære indenfor hjerneforskning. Ved hjæp af sådanne modelleringsmetoderne forsger forskere at prdiktere en eksperimentelt defineret mental tilstand ud fra hjernescanningsdata. Afhandlingen omhandler emner, der kan inddeles i to dele.Første del undersger hvorled...
Voltammetry: mathematical modelling and Inverse Problem
Koshev, N A; Kuzina, V V
2016-01-01
We propose the fast semi-analytical method of modelling the polarization curves in the voltammetric experiment. The method is based on usage of the special func- tions and shows a big calculation speed and a high accuracy and stability. Low computational needs of the proposed algorithm allow us to state the set of Inverse Problems of voltammetry for the reconstruction of metal ions concentrations or the other parameters of the electrolyte under investigation.
A mathematical model of insulin secretion.
Shannon, A G; Hogg, J M; Ollerton, R L; Luzio, S; Owens, D R
1994-01-01
Diabetes mellitus is a chronic state of excessive blood glucose levels (hyperglycaemia), which may result from many environmental and genetic factors, often acting jointly. The major regulator of glucose concentration in the blood is insulin. It is known that about 50% of the insulin is taken up by the liver on passing through it after secretion from the pancreas. The precise value of this fractional uptake is not known, so the prehepatic insulin secretion rates cannot be readily estimated from the plasma insulin concentration levels. By utilizing the equimolar secretion of insulin and connecting peptide (C-peptide) from the pancreas, a noninvasive method has been formulated. This was based on a compartmental model which involved the pancreas, liver, and plasma. The resulting differential equation yielded a gamma variate solution which could be readily linearized. The model was then tested on 56 normal (51 nonobese and 5 obese) subjects, and three groups of subjects with diabetes who could be labelled as mild, moderate, and severe (based on the fasting plasma glucose concentration) with 83, 88, and 64 subjects respectively. We have focused on the human patient environment of the clinician to produce a distinct model which gave a consistent pattern within all four groups with good fits between observed and theoretical values of the plasma insulin levels. The consequent rates for insulin secretion were consistent across the groups and were clinically meaningful.
A New Model for the Integration of Science and Mathematics: The Balance Model
Kiray, S. Ahmet
2012-01-01
The aim of this study is to develop an integrated scientific and mathematical model that is suited to the background of Turkish teachers. The dimensions of the model are given and compared to the models which have been previously developed and the findings of earlier studies on the topic. The model is called the balance, reflecting the…
Mathematical models of a diffusion-convection in porous media
Directory of Open Access Journals (Sweden)
Anvarbek M. Meirmanov
2012-06-01
Full Text Available Mathematical models of a diffusion-convection in porous media are derived from the homogenization theory. We start with the mathematical model on the microscopic level, which consist of the Stokes system for a weakly compressible viscous liquid occupying a pore space, coupled with a diffusion-convection equation for the admixture. We suppose that the viscosity of the liquid depends on a concentration of the admixture and for this nonlinear system we prove the global in time existence of a weak solution. Next we rigorously fulfil the homogenization procedure as the dimensionless size of pores tends to zero, while the porous body is geometrically periodic. As a result, we derive new mathematical models of a diffusion-convection in absolutely rigid porous 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 model of an air-filled alpha stirling refrigerator
McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir
2013-10-01
This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.
Mathematically Modeling Parameters Influencing Surface Roughness in CNC Milling
Directory of Open Access Journals (Sweden)
Engin Nas
2012-01-01
Full Text Available In this study, steel AISI 1050 is subjected to process of face milling in CNC milling machine and such parameters as cutting speed, feed rate, cutting tip, depth of cut influencing the surface roughness are investigated experimentally. Four different experiments are conducted by creating different combinations for parameters. In conducted experiments, cutting tools, which are coated by PVD method used in forcing steel and spheroidal graphite cast iron are used. Surface roughness values, which are obtained by using specified parameters with cutting tools, are measured and correlation between measured surface roughness values and parameters is modeled mathematically by using curve fitting algorithm. Mathematical models are evaluated according to coefficients of determination (R2 and the most ideal one is suggested for theoretical works. Mathematical models, which are proposed for each experiment, are estipulated.
Random curds as mathematical models of fractal rhythm in architecture
Directory of Open Access Journals (Sweden)
Ćirović Ivana
2014-01-01
Full Text Available The author Carl Bovill has suggested and described a method for generating rhythm in architecture with the help of random curds, as they are the mathematical models of unpredictable and uneven groupings which he recognizes in natural shapes and in natural processes. He specified the rhythm generated in this way as the fractal rhythm. Random curds can be generated by a simple process of curdling, as suggested by B. Mandelbrot. This paper examines the way in which the choice of probability for every stage or level of the curdling process, and the number of stages in the procedure of curdling, affect the characteristics of the obtained fractal object as a potential mathematical model of rhythm in the design process. At the same time, this paper examines the characteristics of rhythm in architecture which determine whether the obtained fractal object will be accepted as an appropriate mathematical model of the observed rhythm.
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.
Mathematical models for the EPIC code
Energy Technology Data Exchange (ETDEWEB)
Buchanan, H.L.
1981-06-03
EPIC is a fluid/envelope type computer code designed to study the energetics and dynamics of a high energy, high current electron beam passing through a gas. The code is essentially two dimensional (x, r, t) and assumes an axisymmetric beam whose r.m.s. radius is governed by an envelope model. Electromagnetic fields, background gas chemistry, and gas hydrodynamics (density channel evolution) are all calculated self-consistently as functions of r, x, and t. The code is a collection of five major subroutines, each of which is described in some detail in this report.
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
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......, Ontario, Canada), NebuChamber (Astra, Södirtälje, Sweden) and Nebuhaler (Astra) adapted for babies. The dose of fluticasone proportionate delivered by the Babyhaler (Glaxco Wellcome, Oxbridge, Middlesex, UK) was 80% of that predicted, probably because of incomplete priming of this spacer. Of the above...
Mathematical Viscosity Models for Ternary Metallic and Silicate Melts
Institute of Scientific and Technical Information of China (English)
FU Yuan-kun; MENG Xian-min; GUO Han-jie
2004-01-01
The mathematical viscosity models for metallic melts were discussed. The experimental data of Ag-Au-Cu systems were used to verify the models based on Chou's general geometric thermodynamic model and the calculated results are consistent with the reported experimental data. A new model predicting the viscosity of multi-component silicate melts was established. The CaO-MnO-SiO2, CaO-FeO-SiO2 and FeO-MnO-SiO2 silicate slag systems were used to verify the model.
Directory of Open Access Journals (Sweden)
Arkady Plotnitsky
2017-06-01
Full Text Available The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, that may be helpful or even necessary there or in physics itself. I shall, in closing, suggest one possible type of such models, singularized probabilistic models, SP-models, some
Mathematical model of a cell size checkpoint.
Directory of Open Access Journals (Sweden)
Marco Vilela
Full Text Available How cells regulate their size from one generation to the next has remained an enigma for decades. Recently, a molecular mechanism that links cell size and cell cycle was proposed in fission yeast. This mechanism involves changes in the spatial cellular distribution of two proteins, Pom1 and Cdr2, as the cell grows. Pom1 inhibits Cdr2 while Cdr2 promotes the G2 → M transition. Cdr2 is localized in the middle cell region (midcell whereas the concentration of Pom1 is highest at the cell tips and declines towards the midcell. In short cells, Pom1 efficiently inhibits Cdr2. However, as cells grow, the Pom1 concentration at midcell decreases such that Cdr2 becomes activated at some critical size. In this study, the chemistry of Pom1 and Cdr2 was modeled using a deterministic reaction-diffusion-convection system interacting with a deterministic model describing microtubule dynamics. Simulations mimicked experimental data from wild-type (WT fission yeast growing at normal and reduced rates; they also mimicked the behavior of a Pom1 overexpression mutant and WT yeast exposed to a microtubule depolymerizing drug. A mechanism linking cell size and cell cycle, involving the downstream action of Cdr2 on Wee1 phosphorylation, is proposed.
Mathematical Modeling of Routing in DHTs
Kersch, Peter; Szabo, Robert
Although most Distributed Hash Table (DHT) overlays are structurally similar to the "small-world" navigation model of Kleinberg - architectural and algorithmic details of different DHT variants differ significantly. Lookup performance of DHTs depends on a sets of different and often incompatible parameters, which makes analytical comparison rather difficult. The objective of this chapter is to review existing analytical models for DHT routing performance and to introduce a novel framework for the per-hop routing progress analysis of long-range DHT connections based on a logarithmic transformation. With the logarithmic transformation of the DHT metric space we analyze the distribution of the per-hop routing progress in general and also for the special cases of the deterministic and probabilistic power-law routing overlays. Based on the proposed analytical framework routing performance of DHTs can be described by a triple: the long-range connection density, its coefficient of variation and the number of short-range connections. Finally, we derive upper bound on the expected number of routing hops as a function of network size and the parameter triple.
