Gupta, CB; Kumar, V
2009-01-01
About the Book: This book `Advanced Mathematics` is primarily designed for B.Tech., IV Semester (EE and EC branch) students of Rajasthan Technical University. The subject matter is discussed in a lucid manner. The discussion is covered in five units: Unit I: deals with Numerical Analysis, Unit-II: gives different aspects of Numerical Analysis, Unit-III: Special Function, Unit-IV:Statistics and Probability, Calculus of Variation and Transforms are discussed in Unit V. All the theoretical concepts are explained through solved examples. Besides, a large number of unsolved problems on each top
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
Advanced Mathematical Model to Describe the Production of Biodiesel Process
Directory of Open Access Journals (Sweden)
Ahmmed S. Ibrehem
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.4.2.7109.37-42][How to Link/DOI: http://dx.doi.org/10.9767/bcrec.4.2.7109.37-42 || or local: http://ejournal.undip.ac.id/index.php/bcrec/article/view/7109 ]
Copper Oxide Nanoparticles for Advanced Refrigerant Thermophysical Properties: Mathematical Modeling
Directory of Open Access Journals (Sweden)
S. A. Fadhilah
2014-01-01
Full Text Available In modern days, refrigeration systems are important for industrial and domestic applications. The systems consume more electricity as compared to other appliances. The refrigeration systems have been investigated thoroughly in many ways to reduce the energy consumption. Hence, nanorefrigerant which is one kind of nanofluids has been introduced as a superior properties refrigerant that increased the heat transfer rate in the refrigeration system. Many types of materials could be used as the nanoparticles to be suspended into the conventional refrigerants. In this study, the effect of the suspended copper oxide (CuO nanoparticles into the 1,1,1,2-tetrafluoroethane, R-134a is investigated by using mathematical modeling. The investigation includes the thermal conductivity, dynamic viscosity, and heat transfer rate of the nanorefrigerant in a tube of evaporator. The results show enhanced thermophysical properties of nanorefrigerant compared to the conventional refrigerant. These advanced thermophysical properties increased the heat transfer rate in the tube. The nanorefrigerant could be a potential working fluid to be used in the refrigeration system to increase the heat transfer characteristics and save the energy usage.
Advanced engineering mathematics
Jeffrey, Alan
2001-01-01
Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...
Energy Technology Data Exchange (ETDEWEB)
1990-12-01
The issue of global warming and related climatic changes from increasing concentrations of greenhouse gases in the atmosphere has received prominent attention during the past few years. The Computer Hardware, Advanced Mathematics, and Model Physics (CHAMMP) Climate Modeling Program is designed to contribute directly to this rapid improvement. The goal of the CHAMMP Climate Modeling Program is to develop, verify, and apply a new generation of climate models within a coordinated framework that incorporates the best available scientific and numerical approaches to represent physical, biogeochemical, and ecological processes, that fully utilizes the hardware and software capabilities of new computer architectures, that probes the limits of climate predictability, and finally that can be used to address the challenging problem of understanding the greenhouse climate issue through the ability of the models to simulate time-dependent climatic changes over extended times and with regional resolution.
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.
Multi-band effective mass approximations advanced mathematical models and numerical techniques
Koprucki, Thomas
2014-01-01
This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operational principle. Secondly, they allow us to predict and optimize in advance the qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used wit...
Advances in biomolecular surface meshing and its applications to mathematical modeling
Institute of Scientific and Technical Information of China (English)
CHEN MinXin; LU BenZhuo
2013-01-01
In the field of molecular modeling and simulation,molecular surface meshes are necessary for many problems,such as molecular structure visualization and analysis,docking problem and implicit solvent modeling and simulation.Recently,with the developments of advanced mathematical modeling in the field of implicit solvent modeling and simulation,providing surface meshes with good qualities efficiently for large real biomolecular systems becomes an urgent issue beyond its traditional purposes for visualization and geometry analyses for molecular structure.In this review,we summarize recent works on this issue.First,various definitions of molecular surfaces and corresponding meshing methods are introduced.Second,our recent meshing tool,TMSmesh,and its performances are presented.Finally,we show the applications of the molecular surface mesh in implicit solvent modeling and simulations using boundary element method (BEM) and finite element method (FEM).
Moscardini, Alfredo
1994-01-01
As the role of the modern engineer is markedly different from that of even a decade ago, the theme of engineering mathematics educa tion (EME) is an important one. The need for mathematical model ling (MM) courses and consideration of the educational impact of computer-based technology environments merit special attention. This book contains the proceeding of the NATO Advanced Research Workshop held on this theme in July 1993. We have left the industrial age behind and have entered the in formation age. Computers and other emerging technologies are penetrating society in depth and gaining a strong influence in de termining how in future society will be organised, while the rapid change of information requires a more qualified work force. This work force is vital to high technology and economic competitive ness in many industrialised countries throughout the world. Within this framework, the quality of EME has become an issue. It is expected that the content of mathematics courses taught in schools o...
Advances in mathematical economics
Maruyama, Toru
2016-01-01
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
Advances in mathematical economics
Maruyama, Toru
2015-01-01
The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.
Advances in mathematical economics
Yamazaki, Akira
2006-01-01
A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions.Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.
Advances in mathematical economics
Maruyama, Toru
2014-01-01
A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research.
Advances in mathematical economics
Yamazaki, Akira
2006-01-01
A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.
A bridge to advanced mathematics
Sentilles, Dennis
2011-01-01
This helpful workbook-style ""bridge"" book introduces students to the foundations of advanced mathematics, spanning the gap between a practically oriented calculus sequence and subsequent courses in algebra and analysis with a more theoretical slant. Part 1 focuses on logic and number systems, providing the most basic tools, examples, and motivation for the manner, method, and concerns of higher mathematics. Part 2 covers sets, relations, functions, infinite sets, and mathematical proofs and reasoning. Author Dennis Sentilles also discusses the history and development of mathematics as well a
Advances in mathematical economics
Yamazaki, Akira
2005-01-01
A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. The editorial board of this series comprises the following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors: R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont...
Computer Hardware, Advanced Mathematics and Model Physics pilot project final report
International Nuclear Information System (INIS)
The Computer Hardware, Advanced Mathematics and Model Physics (CHAMMP) Program was launched in January, 1990. A principal objective of the program has been to utilize the emerging capabilities of massively parallel scientific computers in the challenge of regional scale predictions of decade-to-century climate change. CHAMMP has already demonstrated the feasibility of achieving a 10,000 fold increase in computational throughput for climate modeling in this decade. What we have also recognized, however, is the need for new algorithms and computer software to capitalize on the radically new computing architectures. This report describes the pilot CHAMMP projects at the DOE National Laboratories and the National Center for Atmospheric Research (NCAR). The pilot projects were selected to identify the principal challenges to CHAMMP and to entrain new scientific computing expertise. The success of some of these projects has aided in the definition of the CHAMMP scientific plan. Many of the papers in this report have been or will be submitted for publication in the open literature. Readers are urged to consult with the authors directly for questions or comments about their papers
W.A. Stolk (Wilma); S.J. de Vlas (Sake); J.D.F. Habbema (Dik)
2006-01-01
textabstractMathematical simulation models for transmission and control of lymphatic filariasis are useful tools for studying the prospects of lymphatic filariasis elimination. Two simulation models are currently being used. The first, EPIFIL, is a population-based, deterministic model that simulate
How can mathematical models advance tuberculosis control in high HIV prevalence settings?
Houben, RM; Dowdy, DW; Vassall, A.; Cohen, T; Nicol, MP; Granich, RM; Shea, JE; Eckhoff, P.; Dye, C.; Kimerling, ME; White, RG; TB MAC TB-HIV meeting participants
2014-01-01
Existing approaches to tuberculosis (TB) control have been no more than partially successful in areas with high human immunodeficiency virus (HIV) prevalence. In the context of increasingly constrained resources, mathematical modelling can augment understanding and support policy for implementing those strategies that are most likely to bring public health and economic benefits. In this paper, we present an overview of past and recent contributions of TB modelling in this key area, and sugges...
Results of mathematical modeling of an advanced Joule-heated nuclear waste glass melter
International Nuclear Information System (INIS)
Three-dimensional mathematical modeling of a Joule-heated, liquid-fed nuclear waste glass melter is described. The method used for the solution of the governing differential equations was the finite control-volume approach. Results are presented including the electric field in the glass pool, the distribution of Joule-heat and temperature, and the flow field. The computer simulations were performed for a melter model containing glass of normal melt properties throughout the glass pool, and for one in which noble metals segregations were assumed. It is shown, that modeling helps to predict the performance of the system under standard and off-standard conditions. (author)
DEFF Research Database (Denmark)
Martens, Sebastian; Mijatovic, Nenad; Holbøll, Joachim;
2015-01-01
many areas of electrical machine analysis. However, for fault investigations, the phase-coordinate representation has been found more suitable. This paper presents a mathematical model in phase coordinates of the DFIG with two parallel windings per rotor phase. The model has been implemented in Matlab...... and its properties in context of fault simulations and investigations has been investigated. Some of the most common faults have been simulated, namely broken rotor bars or windings, dynamic eccentricities and stator phase winding short circuits. These fault conditions propagate to the stator current...
Advances in mechanics and mathematics
Ogden, Ray
2002-01-01
Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.
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…
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
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
Computational experiment approach to advanced secondary mathematics curriculum
Abramovich, Sergei
2014-01-01
This book promotes the experimental mathematics approach in the context of secondary mathematics curriculum by exploring mathematical models depending on parameters that were typically considered advanced in the pre-digital education era. This approach, by drawing on the power of computers to perform numerical computations and graphical constructions, stimulates formal learning of mathematics through making sense of a computational experiment. It allows one (in the spirit of Freudenthal) to bridge serious mathematical content and contemporary teaching practice. In other words, the notion of teaching experiment can be extended to include a true mathematical experiment. When used appropriately, the approach creates conditions for collateral learning (in the spirit of Dewey) to occur including the development of skills important for engineering applications of mathematics. In the context of a mathematics teacher education program, this book addresses a call for the preparation of teachers capable of utilizing mo...
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 process...... 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 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...
International Conference on Advances in Applied Mathematics
Hammami, Mohamed; Masmoudi, Afif
2015-01-01
This contributed volume presents some recent theoretical advances in mathematics and its applications in various areas of science and technology. Written by internationally recognized scientists and researchers, the chapters in this book are based on talks given at the International Conference on Advances in Applied Mathematics (ICAAM), which took place December 16-19, 2013, in Hammamet, Tunisia. Topics discussed at the conference included spectral theory, operator theory, optimization, numerical analysis, ordinary and partial differential equations, dynamical systems, control theory, probability, and statistics. These proceedings aim to foster and develop further growth in all areas of applied mathematics.
Mathematics for natural scientists II advanced methods
Kantorovich, Lev
2016-01-01
This book covers the advanced mathematical techniques useful for physics and engineering students, presented in a form accessible to physics students, avoiding precise mathematical jargon and laborious proofs. Instead, all proofs are given in a simplified form that is clear and convincing for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each chapter. Mathematics for Natural Scientists II: Advanced Methods is the second of two volumes. It follows the first volume on Fundamentals and Basics.
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.
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Mathematical 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.
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 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.
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Reassessing the economic value of advanced level mathematics
Adkins, Michael; Noyes, Andrew
2016-01-01
In the late 1990s, the economic return to Advanced level (A-level) mathematics was examined. The analysis was based upon a series of log-linear models of earnings in the 1958 National Child Development Survey (NCDS) and the National Survey of 1980 Graduates and Diplomates. The core finding was that A-level mathematics had a unique earnings premium of 7-10% at age 33. In recent years, this finding has contributed to the government’s agenda of increasing participation in post-16 study of advanc...
Advances in interdisciplinary applied discrete mathematics
Kaul, Hemanshu
2010-01-01
In the past 50 years, discrete mathematics has developed as a far-reaching and popular language for modeling fundamental problems in computer science, biology, sociology, operations research, economics, engineering, etc. The same model may appear in different guises, or a variety of models may have enough similarities such that same ideas and techniques can be applied in diverse applications. This book focuses on fields such as consensus and voting theory, clustering, location theory, mathematical biology, and optimization that have seen an upsurge of new and exciting works over the past two d
Mathematical Modeling: Convoying Merchant Ships
Mathews, Susann M.
2004-01-01
This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…
Directory of Open Access Journals (Sweden)
LIVIU S. BOCÎI
2013-06-01
Full Text Available This paper establishes a mathematical model of induction machine connected to a frequency inverter necessary to adjust the electric motor drive. The mathematical model based on the Park's theory allows the analysis of the whole spectrum (electric car – frequency inverter to drive the electric trolley bus made on ASTRA Bus Arad (Romania. To remove higher order harmonics, the PWM waveform of supply voltage is used, set in the general case. Operating characteristics of electric motor drive are set to sub-nominal frequency (f Bele 2007.Este documento estabelece um modelo matemático de máquina de indução conectado a um inversor de frequência necessário para ajustar o motor de acionamento elétrico. O modelo matemático baseado na Teoria de Park permite a análise de todo o espectro (carro elétrico com inversor de frequência para dirigir o ônibus elétrico feito em ASTRA Bus Arad (Romênia. Para remover harmônicas de ordem mais alta, a forma de onda da tensão de alimentação PWM é utilizado, definido no caso geral. Características de funcionamento do motor de acionamento elétrico são definidas para frequência sub-nominal (f
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 Modeling in Mathematics Education: Basic Concepts and Approaches
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Introduction to mathematical modeling and chaotic dynamics
Upadhyay, Ranjit Kumar
2013-01-01
""The presentation is so clear that anyone with even a basic mathematical background can study it and get a clear picture. … Unlike many other similar textbooks, a rich reference section is given at the end of each chapter. The cautious selection of worked out examples and exercises throughout the book is superb. For anyone with previous experience of having run into books in mathematical modeling and chaotic dynamics that rapidly move into advanced mathematical content, the book offers a pleasant recourse at an introductory level and therefore can be very inspirational.""-MAA Reviews, Decembe
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...
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
Advanced Mathematics Course-Taking: A Focus on Gender Equifinality
You, Sukkyung; Sharkey, Jill D.
2012-01-01
High school mathematics achievement predicts future success. Potentially different factors that lead to success for boys versus girls, termed equifinality, are not well understood. Such factors are needed to inform interventions to increase numbers of students taking advanced mathematics courses and going on into science and mathematics careers.…
Adding structure to the transition process to advanced mathematical activity
Engelbrecht, Johann
2010-03-01
The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.
Campbell, D. Michael
The lack of preparation, participation, and equal access of students in mathematics and the science education continues to afflict America's high school system (Ratliff, 2001). Additionally, gender and ethnic status have become significant factors as females and minority subgroups such as African Americans and Hispanics continue to be underrepresented in these two subject fields. Recognizing and understanding these trends is extremely important for the future of this country. As fewer minorities and females become involved in advanced mathematics and science curriculum there will be a continued lack of minorities and females in mathematics and science careers. Additionally, this insufficient representation leads to fewer numbers of females and minorities in industry and educational leadership positions in mathematics and science to promote participation and equality in these fields. According to Brainard and Carlin (2003) as trends currently stand, these two groups will be under-represented in the fields of math and science and will continue to be denied economic and social power. Thus, a better understanding of these trends in participation in mathematics and science among these groups of students is warranted. This study is intended to accomplish four objectives. The first objective is to identify the extent to which opportunities are increasing or decreasing for students in high schools taking mathematics and science Advanced Placement exams by examining six years of student testing data from the College Board. A second objective is to identify features of high schools that relate to greater expansion in Advanced Placement test taking for females and minority groups in the areas of both math and science. A third objective is to explore whether, and to what extent, any social or educational features such as economic status, regional school and living locations, and ethnic backgrounds have enhanced or reduced Advanced Placement testing in these schools. Lastly
Biodistribution of radiopharmaceuticals - mathematic models
International Nuclear Information System (INIS)
Characteristic biodistributions of radiopharmaceuticals were investigated by means of mathematical pharmacokinetics. Beside linear concentration dependent transport processes the existence of chemical equilibria in corresponding compartments producing chemically different transport and permeating species were included. The derived relations have been demonstrated by mathematical organ models comprising the renal excretion, the distribution of an osteotropic radiopharmaceutical between the skelet and the tumour compartment as well as a kidney model. (author)
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)
Koichu, Boris
2010-01-01
This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…
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...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated as...
Mathematical applications and modelling yearbook 2010, Association of Mathematics Educators
Scientific, World
2010-01-01
Mathematical Applications and Modelling is the second in the series of the yearbooks of the Association of Mathematics Educators in Singapore. The book is unique as it addresses a focused theme on mathematics education. The objective is to illustrate the diversity within the theme and present research that translates into classroom pedagogies.The book, comprising of 17 chapters, illuminates how application and modelling tasks may help develop the capacity of students to use mathematics in their present and future lives. Several renowned international researchers in the field of mathematical mo
Mathematical Models of Gene Regulation
Mackey, Michael C.
2004-03-01
This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.
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 circulatory system model
Lakin, William D. (Inventor); Stevens, Scott A. (Inventor)
2010-01-01
A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.
Mathematical Modeling: A Bridge to STEM Education
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…
All Students Need Advanced Mathematics. Math Works
Achieve, Inc., 2013
2013-01-01
This fact sheet explains that to thrive in today's world, all students will need to graduate with very strong math skills. That can only mean one thing: advanced math courses are now essential math courses. Highlights of this paper include: (1) Advanced math equals college success; (2) Advanced math equals career opportunity; and (3) Advanced math…
Mathematics teachers’ ideas about mathematical models: a diverse landscape
Alfredo Bautista; 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 questions through content analysis. A varied landscape of ideas was identified. Teachers referred to different entities as constituting models, expresse...
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments
Mathematical modelling of reservoir ecosystems
Czech Academy of Sciences Publication Activity Database
Růžička, Martin; Hejzlar, Josef; Kafková, Dagmar; Balejová, Marcela; Thébault, J. M.
2001-01-01
Roč. 49, č. 2 (2001), s. 109-124. ISSN 0042-790X R&D Projects: GA ČR GA103/98/0281; GA AV ČR IAA3042903 Keywords : mathematical model ling * ecosystems * reservoir Rimov Subject RIV: BK - Fluid Dynamics
10th European Conference on Numerical Mathematics and Advanced Applications
Deparis, Simone; Kressner, Daniel; Nobile, Fabio; Picasso, Marco
2015-01-01
This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.
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…
Mathematical models of bipolar disorder
Daugherty, D; Roque-Urrea, T; Urrea-Roque, J; DE TROYER, J; Wirkus, S; Porter, M. A.
2009-01-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using ...
Mathematical Models of Bipolar Disorder
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Snyder, Jessica; Wirkus, Stephen; Mason A. Porter
2003-01-01
We use limit cycle oscillators to model Bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about one percent of the United States adult population. We consider two nonlinear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individual...
Mathematical Model for Photovoltaic Cells
Wafaa ABD EL-BASIT; Ashraf Mosleh ABD El–MAKSOOD; Fouad Abd El-Moniem Saad SOLIMAN
2013-01-01
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 ...
Logical Tree of Mathematical Modeling
Directory of Open Access Journals (Sweden)
László Pokorádi
2015-04-01
Full Text Available During setting up a mathematical model, it can be very important and dicult task to choose input parametersthat should be known for solution of this problem. A similar problem might come up when someone wants to carryout an engineering calculation task. A very essential aim technical education is developing of good logical engineeringthinking. One main part of this thinking is to determine the potential sets of required input parameters of anengineering calculation. This paper proposes a logical tree based method to determine the required parameters of amathematical model. The method gives a lively description about needed data base, and computational sequence forus to get to determine the set of required output parameter. The shown method is named LogTreeMM - Logical Treeof Mathematical Modeling.
Mathematical Model of Age Aggression
Golovinski, P. A.
