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.
Workshop on Advanced Modelling in Mathematical Finance : in Honour of Ernst Eberlein
Papapantoleon, Antonis
2016-01-01
This Festschrift resulted from a workshop on “Advanced Modelling in Mathematical Finance” held in honour of Ernst Eberlein’s 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein’s long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.
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...
Nonstandard Analysis Applied to Advanced Undergraduate Mathematics - Infinitesimal Modeling
Herrmann, Robert A.
2003-01-01
This is a Research and Instructional Development Project from the U. S. Naval Academy. In this monograph, the basic methods of nonstandard analysis for n-dimensional Euclidean spaces are presented. Specific rules are deveoped and these methods and rules are applied to rigorous integral and differential modeling. The topics include Robinson infinitesimals, limited and infinite numbers; convergence theory, continuity, *-transfer, internal definition, hyprefinite summation, Riemann-Stieltjes int...
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...
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.
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...
Advanced engineering mathematics
Kreyszig, Erwin
1972-01-01
Introducing those areas of mathematics which are most important to practical problem solving in the field, this book pays particular attention to ordinary differential equations, linear algebra and vector analysis, complex analysis, and numerical methods. Fourier series and partial differential equations are also covered thoroughly. The problem sets in this edition have been updated and revised to give greater weight to modeling, phase-plane and numerical multi-step methods, and applications. Each section includes examples and problems illustrating concepts, methods and results, and their engineering applications.
DEFF Research Database (Denmark)
Carugati, Andrea
. The resulting methodology builds on these four results. The methodology is based on an emergent and iterative process focused on the discussion of software prototypes built as boundary objects: visual, usable, bi-directional, and up-to-date. Iterations are kept short so that the prototypes remain simple enough...... modeling (AMM) in scheduling and control systems. Advanced mathematical techniques are relatively new in scheduling and control systems, at least in real production situations, and therefore the project included the research of methods and tools for the development of these systems. Because of the novelty...... with a relativist approach. Arriving at the design of an ISD methodology required the combination of previous theoretical results with the observations from the case study. The case study showed some of the key elements to be integrated in the methodology. Firstly, plans and models are subject of a high degree...
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
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
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
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
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...
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
DEFF Research Database (Denmark)
Martens, Sebastian; Mijatovic, Nenad; Holbøll, Joachim
2015-01-01
Efficient fault detection in generators often require prior knowledge of fault behavior, which can be obtained from theoretical analysis, often carried out by using discrete models of a given generator. Mathematical models are commonly represented in the DQ0 reference frame, which is convenient...... in 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...
Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues
Directory of Open Access Journals (Sweden)
MunJu eKim
2013-11-01
Full Text Available Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
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.
Cognitive Correlates of Performance in Advanced Mathematics
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
2012-01-01
Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…
Mathematical problems in meteorological modelling
Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella
2016-01-01
This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...
Mathematical Modelling for EOQ Inventory System with Advance Payment and Fuzzy Parameters
Directory of Open Access Journals (Sweden)
S Priyan
2014-11-01
Full Text Available This study considers an EOQ inventory model with advance payment policy in a fuzzy situation by employing two types of fuzzy numbers that are trapezoidal and triangular. Two fuzzy models are developed here. In the first model the cost parameters are fuzzified, but the demand rate is treated as crisp constant. In the second model, the demand rate is fuzzified but the cost parameters are treated as crisp constants. For each fuzzy model, we use signed distance method to defuzzify the fuzzy total cost and obtain an estimate of the total cost in the fuzzy sense. Numerical example is provided to ascertain the sensitiveness in the decision variables about fuzziness in the components. In practical situations, costs may be dependent on some foreign monetary unit. In such a case, due to a change in the exchange rates, the costs are often not known precisely. The first model can be used in this situation. In actual applications, demand is uncertain and must be predicted. Accordingly, the decision maker faces a fuzzy environment rather than a stochastic one in these cases. The second model can be used in this situation. Moreover, the proposed models can be expended for imperfect production process.
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
Gestures and insight in advanced mathematical thinking
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
2011-10-01
What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding - in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities. One participant uses gestures to clarify the relationships between a function, its derivative and its antiderivative. We show how these gestures help create a virtual mathematical construct, which in turn leads to a new problem-solving strategy. These results suggest that gestures are a productive, but potentially undertapped resource for generating new insights in advanced levels of mathematics.