Mathematical modeling of a convective textile drying process
Directory of Open Access Journals (Sweden)
G. Johann
2014-12-01
Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.
Mathematical Existence Results for the Doi-Edwards Polymer Model
Chupin, Laurent
2017-01-01
In this paper, we present some mathematical results on the Doi-Edwards model describing the dynamics of flexible polymers in melts and concentrated solutions. This model, developed in the late 1970s, has been used and extensively tested in modeling and simulation of polymer flows. From a mathematical point of view, the Doi-Edwards model consists in a strong coupling between the Navier-Stokes equations and a highly nonlinear constitutive law. The aim of this article is to provide a rigorous proof of the well-posedness of the Doi-Edwards model, namely that it has a unique regular solution. We also prove, which is generally much more difficult for flows of viscoelastic type, that the solution is global in time in the two dimensional case, without any restriction on the smallness of the data.
Mathematical Model of Hot Metal Desulfurization by Powder Injection
Directory of Open Access Journals (Sweden)
Yolanda Cepeda Rodríguez
2012-01-01
Full Text Available Although there have been a numerous number of studies on mathematical model of hot metal desulfurization by deep injection of calcium carbide, the research field as a whole is not well integrated. This paper presents a model that takes into account the kinetics, thermodynamics, and transport processes to predict the sulfur levels in the hot metal throughout a blow. The model could be utilized to assess the influence of the treatment temperature, rate of injection, gas flow rate, and initial concentration of sulfur on the desulfurization kinetics. In the second part of this paper an analysis of the industrial data for injection of calcium carbide using this model is described. From a mathematical model that describes the characteristics of a system, it is possible to predict the behavior of the variables involved in the process, resulting in savings of time and money. Discretization is realized through the finite difference method combined with interpolation in the border domain by Taylor series.
BUILDING MATHEMATICAL MODELS IN DYNAMIC PROGRAMMING
Directory of Open Access Journals (Sweden)
LIANA RODICA PATER
2012-05-01
Full Text Available In short, we can say that dynamic programming is a method of optimization of systems, using their mathematical representation in phases or sequences or as we say, periods. Such systems are common in economic studies at the implementation of programs on the most advanced techniques, such as for example that involving cosmic navigation. Another concept that is involved in the study of dynamic programs is the economic horizon (number of periods or phases that a dynamic program needs. This concept often leads to the examination of the convergence of certain variables on infinite horizon. In many cases from the real economy by introducing updating, dynamic programs can be made convergent.
Mass Extinction in a Simple Mathematical Biological Model
Tokita, K; Tokita, Kei; Yasutomi, Ayumu
1997-01-01
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system initially has a large number of species ( diversity). The extinction dynamics shows several significant features such as a power law in basin size distribution, induction time, etc. The present theory can be a mathematical foundation of the species-area effect in the paleontologic theory for mass extinction.
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 models of magnetite desliming for automated quality control systems
Olevska, Yu.; Mishchenko, V.; Olevskyi, V.
2016-10-01
The aim of the study is to provide multifactor mathematical models suitable for use in automatic control systems of desliming process. For this purpose we described the motion of a two-phase environment regard to the shape the desliming machine and technological parameters of the enrichment process. We created the method for preparation of dependences of the enrichment process quality from the technological and design parameters. To automate the process we constructed mathematical models to justify intensive technological modes and optimal parameters for design of desliming machine.
Mathematical modelling in the computer-aided process planning
Mitin, S.; Bochkarev, P.
2016-04-01
This paper presents new approaches to organization of manufacturing preparation and mathematical models related to development of the computer-aided multi product process planning (CAMPP) system. CAMPP system has some peculiarities compared to the existing computer-aided process planning (CAPP) systems: fully formalized developing of the machining operations; a capacity to create and to formalize the interrelationships among design, process planning and process implementation; procedures for consideration of the real manufacturing conditions. The paper describes the structure of the CAMPP system and shows the mathematical models and methods to formalize the design procedures.
Mathematical model in controlling dengue transmission with sterile mosquito strategies
Aldila, D.; Nuraini, N.; Soewono, E.
2015-09-01
In this article, we propose a mathematical model for controlling dengue disease transmission with sterile mosquito techniques (SIT). Sterile male introduced from lab in to habitat to compete with wild male mosquito for mating with female mosquito. Our aim is to displace gradually the natural mosquito from the habitat. Mathematical model analysis for steady states and the basic reproductive ratio are performed analytically. Numerical simulation are shown in some different scenarios. We find that SIT intervention is potential to controlling dengue spread among humans population
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 models and numerical simulation in electromagnetism
Bermúdez, Alfredo; Salgado, Pilar
2014-01-01
The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell’s equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.
A Mathematical Model of Democratic Elections
Directory of Open Access Journals (Sweden)
Mato Nagel
2010-09-01
Full Text Available Democratic election is the preferred method for determining political administrators nowadays. The intention is to find the best possible leader in order to improve the group's competitiveness and success. Though preferred, democratic election is far from being optimal in this respect, and is increasingly becoming the target for fraud. A model was developed to scientifically analyze the present electoral system's insufficiency. It is based on fauceir assumptions. Its calculations enable principles to be developed that optimize the election process, while also revealing the limits of elections in societies growing ever more complex, so that in the end elections have to be replaced by processes similar to what has proved optimal throughout naturally occurring evolution-natural selection.
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.
A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy.
Li, Xuefang; Xu, Jian-Xin
2016-10-07
Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon-γ (IFN-γ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013). The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model.
Frejd, Peter
2014-01-01
The relevance of using mathematics in and for out-of-school activities is one main argument for teaching mathematics in education. Mathematical modelling is considered as a bridge between the mathematics learned and taught in schools and the mathematics used at the workplace and in society and it is also a central notion in the present Swedish mathematical syllabus for upper secondary school. This doctoral thesis reports on students’, teachers’ and modelling experts’ experiences of, learning,...
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.
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.
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.
Mathematical Modelling of Coal Gasification Processes
Sundararajan, T.; Raghavan, V.; Ajilkumar, A.; Vijay Kumar, K.
2017-07-01
experimental and modelling work has been undertaken to investigate the gasification characteristics of high ash Indian coals and compare the yield with those of high grade Australian and Japanese coals. A 20 kW capacity entrained flow gasifier has been constructed and the gasification characteristics have been studied for Indian coals for different particle sizes, system pressures and air flow rates. The theoretical model incorporates the effects of Knudsen diffusion, devolatilization and various heterogenous and homogenous kinetic steps as well as two-phase flow interactions involving the gaseous and particle phases. Output parameters such as carbon conversion, cold gas efficiency and syngas composition have been compared for different grades of coals under a wide range of operating conditions. The model developed for the entrained flow gasifier predicts the gasification characteristics of both Indian and foreign coals well. Apart from the entrained flow gasifier, a bubbling bed gasifier of 100 kW capacity has also been studied. A pilot plant for the gasification of Indian coals has been set up for this capacity and its performance has been investigated experimentally as well as theoretically at different air and steam flow rates. Carbon conversion efficiency of more than 80% has been achieved.
Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling
Energy Technology Data Exchange (ETDEWEB)
Du, Qiang [Pennsylvania State Univ., State College, PA (United States)
2014-11-12
The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of which is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next
The mathematical model of a LUNG simulator
Directory of Open Access Journals (Sweden)
František Šolc
2014-12-01
Full Text Available The paper discusses the design, modelling, implementation and testing of a specific LUNG simulator,. The described research was performed as a part of the project AlveoPic – Advanced Lung Research for Veterinary Medicine of Particles for Inhalation. The simulator was designed to establish a combined study programme comprising Biomedical Engineering Sciences (FEEC BUT and Healthcare and Rehabilitation Technology (FH Technikum Wien. The simulator is supposed to be an advanced laboratory equipment which should enhance the standard of the existing research activities within the above-mentioned study programs to the required level. Thus, the proposed paper introduces significant technical equipment for the laboratory education of students at both FH Technikum Wien and the Faculty of Electrical Engineering and Communication, Brno University of Technology. The apparatuses described here will be also used to support cooperative research activities. In the given context, the authors specify certain technical solutions and parameters related to artificial lungs, present the electrical equipment of the system, and point out the results of the PC-based measurement and control.