2013-01-01
We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...
Mathematical 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 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: A Bridge to STEM Education
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may contribute to theoretical conceptualization of STEM education by specifically addressing the professional competencies that teachers need. The discussio...
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.
Mathematical models of bipolar disorder
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
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.
Mathematical models of viscous friction
Buttà, Paolo; Marchioro, Carlo
2015-01-01
In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...
Mathematical model for classification of EEG signals
Ortiz, Victor H.; Tapia, Juan J.
2015-09-01
A mathematical model to filter and classify brain signals from a brain machine interface is developed. The mathematical model classifies the signals from the different lobes of the brain to differentiate the signals: alpha, beta, gamma and theta, besides the signals from vision, speech, and orientation. The model to develop further eliminates noise signals that occur in the process of signal acquisition. This mathematical model can be used on different platforms interfaces for rehabilitation of physically handicapped persons.
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 Foundations of Quantum Mechanics: An Advanced Short Course
Moretti, Valter
2015-01-01
This paper collects and extends the lectures given by the author at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C*-) algebraic formulation of quantum theories.
GEM - A Platform for Advanced Mathematical Geosimulations
Czech Academy of Sciences Publication Activity Database
Blaheta, Radim; Jakl, Ondřej; Kohut, Roman; Starý, Jiří
Vol. Part 1. Berlin, Heidelberg, New York : Springer - Verlag, 2010 - (Wyrzykowski, R.; Dongarra, J.; Karczewski, K.; Wasniewski, J.), s. 266-275 ISBN 978-3-642-14389-2. ISSN 0302-9743. - (Lecture Notes in Computer Science. LNCS. 6067). [International Conference, PPAM 2009 /8./. Wroclaw (PL), 13.09.2009-16.09.2009] R&D Projects: GA ČR GA105/09/1830 Institutional research plan: CEZ:AV0Z30860518 Keywords : finite element modelling * parallel solvers * applications in geosciences Subject RIV: JC - Computer Hardware ; Software http://www.springerlink.com/content/e68qgt23t51x1605/fulltext.pdf
Particles in thickening: mathematical model
International Nuclear Information System (INIS)
A mathematical model to describe the changes in the particle size distribution immediately below the solid/liquid interface in gravity thickening was formulated and tested against experimental results. The distribution is predicted to change by coagulation and differential sedimentation. Modifications to the collision efficiency functions for Brownian motion, fluid shear, and differential sedimentation were necessary to account for the high concentrations in thickening. The model correctly predicted the observed trends for both the coagulation and differential sedimentation aspects of the experimental results for changes with time, solids concentration, particle stability, and the subsidence velocity of the interface. The model is limited by the fact that the subsidence velocity cannot be predicted and by the simplified approach to the hydrodynamics of differential sedimentation which is incorporated. The substantial agreement between the model and experimental results indicates that the conceptual approach of the model is well-founded. The lack of agreement in some cases also has led to further insight into the mechanisms of particle transport in a concentrated heterodisperse suspension
Nechako Reservoir mathematical modelling studies
International Nuclear Information System (INIS)
The addition of 540 MW of hydroelectric generating capacity to the Nechako Reservoir involves the increased diversion of water from the headwaters of the Nechako River in the Fraser River drainage to the Kemano River on the Pacific coast. Approval of the project requires a two level release structure at Kenney Dam at the head of the Nechako Canyon to manage downstream flows and water temperatures to conserve and protect chinook and sockeye populations. Two- and three-dimensional mathematical models were used to evaluate the hydrothermal characteristics of the Nechako Reservoir and to assess the capability of the proposed structure to provide releases necessary to meet downstream objectives. Results of the modelling show that deep water intake temperatures are sensitive to reservoir surface elevation and the deep water intake elevation. Modelling results for maximum release of 200 m3/s show that the deep water intake invert should be located at an elevation of 795 m to ensure water temperature criteria are met. The three dimensional modelling showed that little, if any additional bottom water mixing beyond that indicated by the two dimensional results for a nearby lake is likely to occur as a result of the Kenamo completion project. Extreme condition analysis shows that there exists sufficient volumes of cold water in the Nechako reservoir to ensure that the 10 degree C water release criteria can be met for the required period. 4 refs., 1 fig
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,...
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Mathematical 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.
Energy Technology Data Exchange (ETDEWEB)
J.K. Brimacombe; I.V. Samarasekera; E.B. Hawbolt; T.R. Meadowcroft; M. Militzer; W.J. Pool; D.Q. Jin
1999-07-31
This report describes the work of developing an integrated model used to predict the thermal history, deformation, roll forces, microstructural evolution and mechanical properties of steel strip in a hot-strip mill. This achievement results from a joint research effort that is part of the American Iron and Steel Institute's (AIS) Advanced Process Control Program, a collaboration between the U.S. DOE and fifteen North American Steelmakers.
Advanced mathematical study and the development of conditional reasoning skills.
Directory of Open Access Journals (Sweden)
Nina Attridge
Full Text Available Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general 'thinking skills'. Today, this argument, known as the 'Theory of Formal Discipline' is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought.
Modelling and Optimizing Mathematics Learning in Children
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
Mathematical Modelling as a Professional Task
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
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...
Mathematical Model of Gravitational and Electrostatic Forces
Krouglov, A
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.
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
Towards the mathematical modelling of human behavior
Jódar Sánchez, Lucas Antonio; Cortés López, Juan Carlos; Acedo Rodríguez, Luis
2011-01-01
Jódar Sánchez, LA.; Cortés López, JC.; Acedo Rodríguez, L. (2011). Towards the mathematical modelling of human behavior. Mathematical and Computer Modelling. 54(7):1625-1625. doi:10.1016/j.mcm.2010.10.009. Senia 1625 1625 54 7
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.
Rival approaches to mathematical modelling in immunology
Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.
2007-08-01
In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.
Mathematical models for interpretation of tracer data in groundwater hydrology
International Nuclear Information System (INIS)
The Advisory Group Meeting had the overall objective of discussing in detail the methodologies and approaches in the development of mathematical models for quantitative evaluations of tracer data in groundwater hydrology and reviewing the recent advances in this field. A separate abstract was prepared for each of the eight papers
A mathematical model for iodine kinetics
International Nuclear Information System (INIS)
A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case
ECONOMIC-MATHEMATICAL CLUSTER’S MODELS
Directory of Open Access Journals (Sweden)
Nikolay Dmitriyevich Naydenov
2015-11-01
Full Text Available The article describes the economic and mathematical models of cluster formations: a model city on the line, the model of network competition consumers one-agent cluster model, the multi-agent playing model of cluster growth, the model comprehensive income cluster members, the artificial neural networks, the balance cluster model, the stability of the cluster model. The article shows that the economic-mathematical modeling processes, clustering as the method allows to improve forecasting, planning and evaluation of the level of clustering in the region.Purpose. Show the level of development of economic and mathematical models as a tool for the analysis of clusters of integration associations in the regions.Methodology. Economic-mathematical modeling, analysis, synthesis, comparison, statistical surveys.Results. The high activity of research in the field of economic and mathematical modeling of cluster formations revealed. The essential characteristics of cluster formations using economic and mathematical models investigated.Practical implications. The economic policy of the regions, countries and municipalities.
Mathematical Models in Danube Water Quality
Directory of Open Access Journals (Sweden)
Valerian Antohe
2009-01-01
Full Text Available The mathematical shaping in the study of water quality has become a branch of environmental engineering. The comprehension and effective application of mathematical models in studying environmental phenomena keep up with the results in the domain of mathematics and the development of specialized software as well. Integrated software programs simulate and predict extreme events, propose solutions, analyzing and processing data in due time. This paper presents a browsing through some mathematical categories of processing the statistical data, examples and their analysis concerning the degree of water pollution downstream the river Danube.
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 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...
U.S. Department of Health & Human Services — The Advance Payment Model is designed for physician-based and rural providers who have come together voluntarily to give coordinated high quality care to the...
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 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 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 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.
Mathematical modelling of the cardiovascular system
Quarteroni, Alfio
2003-01-01
In this paper we will address the problem of developing mathematical models for the numerical simulation of the human circulatory system. In particular, we will focus our attention on the problem of haemodynamics in large human arteries.
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...
Students’ mathematical learning in modelling activities
DEFF Research Database (Denmark)
Kjeldsen, Tinne Hoff; Blomhøj, Morten
2013-01-01
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......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...... 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....
NATO Advanced Study Institute on Advanced Physical Oceanographic Numerical Modelling
1986-01-01
This book is a direct result of the NATO Advanced Study Institute held in Banyuls-sur-mer, France, June 1985. The Institute had the same title as this book. It was held at Laboratoire Arago. Eighty lecturers and students from almost all NATO countries attended. The purpose was to review the state of the art of physical oceanographic numerical modelling including the parameterization of physical processes. This book represents a cross-section of the lectures presented at the ASI. It covers elementary mathematical aspects through large scale practical aspects of ocean circulation calculations. It does not encompass every facet of the science of oceanographic modelling. We have, however, captured most of the essence of mesoscale and large-scale ocean modelling for blue water and shallow seas. There have been considerable advances in modelling coastal circulation which are not included. The methods section does not include important material on phase and group velocity errors, selection of grid structures, advanc...
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.
Ei, Shin-ichiro; Koiso, Miyuki; Ochiai, Hiroyuki; Okada, Kanzo; Saito, Shingo; Shirai, Tomoyuki
2014-01-01
This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.
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
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…
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 Models of Hydraulic Systems, Examples, Analysis
Czech Academy of Sciences Publication Activity Database
Straškraba, Ivan
Praha : ÚT AV ČR, 2006 - (Příhoda, J.; Kozel, K.), s. 159-162 ISBN 80-85918-98-6. [Conference Topical Problems of Fluid Mechanics 2006. Praha (CZ), 22.02.2006-24.02.2006] R&D Projects: GA ČR(CZ) GA201/05/0005 Institutional research plan: CEZ:AV0Z10190503 Keywords : hydraulic systems * fluid flow * mathematical models Subject RIV: BA - General Mathematics
Mathematical Modelling of Running Crown Forest Fires
Taranchuk, V. B.; Barovik, D. V.
2010-01-01
Adapted mathematical model of running crown forest fire propagation is considered. Simplifying assumptions, equations of the model, initial and boundary conditions, finite diference approximations are introduced. The results of computer modelling and the peculiarities of forest fire behavior in heterogeneous forests are discussed
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...
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...
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...
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 Models of Tuberculosis Reactivation and Relapse
Wallis, Robert S.
2016-01-01
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 etiologic mechanism of tuberculosis in patients treated with tumor necrosis factor blockers, 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. PMID:27242697
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 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 Model of the Jet Engine Fuel System
Klimko Marek
2015-01-01
The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor) engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator) will be described, with respect to advanced predetermined simplifications.
Mathematical Model of the Jet Engine Fuel System
Directory of Open Access Journals (Sweden)
Klimko Marek
2015-01-01
Full Text Available The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator will be described, with respect to advanced predetermined simplifications.
Examination of Primary Mathematics Student Teachers’ Modelling Competencies
Directory of Open Access Journals (Sweden)
Ayşe Tekin Dede
2013-12-01
Full Text Available Modelling competencies are the competencies to understand the real problem and to set up a model based on reality, to set up a mathematical model from the real model, to solve mathematical questions within this mathematical model, to interpret mathematical results in a real situation, and to validate the solution (Blum & Kaiser, 1997, cited in Maaß, 2006. The purpose of this study is to examine modelling competencies of primary mathematics student teachers in the solution process of a modelling problem. The approaches primary mathematics student teachers were videotaped and analyzed using thematic coding. In accordance with the data obtained from the study, it was identified that the participants showed approaches in the context of all competencies except the competencies to interpret mathematical results in a real situation. The participants showed inadequate approaches on interpreting the obtained mathematical results.Key Words: Mathematical modelling, modelling problem, modelling competencies, primary mathematics student teachers
Mathematical model for predicting human vertebral fracture
Benedict, J. V.
1973-01-01
Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.
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 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
Bélair, Jacques; Kunze, Herb; Makarov, Roman; Melnik, Roderick; Spiteri, Raymond J
2016-01-01
Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science a...
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
This progress report contains notes on four aspects of hydrological modelling. The first three describe the development of transport models for solute moving with groundwater in fractured rock and the application of the models to field experiments in Cornwall, UK and Chalk River, Canada. The fourth section describes network models which have been used to estimate hydrodynamic dispersion and are in process of being extended to three dimensional systems. (author)
Mathematical modelling of membrane separation
Vinther, Frank; Brøns, Morten; Meyer, Anne S.
2015-01-01
Denne afhandling omhandler matematisk modellering af membranseparation. Afhandlingen består af indledende teori omhandlende membranseparation, ligninger fra fluiddynamik og egenskaber for dextran, som er det stof der ønskes separeret. Ydermere består den af tre separate matematiske modeller, med hver deres tilgang til membranseparation.Den første model er en statistisk model, som undersøger sammenhængen mellem molekyleform og sandsynligheden for at det givne molekyle penetrerer ind i membrane...
THE INSTRUCTIONAL DESIGN MODEL FOR MATHEMATICS EDUCATION
Özdemir, Emine; UYANGÖR, Sevinç MERT
2011-01-01
In this study, to present an instructional model by considering the existing models of instructional design (Addie, ARCS Motivation, Dick and Carey, ASSURE, Seels and Glasgow, Smith and Ragan, Universal, with the elaboration theory of Gerlach and Ely design models) with the nature of mathematics education and to reveal analysis, design, development, implementation, evaluation, and to revise levels with lower levels of the instructional design model were aimed. In this study, the qualitative c...
Mathematical models of information and stochastic systems
Kornreich, Philipp
2008-01-01
From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t
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 Gomaa
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 Modelling of Unmanned Aerial Vehicles
Directory of Open Access Journals (Sweden)
Saeed Sarwar
2013-04-01
Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV
Mathematical modelling of unmanned aerial vehicles
International Nuclear Information System (INIS)
UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)
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 ...
Physical and mathematical modeling of antimicrobial photodynamic therapy
Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang
2014-07-01
Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.
Mathematical Modelling of Network Traffic
Li, Yu
2015-01-01
ncreasing access to the Internet is producing profound influence around the World. More and more people are taking advantage of the Internet to obtain information, communicate with each other far away and enjoy various recreations. This largely increased demand for the Internet requires better and more effective models. During the 1990s, a number of studies show that due to a different nature from telephonic traffic, in particular a bursty nature, traditional queuing models are not applicable...
A mathematical model of leptin resistance
Jacquier, Marine; Hédi A Soula; Crauste, Fabien
2015-01-01
Obesity is often associated with leptin resistance, which leads to a physiological system with high leptin concentration but unable to respond to leptin signals and to regulate food intake. We propose a mathematical model of the leptin-leptin receptors system, based on the assumption that leptin is a regulator of its own receptor activity, and investigate its qualitative behavior. Based on current knowledge and previous models developed for body weight dynamics in rodents, the model includes ...
Mathematical efficiency modeling of static power converters
Hoff Dupont, Fabrício; Zaragoza Bertomeu, Jordi; Rech, Cassiano; Pinheiro, José Renes
2015-01-01
This paper presents a review and a comparative analysis between mathematical models for the efficiency of power converters. Two different types of models are considered, being one for converters subject solely for output power variations, and a second one also considering input voltage variations. Both cases are particularly important for systems fed by renewable sources as photovoltaic panels or wind turbines. Knowledge of the appropriate models is of interest in the dev...
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
Mathematical Models Issues of Environmental Management
Directory of Open Access Journals (Sweden)
Pop Viorel
2015-05-01
Full Text Available Today the world is facing, more and more, different sources of pollution, the most affected areas being the proximity of big industrial centers (e.g.: chemistry, mining and metallurgy, machinery building etc.. Baia Mare industrial area is a typical one for such a situation. To maintain a clean and healthy environment in Baia Mare city and in the surrounding areas, important costs are needed. The usefulness of the mathematical models consists in the possibility of mathematical processing of industrial parameters evolutions, with relevant interpretations on various influences and their correction for achieving the set goals (maximizing financial efficiency, environmental protection with the compliance of legal requirements etc.
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
This progress report contains notes on three aspects of hydrological modelling. Work on hydrodynamic dispersion in fractured media has been extended to transverse dispersion. Further work has been done on diffusion into the rock matrix and its effect on solute transport. The program NAMSOL has been used for the MIRAGE code comparison exercise being organised by Atkins R and D. (author)
Analysis of mathematical models of radioisotope gauges
International Nuclear Information System (INIS)
Radioisotope gauges as industrial sensors were briefly reviewed. Regression models of instruments based on various principles developed in Institute of Nuclear Research and Institute of Nuclear Chemistry and Technology were analysed and their mathematical models assessed. It was found that for one - dimensional models the lowest value of standard error of estimate was achieved when calibration procedure was modelled by logarithmic function. Mathematical expressions for variance and mean value of intrinsic error for linear and non - linear one - as well as for multi - dimensional models of radioisotope gauges were derived. A conclusion was drawn that optimal model of calibration procedure determined by regression analysis method not always corresponds to the minimum value of the intrinsic error variance. Influence of cutting off of probability distribution function of measured quantity and its error at the lower upper limit of measurement range on variance and mean value of intrinsic error was evaluated. Feasibility study for application of some aspects of Shannon's information theory for evaluation of mathematical models of radioisotope gauges was accomplished. Its usefulness for complex evaluation of multidimensional models was confirmed. 105 refs. (author)
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)
1996-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
Mathematical modeling 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
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.
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.
Models and structures: mathematical physics
International Nuclear Information System (INIS)
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 of leptin resistance
Jacquier, Marine; Soula, Hédi A; Crauste, Fabien
2015-01-01
International audience Obesity is often associated with leptin resistance, which leads to a physiological system with high leptin concentration but unable to respond to leptin signals and to regulate food intake. We propose a mathematical model of the leptin-leptin receptors system, based on the assumption that leptin is a regulator of its own receptor activity, and investigate its qualitative behavior. Based on current knowledge and previous models developed for body weight dynamics in ro...
Mathematical Modeling of Magnetic Regenerator Refrigeration Systems
Salarvand, Navid
2009-01-01
ABSTRACT: Active magnetic regenerative refrigeration (AMRR) systems are designed based on magnetocaloric effect of some special solid materials, such as Gadolinium-Silicon-Germanium, Ferrum-Rhodium, etc. During the last three decades, a variety of cooling systems have been proposed using magnetic materials at room temperature. In this thesis, an AMRR system using FeRh as refrigerant is studied. For the simulation, a one-dimensional, time-varying mathematical model is developed. This model co...
Mathematical Modelling of Immune Response in Tissues
Su, B; Zhou, W; K. S. Dorman; Jones, D. E.
2009-01-01
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...
Mathematical Modeling of Multienzyme Biosensor System
SP. Ganesan; K Saravanakumar; Rajendran, L.
2014-01-01
A mathematical model of hybrid inhibitor biosensor system is discussed. This model consists of five nonlinear partial differential equations for bisubstrate sensitive amperometric system. Simple and closed form of analytical expressions for concentration of glucose-6-phosphate (substrate), potassium dihydrogen phosphate (inhibitor), oxygen (co-substrate), glucose (product 1), and hydrogen peroxide (product 3) is obtained in terms of rate constant using modified Adomian decomposition method (M...
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 Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
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 to as a geomag......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...... to as a geomagnetic field model. Such models can be used to produce maps. More importantly, they form the basis for the geophysical interpretation of the geomagnetic field, by providing the possibility of separating fields produced by various sources and extrapolating those fields to places where they cannot...... 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...
From mathematical modelling to computational simulation: mathematical experimentation on teaching
Oliveira, Margarida Cristina Pereira da Silva
2015-01-01
With recent technological developments and ease of access to knowledge and information, the teaching paradigm must be in permanent update and change, especially, the teaching paradigm of Mathematics. The current teaching system must prepare students, both from high schools and universities, to their entrance in the global labor market, that, more than ever before, demands for more innovation capacity, concerning the integrated usage of scientific knowledge, Mathematics and new technologies. ...