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....
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...
Teaching Mathematical Modelling.
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Gestures and Insight in Advanced Mathematical Thinking
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
2011-01-01
What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…
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
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.
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 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.
Mathematical modelling of metabolism
DEFF Research Database (Denmark)
Gombert, Andreas Karoly; Nielsen, Jens
2000-01-01
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...
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.
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Concepts of mathematical modeling
Meyer, Walter J
2004-01-01
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec
Mathematical modeling in biomedical imaging
2012-01-01
This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed mathematical and computational tools. It is particularly suitable for researchers and graduate students in applied mathematics and biomedical engineering.
Mathematical models of hysteresis
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-08-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
Mathematical modeling in psychological researches
Directory of Open Access Journals (Sweden)
Aleksandra Zyolko
2013-04-01
Full Text Available The author considers the nature of mathematical modeling and its significance in psychological researches. The author distinguishes the types of mathematical models: deterministic, stochastic models and synergetic models. The system approach is proposed as an instrument of implementation of mathematical modelling in psychological research.
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.
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
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…
Research on Lesson Planing Model of Advanced Mathematics%高等数学备课模式的研究
Institute of Scientific and Technical Information of China (English)
邱云兰
2014-01-01
Lesson planning is an endless re-creation proj ect,it needs the grasp of the knowledge and skills,processes and methods,attitudes and values.New curriculum not only challenges the traditional or-ganizational model,but also the lesson planning.Prepareing the lesson planning and grasp the main idea are tne key.In teaching process,there should be included interesting mathematical problems,mathematical col-orful anecdotes and outstanding mathematical conj ecture,which can serve the students a strong desire for knowledge and creativity to explore the unknown mysteries of motivation.%备课是一项无止境的再“创作”工程。备课要把握知识与技能、过程与方法、情感态度与价值观的要求。备教材、备教法、备学生、备学法，对学生学习高等数学（如下简称高数）有较大的影响，影响学生思维、兴趣和素质的提高。将生动有趣的数学名题、多姿多彩的数学轶事、悬而末决的数学猜想、似是而非的数学饽论，巧妙地贯穿在相应的备课环节之中，从而使学生产生对高数学习的浓厚兴趣和创造探索的动力。
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 chronobiology.
Bordyugov, G; Westermark, P O; Korenčič, A; Bernard, S; Herzel, H
2013-01-01
Circadian clocks are autonomous oscillators entrained by external Zeitgebers such as light-dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell-cell coupling, and (3) optimization of chronotherapy.
Advanced Mathematical Thinking in a Technological Workplace.
Magajna, Zlatan; Monaghan, John
2003-01-01
Examines the use of mathematics in a computer-aided design and manufacturing setting, whether this mathematics is related to school mathematics, how technicians understand this mathematics, and the role of technology in the technicians' mathematics-related problem solving activities. Focuses on technician's calculations of the interval volume of…
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...
Advanced mathematics for engineers and scientists
DuChateau, Paul
2012-01-01
This book can be used as either a primary text or a supplemental reference for courses in applied mathematics. Its core chapters are devoted to linear algebra, calculus, and ordinary differential equations. Additional topics include partial differential equations and approximation methods. Each chapter features an ample selection of solved problems. These problems were chosen to illustrate not only how to solve various algebraic and differential equations but also how to interpret the solutions in order to gain insight into the behavior of the system modeled by the equation. In addition to th
Directory of Open Access Journals (Sweden)
Trude Nilsen
2013-10-01
Full Text Available As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal on the application of mathematics in physics education compared with the research related to the conceptual knowledge of physics. In order to clarify the nature of mathematics in physics education, we developed a theoretical framework for mathematical competencies pertinent to various physics tasks based on theoretical frameworks from mathematics and physics education. We used this synthesis of frameworks as a basis to create a model for physics competence. The framework also served as a tool for analyzing and categorizing trend items from the international large-scale survey, TIMSS Advanced 1995 and 2008. TIMSS Advanced assessed students in upper secondary school with special preparation in advanced physics and mathematics. We then investigated the changes in achievements on these categorized items across time for nations who participated in both surveys. The results from our analysis indicate that students whose overall physics achievement declined struggled the most with items requiring mathematics, especially items requiring them to handle symbols, such as manipulating equations. This finding suggests the importance of collaboration between mathematics and physics education as well as the importance of traditional algebra for physics education.