Mathematical Model of Asynchronous Machine in MATLAB Simulink
Directory of Open Access Journals (Sweden)
A A Ansari
2010-05-01
Full Text Available Different mathematical models have been used over the years to examine different problems associated with induction motors. These range from the simple equivalent circuit models to more complex d,q models and abc models which allow the inclusion of various forms of impedance and/or voltage unbalance. Recently, hybrid models have been developed which allow the inclusion of supply side unbalance but with the computational economy of the d,q models. This paper presents these models with typical results and provides guidelines for their use The dynamic simulation of small power induction motor based on mathematical modelling is proposed in this paper. The dynamic simulation is one of the key steps in the validation of the design process of the motor drive systems and it is needed for eliminating inadvertent design mistakes and the resulting error in the prototype construction and testing. This paper demonstrates the simulation of steady-state performance of induction motor by MATLAB Program Threephase induction motor is modeled and simulated with SIMULINK model.
Multiscale mathematical modeling and simulation of cellular dynamical process.
Nakaoka, Shinji
2014-01-01
Epidermal homeostasis is maintained by dynamic interactions among molecules and cells at different spatiotemporal scales. Mathematical modeling and simulation is expected to provide clear understanding and precise description of multiscaleness in tissue homeostasis under systems perspective. We introduce a stochastic process-based description of multiscale dynamics. Agent-based modeling as a framework of multiscale modeling to achieve consistent integration of definitive subsystems is proposed. A newly developed algorithm that particularly aims to perform stochastic simulations of cellular dynamical process is introduced. Finally we review applications of multiscale modeling and quantitative study to important aspects of epidermal and epithelial homeostasis.
Mathematical models with singularities a zoo of singular creatures
Torres, Pedro J
2015-01-01
The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.
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...... of the solute permeability the concentration dependent viscosity decreases the volumetric flux through the membrane at high pressures. This effect is due to a very high concentration at the membrane surface. The model is related to experimental data. There is a good qualitative and a reasonable quantitative...
Heat-pump-assisted dryer: Pt. 1; Mathematical model
Energy Technology Data Exchange (ETDEWEB)
Pendyala, V.R.; Devotta, S.; Patwardhan, V.S. (National Chemical Lab., Poona (India))
1990-07-01
A mathematical model for an integrated heat-pump-assisted dryer has been developed. The dryer has been modelled considering the heat transfer and simultaneous heat and mass transfer zones. The heat-pump heat exchangers have been modelled by writing the enthalpy balance for differential lengths considering the various zones on the air and working-fluid sides. The compressor has been described by the polytropic compression equation. The model has been used for simulating an existing system using R11 to study the effect of approach velocity of air to the evaporator and of the suction superheat on the specific energy consumption of the heat pump assisted dryer. (author).
Mathematical Model of Piston Ring Sealing in Combustion Engine
Koszałka Grzegorz; Guzik Mirosław
2015-01-01
This paper presents a mathematical model of piston-rings-cylinder sealing (TPC) of a combustion engine. The developed model is an itegrated model of gas flow through gaps in TPC unit, displacements and twisting motions of piston rings in ring grooves as well as generation of oil film between ring face surfaces and cylinder liner. Thermal deformations and wear of TPC unit elements as well as heat exchange between flowing gas and surrounding walls, were taken into account in the model. The pape...
A review of mathematical models in economic environmental problems
DEFF Research Database (Denmark)
Nahorski, Z.; Ravn, H.F.
2000-01-01
The paper presents a review of mathematical models used,in economic analysis of environmental problems. This area of research combines macroeconomic models of growth, as dependent on capital, labour, resources, etc., with environmental models describing such phenomena like natural resources...... exhaustion or pollution accumulation and degradation. In simpler cases the models can be treated analytically and the utility function can be optimized using, e.g., such tools as the maximum principle. In more complicated cases calculation of the optimal environmental policies requires a computer solution....
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...
Developing the Roots of Modelling Conceptions: "Mathematical Modelling Is the Life of the World"
Brown, Jill Patricia; Stillman, Gloria Ann
2017-01-01
A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…
Mathematical Modelling of Surfactant Self-assembly at Interfaces
Morgan, C. E.
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 differential equations that couple the rearrangement of surfactant within the multilayer to the surface adsorption kinetics is first derived. This model is then extended to the macroscopic scale by taking the continuum limit that exploits the typically large number of surfactant layers, which results in a novel third-order partial differential equation. The model is generalized to allow for the presence of two adsorbing boundaries, which results in an implicit free-boundary problem. The system predicts physically observed features in multilayer systems such as the initial formation of smaller lamellar structures and the typical number of layers that form in equilibrium.
On the Treatment of Airline Travelers in Mathematical Models
Johansson, Michael A.; Arana-Vizcarrondo, Neysarí; Biggerstaff, Brad J.; Staples, J. Erin; Gallagher, Nancy; Marano, Nina
2011-01-01
The global spread of infectious diseases is facilitated by the ability of infected humans to travel thousands of miles in short time spans, rapidly transporting pathogens to distant locations. Mathematical models of the actual and potential spread of specific pathogens can assist public health planning in the case of such an event. Models should generally be parsimonious, but must consider all potentially important components of the system to the greatest extent possible. We demonstrate and discuss important assumptions relative to the parameterization and structural treatment of airline travel in mathematical models. Among other findings, we show that the most common structural treatment of travelers leads to underestimation of the speed of spread and that connecting travel is critical to a realistic spread pattern. Models involving travelers can be improved significantly by relatively simple structural changes but also may require further attention to details of parameterization. PMID:21799782
Mathematical modeling of elastic inverted pendulum control system
Institute of Scientific and Technical Information of China (English)
Chao XU; Xin YU
2004-01-01
Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering.The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations(ODEs).Complete rigidity is the approximation of practical models;Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller.A new kind of inverted pendulum,elastic inverted pendulum was proposed,and elasticity was considered.Mathematical model was derived from Hamiltonian principle and variational methods,which were formulated by the coupling of partial differential equations(PDE) and ODE.Because of infinite dimensional,system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one.
Mathematical modeling of brain tumors: effects of radiotherapy and chemotherapy
Energy Technology Data Exchange (ETDEWEB)
Powathil, G [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Kohandel, M [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Sivaloganathan, S [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Oza, A [Center for Mathematical Medicine, Fields Institute for Research in Mathematical Sciences, Toronto, Ontario M5T 3J1 (Canada); Milosevic, M [Radiation Medicine Program, Princess Margaret Hospital, and Department of Radiation Oncology, University of Toronto, Toronto, Ontario M5G 2M9 (Canada)
2007-06-07
Gliomas, the most common primary brain tumors, are diffusive and highly invasive. The standard treatment for brain tumors consists of a combination of surgery, radiation therapy and chemotherapy. Over the past few years, mathematical models have been applied to study untreated and treated brain tumors. In an effort to improve treatment strategies, we consider a simple spatio-temporal mathematical model, based on proliferation and diffusion, that incorporates the effects of radiotherapeutic and chemotherapeutic treatments. We study the effects of different schedules of radiation therapy, including fractionated and hyperfractionated external beam radiotherapy, using a generalized linear quadratic (LQ) model. The results are compared with published clinical data. We also discuss the results for combination therapy (radiotherapy plus temozolomide, a new chemotherapy agent), as proposed in recent clinical trials. We use the model to predict optimal sequencing of the postoperative (combination of radiotherapy and adjuvant, neo-adjuvant or concurrent chemotherapy) treatments for brain tumors.
Mathematical modeling of isotope labeling experiments for metabolic flux analysis.
Nargund, Shilpa; Sriram, Ganesh
2014-01-01
Isotope labeling experiments (ILEs) offer a powerful methodology to perform metabolic flux analysis. However, the task of interpreting data from these experiments to evaluate flux values requires significant mathematical modeling skills. Toward this, this chapter provides background information and examples to enable the reader to (1) model metabolic networks, (2) simulate ILEs, and (3) understand the optimization and statistical methods commonly used for flux evaluation. A compartmentalized model of plant glycolysis and pentose phosphate pathway illustrates the reconstruction of a typical metabolic network, whereas a simpler example network illustrates the underlying metabolite and isotopomer balancing techniques. We also discuss the salient features of commonly used flux estimation software 13CFLUX2, Metran, NMR2Flux+, FiatFlux, and OpenFLUX. Furthermore, we briefly discuss methods to improve flux estimates. A graphical checklist at the end of the chapter provides a reader a quick reference to the mathematical modeling concepts and resources.
On the treatment of airline travelers in mathematical models.
Directory of Open Access Journals (Sweden)
Michael A Johansson
Full Text Available The global spread of infectious diseases is facilitated by the ability of infected humans to travel thousands of miles in short time spans, rapidly transporting pathogens to distant locations. Mathematical models of the actual and potential spread of specific pathogens can assist public health planning in the case of such an event. Models should generally be parsimonious, but must consider all potentially important components of the system to the greatest extent possible. We demonstrate and discuss important assumptions relative to the parameterization and structural treatment of airline travel in mathematical models. Among other findings, we show that the most common structural treatment of travelers leads to underestimation of the speed of spread and that connecting travel is critical to a realistic spread pattern. Models involving travelers can be improved significantly by relatively simple structural changes but also may require further attention to details of parameterization.