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.
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.
Editorial: Mathematical modelling of infectious diseases.
Fenton, Andy
2016-06-01
The field of disease ecology - the study of the spread and impact of parasites and pathogens within their host populations and communities - has a long history of using mathematical models. Dating back over 100 years, researchers have used mathematics to describe the spread of disease-causing agents, understand the relationship between host density and transmission and plan control strategies. The use of mathematical modelling in disease ecology exploded in the late 1970s and early 1980s through the work of Anderson and May (Anderson and May, 1978, 1981, 1992; May and Anderson, 1978), who developed the fundamental frameworks for studying microparasite (e.g. viruses, bacteria and protozoa) and macroparasite (e.g. helminth) dynamics, emphasizing the importance of understanding features such as the parasite's basic reproduction number (R 0) and critical community size that form the basis of disease ecology research to this day. Since the initial models of disease population dynamics, which primarily focused on human diseases, theoretical disease research has expanded hugely to encompass livestock and wildlife disease systems, and also to explore evolutionary questions such as the evolution of parasite virulence or drug resistance. More recently there have been efforts to broaden the field still further, to move beyond the standard 'one-host-one-parasite' paradigm of the original models, to incorporate many aspects of complexity of natural systems, including multiple potential host species and interactions among multiple parasite species. PMID:27027318
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)
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.
Lim, L. L.; Tso, T. -Y.; Lin, F. L.
2009-01-01
This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a…
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. PMID:25765193
A mathematical model of the Mafia game
Migdał, 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 de...
Mathematical modelling of Regional Fuel Cycle Centres
International Nuclear Information System (INIS)
The concept of Regional Fuel Cycle Centres (RFCC) has attracted wide interest as a possible approach towards meeting the nuclear fuel cycle needs of many countries. As part of its study of the RFCC concept, the International Atomic Energy Agency is developing mathematical models and associated computer codes to analyse the economics and logistics of various strategies for management of spent nuclear fuel and waste materials. (author)
Topics in the mathematical modelling of nanotoxicology
Jones, Zofia
2012-01-01
Over the last ten years questions related to the safety of nanoparticles and their possible toxic effects have become well-established. The government's Health and Safety Laboratories (HSL) at Buxton are currently attempting to determine their possible toxicity in the workplace. It is their responsibility to establish what levels are exposure can be considered safe in the workplace. This project is a CASE studentship with HSL and aims to start developing mathematical models relating to nan...
Özkan Hıdıroğlu, Yeliz; Hıdıroğlu, Çağlar Naci
2016-01-01
The aim of the study is to examine epistemological beliefs in explaining the mathematical modelling approaches of mathematics teachers. In the study, basically dominated by a qualitative approach, quantitative and qualitative data were gathered concurrently from 35 mathematics teachers who work in Ġzmir and after analysis process while interpreting the findings they were combined and compared. Qualitative data were gathered from written answer sheets of mathematics teachers on mat...
Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors
Zoran Benić; Petar Piljek; Denis Kotarski
2016-01-01
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 mo...
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)
Basic Perforator Flap Hemodynamic Mathematical Model
Tao, Youlun; Ding, Maochao; Wang, Aiguo; Zhuang, Yuehong; Chang, Shi-Min; Mei, Jin; Hallock, Geoffrey G.
2016-01-01
Background: A mathematical model to help explain the hemodynamic characteristics of perforator flaps based on blood flow resistance systems within the flap will serve as a theoretical guide for the future study and clinical applications of these flaps. Methods: There are 3 major blood flow resistance network systems of a perforator flap. These were defined as the blood flow resistance of an anastomosis between artery and artery of adjacent perforasomes, between artery and vein within a perforasome, and then between vein and vein corresponding to the outflow of that perforasome. From this, a calculation could be made of the number of such blood flow resistance network systems that must be crossed for all perforasomes within a perforator flap to predict whether that arrangement would be viable. Results: The summation of blood flow resistance networks from each perforasome in a given perforator flap could predict which portions would likely survive. This mathematical model shows how this is directly dependent on the location of the vascular pedicle to the flap and whether supercharging or superdrainage maneuvers have been added. These configurations will give an estimate of the hemodynamic characteristics for the given flap design. Conclusions: This basic mathematical model can (1) conveniently determine the degree of difficulty for each perforasome within a perforator flap to survive; (2) semiquantitatively allow the calculation of basic hemodynamic parameters; and (3) allow the assessment of the pros and cons expected for each pattern of perforasomes encountered clinically based on predictable hemodynamic observations.
Lew, Kristen; Fukawa-Connelly, Timothy Patrick; Mejía-Ramos , Juan Pablo; Weber, Keith
2016-01-01
We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…
Mathematical models of breast and ovarian cancers.
Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron
2016-07-01
Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review, we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, as answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. WIREs Syst Biol Med 2016, 8:337-362. doi: 10.1002/wsbm.1343 For further resources related to this article, please visit the WIREs website. PMID:27259061
Mathematical modeling and signal processing in speech and hearing sciences
Xin, Jack
2014-01-01
The aim of the book is to give an accessible introduction of mathematical models and signal processing methods in speech and hearing sciences for senior undergraduate and beginning graduate students with basic knowledge of linear algebra, differential equations, numerical analysis, and probability. Speech and hearing sciences are fundamental to numerous technological advances of the digital world in the past decade, from music compression in MP3 to digital hearing aids, from network based voice enabled services to speech interaction with mobile phones. Mathematics and computation are intimately related to these leaps and bounds. On the other hand, speech and hearing are strongly interdisciplinary areas where dissimilar scientific and engineering publications and approaches often coexist and make it difficult for newcomers to enter.
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...
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
generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.
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...... be carefully selected, so that the model and its visualization enhance our ability to interpret brain function. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as...... means for extracting a global summary map from a trained model. Such summary maps provides the investigator with an overview of brain locations of importance to the model’s predictions. The sensitivity map proves as a versatile technique for model visualization. Furthermore, we perform a preliminary...
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...... parameters must be carefully selected, so that the model and its visualization enhance our ability to interpret the brain. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map...... as means for extracting a global summary map from a trained model. Such summary maps provides the investigator with an overview of brain locations of importance to the model’s predictions. The sensitivity map proves as a versatile technique for model visualization. Furthermore, we perform a...
Improved mathematical model for uranium metabolism
International Nuclear Information System (INIS)
An improved mathematical model for uranium metabolism in the primate was developed. Animal and human literature data were the basis for building the model consisting of six compartments: plasma, red cells, short-term bone component, long-term bone component, kidney, and urine. In this model, there is a feedback from the red cells and bone compartments to plasma, and the model is applicable to uranium only from the time it is absorbed into blood. An analytical mathematical solution is proposed that will permit estimation of the distribution of uranium among the various compartments. To verify the model and determine the required time constants, single non-toxic doses of uranium were administered to baboons and plasma, red cells, and urine samples subsequently analyzed. Samples of human skeleton were also measured for normal levels of uranium. These measurements will be used to test whether the model accurately predicts long-term bond concentration. Uranium exists in the mammalian body as the hexavalent uranyl ion which tends to complex with plasma proteins or bicarbonates. Animal experiments indicate that after an iv injection, uranium leaves the bloodstream very rapidly; at 40 min after injection, 50% has been excreted in the urine, with little uranium in tissue other than kidney and bone. The distribution of uranium in humans is similar to that in animals. There was no significant concentration of uranium in any of 21 human tissues and organs, apart from bone and kidney, examined at autopsy
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. PMID:24560011
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.
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 Modeling of Multienzyme Biosensor System
Directory of Open Access Journals (Sweden)
SP. Ganesan
2014-01-01
Full Text Available A mathematical model of hybrid inhibitor biosensor system is discussed. This model consists of five nonlinear partial differential equations for bisubstrate sensitive amperometric system. Simple and closed form of analytical expressions for concentration of glucose-6-phosphate (substrate, potassium dihydrogen phosphate (inhibitor, oxygen (co-substrate, glucose (product 1, and hydrogen peroxide (product 3 is obtained in terms of rate constant using modified Adomian decomposition method (MADM. In this study, behavior of biokinetic parameters is analyzed using this theoretical result. The obtained analytical results (concentrations are compared with the numerical results and are found to be in satisfactory agreement.
Mathematical Model of Suspension Filtration and Its Analytical Solution
Directory of Open Access Journals (Sweden)
Normahmad Ravshanov
2013-01-01
Full Text Available The work develops advanced mathematical model and computing algorithm to analyze, predict and identify the basic parameters of filter units and their variation ranges. Numerical analytic solution of liquid ionized mixtures filtration was got on their basis. Computing experiments results are presented in graphics form. Calculation results analysis enables to determine the optimum performance of filter units, used for liquid ionized mixtures filtration, food preparation, drug production and water purification. Selection of the most suitable parameters contributes to the improvement of economic and technological efficiency of production and filter units working efficiency.
Mathematical Modeling of a Simulated Fixed Bed for Desalting Operation
M.A. OLUTOYE; Mohamed ALHASSAN
2006-01-01
Continue survival of the petrochemical industry in the face of advancement in processing technology must change for better performance. In doing so, the pre-treatment stage of crude, which include desalting will go a long way at improving the overall quality of the product obtained. It is in view of this that a mathematical modeling of adsorption of a fixed simulated bed for desalting operation was carried out to determine the variation of the concentration of adsorbate (mol/l) and the amount...
Origins of the brain networks for advanced mathematics in expert mathematicians.
Amalric, Marie; Dehaene, Stanislas
2016-05-01
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124
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 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...
Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin
2013-04-01
The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.
Assessment of Primary 5 Students' Mathematical Modelling Competencies
Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia
2012-01-01
Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…
Mathematical Modeling of Extinction of Inhomogeneous Populations.
Karev, G P; Kareva, I
2016-04-01
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed of clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the "unobserved heterogeneity," i.e., the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of "internal population time" is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117
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—
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)
5th Conference on Advanced Mathematical and Computational Tools in Metrology
Cox, M G; Filipe, E; Pavese, F; Richter, D
2001-01-01
Advances in metrology depend on improvements in scientific and technical knowledge and in instrumentation quality, as well as on better use of advanced mathematical tools and development of new ones. In this volume, scientists from both the mathematical and the metrological fields exchange their experiences. Industrial sectors, such as instrumentation and software, will benefit from this exchange, since metrology has a high impact on the overall quality of industrial products, and applied mathematics is becoming more and more important in industrial processes.This book is of interest to people
Mathematical Modeling of Diaphragm Pneumatic Motors
Directory of Open Access Journals (Sweden)
Fojtášek Kamil
2014-03-01
Full Text Available Pneumatic diaphragm motors belong to the group of motors with elastic working parts. This part is usually made of rubber with a textile insert and it is deformed under the pressure of a compressed air or from the external mass load. This is resulting in a final working effect. In this type of motors are in contact two different elastic environments – the compressed air and the esaltic part. These motors are mainly the low-stroke and working with relatively large forces. This paper presents mathematical modeling static properties of diaphragm motors.
A mathematical model of 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......-mentioned factors, initial loss of aerosol by impact on the chamber wall is most important for the efficiency of a spacer. With a VT of 195 mL, the AeroChamber and Babyhaler were emptied in two breaths, the NebuChamber in four breaths, and the Nebuhaler in six breaths. Insufficiencies of the expiratory valves were...
PREFACE: Physics-Based Mathematical Models for Nanotechnology
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines
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.
Mathematical and computational modeling and simulation fundamentals and case studies
Moeller, Dietmar P F
2004-01-01
Mathematical and Computational Modeling and Simulation - a highly multi-disciplinary field with ubiquitous applications in science and engineering - is one of the key enabling technologies of the 21st century. This book introduces to the use of Mathematical and Computational Modeling and Simulation in order to develop an understanding of the solution characteristics of a broad class of real-world problems. The relevant basic and advanced methodologies are explained in detail, with special emphasis on ill-defined problems. Some 15 simulation systems are presented on the language and the logical level. Moreover, the reader can accumulate experience by studying a wide variety of case studies. The latter are briefly described within the book but their full versions as well as some simulation software demos are available on the Web. The book can be used for University courses of different level as well as for self-study. Advanced sections are marked and can be skipped in a first reading or in undergraduate courses...
Mathematical modeling of the Phoenix Rising pathway.
Directory of Open Access Journals (Sweden)
Chad Liu
2014-02-01
Full Text Available Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2, a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3, caspase 7 (C7, and nuclear factor κB (NFκB. In addition, we simulated the effects of cyclooxygenase-2 (COX2 inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.
Mathematical Modeling of 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
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.…
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.
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
Distributed Mathematical Model Simulation on a Parallel Architecture
Kvasnica, Peter; Kvasnica, Igor
2012-01-01
The aim of this article is to discuss the design of distributed mathematical models and suitable parallel architecture of computers. The paper summarises the author’s experience with mathematical modelling of decomposed information systems of a simulator. Conclusions are based on the theory of the design of the computer control systems. The author describes computers that create a distributed computer system of a flight simulator. Modelling of a time precision of mathematical model of the spe...
Models for harnessing the Internet in mathematics education
Kissane, Barry
2012-01-01
In recent years, the Internet has increasingly been used to provide significant resources for student to learn mathematics and to learn about mathematics, as well as significant resources for teachers to support these. Effective access to and use of these has been hampered in practice by limited facilities in schools and the limited experience of many mathematics teachers with the Internet for mathematical purposes. This paper offers models for understanding the effective use of Internet reso...
Laser interaction with biological material mathematical modeling
Kulikov, Kirill
2014-01-01
This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.
Mathematical modeling of a thermovoltaic cell
White, Ralph E.; Kawanami, Makoto
1992-01-01
A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.
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......-mentioned factors, initial loss of aerosol by impact on the chamber wall is most important for the efficiency of a spacer. With a VT of 195 mL, the AeroChamber and Babyhaler were emptied in two breaths, the NebuChamber in four breaths, and the Nebuhaler in six breaths. Insufficiencies of the expiratory valves were...
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...
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.
Recent advances in modeling nutrient utilization in ruminants1
Kebreab, E.; Dijkstra, J.; Bannink, A.; France, J.
2009-01-01
Mathematical modeling techniques have been applied to study various aspects of the ruminant, such as rumen function, post-absorptive metabolism and product composition. This review focuses on advances made in modeling rumen fermentation and its associated rumen disorders, and energy and nutrient uti
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...
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).
Modeling in school mathematics: generating active learning environments
Sakonidis, Haralambos
2003-01-01
Models and the modeling process are at the heart of mathematics. The paper discusses the importance of developing pupils’ modeling abilities and skills in the context of school mathematics and focuses in particular on the content, structure and the educational exploitation of a set of activities constructed to serve this purpose in a computational modeling environment.
Mathematical model of tumor-immune surveillance.
Mahasa, Khaphetsi Joseph; Ouifki, Rachid; Eladdadi, Amina; Pillis, Lisette de
2016-09-01
We present a novel mathematical model involving various immune cell populations and tumor cell populations. The model describes how tumor cells evolve and survive the brief encounter with the immune system mediated by natural killer (NK) cells and the activated CD8(+) cytotoxic T lymphocytes (CTLs). The model is composed of ordinary differential equations describing the interactions between these important immune lymphocytes and various tumor cell populations. Based on up-to-date knowledge of immune evasion and rational considerations, the model is designed to illustrate how tumors evade both arms of host immunity (i.e. innate and adaptive immunity). The model predicts that (a) an influx of an external source of NK cells might play a crucial role in enhancing NK-cell immune surveillance; (b) the host immune system alone is not fully effective against progression of tumor cells; (c) the development of immunoresistance by tumor cells is inevitable in tumor immune surveillance. Our model also supports the importance of infiltrating NK cells in tumor immune surveillance, which can be enhanced by NK cell-based immunotherapeutic approaches. PMID:27317864
Mathematical problems in modeling artificial heart
Directory of Open Access Journals (Sweden)
Ahmed N. U.
1995-01-01
Full Text Available In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate. On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.
The use of mathematical models in teaching wastewater treatment engineering
DEFF Research Database (Denmark)
Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.
2002-01-01
Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...... efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available....
Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors
Rash, Agnes M.; Zurbach, E. Peter
2004-01-01
The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…
Czech Academy of Sciences Publication Activity Database
Nedoma, Jiří
Hauppauge : Nova Science Publishers, 2012 - (Tarasov, A.; Demidov, M.), s. 107-196 ISBN 978-1-61942-235-3. - ( Oceanography and Ocean Engineering Natural Disaster Research, Prediction and Mitigation) Institutional support: RVO:67985807 Keywords : Hurricanes * consequences of hurricanes * mathematical modelling * computational methods * algorithms Subject RIV: BA - General Mathematics https://www.novapublishers.com/catalog/product_info.php?products_id=27159
Increasing Problem Solving Skills in Fifth Grande Advanced Mathematics Students
Jobrina Gale Ellison
2009-01-01
Because No Child Left Behind (NCLB) calls for every student to make gains during every school year, even advanced students who are already performing at the top must make these gains. Teachers need to find areas to target with advanced students. One area that could be targeted to strengthen is problem solving skills. Research shows that daily practice and strategy instruction in problem solving skills will increase students’ problem solving abilities. I dedicated 5-10 minutes per day to probl...
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 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 Modeling of the Origins of Life
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Mathematical 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.
Noise in restaurants: Levels and mathematical model
Directory of Open Access Journals (Sweden)
Wai Ming To
2014-01-01
Full Text Available Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (Leq,1-h was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Mathematical modeling of endovenous laser treatment (ELT
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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
On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process
Directory of Open Access Journals (Sweden)
Jennifer A Flegg
2015-09-01
Full Text Available Over the last thirty years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e. capillary sprout growth has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made towards the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.
Mathematical modeling plasma transport in tokamaks
International Nuclear Information System (INIS)
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 1020/m3 with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%
Mathematical Modeling Social Responsibility for Dynamic Organizations
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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.
Mathematical modeling of hybrid CO2 laser
International Nuclear Information System (INIS)
A Teller-landau six-temperature model describing the dynamic emission of single mode TEA CO2 laser has been adapted. This model has been also used to describe the mechanism of obtaining relatively high-power output pulses from hybrid TE-TEA or CW-TEA CO2 laser consisting of high and low-pressure sections. The suggested mathematical model allows to investigate the mechanism which limits the TEA oscillation to single longitudinal mode (SLM) due to the narrow gain bandwidth of low-pressure section, and also to study the effect of the laser input parameters on the smooth output laser pulse parameters. In addition, numerical solutions, of non-linear rate equation system of suggested model are quantitatively discussed. The solutions describe the radiation field intensity, the population inversion, and the energy transfer processes. The calculated values of maximum peak power, total energy in pulse, pulse width, etc. are in a very good agreement with the observed experimental values. (author)
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. PMID:20030966
Mathematical models of physics problems (physics research and technology)
Anchordoqui, Luis Alfredo
2013-01-01
This textbook is intended to provide a foundation for a one-semester introductory course on the advanced mathematical methods that form the cornerstones of the hard sciences and engineering. The work is suitable for first year graduate or advanced undergraduate students in the fields of Physics, Astronomy and Engineering. This text therefore employs a condensed narrative sufficient to prepare graduate and advanced undergraduate students for the level of mathematics expected in more advanced graduate physics courses, without too much exposition on related but non-essential material. In contrast to the two semesters traditionally devoted to mathematical methods for physicists, the material in this book has been quite distilled, making it a suitable guide for a one-semester course. The assumption is that the student, once versed in the fundamentals, can master more esoteric aspects of these topics on his or her own if and when the need arises during the course of conducting research. The book focuses on two cor...
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
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.
An introduction to mathematical modeling a course in mechanics
Oden, Tinsley J
2011-01-01
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...