Recent Advances in Analytical Methods in Mathematical Physics
Ozer, Teoman; Taranov, Vladimir B.; Smirnov, Roman G.; Klemas, Thomas J.; Thamburaja, Prakash; Wijesinghe, Sanith; Polat, Burak
2012-01-01
This special issue of the journal Advances in Mathematical Physics was planned to focus on the most recent advances in analytical techniques of particular use to researchers in the field of mathematical physics that covers a very wide area of topics and has a key role in interdisciplinary studies including mathematics, mechanics, and physics. In this special issue, we were particularly interested in receiving novel contributions detailing analytical methods together with approp...
Mathematical Model for Hit Phenomena
Ishii, Akira; Hayashi, Takefumi; Matsuda, Naoya; Nakagawa, Takeshi; Arakaki, Hisashi; Yoshida, Narihiko
2010-01-01
The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dynamical and non-equilibrium phenomena. The purchase intention for each person is introduced and direct and indirect communications are expressed as two-body and three-body interaction in our model. The mathematical model is expressed as coupled nonlinear differential equations. The important factor in the model is the decay time of rumor for the hit. The calculated results agree very well with revenues of recent 25 movies.
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
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 Models of Biochemical Oscillations
Conrad, Emery David
1999-01-01
The goal of this paper is to explain the mathematics involved in modeling biochemical oscillations. We first discuss several important biochemical concepts fundamental to the construction of descriptive mathematical models. We review the basic theory of differential equations and stability analysis as it relates to two-variable models exhibiting oscillatory behavior. The importance of the Hopf Bifurcation will be discussed in detail for the central role it plays in limit cycle behavior and...
Mathematical Models of Waiting Time.
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)
The Spectrum of Mathematical Models.
Karplus, Walter J.
1983-01-01
Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…
Exposing calculus students to advanced mathematics
Griffiths, Barry J.; Selcuk Haciomeroglu, Erhan
2014-07-01
To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in mathematics. This paper posits that one of the main reasons is that the mathematical community does not expose calculus students to the beauty and complexity of upper-level mathematics, and that by doing so before they fully commit to their programme of study, the number of students with a qualification in mathematics can be increased. The results show a significant increase in the number of students planning to add a minor in mathematics, and an increased likelihood among freshmen and sophomores to change their major.
2015-08-24
dislocations in RDX - family of crystallographic planes on which slip occurs- The (010)[100] screw configuration was found to be unstable. Structure of the (010...Peierls stress (critical stress for dislocation motion), c) we discovered a family of point defects which are rotated and distorted molecules...result needed in crystal plasticity models of hot spot formation, e) we developed a family of coarse grained models for the RDX crystal in which the
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…
Conditional Inference and Advanced Mathematical Study: Further Evidence
Inglis, Matthew; Simpson, Adrian
2009-01-01
In this paper, we examine the support given for the "theory of formal discipline" by Inglis and Simpson (Educational Studies Mathematics 67:187-204, "2008"). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional…
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
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.
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.
Advanced Mathematical Tools in Metrology III
Ciarlini, P.