Mathematical Modeling of Carcinogenesis Based on Chromosome Aberration Data
Institute of Scientific and Technical Information of China (English)
Xiao-bo Li
2009-01-01
Objective: The progression of human cancer is characterized by the accumulation of genetic instability. An increasing number of experimental genetic molecular techniques have been used to detect chromosome aberrations. Previous studies on chromosome abnormalities often focused on identifying the frequent loci of chromosome alterations, but rarely addressed the issue of interrelationship of chromosomal abnormalities. In the last few years, several mathematical models have been employed to construct models of carcinogenesis, in an attempt to identify the time order and cause-and-effect relationship of chromosome aberrations. The principles and applications of these models are reviewed and compared in this paper. Mathematical modeling of carcinogenesis can contribute to our understanding of the molecular genetics of tumor development, and identification of cancer related genes, thus leading to improved clinical practice of cancer.
Mathematical models applied in inductive non-destructive testing
Energy Technology Data Exchange (ETDEWEB)
Wac-Wlodarczyk, A.; Goleman, R.; Czerwinski, D. [Technical University of Lublin, 20 618 Lublin, Nadbystrzycka St 38a (Poland); Gizewski, T. [Technical University of Lublin, 20 618 Lublin, Nadbystrzycka St 38a (Poland)], E-mail: t.gizewski@pollub.pl
2008-10-15
Non-destructive testing are the wide group of investigative methods of non-homogenous material. Methods of computer tomography, ultrasonic, magnetic and inductive methods still developed are widely applied in industry. In apparatus used for non-destructive tests, the analysis of signals is made on the basis of complex system answers. The answer is linearized due to the model of research system. In this paper, the authors will discuss the applications of the mathematical models applied in investigations of inductive magnetic materials. The statistical models and other gathered in similarity classes will be taken into consideration. Investigation of mathematical models allows to choose the correct method, which in consequence leads to precise representation of the inner structure of examined object. Inductive research of conductive media, especially those with ferromagnetic properties, are run with high frequency magnetic field (eddy-currents method), which considerably decrease penetration depth.
Cook, D. P.; Evans, J. W.
1995-02-01
This first of two related articles describes a mathematical model for electromagnetic casting in three dimensions, i.e., where the dependent variables are functions of all three spatial coordinates. It is shown how the method of inductances can be extended to three dimensions in order to solve Maxwell's equations for the electromagnetic field in and around the caster. The principal task here is the calculation of the inductances between loops of irregular shape, and the method by which this is done is described. The computations are self-consistent ones in that the free surface of the molten metal is adjusted in response to the supporting electromagnetic forces which are themselves dependent on the shape of that surface. The computed electromagnetic forces are input into a second phase of the calculation where melt flow is computed in three dimensions using the finite element package FIDAP.
A mathematical model of star formation in the Galaxy
Directory of Open Access Journals (Sweden)
M.A. Sharaf
2012-06-01
Full Text Available This paper is generally concerned with star formation in the Galaxy, especially blue stars. Blue stars are the most luminous, massive and the largest in radius. A simple mathematical model of the formation of the stars is established and put in computational algorithm. This algorithm enables us to know more about the formation of the star. Some real and artificial examples had been used to justify this model.
Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.
Clément, Frédérique
2016-07-01
Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of
Mathematical models for predicting indoor air quality from smoking activity.
Ott, W R
1999-01-01
Much progress has been made over four decades in developing, testing, and evaluating the performance of mathematical models for predicting pollutant concentrations from smoking in indoor settings. Although largely overlooked by the regulatory community, these models provide regulators and risk assessors with practical tools for quantitatively estimating the exposure level that people receive indoors for a given level of smoking activity. This article reviews the development of the mass balanc...
MATHEMATICAL MODEL OF RIVER BED CHANGE DOWNSTREAM OF XIAOLANGDI RESERVOIR
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A mathematical model of river bed change downstream of the Xiaolangdi Reservoir was developed based on the most recent achievement of sediment theory in the Yellow River. The model was verified by the comparison of computed results and measured data from 1986 to 1996. Numerical prediction of the erosion and deposition downstream of the Xiaolangdi Reservoir in its first operation year was carried out, and a series of suggestions were given for reservoir operation mode in its early operation period.
Mathematical Model of Bone Regeneration in a Porous Implant
Maslov, L. B.
2017-07-01
A mathematical model of the reparative regeneration of bone tissue governed by the law of cell differentiation and action of an external periodic mechanical loading is presented. The model allows one to study the recovery processes of injured human locomotor system elements under a dynamic loading and to theoretically substantiate the choice of an optimum periodic impact on the defective tissues for their fastest and steady healing.
Organisation for Economic Cooperation and Development, Paris (France).
The purposes of this volume are to report a survey of current practice in the construction and use of mathematical models for the education sector: to identify the most important technical and substantive problems confronting the model-building effort; and to bridge the gap between the advancing research pursuit of model-building and the lagging…
Mathematical Modelling and Experimental Analysis of Early Age Concrete
DEFF Research Database (Denmark)
Hauggaard-Nielsen, Anders Boe
1997-01-01
The report deals with mathematical models for concrete at early age. In the hardening process chemical reactions take place and the concrete skeleton is created. The processes changes the moisture content and produces heat. The associated temperature rise gives expansion of the material which may...
Engaging Students in Mathematical Modeling through Service-Learning
Carducci, Olivia M.
2014-01-01
I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…
Exploring Student Reflective Practice during a Mathematical Modelling Challenge
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond; Kanasa, Harry
2012-01-01
This paper seeks to compare the reflective writings of two cohorts of students (Year 4/5 and Year 8/9) participating in mathematical modelling challenges. Whilst the reflections of the younger cohort were results oriented, the older cohort's reflections spoke more to the affective domain, group processes, the use of technology and the acquisition…
A Mathematical Model of the Great Solar Eclipse of 1991.
Lamb, John Jr.
1991-01-01
An activity that shows how mathematics can be used to model events in the real world is described. A way to calculate the area of the sun covered by the moon during a partial eclipse is presented. A computer program that will determine the coverage percentage is also included. (KR)
A Mathematical Model for HIV Drug-Resistance
Faedo, Ivan; Raimundo, Silvia Martorano; Venturino, Ezio
2010-09-01
In this paper we present a mathematical model of the transmission of HIV infection here the individuals receive antiretroviral drugs but may not respond to treatment. In such case the latter can be changed to a different therapy, and individuals may or may not respond also to this second set of drugs.
SCIENTIFIC PRINCIPLES AND MATHEMATICAL MODELS OF PROCESSES OF MINING
Kriuchkov, Anatolii Ivanovych
2016-01-01
The connection between mathematical models of the mining industry with the basic scientific principles. The method of simulation of random non-stationary processes in the form of a set of Hamilton-Jacobi equations and Fokker-Planck-Kolmogorov using the principle of duality movement of mass in space
Optlang: An algebraic modeling language for mathematical optimization
DEFF Research Database (Denmark)
Jensen, Kristian; Cardoso, Joao; Sonnenschein, Nikolaus
2016-01-01
Optlang is a Python package implementing a modeling language for solving mathematical optimization problems, i.e., maximizing or minimizing an objective function over a set of variables subject to a number of constraints. It provides a common native Python interface to a series of optimization...
Mathematical Model of Lifetime Duration at Insulation of Electrical Machines
Directory of Open Access Journals (Sweden)
Mihaela Răduca
2009-10-01
Full Text Available Abstract. This paper present a mathematical model of lifetime duration at hydro generator stator winding insulation when at hydro generator can be appear the damage regimes. The estimation to make by take of the programming and non-programming revisions, through the introduction and correlation of the new defined notions.
MATHEMATICAL MODEL OF PURIFICATION PROCESS OF OIL CONTAMINATED WATERS
Directory of Open Access Journals (Sweden)
С. Бойченко
2012-04-01
Full Text Available Sorption properties of carbonic sorbents on natural raw materials for purification of waste waters frompetroleum products are investigated. Temperature influence on sumption properties of sorbents on naturalraw materials to increase the purification degree of water ecosystem is studied. Mathematical model ofpurification process of oil contaminated waters is developed
Mathematical modeling of the aerodynamic characteristics in flight dynamics
Tobak, M.; Chapman, G. T.; Schiff, L. B.
1984-01-01
Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.