Mathematical model insights into arsenic detoxification
Directory of Open Access Journals (Sweden)
Nijhout H Frederik
2011-08-01
Full Text Available Abstract Background Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs, which then undergoes hepatic methylation to methylarsonic acid (MMAs and a second methylation to dimethylarsinic acid (DMAs. Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation. Methods We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects. Results We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic
Manual on mathematical models in isotope hydrogeology
International Nuclear Information System (INIS)
Methodologies based on the use of naturally occurring isotopes are, at present, an integral part of studies being undertaken for water resources assessment and management. Quantitative evaluations based on the temporal and/or spatial distribution of different isotopic species in hydrological systems require conceptual mathematical formulations. Different types of model can be employed depending on the nature of the hydrological system under investigation, the amount and type of data available, and the required accuracy of the parameter to be estimated. This manual provides an overview of the basic concepts of existing modelling approaches, procedures for their application to different hydrological systems, their limitations and data requirements. Guidance in their practical applications, illustrative case studies and information on existing PC software are also included. While the subject matter of isotope transport modelling and improved quantitative evaluations through natural isotopes in water sciences is still at the development stage, this manual summarizes the methodologies available at present, to assist the practitioner in the proper use within the framework of ongoing isotope hydrological field studies. In view of the widespread use of isotope methods in groundwater hydrology, the methodologies covered in the manual are directed towards hydrogeological applications, although most of the conceptual formulations presented would generally be valid. Refs, figs, tabs
Mathematical model “The electric line - wind farm”
Merenco V.
2008-01-01
It is considered the problem of finding of the mathematical model of a circuit “electric line – wind farm” with the purpose of analysis of operating modes by a method of mathematical simulation. The mathematical model is based on a method of characteristics, takes into account heterogeneity of a circuit and allows realizing various modes and changes in structure of a circuit simple change of values of sizes set as the concentrated parameters.
Mathematical modelling: From school to university
Directory of Open Access Journals (Sweden)
Ansie Harding
2009-09-01
Full Text Available The outcomes based education (OBE system is characterised by controversy and the 2008 matric results that rendered admission to an unusually large number of students did nothing to silence critics. The ﬁrst students who completed their full cycle of school education in the OBE system entered universities in 2009 and their preparedness for university mathematics as well as their performance at university level are important as indicaters for estimating the success or otherwise of the OBE system. In a previous study student performance in mathematics admission tests for 2005-2007 was investigated and it was found that students who had had partial exposure to OBE performed worse than had been the case with their predecessors in the categories of modelling and ratio problems. As a result, this study was conducted to investigate how the 2009 intake of students performed in a modelling course at university level. A report is presented which deals with student performance in the course, problems experienced, the effect of remedial intervention on performance and whether students of the OBE system are adequately prepared for mathematical modelling at university level. This study focuses on performance in a ﬁrst year course in mathematical modelling at the University of Pretoria. The course is problem based and is technology intensive, requiring use of the software package Matlab. For investigative purposes the papers of semester tests 1 and 2 of 2005 were used unchanged for tests in 2009. Students of 2009 did not have access to the 2005 papers and the same lecturer taught students of both groups. The lecturer also noted personal experiences in respect of students and was able to draw reasonable comparisons between the 2009 students and previous groups because of her years of involvement with the course. The entrance requirement of 60% for matric mathematics in 2005 was increased to 70% in 2009. Results indicate that the pass percentage decreased in
Modeling anaphora in informal mathematical dialogue
Wolska, Magdalena; Ivana Kruijff-Korbayová
2006-01-01
We analyze anaphoric phenomena in the context of building an input understanding component for a conversational system for tutoring mathematics. In this paper, we report the results of data analysis of two sets of corpora of dialogs on mathematical theorem proving. We exemplify anaphoric phenomena, identify factors relevant to anaphora resolution in our domain and extensions to the input interpretation component to support it.
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…
Application of Mathematical Modeling Activities in Costarican High School Education
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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.
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.
A mathematical model of forgetting and amnesia
Directory of Open Access Journals (Sweden)
JaapM. 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 Models and Economic Forecasting: Some Uses and Mis-Uses of Mathematics in Economics
David Hendry
2011-01-01
We consider three 'cases studies' of the uses and mis-uses of mathematics in economics and econometrics. The first concerns economic forecasting, where a mathematical analysis is essential, and is independent of the specific forecasting model and how the process being forecast behaves. The second concerns model selection with more candidate variables than the number of observations. Again, an understanding of the properties of extended general-to-specific procedures is impossible without adva...
In-Situ Assays Using a New Advanced Mathematical Algorithm - 12400
International Nuclear Information System (INIS)
Current mathematical efficiency modeling software for in-situ counting, such as the commercially available In-Situ Object Calibration Software (ISOCS), typically allows the description of measurement geometries via a list of well-defined templates which describe regular objects, such as boxes, cylinder, or spheres. While for many situations, these regular objects are sufficient to describe the measurement conditions, there are occasions in which a more detailed model is desired. We have developed a new all-purpose geometry template that can extend the flexibility of current ISOCS templates. This new template still utilizes the same advanced mathematical algorithms as current templates, but allows the extension to a multitude of shapes and objects that can be placed at any location and even combined. In addition, detectors can be placed anywhere and aimed at any location within the measurement scene. Several applications of this algorithm to in-situ waste assay measurements, as well as, validations of this template using Monte Carlo calculations and experimental measurements are studied. Presented in this paper is a new template of the mathematical algorithms for evaluating efficiencies. This new template combines all the advantages of the ISOCS and it allows the use of very complex geometries, it also allows stacking of geometries on one another in the same measurement scene and it allows the detector to be placed anywhere in the measurement scene and pointing in any direction. We have shown that the template compares well with the previous ISOCS software within the limit of convergence of the code, and also compare well with the MCNPX and measured data within the joint uncertainties for the code and the data. The new template agrees with ISOCS to within 1.5% at all energies. It agrees with the MCNPX to within 10% at all energies and it agrees with most geometries within 5%. It finally agrees with measured data to within 10%. This mathematical algorithm can now be
Numerical Treatment of the Mathematical Models for Water Pollution
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F. B. Agusto
2007-01-01
Full Text Available To evaluate the environmental impact of pollution, mathematical models play a major role in predicting the pollution level in the regions under consideration. This paper examines the various mathematical models involving water pollutant. We also give the implicit central difference scheme in space, and a forward difference method in time for the evaluation of the generalized transport equation.
Numerical Treatment of the Mathematical Models for Water Pollution
Agusto, F. B.; O. M. Bamigbola
2007-01-01
To evaluate the environmental impact of pollution, mathematical models play a major role in predicting the pollution level in the regions under consideration. This paper examines the various mathematical models involving water pollutant. We also give the implicit central difference scheme in space, and a forward difference method in time for the evaluation of the generalized transport equation.
The Expansion Method, Mathematical Modeling, and Spatial Econometrics
Emilio Casetti
1997-01-01
Consider the mode of enquiry that involves thinking about thinking. The expansion methodology originates within it, from an analysis of the thought processes presiding upon the construction of any mathematical models of any realities. The focal point of this paper is a discussion of the relations between the expansion methodology, mathematical modeling, and spatial econometrics.
Students' Approaches to Learning a New Mathematical Model
Flegg, Jennifer A.; Mallet, Daniel G.; Lupton, Mandy
2013-01-01
In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quantitative data based around the students' approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to…
Models for Decision Making: From Applications to Mathematics... and Back
Crama, Yves
2010-01-01
In this inaugural lecture, I describe some facets of the interplay between mathematics and management science, economics, or engineering, as they come together in operations research models. I intend to illustrate, in particular, the complex and fruitful process through which fundamental combinatorial models find applications in management science, which in turn foster the development of new and challenging mathematical questions.
Mathematical modeling of moving boundary problems in thermal energy storage
Solomon, A. D.
1980-01-01
The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.
Mathematical Formulation Requirements and Specifications for the Process Models
International Nuclear Information System (INIS)
The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments naturally
Advanced Chemistry Basins Model
Energy Technology Data Exchange (ETDEWEB)
Blanco, Mario; Cathles, Lawrence; Manhardt, Paul; Meulbroek, Peter; Tang, Yongchun
2003-02-13
The objective of this project is to: (1) Develop a database of additional and better maturity indicators for paleo-heat flow calibration; (2) Develop maturation models capable of predicting the chemical composition of hydrocarbons produced by a specific kerogen as a function of maturity, heating rate, etc.; assemble a compositional kinetic database of representative kerogens; (3) Develop a 4 phase equation of state-flash model that can define the physical properties (viscosity, density, etc.) of the products of kerogen maturation, and phase transitions that occur along secondary migration pathways; (4) Build a conventional basin model and incorporate new maturity indicators and data bases in a user-friendly way; (5) Develop an algorithm which combines the volume change and viscosities of the compositional maturation model to predict the chemistry of the hydrocarbons that will be expelled from the kerogen to the secondary migration pathways; (6) Develop an algorithm that predicts the flow of hydrocarbons along secondary migration pathways, accounts for mixing of miscible hydrocarbon components along the pathway, and calculates the phase fractionation that will occur as the hydrocarbons move upward down the geothermal and fluid pressure gradients in the basin; and (7) Integrate the above components into a functional model implemented on a PC or low cost workstation.
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)
Mathematical model of radon activity measurements
International Nuclear Information System (INIS)
Present work describes a mathematical model that quantifies the time dependent amount of 222Rn and 220Rn 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 222Rn and 220Rn 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 220Rn 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 222Rn, only. Furthermore, the model also addresses the activity of 220Rn and 222Rn 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)
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...
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.
Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra
Domínguez-García, S.; García-Planas, M. I.; Taberna, J.
2016-01-01
Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…
NATO Advanced Research Workshop on Exploiting Mental Imagery with Computers in Mathematics Education
Mason, John
1995-01-01
The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.
Mathematical modelling of flow over periodic structures
Czech Academy of Sciences Publication Activity Database
Bauer, Petr
Fukuoka: Kyushu University, 2012 - (Beneš, M.; Kimura, M.; Yazaki, S.), s. 3-10. (36). ISSN 1881-4042. [Czech- Japanese Seminar in Applied Mathematics 2010. Praha (CZ), 30.08.2010-04.09.2010] Institutional research plan: CEZ:AV0Z20760514 Keywords : incompressible flow * finite element method * Crouzeix-Raviart elements * multigrid * Vanka type smoothers Subject RIV: BA - General Mathematics
Wear process mathematical modelling of sleeve assembly details of ice
С. А. Загайко
2013-01-01
Features of mathematical modeling of wear process of a cylinder sleeve, piston rings and a piston skirt of an internal combustion engine are considered. Model approbation on the basis of resource tests of an internal combustion engine is carried out.
Symmetrization of mathematical model of charge transport in semiconductors
Directory of Open Access Journals (Sweden)
Alexander M. Blokhin
2002-11-01
Full Text Available A mathematical model of charge transport in semiconductors is considered. The model is a quasilinear system of differential equations. A problem of finding an additional entropy conservation law and system symmetrization are solved.
The 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.
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.
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. PMID:26396161
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.
Advanced methods of solid oxide fuel cell modeling
Milewski, Jaroslaw; Santarelli, Massimo; Leone, Pierluigi
2011-01-01
Fuel cells are widely regarded as the future of the power and transportation industries. Intensive research in this area now requires new methods of fuel cell operation modeling and cell design. Typical mathematical models are based on the physical process description of fuel cells and require a detailed knowledge of the microscopic properties that govern both chemical and electrochemical reactions. ""Advanced Methods of Solid Oxide Fuel Cell Modeling"" proposes the alternative methodology of generalized artificial neural networks (ANN) solid oxide fuel cell (SOFC) modeling. ""Advanced Methods
Energy Technology Data Exchange (ETDEWEB)
Lee, S; Richard Dimenna, R; David Tamburello, D
2008-11-13
The process of recovering the waste in storage tanks at the Savannah River Site (SRS) typically requires mixing the contents of the tank with one to four dual-nozzle jet mixers located within the tank. The typical criteria to establish a mixed condition in a tank are based on the number of pumps in operation and the time duration of operation. To ensure that a mixed condition is achieved, operating times are set conservatively long. This approach results in high operational costs because of the long mixing times and high maintenance and repair costs for the same reason. A significant reduction in both of these costs might be realized by reducing the required mixing time based on calculating a reliable indicator of mixing with a suitably validated computer code. The work described in this report establishes the basis for further development of the theory leading to the identified mixing indicators, the benchmark analyses demonstrating their consistency with widely accepted correlations, and the application of those indicators to SRS waste tanks to provide a better, physically based estimate of the required mixing time. Waste storage tanks at SRS contain settled sludge which varies in height from zero to 10 ft. The sludge has been characterized and modeled as micron-sized solids, typically 1 to 5 microns, at weight fractions as high as 20 to 30 wt%, specific gravities to 1.4, and viscosities up to 64 cp during motion. The sludge is suspended and mixed through the use of submersible slurry jet pumps. To suspend settled sludge, water is added to the tank as a slurry medium and stirred with the jet pump. Although there is considerable technical literature on mixing and solid suspension in agitated tanks, very little literature has been published on jet mixing in a large-scale tank. If shorter mixing times can be shown to support Defense Waste Processing Facility (DWPF) or other feed requirements, longer pump lifetimes can be achieved with associated operational cost and
Energy Technology Data Exchange (ETDEWEB)
Lee, S; Dimenna, R; Tamburello, D
2011-02-14
height from zero to 10 ft. The sludge has been characterized and modeled as micron-sized solids, typically 1 to 5 microns, at weight fractions as high as 20 to 30 wt%, specific gravities to 1.4, and viscosities up to 64 cp during motion. The sludge is suspended and mixed through the use of submersible slurry jet pumps. To suspend settled sludge, water is added to the tank as a slurry medium and stirred with the jet pump. Although there is considerable technical literature on mixing and solid suspension in agitated tanks, very little literature has been published on jet mixing in a large-scale tank. One of the main objectives in the waste processing is to provide feed of a uniform slurry composition at a certain weight percentage (e.g. typically {approx}13 wt% at SRS) over an extended period of time. In preparation of the sludge for slurrying, several important questions have been raised with regard to sludge suspension and mixing of the solid suspension in the bulk of the tank: (1) How much time is required to prepare a slurry with a uniform solid composition? (2) How long will it take to suspend and mix the sludge for uniform composition in any particular waste tank? (3) What are good mixing indicators to answer the questions concerning sludge mixing stated above in a general fashion applicable to any waste tank/slurry pump geometry and fluid/sludge combination?
Study on advancement of in vivo counting using mathematical simulation
Energy Technology Data Exchange (ETDEWEB)
Kinase, Sakae [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
2003-05-01
To obtain an assessment of the committed effective dose, individual monitoring for the estimation of intakes of radionuclides is required. For individual monitoring of exposure to intakes of radionuclides, direct measurement of radionuclides in the body - in vivo counting- is very useful. To advance in a precision in vivo counting which fulfills the requirements of ICRP 1990 recommendations, some problems, such as the investigation of uncertainties in estimates of body burdens by in vivo counting, and the selection of the way to improve the precision, have been studied. In the present study, a calibration technique for in vivo counting application using Monte Carlo simulation was developed. The advantage of the technique is that counting efficiency can be obtained for various shapes and sizes that are very difficult to change for phantoms. To validate the calibration technique, the response functions and counting efficiencies of a whole-body counter installed in JAERI were evaluated using the simulation and measurements. Consequently, the calculations are in good agreement with the measurements. The method for the determination of counting efficiency curves as a function of energy was developed using the present technique and a physiques correction equation was derived from the relationship between parameters of correction factor and counting efficiencies of the JAERI whole-body counter. The uncertainties in body burdens of {sup 137}Cs estimated with the JAERI whole-body counter were also investigated using the Monte Carlo simulation and measurements. It was found that the uncertainties of body burdens estimated with the whole-body counter are strongly dependent on various sources of uncertainty such as radioactivity distribution within the body and counting statistics. Furthermore, the evaluation method of the peak efficiencies of a Ge semi-conductor detector was developed by Monte Carlo simulation for optimum arrangement of Ge semi-conductor detectors for
Study on advancement of in vivo counting using mathematical simulation
International Nuclear Information System (INIS)
To obtain an assessment of the committed effective dose, individual monitoring for the estimation of intakes of radionuclides is required. For individual monitoring of exposure to intakes of radionuclides, direct measurement of radionuclides in the body - in vivo counting- is very useful. To advance in a precision in vivo counting which fulfills the requirements of ICRP 1990 recommendations, some problems, such as the investigation of uncertainties in estimates of body burdens by in vivo counting, and the selection of the way to improve the precision, have been studied. In the present study, a calibration technique for in vivo counting application using Monte Carlo simulation was developed. The advantage of the technique is that counting efficiency can be obtained for various shapes and sizes that are very difficult to change for phantoms. To validate the calibration technique, the response functions and counting efficiencies of a whole-body counter installed in JAERI were evaluated using the simulation and measurements. Consequently, the calculations are in good agreement with the measurements. The method for the determination of counting efficiency curves as a function of energy was developed using the present technique and a physiques correction equation was derived from the relationship between parameters of correction factor and counting efficiencies of the JAERI whole-body counter. The uncertainties in body burdens of 137Cs estimated with the JAERI whole-body counter were also investigated using the Monte Carlo simulation and measurements. It was found that the uncertainties of body burdens estimated with the whole-body counter are strongly dependent on various sources of uncertainty such as radioactivity distribution within the body and counting statistics. Furthermore, the evaluation method of the peak efficiencies of a Ge semi-conductor detector was developed by Monte Carlo simulation for optimum arrangement of Ge semi-conductor detectors for designing a
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.
CHOOSING A MATHEMATICAL MODEL OF HEAT SUPPLY NETWORK ROUTE
V.N.Melkumov; Kuznetsov, I. S.; V. N. Kobelev
2012-01-01
Problem statement. Modern computational technologies allow to develop mathematical modelsfor choosing optimal topology and construction routes of heat supply networks taking into accounta large amount of influencing factors. Important pivots when developing a mathematical model arethe choice of source data representation, of the model of choosing the optimal topology and routeand the computational algorithms for model implementation at computing facilities. The difficultyof choosing a computa...
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.
Mathematical modeling of a convective textile drying process
Johann, G; E. A. Silva; O.C. Motta Lima; N.C. Pereira
2014-01-01
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 s...
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
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.
On the mathematical modelling of measurement
Barzilai, Jonathan
2006-01-01
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions that lead to construction of measurement scales that enable these operations.
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model
Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V.
2016-01-01
Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods. PMID:27387139
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.
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 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-
MAPCLUS: A Mathematical Programming Approach to Fitting the ADCLUS Model.
Arabie, Phipps
1980-01-01
A new computing algorithm, MAPCLUS (Mathematical Programming Clustering), for fitting the Shephard-Arabie ADCLUS (Additive Clustering) model is presented. Details and benefits of the algorithm are discussed. (Author/JKS)
Mathematical modeling of electromechanical processes in a brushless DC motor
Tkachuk, V. I.; V.I. Zhuk
2014-01-01
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 modelling of water radiolysis kinetics under reactor conditions
International Nuclear Information System (INIS)
Experimental data on coolant radiolysis (RBMK-1000 reactor) were used to construct mathematical model of water radiolysis kinetics under reactor conditions. Good agreement of calculation results with the experiment is noted
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.
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.
Directory of Open Access Journals (Sweden)
Rodrigo Dalla Vecchia
2016-02-01
Full Text Available 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 indicate that Big Data may contribute new ways of working with MM in the classroom, helping develop pedagogical objectives associated with the ability to deal with and interpret di
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....... Mathematical arguments as well as hypotheses about the physiological system have been used to construct the models....... 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...
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 of...