The Table of Contents for the book is as follows: * Foreword * Invited Papers * The ISO Guide to the Expression of Uncertainty in Measurement: A Bridge between Statistics and Metrology * Bootstrap Algorithms and Applications * The TTRSs: 13 Oriented Constraints for Dimensioning, Tolerancing & Inspection * Graded Reference Data Sets and Performance Profiles for Testing Software Used in Metrology * Uncertainty in Chemical Measurement * Mathematical Methods for Data Analysis in Medical Applications * High-Dimensional Empirical Linear Prediction * Wavelet Methods in Signal Processing * Software Problems in Calibration Services: A Case Study * Robust Alternatives to Least Squares * Gaining Information from Biomagnetic Measurements * Full Papers * Increase of Information in the Course of Measurement * A Framework for Model Validation and Software Testing in Regression * Certification of Algorithms for Determination of Signal Extreme Values during Measurement * A Method for Evaluating Trends in Ozone-Concentration Data and Its Application to Data from the UK Rural Ozone Monitoring Network * Identification of Signal Components by Stochastic Modelling in Measurements of Evoked Magnetic Fields from Peripheral Nerves * High Precision 3D-Calibration of Cylindrical Standards * Magnetic Dipole Estimations for MCG-Data * Transfer Functions of Discrete Spline Filters * An Approximation Method for the Linearization of Tridimensional Metrology Problems * Regularization Algorithms for Image Reconstruction from Projections * Quality of Experimental Data in Hydrodynamic Research * Stochastic Drift Models for the Determination of Calibration Intervals * Short Communications * Projection Method for Lidar Measurement * Photon Flux Measurements by Regularised Solution of Integral Equations * Correct Solutions of Fit Problems in Different Experimental Situations * An Algorithm for the Nonlinear TLS Problem in Polynomial Fitting * Designing Axially Symmetric Electromechanical Systems of
The 24-Hour Mathematical Modeling Challenge
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
Mathematical Modeling: A Bridge to STEM Education
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…
Ma, Xin
2010-01-01
Based on data from the Longitudinal Study of American Youth (LSAY), students were classified into high-, middle-, and low-ability students. The effects of early acceleration in mathematics on the most advanced mathematics coursework (precalculus and calculus) in high school were examined in each category. Results showed that although early…
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
Mathematical modelling of membrane separation
DEFF Research Database (Denmark)
Vinther, Frank
This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... 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 prolate ellipsoids with the same volume. The porous membrane is assumed isotropic such that the model reduces to a two dimensional model. With this assumption ellipsoids with the same volume reduces to ellipses with the same area. The model finds the probability of entering the pore of the membrane...
An Assessment Model for Proof Comprehension in Undergraduate Mathematics
Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron
2012-01-01
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…
Cognitive development in advanced mathematics using technology
Tall, David
2000-12-01
This paper considers cognitive development in mathematics and its relationship with computer technology, with special emphasis on the use of visual imagery and symbols and the later shift to formal axiomatic theories. At each stage, empirical evidence is presented to show how these forms of thinking are enhanced, changed, or impeded by the use of technology.
Electrorheological fluids modeling and mathematical theory
Růžička, Michael
2000-01-01
This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.
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…
European Conference on Numerical Mathematics and Advanced Applications
Manguoğlu, Murat; Tezer-Sezgin, Münevver; Göktepe, Serdar; Uğur, Ömür
2016-01-01
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH), held every 2 years, provides a forum for discussing recent advances in and aspects of numerical mathematics and scientific and industrial applications. The previous ENUMATH meetings took place in Paris (1995), Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011) and Lausanne (2013). This book presents a selection of invited and contributed lectures from the ENUMATH 2015 conference, which was organised by the Institute of Applied Mathematics (IAM), Middle East Technical University, Ankara, Turkey, from September 14 to 18, 2015. It offers an overview of central recent developments in numerical analysis, computational mathematics, and applications in the form of contributions by leading experts in the field.
Advanced Production Planning Models
Energy Technology Data Exchange (ETDEWEB)
JONES,DEAN A.; LAWTON,CRAIG R.; KJELDGAARD,EDWIN A.; WRIGHT,STEPHEN TROY; TURNQUIST,MARK A.; NOZICK,LINDA K.; LIST,GEORGE F.
2000-12-01
>This report describes the innovative modeling approach developed as a result of a 3-year Laboratory Directed Research and Development project. The overall goal of this project was to provide an effective suite of solvers for advanced production planning at facilities in the nuclear weapons complex (NWC). We focused our development activities on problems related to operations at the DOE's Pantex Plant. These types of scheduling problems appear in many contexts other than Pantex--both within the NWC (e.g., Neutron Generators) and in other commercial manufacturing settings. We successfully developed an innovative and effective solution strategy for these types of problems. We have tested this approach on actual data from Pantex, and from Org. 14000 (Neutron Generator production). This report focuses on the mathematical representation of the modeling approach and presents three representative studies using Pantex data. Results associated with the Neutron Generator facility will be published in a subsequent SAND report. The approach to task-based scheduling described here represents a significant addition to the literature for large-scale, realistic scheduling problems in a variety of production settings.