MATHEMATICAL MODEL OF PURIFICATION PROCESS OF OIL CONTAMINATED WATERS
С. Бойченко; Кучер, О.; Л. Павлюх
2012-01-01
Sorption properties of carbonic sorbents on natural raw materials for purification of waste waters frompetroleum products are investigated. Temperature influence on sumption properties of sorbents on naturalraw materials to increase the purification degree of water ecosystem is studied. Mathematical model ofpurification process of oil contaminated waters is developed
A Mathematical Model of the Great Solar Eclipse of 1991.
Lamb, John Jr.
1991-01-01
An activity that shows how mathematics can be used to model events in the real world is described. A way to calculate the area of the sun covered by the moon during a partial eclipse is presented. A computer program that will determine the coverage percentage is also included. (KR)
Mathematical modelling: a tool for hospital infection control
Grundmann, Hajo; Hellriegel, B.
2006-01-01
Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has
Mathematical modelling : a tool for hospital infection control
Grundmann, H; Hellriegel, B
Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has
Mathematical modelling: a tool for hospital infection control.
Grundmann, Hajo; Hellriegel, B
2006-01-01
Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has
Semantic Web Based Efficient Search Using Ontology and Mathematical Model
Directory of Open Access Journals (Sweden)
K.Palaniammal
2014-01-01
Full Text Available The semantic web is the forthcoming technology in the world of search engine. It becomes mainly focused towards the search which is more meaningful rather than the syntactic search prevailing now. This proposed work concerns about the semantic search with respect to the educational domain. In this paper, we propose semantic web based efficient search using ontology and mathematical model that takes into account the misleading, unmatched kind of service information, lack of relevant domain knowledge and the wrong service queries. To solve these issues in this framework is designed to make three major contributions, which are ontology knowledge base, Natural Language Processing (NLP techniques and search model. Ontology knowledge base is to store domain specific service ontologies and service description entity (SDE metadata. The search model is to retrieve SDE metadata as efficient for Education lenders, which include mathematical model. The Natural language processing techniques for spell-check and synonym based search. The results are retrieved and stored in an ontology, which in terms prevents the data redundancy. The results are more accurate to search, sensitive to spell check and synonymous context. This paper reduces the user’s time and complexity in finding for the correct results of his/her search text and our model provides more accurate results. A series of experiments are conducted in order to respectively evaluate the mechanism and the employed mathematical model.
A novel mathematical model for controllable near-field electrospinning
Directory of Open Access Journals (Sweden)
Changhai Ru
2014-01-01
Full Text Available 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 analysis of intermittent gas injection model in oil production
Tasmi, Silvya, D. R.; Pudjo, S.; Leksono, M.; Edy, S.
2016-02-01
Intermittent gas injection is a method to help oil production process. Gas is injected through choke in surface and then gas into tubing. Gas forms three areas in tubing: gas column area, film area and slug area. Gas column is used to propel slug area until surface. A mathematical model of intermittent gas injection is developed in gas column area, film area and slug area. Model is expanding based on mass and momentum conservation. Using assume film thickness constant in tubing, model has been developed by Tasmi et. al. [14]. Model consists of 10 ordinary differential equations. In this paper, assumption of pressure in gas column is uniform. Model consist of 9 ordinary differential equations. Connection of several variables can be obtained from this model. Therefore, dynamics of all variables that affect to intermittent gas lift process can be seen from four equations. To study the behavior of variables can be analyzed numerically and mathematically. In this paper, simple mathematically analysis approach is used to study behavior of the variables. Variables that affect to intermittent gas injection are pressure in upstream valve and in gas column. Pressure in upstream valve will decrease when gas mass in valve greater than gas mass in choke. Dynamic of the pressure in the gas column will decrease and increase depending on pressure in upstream valve.
Mathematical Modelling of Cation Transport and Regulation in Yeast.
Kahm, Matthiasé; Kschischo, Maik
2016-01-01
Mathematical modelling of ion transport is a strategy to understand the complex interplay between various ionic species and their transporters. Such models should provide new insights and suggest new interesting experiments. Two essential variables in models for ion transport and control are the membrane potential and the intracellular pH, which generates an additional layer of complexity absent from many other models of biochemical reaction pathways. The aim of this text is to introduce the reader to the basic principles and assumptions of modelling in this field. A simplified model of potassium transport will be used as an example and will be derived in a step by step manner. This forms the basis for understanding the advantages and limitations of more complex models. These are briefly reviewed at the end of this chapter.
Modified Mathematical Model For Neutralization System In Stirred Tank Reactor
Directory of Open Access Journals (Sweden)
Ahmmed Saadi Ibrehem
2011-05-01
Full Text Available A modified model for the neutralization process of Stirred Tank Reactors (CSTR reactor is presented in this study. The model accounts for the effect of strong acid [HCL] flowrate and strong base [NaOH] flowrate with the ionic concentrations of [Cl-] and [Na+] on the Ph of the system. In this work, the effect of important reactor parameters such as ionic concentrations and acid and base flowrates on the dynamic behavior of the CSTR is investigated and the behavior of mathematical model is compared with the reported models for the McAvoy model and Jutila model. Moreover, the results of the model are compared with the experimental data in terms of pH dynamic study. A good agreement is observed between our model prediction and the actual plant data. © 2011 BCREC UNDIP. All rights reserved(Received: 1st March 2011, Revised: 28th March 2011; Accepted: 7th April 2011[How to Cite: A.S. Ibrehem. (2011. Modified Mathematical Model For Neutralization System In Stirred Tank Reactor. Bulletin of Chemical Reaction Engineering & Catalysis, 6(1: 47-52. doi:10.9767/bcrec.6.1.825.47-52][How to Link / DOI: http://dx.doi.org/10.9767/bcrec.6.1.825.47-52 || or local: http://ejournal.undip.ac.id/index.php/bcrec/article/view/825 ] | View in
Mathematical Models of Fluid Dynamics Modeling, Theory, Basic Numerical Facts An Introduction
Ansorge, Rainer
2009-01-01
Without sacrificing scientific strictness, this introduction to the field guides readers through mathematical modeling, the theoretical treatment of the underlying physical laws and the construction and effective use of numerical procedures to describe the behavior of the dynamics of physical flow. The book is carefully divided into three main parts:. - The design of mathematical models of physical fluid flow;. - A theoretical treatment of the equations representing the model, as Navier-Stokes, Euler, and boundary layer equations, models of turbulence, in order to gain qualitative as well as q
Mathematical models of wound healing and closure: a comprehensive review.
Jorgensen, Stephanie N; Sanders, Jonathan R
2016-09-01
Wound healing is a complex process comprised of overlapping phases and events that work to construct a new, functioning tissue. Mathematical models describe these events and yield understanding about the overall process of wound healing. Generally, these models are focused on only one phase (or a few phases) to explain healing for a specific system. A review of the literature reveals insights as reported on herein regarding the variety of overlapping inputs and outputs for any given type of model. Specifically, these models have been characterized with respect to the phases of healing and their mathematical/physical basis in an effort to shed light on new opportunities for model development. Though all phases of wound healing have been modeled, previous work has focused mostly on the proliferation and related contraction phases of healing with fewer results presented regarding other phases. As an example, a gap in the literature has been identified regarding models to describe facilitated wound closure techniques (e.g., suturing and its effect on resultant scarring). Thus, an opportunity exists to create models that tie the transient processes of wound healing, such as cell migration, to resultant scarring when considering tension applied to skin with given suturing techniques.
A New Mathematical Modeling Technique for Pull Production Control Systems
Directory of Open Access Journals (Sweden)
O. Srikanth
2013-12-01
Full Text Available The Kanban Control System widely used to control the release of parts of multistage manufacturing system operating under a pull production control system. Most of the work on Kanban Control System deals with multi-product manufacturing system. In this paper, we are proposing a regression modeling technique in a multistage manufacturing system is to be coordinates the release of parts into each stage of the system with the arrival of customer demands for final products. And also comparing two variants stages of the Kanban Control System model and combines with mathematical and Simulink model for the production coordination of parts in an assembly manufacturing systems. In both variants, the production of a new subassembly is authorized only when an assembly Kanban is available. Assembly kanbans become available when finished product is consumed. A simulation environment for the product line system has to generate with the proposed model and the mathematical model have to give implementation against the simulation model in the working platform of MATLAB. Both the simulation and model outputs have provided an in depth analysis of each of the resulting control system for offering model of a product line system.
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.
Mathematical modeling of earth's dynamical systems a primer
Slingerland, Rudy
2011-01-01
Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be f...