Recent advances in opinion modeling: control and social influence
Albi, Giacomo; Toscani, Giuseppe; Zanella, Mattia
2016-01-01
We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our attention on two major advancements: optimal control of opinion formation and influence of additional social aspects, like conviction and number of connections in social networks, which modify the agents' role in the opinion exchange process.
Mathematical Model of Moving Heat-Transfer Agents
Directory of Open Access Journals (Sweden)
R. I. Yesman
2014-07-01
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.
A mathematical model for a copolymer in an emulsion
2007-01-01
In this paper we review some recent results, obtained jointly with Stu Whittington, for a mathematical model describing a copolymer in an emulsion. The copolymer consists of hydrophobic and hydrophilic monomers, concatenated randomly with equal density. The emulsion consists of large blocks of oil and water, arranged in a percolation-type fashion. To make the model mathematically tractable, the copolymer is allowed to enter and exit a neighboring pair of blocks only at diagonally opposite cor...
Partial sum approaches to mathematical parameters of some growth models
Korkmaz, Mehmet
2016-04-01
Growth model is fitted by evaluating the mathematical parameters, a, b and c. In this study, the method of partial sums were used. For finding the mathematical parameters, firstly three partial sums were used, secondly four partial sums were used, thirdly five partial sums were used and finally N partial sums were used. The purpose of increasing the partial decomposition is to produce a better phase model which gives a better expected value by minimizing error sum of squares in the interval used.
A mathematical model of pulmonary gas exchange under inflammatory stress
Reynolds, Angela; Ermentrout, G. Bard; Clermont, Gilles
2010-01-01
During a severe local or systemic inflammatory response, immune mediators target lung tissue. This process may lead to acute lung injury and impaired diffusion of gas molecules. Although several mathematical models of gas exchange have been described, none simulate acute lung injury following inflammatory stress. In view of recent laboratory and clinical progress in the understanding of the pathophysiology of acute lung injury, such a mathematical model would be useful. We first derived a par...
The Mathematical Modelling of Heat Transfer in Electrical Cables
Bugajev Andrej; Jankevičiūtė Gerda; Tumanova Natalija
2014-01-01
This paper describes a mathematical modelling approach for heat transfer calculations in underground high voltage and middle voltage electrical power cables. First of the all typical layout of the cable in the sand or soil is described. Then numerical algorithms are targeted to the two-dimensional mathematical models of transient heat transfer. Finite Volume Method is suggested for calculations. Different strategies of nonorthogonality error elimination are considered. Acute triangles meshes ...
Advances in machining process modeling
International Nuclear Information System (INIS)
Ever increasing speed and affordability of computing resources together with the advances in the modeling techniques made it possible to use the numerical models like finite element method (FEM), to simulate the metal cutting processes numerically. This paper explains the recent technological advances made in the commercial DEFORMTM system to facilitate the modeling of metal cutting process. During the first phase of this work a 2D system has been developed which assumes orthogonal cutting conditions. The second phase of this work has resulted in the development of a modeling system for 3D machining processes with main focus on turning. The modeling tools developed in this project utilize a hybrid procedure including both transient and steady state approaches. Automated remeshing procedure is being used with great success. Multiple coating layers on the insert can be modeled to study their thermal effects. Elastic and thermal response of the insert during the machining process can also be modeled using this system. The Usui's wear model has also been implemented in the system to study the tool wear. The system developed has been validated with various results reported from actual cutting tests and comparisons are found to be reasonably accurate
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...
Mathematical modelling: From school to university
Ansie Harding
2009-01-01
The outcomes based education (OBE) system is characterised by controversy and the 2008 matric results that rendered admission to an unusually large number of students did nothing to silence critics. The ﬁrst students who completed their full cycle of school education in the OBE system entered universities in 2009 and their preparedness for university mathematics as well as their performance at university level are important as indicaters for estimating the success or otherwise of the OBE syst...
Mathematical Formulation Requirements and Specifications for the Process Models
Energy Technology Data Exchange (ETDEWEB)
Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.
2010-11-01
The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments
Advanced Model of Electromagnetic Launcher
Directory of Open Access Journals (Sweden)
Karel Leubner
2015-01-01
Full Text Available An advanced 2D model of electromagnetic launcher is presented respecting the influence of eddy currents induced in the accelerated ferromagnetic body. The time evolution of electromagnetic field in the system, corresponding forces acting on the projectile and time evolutions of its velocity and current in the field circuit are solved numerically using own application Agros2d. The results are then processed and evaluated in Wolfram Mathematica. The methodology is illustrated with an example whose results are discussed.
A Mathematical Model of Intermittent Androgen Suppression for Prostate Cancer
Ideta, Aiko Miyamura; Tanaka, Gouhei; Takeuchi, Takumi; Aihara, Kazuyuki
2008-12-01
For several decades, androgen suppression has been the principal modality for treatment of advanced prostate cancer. Although the androgen deprivation is initially effective, most patients experience a relapse within several years due to the proliferation of so-called androgen-independent tumor cells. Bruchovsky et al. suggested in animal models that intermittent androgen suppression (IAS) can prolong the time to relapse when compared with continuous androgen suppression (CAS). Therefore, IAS has been expected to enhance clinical efficacy in conjunction with reduction in adverse effects and improvement in quality of life of patients during off-treatment periods. This paper presents a mathematical model that describes the growth of a prostate tumor under IAS therapy based on monitoring of the serum prostate-specific antigen (PSA). By treating the cancer tumor as a mixed assembly of androgen-dependent and androgen-independent cells, we investigate the difference between CAS and IAS with respect to factors affecting an androgen-independent relapse. Numerical and bifurcation analyses show how the tumor growth and the relapse time are influenced by the net growth rate of the androgen-independent cells, a protocol of the IAS therapy, and the mutation rate from androgen-dependent cells to androgen-independent ones.
Recent advances in naturally fractured reservoir modeling
International Nuclear Information System (INIS)
Large amounts of oil reserves are contained in naturally fractured reservoirs. Most of these hydrocarbon volumes have been left behind because of the poor knowledge and/or description methodology of those reservoirs. This lack of knowledge has lead to the nonexistence of good quantitative models for this complicated type of reservoirs. The complexity of naturally fractured reservoirs causes the need for integration of all existing information at all scales (drilling, well logging, seismic, well testing, etc.) to provide a reservoir description for such reservoirs. This paper presents an overview of recent advances in naturally fractured reservoir modeling, which were developed to characterize the dual porosity system and to improve hydrocarbon recovery. Two techniques, material balance and numerical simulation, are shown to be supportive of one another. The material balance technique is a good tool for history matching of production performance and defining the system, which is then used as input in the numerical model. However, material balance has significant disadvantages when it comes to prediction, which is the domain of numerical simulation modeling. We present the application of a recently introduced material balance equation based on a dual-system approach. In numerical simulation, the mathematical model to predict fluid flow in anisotropic media is enhanced by using permeability tensors. We also discuss a technique to construct permeability tensors from seismic, well log and well test analysis
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
Mathematical modelling, problem solving, project and ethnomathematics: Confluent points
Salett Biembengut, Maria
2015-01-01
This paper presents a documental study about the con-fluent points among mathematical modelling, problem solving, project and ethnomathematics as methods of research and mathematics teaching. As a result, the study has shown that there are elements that bind these methods structurally together as research methods. Starting from the fact that education should promote knowledge this study provides evidence for these methods. Thus in each one of them, it is required knowledge from the student ab...
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.
Postcorrection and mathematical model of life in Extended Everett's Concept
Mensky, Michael B.
2007-01-01
Extended Everett's Concept (EEC) recently developed by the author to explain the phenomenon of consciousness is considered. A mathematical model is proposed for the principal feature of consciousness assumed in EEC, namely its ability (in the state of sleep, trance or meditation, when the explicit consciousness is disabled) to obtain information from all alternative classical realities (Everett's worlds) and select the favorable realities. To represent this ability, a mathematical operation c...
Mathematical Modelling and Experimental Analysis of Early Age Concrete
DEFF Research Database (Denmark)
Hauggaard-Nielsen, Anders Boe
1997-01-01
lead to cracks in the later cooling phase. The matrial model has intrigate couplings between the involved mechanics, and in the thesis special emphasize is put on the creep behaviour. The mathematical models are based on experimental analysis and numerical implementation of the models in a finite...
A mathematical model on germinal center kinetics andtermination
DEFF Research Database (Denmark)
Kesmir, Can; De Boer, R.J.
1999-01-01
We devise a mathematical model to study germinal center (GC) kinetics. Earlier models for GC kinetics areextended by explicitly modeling 1) the cell division history of centroblasts, 2) the Ag uptake by centrocytes,and 3) T cell dynamics. Allowing for T cell kinetics and T-B cell interactions, we...
Learning and Teaching Mathematics through Real Life Models
Takaci, Djurdjica; Budinski, Natalija
2011-01-01
This paper proposes modelling based learning as a tool for learning and teaching mathematics in high school. We report on an example of modelling real world problems in two high schools in Serbia where students were introduced for the first time to the basic concepts of modelling. Student use of computers and educational software, GeoGebra, was…
Mathematical modelling of dextran filtration through hollow fibre membranes
DEFF Research Database (Denmark)
Vinther, Frank; Pinelo, Manuel; Brøns, Morten; Jonsson, Gunnar Eigil; Meyer, Anne S.
2014-01-01
In this paper we present a mathematical model of an ultrafiltration process. The results of the model are produced using standard numerical techniques with Comsol Multiphysics. The model describes the fluid flow and separation in hollow fibre membranes. The flow of solute and solvent within the h...
Mathematical models for correction of images, obtained at radioisotope scan
International Nuclear Information System (INIS)
The images, which obtained at radioisotope scintigraphy, contain distortions. Distortions appear as a result of absorption of radiation by patient's body's tissues. Two mathematical models for reducing of such distortions are proposed. Image obtained by only one gamma camera is used in the first mathematical model. Unfortunately, this model allows processing of the images only in case, when it can be assumed, that the investigated organ has a symmetric form. The images obtained by two gamma cameras are used in the second model. It gives possibility to assume that the investigated organ has non-symmetric form and to acquire more precise results. (authors)
A Review on Mathematical Modeling for Textile Processes
Chattopadhyay, R.
2015-10-01
Mathematical model is a powerful tool in engineering for studying variety of problems related to design and development of products and processes, optimization of manufacturing process, understanding a phenomenon and predicting product's behaviour in actual use. An insight of the process and use of appropriate mathematical tools are necessary for developing models. In the present paper, a review of types of model, procedure followed in developing them and their limitations have been discussed. Modeling techniques being used in few textile processes available in the literature have been cited as examples.
International Nuclear Information System (INIS)
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed
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.
MATHEMATICAL MODELING FOR DURABILITY CHARACTERISTICS OF FLY ASH CONCRETE
Directory of Open Access Journals (Sweden)
JINO JOHN
2012-01-01
Full Text Available This paper presents the results obtained from the mathematical modeling for the durability characteristics of fly ash concrete. A mathematical model is employed to predict the saturated water absorption, permeability, sorpitivity and acid resistance of the concrete containing fly ash as a replacement of cement at a range of 0%, 10%, 20%, 30%, 40% and 50 %. This model is valid for mixes with cement quantity 208 to 416 kg/m3, water cement ratio 0.38 to 0.76, flyash 0 to 208 kg/m3 and cement/ total aggregate ratio varying from 0.11 to 0.22. Fly ash content and water cement ratio are the main parameters which influence the durability characteristics. The predicted mathematical model for saturated water absorption, permeability, sorpitivity and acid resistance produced accurate results for the respective ages when compared with the experimental results.
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
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.
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 a rotary hearth coke calciner
Hilde C. Meisingset; Jens G. Balchen
1995-01-01
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 p...
Mathematical Modeling of Vascular Tumor Growth and Development
Cooper, Michele
2010-01-01
Mathematical modeling of cancer is of significant interest due to its potential to aid in our understanding of the disease, including investigation into which factors are most important in the progression of cancer. With this knowledge and model different paths of treatment can be examined; (e.g. simulation of different treatment techniques followed by the more costly venture of testing on animal models). Significant work has been done in the field of cancer modeling with models ranging from ...
Mathematical Modeling of Food Freezing in Air-Blast Freezer
Guiqiang Wang; Pinghua Zou
2014-01-01
A mathematical model for simulating the heat transfer during food freezing was presented. The model consists of three steps. First, the flow field inside the freezing chamber was modeled using the CFD method, based on which the freezing condition, including the temperature and velocity around the food, was calculated. Second, the heat transfer coefficient between food and air was calculated in the CFD model. Third, a finite-difference model was employed to simulate the heat transfer inside th...
Mathematical modelling of slow drug release from collagen matrices
Erichsen, Birgitte Riisøen
2014-01-01
This master's thesis is about controlled drug release, which is a relatively new area of mathematical modelling. In this thesis there have been two major focuses. The first is to further understand the model for drug release from collagen matrices developed earlier by solving it with a different numerical scheme, and the second to develop a new model based on a different geometry. Both models are based on mass conservation and Fick's law, and are therefore possible to compare. The two models ...
Applying Mathematical Models to Surgical Patient Planning
Oostrum, Jeroen
2009-01-01
textabstractOn a daily basis surgeons, nurses, and managers face cancellation of surgery, peak demands on wards, and overtime in operating rooms. Moreover, the lack of an integral planning approach for operating rooms, wards, and intensive care units causes low resource utilization and makes patient flows unpredictable. An ageing population and advances in medicine are putting the available healthcare budget under great pressure. Under these circumstances, hospitals are seeking innovative way...
A Numerical Method for Solving the Mathematical Model of Controlled Drug Release
Öztürk, Yalçın; GÜLSU, Aydan; Gülsu, Mustafa
2013-01-01
Over the past few decades, significant medical advances have been made in the area of drug delivery with the development of controlled release dosage forms. Controlled release formulations bring scientists in different fields to work together with the common aim of realizing more and more effective products. For this purpose, the use of mathematical modeling turns out to be very useful as this approach enables, in the best case, the prediction of release kinetics before the release systems ar...
Modeling Tool Advances Rotorcraft Design
2007-01-01
Continuum Dynamics Inc. (CDI), founded in 1979, specializes in advanced engineering services, including fluid dynamic modeling and analysis for aeronautics research. The company has completed a number of SBIR research projects with NASA, including early rotorcraft work done through Langley Research Center, but more recently, out of Ames Research Center. NASA Small Business Innovation Research (SBIR) grants on helicopter wake modeling resulted in the Comprehensive Hierarchical Aeromechanics Rotorcraft Model (CHARM), a tool for studying helicopter and tiltrotor unsteady free wake modeling, including distributed and integrated loads, and performance prediction. Application of the software code in a blade redesign program for Carson Helicopters, of Perkasie, Pennsylvania, increased the payload and cruise speeds of its S-61 helicopter. Follow-on development resulted in a $24 million revenue increase for Sikorsky Aircraft Corporation, of Stratford, Connecticut, as part of the company's rotor design efforts. Now under continuous development for more than 25 years, CHARM models the complete aerodynamics and dynamics of rotorcraft in general flight conditions. CHARM has been used to model a broad spectrum of rotorcraft attributes, including performance, blade loading, blade-vortex interaction noise, air flow fields, and hub loads. The highly accurate software is currently in use by all major rotorcraft manufacturers, NASA, the U.S. Army, and the U.S. Navy.
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…
Safety analyses of the LVR-15 reactor (mathematical model)
International Nuclear Information System (INIS)
A mathematical model is described of the LVR-15 experimental reactor core and primary circuit. Described are the thermal hydraulics of main primary circuit components, a model of point kinetics for reactor output calculations, and equations for residual heat. An approach to numerical solution is presented and computer programs briefly described. (author). 6 figs., 4 tabs., 28 refs
Mathematical model of bisubject qualimetric arbitrary objects evaluation
Morozova, A.
2016-04-01
An analytical basis and the process of formalization of arbitrary objects bisubject qualimetric evaluation mathematical model information spaces are developed. The model is applicable in solving problems of control over both technical and socio-economic systems for objects evaluation using systems of parameters generated by different subjects taking into account their performance and priorities of decision-making.
Use of mathematical modeling in nuclear measurements projects
International Nuclear Information System (INIS)
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)
Preparation of mathematical model of electronic regulator to calculation researches
Лисовал, А. А.
2008-01-01
The stage of design of microprocessor regulator for a diesel with supercharger is presented: the development of a dynamic mathematical model of an electronic regulator. Adequacy of the created model is confirmed during realization of her in the software environment of MATLAB/Simulink. Il. 6. Bibliogr. 7 names.
Mathematical Model Analysis of Intra-organisational Collaboration
Anliang Ning; Xiaojing Li; Chunxian Wang
2013-01-01
Collaboration means working together to achieve a common goal or to solve a problem. Grounded on complex network theory and collaborative design research, a mathematical model for analysing collaboration level in organisations is proposed. The concepts for characterising organisational structures for collaboration and indicators for assessing organisational behaviour were defined. The article concludes by discussing the limitations of the proposed model.
MATHEMATICAL MODEL OF ELECTROSTATIC PRECIPITATION (REVISION 3): SOURCE CODE
This tape contains the source code (FORTRAN) for Revision 3 of the Mathematical Model of Electrostatic Precipitation. Improvements found in Revision 3 of the model include a new method of calculating the solutions to the electric field equations, a dynamic method for calculating ...
Mathematical model of desublimation process of volatile metal fluorides
Smolkin, P. А.; Buynovskiy, А. S.; Lazarchuk, V. V.; Matveev, А. А.; Sofronov, V. L.
2007-01-01
Mathematical model for calculation of optimal temperature desublimation in metal fluorides and the number of desublimation stages has been developed; it permits achieving the degree of base product recovery from gas-vapour mixture nearly to 100 %. Experimental checking of modeling results at uranium hexafluoride desublimation shows a good correlation with the theoretical data.
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.
CHOOSING A MATHEMATICAL MODEL OF HEAT SUPPLY NETWORK ROUTE
Directory of Open Access Journals (Sweden)
V. N. Melkumov
2012-02-01
Full Text Available Problem statement. Modern computational technologies allow to develop mathematical modelsfor choosing optimal topology and construction routes of heat supply networks taking into accounta large amount of influencing factors. Important pivots when developing a mathematical model arethe choice of source data representation, of the model of choosing the optimal topology and routeand the computational algorithms for model implementation at computing facilities. The difficultyof choosing a computational method, aside from the nature of topological models, is complicatedby a large amount of limiting factors. This is the reason why the choice of forms of representationof mathematical models and the efficiency of computational methods of their solution is actualwhen used in practical applications.Results. A mathematical model of the cost of construction of heat supply networks has been developedwhich, as opposed to traditional models, leaves the necessary degrees of freedom for determiningacceptable and optimal topology and construction route for account of using multicriterionoptimization. A method of weighted summation has been proposed for usage for combiningraster maps corresponding to different routing criteria.Conclusions. The considered method allows to take account of the whole system of factors influencingthe construction route of heat supply network and to conduct route optimization basedon several criteria, which allows to choose the optimal topology and construction route under theinfluence of multiple external and internal factors.
Asymptotic properties of mathematical models of excitability
Biktasheva, I. V.; Simitev, R. D.; Suckley, R.; Biktashev, V. N.
2005-01-01
We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (1952) model of nerve axon, Noble (1962) model of heart Purkinje fibres, and Courtemanche et al. (1998) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic timescales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analy...
Mathematical model of seed germination process
International Nuclear Information System (INIS)
An analytical model of seed germination process was described. The model based on proposed working hypothesis leads - by analogy - to a law corresponding with Verhulst-Pearl's law, known from the theory of population kinetics. The model was applied to describe the germination kinetics of tomato seeds, Promyk field cultivar, biostimulated by laser treatment. Close agreement of experimental and model data was obtained
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.
A full body mathematical model of an oil palm harvester
Tumit, NP; Rambely, A. S.; BMT, Shamsul; Shahriman A., B.; Ng Y., G.; Deros, B. M.; Zailina, H.; Goh Y., M.; Arumugam, Manohar; Ismail I., A.; Abdul Hafiz A., R.