Mathematical modeling applied to the left ventricle of heart
Ranjbar, Saeed
2014-01-01
Background: How can mathematics help us to understand the mechanism of the cardiac motion? The best known approach is to take a mathematical model of the fibered structure, insert it into a more-or-less complex model of cardiac architecture, and then study the resulting fibers of activation that propagate through the myocardium. In our paper, we have attempted to create a novel software capable of demonstrate left ventricular (LV) model in normal hearts. Method: Echocardiography was performed on 70 healthy volunteers. Data evaluated included: velocity (radial, longitudinal, rotational and vector point), displacement (longitudinal and rotational), strain rate (longitudinal and circumferential) and strain (radial, longitudinal and circumferential) of all 16 LV myocardial segments. Using these data, force vectors of myocardial samples were estimated by MATLAB software, interfaced in the echocardiograph system. Dynamic orientation contraction (through the cardiac cycle) of every individual myocardial fiber could ...
Mathematical models in cell biology and cancer chemotherapy
Eisen, Martin
1979-01-01
The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on...
Model answers in pure mathematics for a-level students
Pratt, GA; Schofield, C W
1967-01-01
Model Answers in Pure Mathematics for A-Level Students provides a set of solutions that indicate what is required and expected in an Advanced Level examination in Pure Mathematics. This book serves as a guide to the length of answer required, layout of the solution, and methods of selecting the best approach to any particular type of math problem. This compilation intends to supplement, not replace, the normal textbook and provides a varied selection of questions for practice in addition to the worked solutions. The subjects covered in this text include algebra, trigonometry, coordinate geomet
Mathematical modeling/problem solving in global oxygen transport.
Farrell, Kevin; Hill, Andrew; Dent, Leon; Nguyen, Minh Ly
2009-08-01
A simplified approach to mathematical modeling/problem solving in global oxygen transport is presented. In addition to standard oxygen transport formulae, it uses the S-Factor and a mathematical relationship relating SvO(2) to the ratio DO(2)/VO(2). This method allows the determination or specification of SvO(2), PvO(2), P(50), and systemic shunting in the context of this simplified approach. Heretofore this has not been possible. With this approach, essentially all clinical problems in global oxygen transport can be dealt with. This is illustrated by the broad scope of the five problems presented.
Mathematical Modeling of Neuro-Vascular Coupling in Rat Cerebellum
DEFF Research Database (Denmark)
Rasmussen, Tina
Activity in the neurons called climbing fibers causes blood flow changes. But the physiological mechanisms which mediate the coupling are not well understood. This PhD thesis investigates the mechanisms of neuro-vascular coupling by means of mathematical methods. In experiments, the extracellularly...... measured field potential is used as an indicator of neuronal activity, and the cortical blood flow is measured by means of laser-Doppler flowmetry. Using system identification methods, these measurements have been used to construct and validate parametric mathematical models of the neuro-vascular system...
Mathematical model for corundum single crystal growth by Verneuil method
Grzymkowski, Radosław; Mochnacki, Bohdan; Suchy, Józef
1983-05-01
A mathematical model which is an attempt to describe the complex process of monocrystallization by the Verneuil method is presented. The problem has been solved through the method of finite differences and at the same time making use of a certain modification of the mathematical description of Stefan's problem called the the alternating phase truncation method [9]. The elaborated algorithm and the examples of solutions given at the end of the present study point at the usefulness of the presented method of numerical simulation for modern designing and controlling the processes of crystal production.
Transmission dynamics of cholera: Mathematical modeling and control strategies
Sun, Gui-Quan; Xie, Jun-Hui; Huang, Sheng-He; Jin, Zhen; Li, Ming-Tao; Liu, Liqun
2017-04-01
Cholera, as an endemic disease around the world, has generated great threat to human society and caused enormous morbidity and mortality with weak surveillance system. In this paper, we propose a mathematical model to describe the transmission of Cholera. Moreover, basic reproduction number and the global dynamics of the dynamical model are obtained. Then we apply our model to characterize the transmission process of Cholera in China. It was found that, in order to avoid its outbreak in China, it may be better to increase immunization coverage rate and make effort to improve environmental management especially for drinking water. Our results may provide some new insights for elimination of Cholera.
Mathematical modelling of the combustion of a single wood particle
Energy Technology Data Exchange (ETDEWEB)
Porteiro, J.; Miguez, J.L.; Granada, E.; Moran, J.C. [Departamento de Ingenieria Mecanica, Maquinas y Motores Termicos y Fluidos. Universidad de Vigo, Lagoas Marcosende 9 36200 Vigo (Spain)
2006-01-15
A mathematical model describing the thermal degradation of densified biomass particles is presented here. The model uses a novel discretisation scheme and combines intra-particle combustion processes with extra-particle transport processes, thereby including thermal and diffusional control mechanisms. The influence of structural changes on the physical-thermal properties of wood in its different stages is studied together with shrinkage of the particle during its degradation. The model is used to compare the predicted data with data on the mass loss dynamics and internal temperature of several particles from previous works and relevant literature, with good agreement. (author)
Mathematical model of the dynamics of countercurrent chromatography
Institute of Scientific and Technical Information of China (English)
陆向红; 任其龙; 吴平东
2002-01-01
A mathematical model of the dynamic behavior of countercurrent chromatography was proposed, and the model parameters, including the partition coefficient, the axial dispersion coefficient, the intraparticle diffusion coefficient and the external mass ransfer coefficient were calculated by the method of chromatogram moment analysis. Comparison of the experimental chromatograms of caffeine and theophylline determined in this work with the simulated curves computed by the proposed model showed fairly good agreement. Further, the difference between the average identified the partition coefficients by chromatogram moment analysis and the experimental values was small also, and the relationship between the external mass transfer rate and the linear velocity was similar to that obtained with solid-liquid chromatography.
Mathematical model for the gasification of coal under pressure
Energy Technology Data Exchange (ETDEWEB)
Biba, V.; Macak, J.; Kloss, E.; Malecha, J.
1978-01-01
A mathematical model for the the high-pressure gasification of solid fuels in the charged layer is presented which permits the quantitative description of the the static behavior of the generator. Deals with the parameters of reaction kinetics and of the transfer of matter and energy which are necessary for developing the model of a fixed-bed reactor. To obtain a practical model, simplifications are needed which concern the gasification, degasification, and drying processes. They are dealt with individually. For calculating the concentration and temperature profiles for the solid and gas phases along the gasification bed height, a system of differential equations was obtained which was supplemented by some algebraic equations.
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)
The limitations of mathematical modeling in high school physics education
Forjan, Matej
The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems
Mathematical Modeling of Contact Resistance in Silicon Photovoltaic Cells
Black, J. P.
2013-10-22
In screen-printed silicon-crystalline solar cells, the contact resistance of a thin interfacial glass layer between the silicon and the silver electrode plays a limiting role for electron transport. We analyze a simple model for electron transport across this layer, based on the driftdiffusion equations. We utilize the size of the current/Debye length to conduct asymptotic techniques to simplify the model; we solve the model numerically to find that the effective contact resistance may be a monotonic increasing, monotonic decreasing, or nonmonotonic function of the electron flux, depending on the values of the physical parameters. © 2013 Society for Industrial and Applied Mathematics.
A Mathematical Model of the Thermo-Anemometric Flowmeter
Directory of Open Access Journals (Sweden)
Igor Korobiichuk
2015-09-01
Full Text Available 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 analysis of partial differential equations modeling electrostatic MEMS
Esposito, Pierpaolo; Guo, Yujin
2010-01-01
Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed
MATHEMATICAL MODEL FOR DETERMINING THE INDICATORS OF TRACTIVE VEHICLES
Directory of Open Access Journals (Sweden)
A. F. Golovchuk
2017-06-01
Full Text Available Purpose. The research paper involves solving of the following tasks: 1 refinement of the mathematical model for determining the traction and dynamic, fuel and economic, environmental indicators of mobile energy facilities; 2 methodology development of theoretical studies of automatic control systems, static and dynamic characteristics automotive-tractor diesel with a gas turbine supercharger and a mobile power facility. Methodology. The work studies the working processes of vehicles and machine-tractor aggregates by mathematical simulation and the development of algorithms and programs for the calculation of these processes in actual operational conditions. The system of equations has been developed for theoretical research. It describes a nonlinear mathematical model of the automatic control system of an automotive-tractor diesel rotating frequency. In addition to the differential equations of the first and second order, equations are used in mathematical simulation of working processes of traction vehicles. These equations describe experimental characteristics of an automatic regulator, a high-pressure fuel pump, a turbocharger and an engine, as well as moments of engine mechanical losses and an external load. Findings. The developed mathematical model allows determining the effectiveness of new design, operational and technological developments, as well as various measures in order to improve the fuel-economic and environmental performances of vehicles and machine-tractor aggregates in operating conditions. Originality. For the first time, the mathematical model "Tractor driver – machine-tractor aggregate – road (field" was developed. It allows conducting research of transport tractor aggregates by driving cycles, taking into account the processes of starting and speeding up the mobile-power sources with gear shift. Practical value. In conditions of a protracted economic crisis, in the absence of the necessary equipment, instruments
Mathematical modeling of the neuron morphology using two dimensional images.
Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja
2016-02-01
In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.
Analyzing electrical activities of pancreatic β cells using mathematical models.
Cha, Chae Young; Powell, Trevor; Noma, Akinori
2011-11-01
Bursts of repetitive action potentials are closely related to the regulation of glucose-induced insulin secretion in pancreatic β cells. Mathematical studies with simple β-cell models have established the central principle that the burst-interburst events are generated by the interaction between fast membrane excitation and slow cytosolic components. Recently, a number of detailed models have been developed to simulate more realistic β cell activity based on expanded findings on biophysical characteristics of cellular components. However, their complex structures hinder our intuitive understanding of the underlying mechanisms, and it is becoming more difficult to dissect the role of a specific component out of the complex network. We have recently developed a new detailed model by incorporating most of ion channels and transporters recorded experimentally (the Cha-Noma model), yet the model satisfies the charge conservation law and reversible responses to physiological stimuli. Here, we review the mechanisms underlying bursting activity by applying mathematical analysis tools to representative simple and detailed models. These analyses include time-based simulation, bifurcation analysis and lead potential analysis. In addition, we introduce a new steady-state I-V (ssI-V) curve analysis. We also discuss differences in electrical signals recorded from isolated single cells or from cells maintaining electrical connections within multi-cell preparations. Towards this end, we perform simulations with our detailed pancreatic β-cell model.
Advanced Mathematical Model to Describe the Production of Biodiesel Process
Directory of Open Access Journals (Sweden)
Hikmat S. Al-Salim
2009-12-01
Full Text Available Advanced mathematical model was used to capture the batch reactor characteristics of reacting compounds. The model was applied to batch reactor for the production of bio-diesel from palm and kapok oils. Results of the model were compared with experimental data in terms of conversion of transesterification reaction for the production of bio-diesel under unsteady state. A good agreement was obtained between our model predictions and the experimental data. Both experimental and modeling results showed that the conversion of triglycerides to methyl ester was affected by the process conditions. The transesterification process with temperature of about 70 oC, and methanol ratio to the triglyceride of about 5 times its stoichiometry, and the NAOH catalyst of wt 0.4%, appear to be acceptable process conditions for bio diesel process production from palm oil and kapok oil. The model can be applied for endothermic batch process. © 2009 BCREC UNDIP. All rights reserved[Received: 12 August 2009, Revised: 15 October 2009; Accepted: 18 October 2009][How to Cite: A.S. Ibrehem, H. S. Al-Salim. (2009. Advanced Mathematical Model to Describe the Production of Biodiesel Process. Bulletin of Chemical Reaction Engineering and Catalysis, 4(2: 37-42. doi:10.9767/bcrec.4.2.28.37-42][How to Link/DOI: http://dx.doi.org/10.9767/bcrec.4.2.28.37-42
Dr. S. Jayakumar; Geetha, S.
2017-01-01
Mathematical Model is an idealization of the real world Phenomenon and never a completely accurate representation. Any Model has its limitations a good one can provide valuable results and conclusions. Mathematical Model as a mathematical construct designed to study a particular real world systems or behavior of Interest. The Model allows us to reach mathematical conclusions about the behavior; These conclusions can be interpreted to help a decision maker plan for the future. Most models simp...
Preventing clonal evolutionary processes in cancer: Insights from mathematical models.
Rodriguez-Brenes, Ignacio A; Wodarz, Dominik
2015-07-21
Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.
Mathematical Modeling and Analysis of Multirobot Cooperative Hunting Behaviors
Directory of Open Access Journals (Sweden)
Yong Song
2015-01-01
Full Text Available This paper presents a mathematical model of multirobot cooperative hunting behavior. Multiple robots try to search for and surround a prey. When a robot detects a prey it forms a following team. When another “searching” robot detects the same prey, the robots form a new following team. Until four robots have detected the same prey, the prey disappears from the simulation and the robots return to searching for other prey. If a following team fails to be joined by another robot within a certain time limit the team is disbanded and the robots return to searching state. The mathematical model is formulated by a set of rate equations. The evolution of robot collective hunting behaviors represents the transition between different states of robots. The complex collective hunting behavior emerges through local interaction. The paper presents numerical solutions to normalized versions of the model equations and provides both a steady state and a collaboration ratio analysis. The value of the delay time is shown through mathematical modeling to be a strong factor in the performance of the system as well as the relative numbers of the searching robots and the prey.
Mathematical and computer modeling of component surface shaping
Lyashkov, A.
2016-04-01
The process of shaping technical surfaces is an interaction of a tool (a shape element) and a component (a formable element or a workpiece) in their relative movements. It was established that the main objects of formation are: 1) a discriminant of a surfaces family, formed by the movement of the shape element relatively the workpiece; 2) an enveloping model of the real component surface obtained after machining, including transition curves and undercut lines; 3) The model of cut-off layers obtained in the process of shaping. When modeling shaping objects there are a lot of insufficiently solved or unsolved issues that make up a single scientific problem - a problem of qualitative shaping of the surface of the tool and then the component surface produced by this tool. The improvement of known metal-cutting tools, intensive development of systems of their computer-aided design requires further improvement of the methods of shaping the mating surfaces. In this regard, an important role is played by the study of the processes of shaping of technical surfaces with the use of the positive aspects of analytical and numerical mathematical methods and techniques associated with the use of mathematical and computer modeling. The author of the paper has posed and has solved the problem of development of mathematical, geometric and algorithmic support of computer-aided design of cutting tools based on computer simulation of the shaping process of surfaces.
Mathematical modelling of the growth of human fetus anatomical structures.
Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech
2016-07-08
The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.
Mathematical modeling of normal pharyngeal bolus transport: a preliminary study.
Chang, M W; Rosendall, B; Finlayson, B A
1998-07-01
Dysphagia (difficulty in swallowing) is a common clinical symptom associated with many diseases, such as stroke, multiple sclerosis, neuromuscular diseases, and cancer. Its complications include choking, aspiration, malnutrition, cachexia, and dehydration. The goal in dysphagia management is to provide adequate nutrition and hydration while minimizing the risk of choking and aspiration. It is important to advance the individual toward oral feeding in a timely manner to enhance the recovery of swallowing function and preserve the quality of life. Current clinical assessments of dysphagia are limited in providing adequate guidelines for oral feeding. Mathematical modeling of the fluid dynamics of pharyngeal bolus transport provides a unique opportunity for studying the physiology and pathophysiology of swallowing. Finite element analysis (FEA) is a special case of computational fluid dynamics (CFD). In CFD, the flow of a fluid in a space is modeled by covering the space with a grid and predicting how the fluid moves from grid point to grid point. FEA is capable of solving problems with complex geometries and free surfaces. A preliminary pharyngeal model has been constructed using FEA. This model incorporates literature-reported, normal, anatomical data with time-dependent pharyngeal/upper esophageal sphincter (UES) wall motion obtained from videofluorography (VFG). This time-dependent wall motion can be implemented as a moving boundary condition in the model. Clinical kinematic data can be digitized from VFG studies to construct and test the mathematical model. The preliminary model demonstrates the feasibility of modeling pharyngeal bolus transport, which, to our knowledge, has not been attempted before. This model also addresses the need and the potential for CFD in understanding the physiology and pathophysiology of the pharyngeal phase of swallowing. Improvements of the model are underway. Combining the model with individualized clinical data should potentially
Wright, Vince
2014-03-01
Pirie and Kieren (1989 For the learning of mathematics, 9(3)7-11, 1992 Journal of Mathematical Behavior, 11, 243-257, 1994a Educational Studies in Mathematics, 26, 61-86, 1994b For the Learning of Mathematics, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which learners develop their mathematical understanding. The model was adapted to create the teaching model used in the New Zealand Numeracy Development Projects (Ministry of Education, 2007). A case study of a 3-week sequence of instruction with a group of eight 12- and 13-year-old students provided the data. The teacher/researcher used folding back to materials and images and progressing from materials to imaging to number properties to assist students to develop their understanding of frequencies as proportions. The data show that successful implementation of the model is dependent on the teacher noticing and responding to the layers of understanding demonstrated by the students and the careful selection of materials, problems and situations. It supports the use of the model as a useful part of teachers' instructional strategies and the importance of pedagogical content knowledge to the quality of the way the model is used.
Analysing the Competency of Mathematical Modelling in Physics
Redish, Edward F
2016-01-01
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of the maths we draw on grows as our students progress through a physics curriculum. Despite much research on the learning of both physics and math, the problem of how to successfully teach most of our students to use maths in physics effectively remains unsolved. A fundamental issue is that in physics, we don't just use maths, we think about the physical world with it. As a result, we make meaning with math-ematical symbology in a different way than mathematicians do. In this talk we analyze how developing the competency of mathematical modeling is more than just "learning to do math" but requires learning to blend physical meaning into mathematical representations and use that physical meaning in solving problems. Examples are drawn from across the curriculum.