2015-09-01
The main purpose of this article is to develop a mathematical model of human body during harvesting via Kane's method. This paper is an extension model of previous biomechanical model representing a harvester movement during harvesting a Fresh Fruit Bunch (FFB) from a palm oil tree. The ten segment model consists of foot, leg, trunk, the head and the arms segment. Finally, the inverse dynamic equations are represented in a matrix form.
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
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 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.
Rock Burst Mechanics: Insight from Physical and Mathematical Modelling
Vacek, J.; J. Chocholoušová
2008-01-01
Rock burst processes in mines are studied by many groups active in the field of geomechanics. Physical and mathematical modelling can be used to better understand the phenomena and mechanisms involved in the bursts. In the present paper we describe both physical and mathematical models of a rock burst occurring in a gallery of a coal mine.For rock bursts (also called bumps) to occur, the rock has to possess certain particular rock burst properties leading to accumulation of energy and the pot...
An Advanced Time Averaging Modelling Technique for Power Electronic Circuits
Jankuloski, Goce
For stable and efficient performance of power converters, a good mathematical model is needed. This thesis presents a new modelling technique for DC/DC and DC/AC Pulse Width Modulated (PWM) converters. The new model is more accurate than the existing modelling techniques such as State Space Averaging (SSA) and Discrete Time Modelling. Unlike the SSA model, the new modelling technique, the Advanced Time Averaging Model (ATAM) includes the averaging dynamics of the converter's output. In addition to offering enhanced model accuracy, application of linearization techniques to the ATAM enables the use of conventional linear control design tools. A controller design application demonstrates that a controller designed based on the ATAM outperforms one designed using the ubiquitous SSA model. Unlike the SSA model, ATAM for DC/AC augments the system's dynamics with the dynamics needed for subcycle fundamental contribution (SFC) calculation. This allows for controller design that is based on an exact model.
Mathematical model for spreading dynamics of social network worms
International Nuclear Information System (INIS)
In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks
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 model of the dynamics of psychotherapy
Larry S. Liebovitch; Peluso, Paul R.; Norman, Michael D.; Su, Jessica; Gottman, John M.
2011-01-01
The success of psychotherapy depends on the nature of the therapeutic relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. Previously Gottman et al. used a very similar approach (physical-sciences paradigm) for modeling and making predictions about husband–wife relationshi...
Mathematical modelling and optimal control of anthracnose
Fotsa, David; Houpa, Elvis; Békollé, David; Thron, Christopher; Ndoumbé, Michel
2013-01-01
In this paper we propose two nonlinear models for the control of anthracnose disease. The first is an ordinary differential equation (ODE) model which represents the within-host evolution of the disease. The second includes spatial diffusion of the disease in a bounded domain. We demonstrate the well-posedness of those models by verifying the existence of solutions for given initial conditions and positive invariance of the positive cone. By considering a quadratic cost functional and applyin...
Mathematical Models for Room Air Distribution - Addendum
DEFF Research Database (Denmark)
Nielsen, Peter V.
1982-01-01
removed from the room at constant penetration length is proportional to the cube of the velocities in the occupied zone. It is also shown that a large number of diffusers increases the amount of heat which may be removed without affecting the thermal conditions. Control strategies for dual duct and single......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...
Mathematical Models for Room Air Distribution
DEFF Research Database (Denmark)
Nielsen, Peter V.
1982-01-01
removed from the room at constant penetration length is proportional to the cube of the velocities in the occupied zone. It is also shown that a large number of diffusers increases the amount of heat which may be removed without affecting the thermal conditions. Control strategies for dual duct and single......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...
A Mathematical Model for Segmenting ECG Signals
Feier, Horea; Roşu, Doina; Falniţǎ, Lucian; Roşu, Şerban; Pater, Liana
2010-09-01
This paper deals with the behavior of the modulus of the continuous wavelet transform (CWT) for some known mother wavelets like the Morlet wavelet and the Mexican Hat. By exploiting these properties, the models presented can behave as a segmentation/ recognition signal processing tool by modeling the temporal structure of the observed surface ECG.
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.
Czech Academy of Sciences Publication Activity Database
Nedoma, Jiří
Hauppauge: Nova Science Publishers, 2015 - (Linwood, K.), s. 21-97. (Natural Disaster Research, Prediction and Mitigation). ISBN 978-1-63463-309-3 Institutional support: RVO:67985807 Keywords : earthquakes * tsunamiearthquakes * typhoons * tsunamis * landslides * mudslides * mathematical models * varionational formulations of corresponding model problems * computational methods and algorithms Subject RIV: BA - General Mathematics
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.
Development of a revised mathematical model of the gastrointestinal tract
International Nuclear Information System (INIS)
The objectives of this research are as follows. First, to incorporate new biological data into a revised mathematical adult gastrointestinal tract model that includes: ingestion in both liquid and solid forms; consideration of absorption in the stomach, small intestine, ascending colon, transverse colon or not at all; gender and age of the adult; and whether the adult is a smoker or not. Next, to create a computer program in basic language for calculating residence times in each anatomical section of the GI tract for commonly used radionuclides. Also, to compare and contrast the new model with the ICRP 30 GI tract model in terms of physiological concepts, mathematical concepts, and revised residence times for several commonly used radionuclides. Finally, to determine whether the new model is sufficiently better than the current model to warrant its use as a replacement for the Eve model
A Computational and Mathematical Model for Device Induced Thrombosis
Wu, Wei-Tao; Aubry, Nadine; Massoudi, Mehrdad; Antaki, James
2015-11-01
Based on the Sorenson's model of thrombus formation, a new mathematical model describing the process of thrombus growth is developed. In this model the blood is treated as a Newtonian fluid, and the transport and reactions of the chemical and biological species are modeled using CRD (convection-reaction-diffusion) equations. A computational fluid dynamic (CFD) solver for the mathematical model is developed using the libraries of OpenFOAM. Applying the CFD solver, several representative benchmark problems are studied: rapid thrombus growth in vivo by injecting Adenosine diphosphate (ADP) using iontophoretic method and thrombus growth in rectangular microchannel with a crevice which usually appears as a joint between components of devices and often becomes nidus of thrombosis. Very good agreements between the numerical and the experimental results validate the model and indicate its potential to study a host of complex and practical problems in the future, such as thrombosis in blood pumps and artificial lungs.
A Mathematical Model For Forest Fires Blowup
Viegas, Domingos Xavier
2004-01-01
The very quick fire spread that occurs in some forest fires has been the cause of many fatalities in the past among fire fighters throughout the world. A theoretical model describing the convective interaction between the fire front and the surrounding air is proposed to explain the blowup phenomenon that is observed in nature. This model is based on a set of laboratory experiments of fire blowup in canyons that was used to validate it. The model predicts quite well the general fire behavior ...
A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy.
Li, Xuefang; Xu, Jian-Xin
2016-10-01
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. PMID:27338302
Discrete mathematical physics and particle modeling
International Nuclear Information System (INIS)
The theory and application of the arithmetic approach to the foundations of both Newtonian and special relativistic mechanics are explored. Using only arithmetic, a reformulation of the Newtonian approach is given for: gravity; particle modeling of solids, liquids, and gases; conservative modeling of laminar and turbulent fluid flow, heat conduction, and elastic vibration; and nonconservative modeling of heat convection, shock-wave generation, the liquid drop problem, porous flow, the interface motion of a melting solid, soap films, string vibrations, and solitons. An arithmetic reformulation of special relativistic mechanics is given for theory in one space dimension, relativistic harmonic oscillation, and theory in three space dimensions. A speculative quantum mechanical model of vibrations in the water molecule is also discussed. 82 references
Mathematical Modelling of Metabolic Regulation in Aging
Directory of Open Access Journals (Sweden)
Mark T. Mc Auley
2015-04-01
Full Text Available The underlying cellular mechanisms that characterize aging are complex and multifaceted. However, it is emerging that aging could be regulated by two distinct metabolic hubs. These hubs are the pathway defined by the mammalian target of rapamycin (mTOR and that defined by the NAD+-dependent deacetylase enzyme, SIRT1. Recent experimental evidence suggests that there is crosstalk between these two important pathways; however, the mechanisms underpinning their interaction(s remains poorly understood. In this review, we propose using computational modelling in tandem with experimentation to delineate the mechanism(s. We briefly discuss the main modelling frameworks that could be used to disentangle this relationship and present a reduced reaction pathway that could be modelled. We conclude by outlining the limitations of computational modelling and by discussing opportunities for future progress in this area.
Economics, Mathematical Models, and Environmental Policy
Conrad, John M.
1987-01-01
This paper briefly reviews several models of externality which provide the theoretical basis of environmental economics. An externality may be defined as a situation where the output or action of a firm or individual affects the production possibilities or welfare of another firm or individual who has no direct control over the initial level of the output or activity. Pollution, resulting from the disposal of residual wastes, is a classic example of externality. Three static models examine th...
MATHEMATICAL MODELS FOR MICROSTRUCTURE EVOLUTION IN THE SEAMLESS TUBE ROLLING
Ricardo Nolasco de Carvalho; Marcelo Almeida Cunha Ferreira; Dagoberto Brandão Santos; Ronaldo Antônio Neves Marques Barbosa
2013-01-01
The goal of this work is to present recent developments on mathematical modeling for microstructure evolution in different steel types, applied to a continuous rolling of seamless tubes. The development of these models depends on careful characterization of the thermomechanical cycle and/on correct selection and adjustment of equations which describes the several metallurgical phenomena involved on this process. The adjustments of these models are done using the results obtained i...
A Mathematical Model of Tripartite Synapse: Astrocyte Induced Synaptic Plasticity
Tewari, Shivendra; Majumdar, Kaushik
2011-01-01
In this paper we present a biologically detailed mathematical model of tripartite synapses, where astrocytes modulate short-term synaptic plasticity. The model consists of a pre-synaptic bouton, a post-synaptic dendritic spine-head, a synaptic cleft and a peri-synaptic astrocyte controlling Ca2+ dynamics inside the synaptic bouton. This in turn controls glutamate release dynamics in the cleft. As a consequence of this, glutamate concentration in the cleft has been modeled, in which glutamate ...
Mathematical modeling of recombinant Escherichia coli aerobic batch fermentations
Costa, Rafael S; Rocha, I; Ferreira, E. C.
2008-01-01
In this work, three competing unstructured mathematical models for the biomass growth by recombinant E. coli strains with different acetate inhibition kinetics terms were evaluated for batch processes at constant temperature and pH. The models considered the dynamics of biomass growth, acetate accumulation, substrate consumption, Green Fluorescence Protein (GFP) production and three metabolic pathways for E. coli. Parameter estimation and model validation was carried out usi...
Mathematical Model to Simulate Tuberculosis Disease Population Dynamics
Directory of Open Access Journals (Sweden)
O. K. Koriko
2008-01-01
Full Text Available A mathematical model to depict Tuberculosis disease population dynamics was presented. The model population was compartmentalised as appropriate and the resulting model equations were solved numerically while different instances of the disease transmission were simulated. The graphical profiles of the various sub-populations with time were presented and discussed based on the results from our simulations. Also, the disease-free and endemic equilibrium of the system were established and analyzed for stability.
Mathematical Model of Hot Metal Desulfurization by Powder Injection
Yolanda Cepeda Rodríguez; Guillermo González Múzquiz; José Refugio Parga Torres; Luciano Eliezer Ramírez Vidaurri
2012-01-01
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 c...
Strategic and Tactical Crude Oil Supply Chain: Mathematical Programming Models
Sahebishahemabadi, Hadi
2013-01-01
Crude oil industry very fast became a strategic industry. Then, optimization of the Crude Oil Supply Chain (COSC) models has created new challenges. This fact motivated me to study the COSC mathematical programming models. We start with a systematic literature review to identify promising avenues. Afterwards, we elaborate three concert models to fill identified gaps in the COSC context, which are (i) joint venture formation, (ii) integrated upstream, and (iii) environmentally conscious design.
Comprehensive Mathematical Model for Simulating Electroslag Remelting
Dong, Yan-Wu; Jiang, Zhou-Hua; Fan, Jin-Xi; Cao, Yu-Long; Hou, Dong; Cao, Hai-Bo
2016-04-01
Droplet formation and departure from an electrode tip affect the temperature distribution in liquid slag and a molten steel pool, as well as the removal of nonmetallic inclusions in the electroslag remelting process. In this article, magneto-hydrodynamics modules coupled with a volume of fluid (VOF) model (as described in VOF model theory) for tracking phase distribution have been employed to develop the electrode fusion model and to investigate formation and departure of a droplet from the electrode tip. Subsequently, the remelting rate and molten steel pool have been achieved based on the electrode fusion model. Results indicate that a droplet can increase the flow rate of liquid slag, especially the region of droplet fall through the slag pool; yet it has little impact on the flow distribution. Asymmetric flow can take place in a slag pool due to the action of the droplet. The depth of the molten steel pool increases in the presence of droplets, but the width of the mushy zone decreases. In addition, the shape of the electrode tip is not constant but changes with its fusion. The remelting rate is calculated instead of being imposed in this work. The development of the model supports further understanding of the process and the ability to set the appropriate operating parameters, especially for expensive and easy segregation materials.
Mathematical model for safety analysis of heavy water power reactor
International Nuclear Information System (INIS)
Fundamental information in formulating the mathematical model for accident analysis is concerned with reactivity changes of the system. These parameters are: changes of fuel and moderator temperature, changes of the upper reflector thickness, reactivity changes due to moderator density variation dependent on the steam quantity and neutron flux distribution in the core
Mathematical models and dynamic characteristics of the WWER-440 unit
International Nuclear Information System (INIS)
Dynamic characteristics of the WWER-440 unit are determined. Using suitable mathematical models the dynamic properties of the reactor fuel channel, steam generator and individual parts of the secondary circuit were investigated. General relations of the corresponding transfer function and its numerical value are calculated as well as the transfer functions of different configurations of two parallel lines of the secondary circuit. (author)
Mathematical model of non-isothermal creep based anisotropic damage
Галаган, Ю. Н.; Лысенко, С. В.; Львов, Г. И.
2008-01-01
А mathematical model of nonisothermic creep for anisotropic damage case is considered. Constitutive relation of creep rate and kinematic equation of damage evolution are assumed temperature dependent. A second range tensor is used for description damage. A technique based on existing experimental curves for the identification of material creep constants is presented.
Conceptualizing professional development in mathematics: elements of a model
Sztajn, Paola; Campbell, Mathew; Yoon, Kwang Suk
2011-01-01
This theoretical paper discusses the concept of models for mathematics professional development. After examining the related literature, we propose a definition of this concept that includes four elements: goals, theories, contexts, and structure. We present aspects of professional development that comprise each element.
Mathematical Model for Pressurized Solvent Extraction from Leuzea carthamoides
Czech Academy of Sciences Publication Activity Database
Machalová, Zdeňka
Prague : Institute of Chemical Process Fundamental of the CAS, v. v. i, 2015 - (Bendová, M.; Wagner, Z.), s. 9-10 ISBN 978-80-86186-70-2. [Bažant Postgraduate Conference 2015. Prague (CZ)] Institutional support: RVO:67985858 Keywords : mathematical modelling * extraction * leuzea carthamoides Subject RIV: CI - Industrial Chemistry, Chemical Engineering
Optimization of a new mathematical model for bacterial growth
The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...
MATHEMATICAL MODEL OF A DRYING PROCESS OF CORRUGATED CARDBOARD
Piotrovskiy D. L.; Cherny R. R.
2016-01-01
The feature of the process of drying of corrugated cardboard is different drying processes on three sections of the drying table. The article solves the problem of obtaining a mathematical model of drying process of corrugated cardboard. This structural identification process, defined the input and output parameters, denoted the transmission coefficients for the control channels and indignation
MATHEMATICAL MODEL OF A DRYING PROCESS OF CORRUGATED CARDBOARD
Directory of Open Access Journals (Sweden)
Piotrovskiy D. L.
2016-01-01
Full Text Available The feature of the process of drying of corrugated cardboard is different drying processes on three sections of the drying table. The article solves the problem of obtaining a mathematical model of drying process of corrugated cardboard. This structural identification process, defined the input and output parameters, denoted the transmission coefficients for the control channels and indignation
The mathematical models of solution mining and case study
International Nuclear Information System (INIS)
The mathematical model of parameters which describe solution mining and the principle of ore leaching are presented theoretically and thoroughly with the emphasis on in-situ leaching with a biolixiviant, furthermore, the example of bioleach mining, or biomining, in an abandoned underground copper mine is discussed
Mathematical Model for Pressurized Solvent Extraction from Leuzea carthamoides
Czech Academy of Sciences Publication Activity Database
Machalová, Zdeňka
Prague: Institute of Chemical Process Fundamental of the CAS, v. v. i, 2015 - (Bendová, M.; Wagner, Z.), s. 9-10 ISBN 978-80-86186-70-2. [Bažant Postgraduate Conference 2015. Prague (CZ)] Institutional support: RVO:67985858 Keywords : mathematical modelling * extraction * leuzea carthamoides Subject RIV: CI - Industrial Chemistry, Chemical Engineering
Unlocking pathogen genotyping information for public health by mathematical modeling
M. Kretzschmar; M.G. M. Gomes; R.A. Coutinho; J.S. Koopman
2010-01-01
Molecular typing and mathematical modeling have gone through rapid development in the past decade. Both offer new insights into the epidemiology of infectious diseases, thereby contributing to a better understanding of transmission dynamics. Infectious disease surveillance and control benefit from t
Evolution and History in a new "Mathematical SETI" model
Maccone, Claudio
2014-01-01
important exact equations yielding the b-lognormal when its birth time, senility-time (descending inflexion point) and death time (where the tangent at senility intercepts the time axis) are known. These also are brand-new results. In particular, the σ=1 b-lognormals are shown to be related to the golden ratio, so famous in the arts and in architecture, and these special b-lognormals we call "golden b-lognormals". Applying this new mathematical apparatus to Human History leads to the discovery of the exponential trend of progress between Ancient Greece and the current USA Empire as the envelope of the b-lognormals of all Western Civilizations over a period of 2500 years. We then invoke Shannon's Information Theory. The entropy of the obtained b-lognormals turns out to be the index of "development level" reached by each historic civilization. As a consequence, we get a numerical estimate of the entropy difference (i.e. the difference in the evolution levels) between any two civilizations. In particular, this was the case when Spaniards first met with Aztecs in 1519, and we find the relevant entropy difference between Spaniards an Aztecs to be 3.84 bits/individual over a period of about 50 centuries of technological difference. In a similar calculation, the entropy difference between the first living organism on Earth (RNA?) and Humans turns out to equal 25.57 bits/individual over a period of 3.5 billion years of Darwinian Evolution. Finally, we extrapolate our exponentials into the future, which is of course arbitrary, but is the best Humans can do before they get in touch with any alien civilization. The results are appalling: the entropy difference between aliens 1 million years more advanced than Humans is of the order of 1000 bits/individual, while 10,000 bits/individual would be requested to any Civilization wishing to colonize the whole Galaxy (Fermi Paradox). In conclusion, we have derived a mathematical model capable of estimating how much more advanced than humans
Mathematical Model for Post-Irradiation Haemopoiesis
International Nuclear Information System (INIS)
A model for haemopoiesis has been constructed based on the following hypothesis: (a) Haemopoietic stem cells have the capability of either reproducing as stem cells or differentiating into specialized blood cells of at least two different types; (b) The size of the stem-cell compartment is in part regulated by the rate of increase due to stem-cell reproduction and in part by the rate of loss of stem cells through differentiation; (c) In addition, the size of the stem-cell compartment is in part regulated by a competitive cell-to-cell interaction between the stem-cells themselves and between the differentiating cells and the stem-cells, such that the presence of an exceptionally large number of either cell type would have a repressive effect on the rate of increase of the stem-cell population. This model has been applied to the post-irradiation erythropoietic behaviour of the rat. In the computer studies with the model, an X-ray dose sufficient to inhibit reproduction in 50% of the erythroid stem cells was assumed. It was also assumed that reproduction and differentiation are genetically separately controlled processes and that, therefore, some part of the reproductively injured cells were still capable of differentiation. Under these conditions the model predicted an abortive rise in reticulocyte number, peaking at about 6 days. True recovery was predicted to occur at about 16 days. Both the abortive rise and the true recovery were also present in those segments of the model representing earlier erythroid cells, occurring at progressively earlier times in progressively more primitive cells. Comparison of the model's predictions with experimentally obtained data for post-irradiation erythroid recovery showed a good agreement both with respect to the time of the abortive peak and the time of true recovery. (author)
International Nuclear Information System (INIS)
second book under consideration, that of Schwabl, contains 'Advanced' elements of quantum theory; it is designed for a course following on from one for which Gottfried and Yan, or Schwabl's own 'Quantum Mechanics' might be recommended. Many useful student problems are included. The presentation is said to be rigorous, but again this is a book for the physicist rather than the mathematician. The third book under consideration, that by Gustafson and Sigal is very different from the others. In academic level, at least the initial sections may actually be slightly lower; the book covers a one-term course taken by senior undergraduates or junior graduate students in mathematics or physics, and the initial chapters are on basic topics, such as the physical background, basic dynamics, observables and the uncertainty principle. However the level of mathematical sophistication is far higher than in the other books. While the mathematical prerequisites are modest, a third of the book is made up of what are called mathematical supplements. On the basis of these supplements, the level of mathematical sophistication and difficulty is increased substantially in the middle section of the book, where the topics considered are many-particle systems, density matrices, positive temperatures, the Feynman path integral, and quasi-classical analysis, and there is a final substantial step for the concluding chapters on resonances, an introduction to quantum field theory, and quantum electrodynamics of non-relativistic particles. A supplementary chapter contains an interesting approach to the renormalization group due to Bach, Froehlich and Sigal himself. This book is well-written, and the topics discussed have been well thought-out. It would provide a useful approach to quantum theory for the mathematician, and would also provide access for the physicist to some mathematically advanced methods and topics, but the physicist would definitely have to be prepared to work hard at the mathematics
Mathematical modelling of thermal storage systems for the food industry
Energy Technology Data Exchange (ETDEWEB)
Lopez, A.; Lacarra, G. [Universidad Publica de Navarra Campus Arrosadia, Pamplona (Spain). Area de Tecnologia de Alimentos
1999-07-01
Dynamic mathematical models of two thermal storage systems used in the food industry to produce chilled water are presented; an ice-bank system and a holding tank system. The variability of the refrigeration demand with time was taken into account in the model. A zoned approach using mass and energy balances was applied. Heat transfer phenomena in the evaporator were modelled using empirical correlations. The experimental validation of the mathematical models on an ice-bank system at pilot plant scale, and a centralized refrigeration system with a holding tank in a winery, showed accurate prediction. Simple models are adequate to predict the dynamic behaviour of these refrigeration systems under variable heat loads. (Author)
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.
A mathematical model of the dynamics of antitumor laser immunotherapy
Dawkins, Bryan A.; Laverty, Sean M.
2014-02-01
We use a mathematical model to describe and predict the population dynamics of tumor cells, immune cells, and other immune components in a host undergoing laser immunotherapy treatment against metastatic cancer. We incorporate key elements of the treatment into the model: a function describing the laser-induced primary tumor cell death and parameters capturing the role and strength of the primary immunoadjuvant, glycated chitosan. We focus on identifying conditions that ensure a successful treatment. In particular, we study the patient response (i.e., anti-tumor immune dynamics and treatment outcome) in two different but related mathematical models as we vary quantitative features of the immune system (supply, proliferation, death, and interaction rates). We compare immune dynamics of a `baseline' immune model against an `augmented' model (with additional cell types and antibodies) and in both, we find that using strong immunoadjuvants, like glycated chitosan, that enhance dendritic cell activity yields more promising patient outcomes.
Analysis of mathematical model of leukemia
Directory of Open Access Journals (Sweden)
Helal Mohamed
2015-01-01
Full Text Available In this paper, a model describing the dynamic of chronic myeloid leukemia is studied. By analyzing the corresponding characteristic equations, the local stability of trivial and nontrivial equilibria are discussed. By establishing appropriate Lyapunov functions, we prove the global stability of the positive constant equilibrium solutions.
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-Volterra...
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...
Mathematical Modelling of Supercritical Fluid Extraction
Czech Academy of Sciences Publication Activity Database
Sovová, Helena
New York: Bentham Science Publishers, 2009 - (Duarte, A.), s. 80-96 ISBN 978-1-60805-046-8 R&D Projects: GA ČR GA104/06/1174 Institutional research plan: CEZ:AV0Z40720504 Keywords : supercritical fluid extraction * models * characteristic times Subject RIV: CI - Industrial Chemistry, Chemical Engineering http://www.benthamdirect.org/pages/b_bookarticle.php
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 sy
Mathematical Modelling of Continuous Biotechnological Processes
Pencheva, T.; Hristozov, I.; Shannon, A. G.
2003-01-01
Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…
A mathematical model of vapour film destabilisation
International Nuclear Information System (INIS)
In a hypothetical reactor accident, destabilisation of an intervening vapour film between the molten fuel and liquid coolant by a weak shock wave (trigger), is considered likely to initiate the molten fuel-coolant interaction. The one-dimensional model presented here is part of a larger programme of fundamental research aimed at improved reactor safety. (U.K.)
Mathematical models for space shuttle ground systems
Tory, E. G.
1985-01-01
Math models are a series of algorithms, comprised of algebraic equations and Boolean Logic. At Kennedy Space Center, math models for the Space Shuttle Systems are performed utilizing the Honeywell 66/80 digital computers, Modcomp II/45 Minicomputers and special purpose hardware simulators (MicroComputers). The Shuttle Ground Operations Simulator operating system provides the language formats, subroutines, queueing schemes, execution modes and support software to write, maintain and execute the models. The ground systems presented consist primarily of the Liquid Oxygen and Liquid Hydrogen Cryogenic Propellant Systems, as well as liquid oxygen External Tank Gaseous Oxygen Vent Hood/Arm and the Vehicle Assembly Building (VAB) High Bay Cells. The purpose of math modeling is to simulate the ground hardware systems and to provide an environment for testing in a benign mode. This capability allows the engineers to check out application software for loading and launching the vehicle, and to verify the Checkout, Control, & Monitor Subsystem within the Launch Processing System. It is also used to train operators and to predict system response and status in various configurations (normal operations, emergency and contingent operations), including untried configurations or those too dangerous to try under real conditions, i.e., failure modes.
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.
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
Mathematical modeling to predict residential solid waste generation
International Nuclear Information System (INIS)
One of the challenges faced by waste management authorities is determining the amount of waste generated by households in order to establish waste management systems, as well as trying to charge rates compatible with the principle applied worldwide, and design a fair payment system for households according to the amount of residential solid waste (RSW) they generate. The goal of this research work was to establish mathematical models that correlate the generation of RSW per capita to the following variables: education, income per household, and number of residents. This work was based on data from a study on generation, quantification and composition of residential waste in a Mexican city in three stages. In order to define prediction models, five variables were identified and included in the model. For each waste sampling stage a different mathematical model was developed, in order to find the model that showed the best linear relation to predict residential solid waste generation. Later on, models to explore the combination of included variables and select those which showed a higher R2 were established. The tests applied were normality, multicolinearity and heteroskedasticity. Another model, formulated with four variables, was generated and the Durban-Watson test was applied to it. Finally, a general mathematical model is proposed to predict residential waste generation, which accounts for 51% of the total
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 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.
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.
Solar Panel Mathematical Modeling Using Simulink
Chandani Sharma; Anamika Jain
2014-01-01
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 librarie...
Mathematical modeling of gas turbine cooled elements
Energy Technology Data Exchange (ETDEWEB)
Pashayev, A.; Askerov, D.; Sadiqov, R.; Samedov, A. [Academy of Aviation, Baku (Azerbaijan). Dept. of Mathematical Modeling and Design of Gas Turbine Engines
2007-07-01
The profile section of a gas turbine blade with convective cooling was modelled. Converging quadrature processes were used to determine the stationary and quasi-stationary temperature field of the profile part of the blade. Profiles were visualized using the least squares method along with automatic conjecture, device spline, smooth replenishment, and neural nets. Heat exchange boundary conditions were characterized using the finite difference method; finite element analysis (FEA); the Monte Carlo method; and the boundary integral equations method (BIEM). Boundary conditions included the heat quantity assigned by convection of the cooler transmitted by heat conduction of the blade material to the surface of cooling channels. Errors were investigated using a quadratures method and Tikhonov regularization. A Kirchhoff permutation was used to linearize tasks. The developed equation was then transformed into a Laplace equation. The model was then compared with experimental investigations to validate heat and hydraulic characteristics, as well as the temperature field of the blade cross section. It was concluded that the model can be used to assess the reliability of gas turbine engine designs. 3 refs., 1 fig.
Experimentally supported mathematical modeling of continuous baking processes
DEFF Research Database (Denmark)
Stenby Andresen, Mette
The scope of the PhD project was to increase knowledge on the process-to-product interactions in continuous tunnel ovens. The work has focused on five main objectives. These objectives cover development of new experimental equipment for pilot plant baking experiments, mathematical modeling of heat...... and temperature) and control the process (air flow, temperature, and humidity) are therefore emphasized. The oven is furthermore designed to work outside the range of standard tunnel ovens, making it interesting for manufacturers of both baking products and baking equipment. A mathematical model describing...... the heat and mass transfer in butter cookies during baking was formulated. The model was solved numerically by the use of a finite element method. Model optimization and validation was successfully carried out against experimental data obtained in the new pilot plant oven. The effect of the baking tray...
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 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 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.
Mathematical models applied in inductive non-destructive testing
International Nuclear Information System (INIS)
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
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.
Mathematical modeling in biology: A critical assessment
International Nuclear Information System (INIS)
The molecular revolution and the development of biology-derived industry have led in the last fifty years to an unprecedented 'lead forward' of life sciences in terms of experimental data. Less success has been achieved in the organisation of such data and in the consequent development of adequate explanatory and predictive theories and models. After a brief historical excursus inborn difficulties of mathematisation of biological objects and processes derived from the complex dynamics of life are discussed along with the logical tools (simplifications, choice of observation points etc.) used to overcome them. 'Autistic', monodisciplinary attitudes towards biological modeling of mathematicians, physicists, biologists aimed in each case at the use of the tools of other disciplines to solve 'selfish' problems are also taken into account and a warning against derived dangers (reification of mono disciplinary metaphors, lack of falsification etc.) is given. Finally 'top.down' (deductive) and 'bottom up' (inductive) heuristic interactive approaches to mathematisation are critically discussed with the help of serie of examples
Mathematical Modeling of Competition in Sponsored Search Market
Liu, Jian; Chiu, Dah Ming
2010-01-01
Sponsored search mechanisms have drawn much attention from both academic community and industry in recent years since the seminal papers of [13] and [14]. However, most of the existing literature concentrates on the mechanism design and analysis within the scope of only one search engine in the market. In this paper we propose a mathematical framework for modeling the interaction of publishers, advertisers and end users in a competitive market. We first consider the monopoly market model and ...
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 models of a liquid filtration from reservoirs
Anvarbek Meirmanov; Nelly Erygina; Saltanbek Mukhambetzhanov
2014-01-01
This article studies the filtration from reservoirs into porous media under gravity. We start with the exact mathematical model at the microscopic level, describing the joint motion of a liquid in reservoir and the same liquid and the elastic solid skeleton in the porous medium. Then using a homogenization procedure we derive the chain of macroscopic models from the poroelasticity equations up to the simplest Darcy's law in the porous medium and hydraulics in the reser...
Mathematical models of a liquid filtration from reservoirs
Directory of Open Access Journals (Sweden)
Anvarbek Meirmanov
2014-02-01
Full Text Available This article studies the filtration from reservoirs into porous media under gravity. We start with the exact mathematical model at the microscopic level, describing the joint motion of a liquid in reservoir and the same liquid and the elastic solid skeleton in the porous medium. Then using a homogenization procedure we derive the chain of macroscopic models from the poroelasticity equations up to the simplest Darcy's law in the porous medium and hydraulics in the reservoir.
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 modeling of human behaviors during catastrophic events
Verdière, Nathalie; Lanza, Valentina; Charrier, Rodolphe; Provitolo, Damienne; Dubos-Paillard, Edwige; Bertelle, Cyrille; Aziz-Alaoui, Moulay
2014-01-01
In this paper, we introduce a new approach for modeling the human collective behaviors in the speci c scenario of a sudden catastrophe, this catastrophe can be natural (i.e. earthquake, tsunami) or technological (nuclear event). The novelty of our work is to propose a mathematical model taking into account di erent concurrent behaviors in such situation and to include the processes of transition from one behavior to the other during the event. Here, we focus more on the sequence of behaviors ...
Nonaxisymmetric mathematical model of the cardiac left ventricle anatomy
Pravdin, Sergey
2013-01-01
We describe a mathematical model of the shape and fibre direction field of the cardiac left ventricle. The ventricle is composed of surfaces which model myocardial sheets. On each surface, we construct a set of curves corresponding to myocardial fibres. Tangents to these curves form the myofibres direction field. The fibres are made as images of semicircle chords parallel to its diameter. To specify the left ventricle shape, we use a special coordinate system where the left ventricle boundari...
Grip Forces During Object Manipulation: Experiment, Mathematical Model & Validation
Slota, Gregory P.; Latash, Mark L.; Zatsiorsky, Vladimir M.
2011-01-01
When people transport handheld objects, they change the grip force with the object movement. Circular movement patterns were tested within three planes at two different rates (1.0, 1.5 Hz), and two diameters (20, 40 cm). Subjects performed the task reasonably well, matching frequencies and dynamic ranges of accelerations within expectations. A mathematical model was designed to predict the applied normal forces from kinematic data. The model is based on two hypotheses: (a) the grip force chan...
Mathematical model of induced flow on the airplane vertical tail
Rotaru, Constantin; Cîrciu, Ionicǎ; Edu, Raluca Ioana
2016-06-01
In this paper is presented a mathematical model of the flow around the vertical tail of an airplane, based on the general elements of the aerodynamic design, with details leading to the separate formulation of the Fourier coefficients in the series solution of the Prandtl's lifting-line equation. Numerical results are obtained in Maple soft environment, for a standard configuration of an airplane geometry. The results include the discussion of the vortex model for the sidewash gradient on the vertical stabilizer.
Mathematical Modelling of Quorum Sensing and Bioluminescence in Bacteria
Directory of Open Access Journals (Sweden)
Sarangam Majumdar
2012-09-01
Full Text Available Different types of Quorum Sensing in Bacteria, both intra-species and inter-species, have been analyzed over the last decade. A number of Mathematical Models has been proposed to explain the process of Quorum Sensing which depends on a threshold concentration of autoinducers (or QSM reflecting high bacterial density. Stability of the solution of the differential equations of such an intra-species model for Vibrio fischeri is discussed in this paper.
Testing a Mathematical Model of the Yeast Cell Cycle
Cross, Frederick R.; Archambault, Vincent; Miller, Mary; Klovstad, Martha
2002-01-01
We derived novel, testable predictions from a mathematical model of the budding yeast cell cycle. A key qualitative prediction of bistability was confirmed in a strain simultaneously lacking cdc14 and G1 cyclins. The model correctly predicted quantitative dependence of cell size on gene dosage of the G1 cyclin CLN3, but it incorrectly predicted strong genetic interactions between G1 cyclins and the anaphase- promoting complex specificity factor Cdh1. To provide cons...
Mathematical Modeling of lndustrial Robots Based on Hamiltonian Mechanics
Czech Academy of Sciences Publication Activity Database
Záda, V.; Belda, Květoslav
Košice: Slovak Society for Applied Cybernetics and Informatics (SSAKI), 2016, s. 813-818. ISBN 978-1-4673-8606-7. [17th International Carpathian Control Conference (ICCC). Tatranská Lomnica (SK), 29.05.2016-01.06.2016] Institutional support: RVO:67985556 Keywords : Robot -manipulator * Hamiltonian formalism * mathematical modeling * PD control * model-oreinted motion control Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2016/AS/belda-0459855.pdf
A mathematical model for the dynamics and synchronization of cows
Sun, J.; Bollt, E. M.; Porter, M. A.; Dawkins, M S
2011-01-01
We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract ...
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.
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.
A novel mathematical model for controllable near-field electrospinning
International Nuclear Information System (INIS)
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
Mathematically modeling the biological properties of gliomas: A review.
Martirosyan, Nikolay L; Rutter, Erica M; Ramey, Wyatt L; Kostelich, Eric J; Kuang, Yang; Preul, Mark C
2015-08-01
Although mathematical modeling is a mainstay for industrial and many scientific studies, such approaches have found little application in neurosurgery. However, the fusion of biological studies and applied mathematics is rapidly changing this environment, especially for cancer research. This review focuses on the exciting potential for mathematical models to provide new avenues for studying the growth of gliomas to practical use. In vitro studies are often used to simulate the effects of specific model parameters that would be difficult in a larger-scale model. With regard to glioma invasive properties, metabolic and vascular attributes can be modeled to gain insight into the infiltrative mechanisms that are attributable to the tumor's aggressive behavior. Morphologically, gliomas show different characteristics that may allow their growth stage and invasive properties to be predicted, and models continue to offer insight about how these attributes are manifested visually. Recent studies have attempted to predict the efficacy of certain treatment modalities and exactly how they should be administered relative to each other. Imaging is also a crucial component in simulating clinically relevant tumors and their influence on the surrounding anatomical structures in the brain. PMID:25974347
Mathematical Properties Relevant to Geomagnetic FieldModeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
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 to as a geomagn......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...... to as a geomagnetic field model. Such models can be used to produce maps.More importantly, they form the basis for the geophysical interpretation of the geomagnetic field, by providing the possibility of separating fields produced by various sources and extrapolating those fields to places where they cannot...... 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...
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.
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.
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...
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 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...
Aspects of Mathematical Modelling of Pressure Retarded Osmosis
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Yuri G. Anissimov
2016-02-01
Full Text Available In power generating terms, a pressure retarded osmosis (PRO energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed.
Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification
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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 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.
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....
Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience
Charpin, J. P. F.; O'Hara, S.; Mackey, D.
2013-01-01
In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…
Michelsen, Claus
2015-07-01
Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students’ achievement and attitude in both physics and mathematics. But although there are overwhelming amounts of literature on modeling in science and mathematics education, the interdisciplinary position is seldom addressed explicitly. Furthermore, there has been a striking lack of exposure of the question of how future teachers, who are largely educated in a mono-disciplinary fashion, can best become equipped to introduce genuinely interdisciplinary teaching activities to their future pupils. This paper presents some preliminary reflections upon a graduate course, which aims to prepare future physics and mathematics teachers for interdisciplinary teaching, and which has been designed on the basis of influential theoretical expositions of the concept of interdisciplinarity.
MATHEMATICAL MODELING OF ELECTROCONVECTION IN THE CAPILLARIES. TRANSIENT BEHAVIOR
Directory of Open Access Journals (Sweden)
Kovalenko A. V.