A Mathematical Model to Improve the Performance of Logistics Network
Directory of Open Access Journals (Sweden)
Muhammad Izman Herdiansyah
2012-01-01
Full Text Available The role of logistics nowadays is expanding from just providing transportation and warehousing to offering total integrated logistics. To remain competitive in the global market environment, business enterprises need to improve their logistics operations performance. The improvement will be achieved when we can provide a comprehensive analysis and optimize its network performances. In this paper, a mixed integer linier model for optimizing logistics network performance is developed. It provides a single-product multi-period multi-facilities model, as well as the multi-product concept. The problem is modeled in form of a network flow problem with the main objective to minimize total logistics cost. The problem can be solved using commercial linear programming package like CPLEX or LINDO. Even in small case, the solver in Excel may also be used to solve such model.Keywords: logistics network, integrated model, mathematical programming, network optimization
Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics
Agoshkov, V. I.; Zalesny, V. B.
2012-03-01
Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of Numerical Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and space coordinates. Numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples. These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean dynamics model with an observed data assimilation procedure.
A Mathematical Model to Improve the Performance of Logistics Network
Directory of Open Access Journals (Sweden)
Muhammad Izman Herdiansyah
2012-01-01
Full Text Available The role of logistics nowadays is expanding from just providing transportation and warehousing to offering total integrated logistics. To remain competitive in the global market environment, business enterprises need to improve their logistics operations performance. The improvement will be achieved when we can provide a comprehensive analysis and optimize its network performances. In this paper, a mixed integer linier model for optimizing logistics network performance is developed. It provides a single-product multi-period multi-facilities model, as well as the multi-product concept. The problem is modeled in form of a network flow problem with the main objective to minimize total logistics cost. The problem can be solved using commercial linear programming package like CPLEX or LINDO. Even in small case, the solver in Excel may also be used to solve such model.Keywords: logistics network, integrated model, mathematical programming, network optimization
Mathematical model and simulation of partial penetrated weld pool
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The qualitative analysis on the behavior of partial penetrated weld pool transferring from pulsed peak current to base current in pulsed TIG welding is carried out in this paper. Based on the analysis results, the mathematical models for 3D liquid surface shape of partial penetrated weld pool in pulsed TIG welding are created including surface potential energy model, gravitational energy model and volumetric potential energy. The numerical simulation with these models and the experiments on low carbon steel are carried out using the software Surface Evolver. The simulation results and model are then amended with experimental results. Two important characteristic quantities, the liquid metal coverage ratio and the stripping width of liquid metal, are put forward in this paper, which paves a way for further weld pool full penetration control.
Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics
Directory of Open Access Journals (Sweden)
Cecilia Noecker
2015-03-01
Full Text Available Upon infection of a new host, human immunodeficiency virus (HIV replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV. First, we found that the mode of virus production by infected cells (budding vs. bursting has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral
Micro-macro models for viscoelastic fluids:modelling,mathematics and numerics
Institute of Scientific and Technical Information of China (English)
LE; BRIS; Claude; LELIVRE; Tony
2012-01-01
This paper is an introduction to the modelling of viscoelastic fluids,with an emphasis on micromacro(or multiscale) models.Some elements of mathematical and numerical analysis are provided.These notes closely follow the lectures delivered by the second author at the Chinese Academy of Science during the Workshop "Stress Tensor E?ects on Fluid Mechanics" in January 2010.
Mathematical models for predicting indoor air quality from smoking activity.
Ott, W R
1999-05-01
Much progress has been made over four decades in developing, testing, and evaluating the performance of mathematical models for predicting pollutant concentrations from smoking in indoor settings. Although largely overlooked by the regulatory community, these models provide regulators and risk assessors with practical tools for quantitatively estimating the exposure level that people receive indoors for a given level of smoking activity. This article reviews the development of the mass balance model and its application to predicting indoor pollutant concentrations from cigarette smoke and derives the time-averaged version of the model from the basic laws of conservation of mass. A simple table is provided of computed respirable particulate concentrations for any indoor location for which the active smoking count, volume, and concentration decay rate (deposition rate combined with air exchange rate) are known. Using the indoor ventilatory air exchange rate causes slightly higher indoor concentrations and therefore errs on the side of protecting health, since it excludes particle deposition effects, whereas using the observed particle decay rate gives a more accurate prediction of indoor concentrations. This table permits easy comparisons of indoor concentrations with air quality guidelines and indoor standards for different combinations of active smoking counts and air exchange rates. The published literature on mathematical models of environmental tobacco smoke also is reviewed and indicates that these models generally give good agreement between predicted concentrations and actual indoor measurements.
Evaluation of Mathematical Models for Tankers’ Maneuvering Motions
Directory of Open Access Journals (Sweden)
Erhan AKSU
2017-03-01
Full Text Available In this study, the maneuvering performance of two tanker ships, KVLCC1 and KVLCC2 which have different stern forms are predicted using a system-based method. Two different 3 DOF (degrees of freedom mathematical models based on the MMG(Maneuvering Modeling Group concept areappliedwith the difference in representing lateral force and yawing moment by second and third order polynomials respectively. Hydrodynamic coefficients and related parameters used in the mathematical models of the same scale models of KVLCC1 and KVLCC2 ships are estimated by using experimental data of NMRI (National Maritime Research Institute. The simulations of turning circle with rudder angle ±35o , zigzag(±10o /±10o and zigzag (±20o /±20o maneuvers are carried out and compared with free running model test data of MARIN (Maritime Research Institute Netherlands in this study. As a result of the analysis, it can be summarised that MMG model based on the third order polynomial is superior to the one based on the second order polynomial in view of estimation accuracy of lateral hull force and yawing moment.
Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming
Colins, Andrea; Gerdtzen, Ziomara P.; Nuñez, Marco T.; Salgado, J. Cristian
2017-01-01
Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex
Mathematical Modelling of Silica Scaling Deposition in Geothermal Wells
Nizami, M.; Sutopo
2016-09-01
Silica scaling is widely encountered in geothermal wells in which produce two-phase geothermal fluid. Silica scaling could be formed due to chemical reacting by mixing a geothermal fluid with other geothermal fluid in different compositions, or also can be caused by changes in fluid properties due to changes pressure and temperature. One of method to overcome silica scaling which is occurred around geothermal well is by workover operation. Modelling of silica deposition in porous medium has been modeled in previously. However, the growth of silica scaling deposition in geothermal wells has never been modeled. Modelling of silica deposition through geothermal is important aspects to determine depth of silica scaling growth and best placing for workover device to clean silica scaling. This study is attempted to develop mathematical models for predicting silica scaling through geothermal wells. The mathematical model is developed by integrating the solubility-temperature correlation and two-phase pressure drop coupled wellbore fluid temperature correlation in a production well. The coupled model of two-phase pressure drop and wellbore fluid temperature correlation which is used in this paper is Hasan-Kabir correlation. This modelling is divided into two categories: single and two phase fluid model. Modelling of silica deposition is constrained in temperature distribution effect through geothermal wells by solubility correlation for silica. The results of this study are visualizing the growth of silica scaling thickness through geothermal wells in each segment of depth. Sensitivity analysis is applied in several parameters, such as: bottom-hole pressure, temperature, and silica concentrations. Temperature is most impact factor for silica scaling through geothermal wellbore and depth of flash point. In flash point, silica scaling thickness has reached maximum because reducing of mole in liquid portion.
Nonlinear Mathematical Modeling in Pneumatic Servo Position Applications
Directory of Open Access Journals (Sweden)
Antonio Carlos Valdiero
2011-01-01
Full Text Available This paper addresses a new methodology for servo pneumatic actuators mathematical modeling and selection from the dynamic behavior study in engineering applications. The pneumatic actuator is very common in industrial application because it has the following advantages: its maintenance is easy and simple, with relatively low cost, self-cooling properties, good power density (power/dimension rate, fast acting with high accelerations, and installation flexibility. The proposed fifth-order nonlinear mathematical model represents the main characteristics of this nonlinear dynamic system, as servo valve dead zone, air flow-pressure relationship through valve orifice, air compressibility, and friction effects between contact surfaces in actuator seals. Simulation results show the dynamic performance for different pneumatic cylinders in order to see which features contribute to a better behavior of the system. The knowledge of this behavior allows an appropriate choice of pneumatic actuator, mainly contributing to the success of their precise control in several applications.
Mathematical modeling and numerical simulation of Czochralski Crystal Growth
Energy Technology Data Exchange (ETDEWEB)
Jaervinen, J.; Nieminen, R. [Center for Scientific Computing, Espoo (Finland)
1996-12-31
A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)