2015-06-01
Full Text Available We propose a mathematical model of ion transport binary salt in electroosmotic flow in a capillary. The capillary is open on one side and immersed in a vessel of large volume, in which the concentration of the solution is maintained constant, and the other side closed ion exchange membrane. The walls are considered wettable, i.e. the solution adheres to the walls. This means that the mathematical modeling used to rate the condition of sticking. We study the boundary value problem for a coupled system of equations Nernst, Planck, Poisson and Navier-Stokes equations. Used boundary conditions of general form. The mathematical model is based on the general laws of transport and contains no adjustable parameters. Using this model, the basic laws of ion transport salt solution liquid flow, the emergence and development electroconvection, distribution of concentration of salt ions in the capillary with a small change in time, ie, in the initial (transitional regime. We have identified the presence of ion-exchange membrane surface electroconvective vortices and their influence on the mechanisms of ion transport of salt and fluid movement in different areas of the capillary. A feature of the capillary transport is to the right of the vortex region stagnant areas with a higher concentration of ions
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 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.
Mathematical modeling and the two-phase constitutive equations
International Nuclear Information System (INIS)
The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations
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)
Mathematical Modelling of Bacterial Populations in Bio-remediation Processes
Vasiliadou, Ioanna A.; Vayenas, Dimitris V.; Chrysikopoulos, Constantinos V.
2011-09-01
An understanding of bacterial behaviour concerns many field applications, such as the enhancement of water, wastewater and subsurface bio-remediation, the prevention of environmental pollution and the protection of human health. Numerous microorganisms have been identified to be able to degrade chemical pollutants, thus, a variety of bacteria are known that can be used in bio-remediation processes. In this study the development of mathematical models capable of describing bacterial behaviour considered in bio-augmentation plans, such as bacterial growth, consumption of nutrients, removal of pollutants, bacterial transport and attachment in porous media, is presented. The mathematical models may be used as a guide in designing and assessing the conditions under which areas contaminated with pollutants can be better remediated.
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 Dimension Reduction in Dynamical Systems
DEFF Research Database (Denmark)
Elmegård, Michael
Processes that change in time are in mathematics typically described by differential equations. These may be applied to model everything from weather forecasting, brain patterns, reaction kinetics, water waves, finance, social dynamics, structural dynamics and electrodynamics to name only a few....... These systems are generically nonlinear and the studies of them often become enormously complex. The framework in which such systems are best understood is via the theory of dynamical systems, where the critical behavior is systematically analyzed by performing bifurcation theory. In that context the current...... thesis is attacking two problems. The first is concerned with the mathematical modelling and analysis of an experiment of a vibro-impacting beam. This type of dynamical system has received much attention in the recent years and they occur frequently in mechanical applications, where they induce noise...
Metallic samples specific activity determination by mathematical modelling
International Nuclear Information System (INIS)
The problem of specific activity determination of metallic samples containing radionuclides has been generally solved for a subject demanded by Iron and Steel Workes Galati. In order to establish the dependence between specific activity and the counting rate furnished by the counting equipment, the method used consists in mathematical modelling of the sample detector assembly as well as of the pertinent physical processes. The method and obtained results are described. (author)
Contribution to mathematical modeling of drive parasitic vibration
Czech Academy of Sciences Publication Activity Database
Kratochvíl, Ctirad; Kalous, J.; Kotek, Vladimír
Praha: Ústav termomechaniky AV ČR, 2000 - (Dobiáš, I.), s. 117-120 ISBN 80-85918-54-4. [National colloquium with international participation Dynamics of machines 2000.. Praha (CZ), 08.02.2000-09.02.2000] R&D Projects: GA ČR GA101/98/0972; GA MŠk VS96122 Keywords : dynamic system * mathematical modeling Subject RIV: BI - Acoustics
Mathematical modeling and simulation of nanopore blocking by precipitation
Wolfram, M-T
2010-10-29
High surface charges of polymer pore walls and applied electric fields can lead to the formation and subsequent dissolution of precipitates in nanopores. These precipitates block the pore, leading to current fluctuations. We present an extended Poisson-Nernst-Planck system which includes chemical reactions of precipitation and dissolution. We discuss the mathematical modeling and present 2D numerical simulations. © 2010 IOP Publishing Ltd.
Mathematical programming models for optimising irrigation water management in Egypt
Bader, Esam
2004-01-01
A major challenge facing Egypt is the ever increasing demand for water against the fixed water supplies. Therefore, a greater emphasis is currently being placed on the need to improve the efficiency in the use of the available water resources for crop production. The study presents a practical approach to manage and optimise the irrigation water use given water, land and organisational constraints. A linear programming (LP) mathematical model was developed to make decisions about irrigation w...
Mathematical modeling and analysis of insulin clearance in vivo
Koschorreck, Markus; Gilles, Ernst Dieter
2008-01-01
Background Analyzing the dynamics of insulin concentration in the blood is necessary for a comprehensive understanding of the effects of insulin in vivo. Insulin removal from the blood has been addressed in many studies. The results are highly variable with respect to insulin clearance and the relative contributions of hepatic and renal insulin degradation. Results We present a dynamic mathematical model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. ...
Mathematical modeling and analysis of insulin clearance in vivo
Koschorreck, M.; Gilles, E. D.
2008-01-01
Background: Analyzing the dynamics of insulin concentration in the blood is necessary for a comprehensive understanding of the effects of insulin in vivo. Insulin removal from the blood has been addressed in many studies. The results are highly variable with respect to insulin clearance and the relative contributions of hepatic and renal insulin degradation. Results: We present a dynamic mathematical model of insulin concentration in the blood and of insulin receptor acti...
Mathematical modeling and analysis of insulin clearance in vivo
Koschorreck, M.; Gilles, E.
2008-01-01
Background: Analyzing the dynamics of insulin concentration in the blood is necessary for a comprehensive understanding of the effects of insulin in vivo. Insulin removal from the blood has been addressed in many studies. The results are highly variable with respect to insulin clearance and the relative contributions of hepatic and renal insulin degradation. Results: We present a dynamic mathematical model of insulin concentration in the blood and of insulin receptor activation in hepatocytes...
Mathematical modeling for digestible protein in animal feeds for tilapia
Luiz Vítor Oliveira Vidal; Wilson Massamitu Furuya; Elias Nunes Martins; Tadeu Orlandi Xavier; Mariana Michelato; Themis Sakaguti Graciano
2012-01-01
The objective of this study was to formulate mathematical models to estimate digestible protein in some animal feeds for tilapia. Literature results of the proximate composition of crude protein, ether extract, and mineral matter, as well as digestible protein obtained in biological assays, were used. The data were subjected to multiple linear stepwise backward regression. Path analysis was performed to measure the direct and indirect effects of each independent variable on the dependent one....
Mathematical Modeling Predicts How Proteins Affect Cellular Communication
Lee Ethan; Salic Adrian; Krüger Roland; Heinrich Reinhart; Kirschner Marc W
2003-01-01
Wnt signaling plays an important role in both oncogenesis and development. Activation of the Wnt pathway results in stabilization of the transcriptional coactivator beta-catenin. Recent studies have demonstrated that axin, which coordinates beta-catenin degradation, is itself degraded. Although the key molecules required for transducing a Wnt signal have been identified, a quantitative understanding of this pathway has been lacking. We have developed a mathematical model for the canonical Wnt...
Mathematical model of delay lines based on magnetostatic waves
Directory of Open Access Journals (Sweden)
E. V. Kudinov
2010-12-01
Full Text Available On the example of the delay line have demonstrated the possibility of applying the principle of decomposition to construct mathematical models of microwave devices using magnetostatic waves (MSW in a magnetized epitaxial ferrite films, which allows for a unified methodological basis and the lowest cost to the experimental optimization design of MSW devices for various applications
Input physical properties in mathematical model of steel quenching
B. Smoljan; D. Iljkić; L. Pomenić
2013-01-01
Purpose: Developing of new methods for input data of mathematical model is established.Design/methodology/approach: Temperature dependency of both, heat transfer for quenchant with Grossmann severity of quenching H=0.35, which are adequate for oil and heat conductivity coefficients has been calibrated on the base of Crafts-Lamont diagrams.Findings: Evaluation of physical properties such as specific heat capacity, c, heat conductivity coefficient, λ, density, ρ, heat transfer coefficient, α in...
Mathematical model of processes of reactor with gasified fluidized bed
International Nuclear Information System (INIS)
An original scheme of steam generator with gasifying fluidized bed has been presented as a possible solution for reconstruction of furnace with pulverized burning of coal. The method is effective when applied in combination with desulfurization for the purpose of reducing the CO2 emissions level. A mathematical model has been developed, which determines the correlation primary (fluidizing) and (burning out) secondary air with sufficient for the practice accuracy
Territorial intrusion risk and antipredator behaviour: a mathematical model.
Díaz-Uriarte, R.
2001-01-01
In territorial animals that hide to avoid predators, a predatory attack creates a conflict because a hiding animal cannot defend its territory from conspecific intruders. When intruders are persistent, a past conspecific intrusion informs a territorial resident that future intrusions by the same animal are likely. Using a mathematical model, I examine the effects that past territorial intrusions can have on antipredator behaviour. Past territorial intrusions rarely affect a resident animal's ...
Mathematical Model of Oxygen Transport in Tuberculosis Granulomas
Datta, Meenal; Via, Laura E.; Chen, Wei; Baish, James W.; Xu, Lei; Barry, Clifton E.; Jain, Rakesh K.
2015-01-01
Pulmonary granulomas—the hallmark of Mycobacterium tuberculosis (MTB) infection—are dense cellular lesions that often feature regions of hypoxia and necrosis, partially due to limited transport of oxygen. Low oxygen in granulomas can impair the host immune response, while MTB are able to adapt and persist in hypoxic environments. Here, we used a physiologically based mathematical model of oxygen diffusion and consumption to calculate oxygen profiles within the granuloma, assuming Michaelis–Me...
Heart failure support in mathematical model with baroreflex control
Czech Academy of Sciences Publication Activity Database
Musil, Jan; Převorovská, Světlana; Maršík, František
Olomouc : Palacký University, 2000 - (Vaverka, F.; Janura, M.), s. 154 -157 ISBN 80-244-0193-2. [Conference of the Czech Society of biomechanics with international participation Biomechanics of man 2000. Olomouc (CZ), 24.11.2000-25.11.2000] R&D Projects: GA ČR GA106/98/1373; GA AV ČR KSK1076602 Keywords : mathematical model * mechanical support * failing heart Subject RIV: CE - Biochemistry
Nonlinear dynamics mathematical models for rigid bodies with a liquid
Lukovsky, Ivan A
2015-01-01
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approaches to fluid-structure interaction problems, the fundamental mathematical background and modeling the dynamics of such complex mechanical systems.
A New Mathematical Model for Coanda Effect Velocity Approximation
Valeriu DRĂGAN
2012-01-01
This paper addresses the problem of obtaining a set of mathematical equations that can accurately describe the velocity flow field near a cylindrical surface influenced by the Coandă effect. The work is relevant since the current state of the art Reynolds Averaged Navier Stokes models with curvature correction do not completely describe the properties of the flow in accordance with the experimental data. Semi-empirical equations are therefore deduced based on experimental and theoretical stat...
Mathematical modelling of drying food products: application to tropical fruits
Shahari, Nor Azni
2012-01-01
Drying is an old traditional method of removing liquid from inside material, suchas wood, food, paper, ceramics, building materials, textiles, granular products, pharmaceutical and electronic devices. The kinetics of this liquid removal depends on the material properties of the solid phase as well as on cellular structure. The aim of this project is to understand the effect of complex interaction of heat, moisture and shrinkage to create a detailed mathematical modelling to quantify the ...
Mathematical model of delay lines based on magnetostatic waves
E. V. Kudinov
2010-01-01
On the example of the delay line have demonstrated the possibility of applying the principle of decomposition to construct mathematical models of microwave devices using magnetostatic waves (MSW) in a magnetized epitaxial ferrite films, which allows for a unified methodological basis and the lowest cost to the experimental optimization design of MSW devices for various applications
MATHEMATICAL MODELING OF UNSTEADY HEAT EXCHANGE IN A PASSENGER CAR
Khomenko, I.
2013-01-01
Purpose. Existing mathematical models of unsteady heat exchange in a passenger car do not satisfy the need of the different constructive decisions of the life support system efficiency estimation. They also don’t allow comparing new and old life support system constructions influence on the inner environment conditions. Moreover quite frequently unsteady heat exchange processes were studied at the initial car motion stage. Due to the new competitive engineering decisions of the life support s...
Mathematical modeling of sedimentation process of nanoparticles in gradient medium
Ezhenkova, S. I.; Chivilikhin, S. A.
2015-11-01
Mathematical model describing the motion of a light ray in the medium with a varying index of refraction formed by particles settling in a liquid has been built. We have received size distribution of particles settling in a liquid; calculated the light ray's trajectory in the medium; investigated the dependence of the light ray's trajectory on the initial particles concentration; received the solution of the equation of convective diffusion for nanoparticles.
Two Mathematical Models for Generation of Crowned Tooth Surface
Laszlo Kelemen; Jozsef Szente
2014-01-01
Gear couplings are mechanical components to connect shaft ends and eliminate the misalignments. The most important element of the gear coupling is the hub which is an external gear having crowned teeth. The crowned teeth on the hub are typically produced by hobbing. The resulting tooth surface depends on several parameters. It is influenced by the size of the hob and the feed. In this paper two mathematical models of the crowned tooth surface are introduced for the generation of the idealized...
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)
A Mathematical Model of the Thermo-Anemometric Flowmeter
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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.
A MATHEMATICAL HEAT TRANSFER MODEL IN STATIC AND CONTINUOUS CASTING
Institute of Scientific and Technical Information of China (English)
R. Ghasemzadeh
2004-01-01
The application of a heat flow model to describe the thermal characteristics of freezing alloys with narrow mushy zones from a refrigerated mould wall was outlined. The extension of the model was to treat the continuous casting of metals with low thermal conductivity,such as steels, which will be outlined. The model was based on the mathematical expedient for replacing thermal resistance of the metal/mould interface by virtual adjuncts of metal/mould material. It provided a good description of the pool profile and the technique exhibits advantages in terms of both computation and versatility of application.
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 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.
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
Mathematically modelling and controlling prostate cancer under intermittent hormone therapy
Institute of Scientific and Technical Information of China (English)
Yoshito Hirata; Gouhei Tanaka; Nicholas Bruchovsky; Kazuyuki Aihara
2012-01-01
In this review,we summarize our recently developed mathematical models that predict the effects of intermittent androgen suppression therapy on prostate cancer (PCa).Although hormone therapy for PCa shows remarkable results at the beginning of treatment,cancer cells frequently acquire the ability to grow without androgens during long-term therapy,resulting in an eventual relapse.To circumvent hormone resistance,intermittent androgen suppression was investigated as an alternative treatment option.However,at the present time,it is not possible to select an optimal schedule of on- and off-treatment cycles for any given patient.In addition,clinical trials have revealed that intermittent androgen suppression is effective for some patients but not for others.To resolve these two problems,we have developed mathematical models for PCa under intermittent androgen suppression.The mathematical models not only explain the mechanisms of intermittent androgen suppression but also provide an optimal treatment schedule for the on- and off-treatment periods.
MATHEMATICAL MODEL OF THE DYNAMICS OF HIV INFECTION WITHOUT TREATMENT
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Ogban G. I.
2015-06-01
Full Text Available This article discusses the mathematical and numerical modeling of the immune system of the course of HIV infection without treatment. Presently a significant number of scientific papers are devoted to the study of this problem. However, HIV infection is highly volatile and there is no effective drug, in that HIV has the ability to mutate and reproduce itself in the presence of chemical substances that are meant to inhibit or destroy it. The mathematical models used in this paper are conceptual and exploratory in nature. The proposed mathematical model allow us to obtain a complete description of the dynamics of HIV infection, and also an understanding of the progression to AIDS. Thus, the results of the numerical solution of differential equations in this work show that: the disease develops, and at low concentration of the virus, a certain level of stability does not depend on the initial concentration of infestation. In the absence of treatment, for interesting competition between virus and the loss of virus caused by immune response should be strictly greater than the rate of multiplication of the virus in the blood; the reproduction rate of the uninfected cells should be stricly greater than the mortality rate of the uninfected cells
Mathematical models of Ebola-Consequences of underlying assumptions.
Feng, Zhilan; Zheng, Yiqiang; Hernandez-Ceron, Nancy; Zhao, Henry; Glasser, John W; Hill, Andrew N
2016-07-01
Mathematical models have been used to study Ebola disease transmission dynamics and control for the recent epidemics in West Africa. Many of the models used in these studies are based on the model of Legrand et al. (2007), and most failed to accurately project the outbreak's course (Butler, 2014). Although there could be many reasons for this, including incomplete and unreliable data on Ebola epidemiology and lack of empirical data on how disease-control measures quantitatively affect Ebola transmission, we examine the underlying assumptions of the Legrand model, and provide alternate formulations that are simpler and provide additional information regarding the epidemiology of Ebola during an outbreak. We developed three models with different assumptions about disease stage durations, one of which simplifies to the Legrand model while the others have more realistic distributions. Control and basic reproduction numbers for all three models are derived and shown to provide threshold conditions for outbreak control and prevention. PMID:27130854
Integration of mathematical models in marketing theory and practice
Directory of Open Access Journals (Sweden)
Ioana Olariu
2012-12-01
Full Text Available This article is a theoretical approach on the main mathematical models used in marketing practice. Application of general systems theory in marketing involves setting behavior assumptions as models of various processes.These models have, on the one hand, to describe the interactions between ambiance and system factors, and, secondly, to identify causal dependencies existing in these interactions.Since the models are the means by which possible solutions can be drawn consequences, they occupy a central role in the design of a system to solve a marketing problem.The model is a simplified representation which is described and conceptualized phenomena and real life situations.The purpose of a model is to facilitate understanding of the real system. Models are widely used in marketing, it takes different forms that facilitate understanding the realities of marketing.
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Directory of Open Access Journals (Sweden)
Nadia Said
Full Text Available Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
(Misinterpreting Mathematical Models: Drift As A Physical Process
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Roberta L. Millstein
2009-12-01
Full Text Available Recently, a number of philosophers of biology (e.g., Matthen and Ariew 2002; Walsh, Lewens, and Ariew 2002; Pigliucci and Kaplan 2006; Walsh 2007 have endorsed views about random drift that, we will argue, rest on an implicit assumption that the meaning of concepts such as drift can be understood through an examination of the mathematical models in which drift appears. They also seem to implicitly assume that ontological questions about the causality (or lack thereof of terms appearing in the models can be gleaned from the models alone. We will question these general assumptions by showing how the same equation — the simple (p + q2 = p2 + 2pq + q2 — can be given radically different interpretations, one of which is a physical, causal process and one of which is not. This shows that mathematical models on their own yield neither interpretations nor ontological conclusions. Instead, we argue that these issues can only be resolved by considering the phenomena that the models were originally designed to represent and the phenomena to which the models are currently applied. When one does take those factors into account, starting with the motivation for Sewall Wright’s and R.A. Fisher’s early drift models and ending with contemporary applications, a very different picture of the concept of drift emerges. On this view, drift is a term for a set of physical processes, namely, indiscriminate sampling processes (Beatty 1984; Hodge 1987; Millstein 2002, 2005.
NATO Advanced Study Institute on Recent Advances in the Modeling of Hydrologic Systems
O’Connell, P
1991-01-01
Modeling of the rainfall-runoff process is of both scientific and practical significance. Many of the currently used mathematical models of hydrologic systems were developed a genera tion ago. Much of the effort since then has focused on refining these models rather than on developing new models based on improved scientific understanding. In the past few years, however, a renewed effort has been made to improve both our fundamental understanding of hydrologic processes and to exploit technological advances in computing and remote sensing. It is against this background that the NATO Advanced Study Institute on Recent Advances in the Modeling of Hydrologic Systems was organized. The idea for holding a NATO ASI on this topic grew out of an informal discussion between one of the co-directors and Professor Francisco Nunes-Correia at a previous NATO ASI held at Tucson, Arizona in 1985. The Special Program Panel on Global Transport Mechanisms in the Geo-Sciences of the NATO Scientific Affairs Division agreed to sp...