Mathematical modelling in solid mechanics
Sofonea, Mircea; Steigmann, David
2017-01-01
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...
7th European Conference on Numerical Mathematics and Advanced Applications
Of, Günther; Steinbach, Olaf
2008-01-01
The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of meetings held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. These proceedings contain a selection of invited plenary lectures, papers presented in minisymposia and contributed papers. Topics include theoretical aspects of new numerical techniques and algorithms as well as of applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scientific computing and their applications.
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Mathematical 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
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…
Who succeeds in advanced mathematics and science courses?
Korpershoek, Hanke; Kuyper, Hans; van der Werf, Greetje; Bosker, Roel; Van der Werf, M.P.C.
2011-01-01
Few students (particularly few girls) currently choose to take their Final School Examination (FSE) in advanced mathematics, chemistry and physics, a combination of subjects that is the best preparation for a science-oriented study in higher education. Are these subjects attainable by more students
A mathematical model of inheritance
Institute of Scientific and Technical Information of China (English)
瞿裕忠; 王志坚; 徐家福
1996-01-01
Inheritance is regarded as the hallmark of object-oriented programming languages.A mathematical model of inheritance is presented.In this model,the graph-sorted signature is introduced to represent the algebraic structure of the program,and an extension function on the graph-sorted signatures is used to formally describe the semantics of inheritance.The program’s algebraic structure reflects the syntactic constraints of the language and the corresponding extension function exposes the character of the language’s inheritance.
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 modeling of kidney transport.
Layton, Anita T
2013-01-01
In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.
Mathematical Modeling in Continuum Mechanics
Temam, Roger; Miranville, Alain
2005-06-01
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
Koichu, Boris
2010-03-01
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 between mathematical knowledge and problem-solving behaviours are analysed in the contexts of solving an insight geometry problem, posing algebraic problems and calculus exploration. A particularly knowledgeable and skilled university student was involved in all the episodes. The presented examples substantiate the claim that advanced mathematical knowledge and advanced problem-solving behaviours do not always support each other. More advanced behaviours were observed when the student worked within her conceptual-embodied mathematical world, and less advanced ones when she worked within her symbolic and formal-axiomatic worlds. Alternative explanations of the findings are discussed. It seems that the most comprehensive explanation is in terms of the Principle of Intellectual Parsimony. Implications for further research are drawn.
A Mathematical Model of Mechanotransduction
Roth, Bradley J
2016-01-01
This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between intracellular and extracellular displacements drive mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two dimensions. In several cases the equations are solved analytically, illustrating how displacements divide into two parts: monodomain displacements are identical in both spaces and therefore do not contribute to mechanotransduction, whereas bidomain displacements cause mechanotransduction. A new length constant depends on the intracellular and extracellular shear moduli and the integrin spring constant, and bidomain effects often occur within a few length constants of the tissue edge. Numerical methods for solving the model equations are being developed. Precursors to the model and potential applications are discussed. The bidomain model...
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 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.
Mathematical foundations of quantum mechanics: An advanced short course
Moretti, Valter
2016-08-01
This paper collects and extends the lectures I gave 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.
Tools of the trade introduction to advanced mathematics
Sally, Jr, Paul J
2008-01-01
This book provides a transition from the formula-full aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics. Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such
Optical Coherence Tomography: Advanced Modeling
DEFF Research Database (Denmark)
Andersen, Peter E.; Thrane, Lars; Yura, Harold T.;
2013-01-01
Analytical and numerical models for describing and understanding the light propagation in samples imaged by optical coherence tomography (OCT) systems are presented. An analytical model for calculating the OCT signal based on the extended Huygens-Fresnel principle valid both for the single......- and multiple-scattering regimes is derived. An advanced Monte Carlo model for calculating the OCT signal is also derived, and the validity of this model is shown through a mathematical proof based on the extended Huygens-Fresnel principle. From the analytical model, an algorithm for enhancing OCT images...... is developed, the so-called true-reflection algorithm in which the OCT signal may be corrected for the attenuation caused by scattering. The algorithm is verified experimentally and by using the Monte Carlo model as a numerical tissue phantom. Applications of extraction of optical properties from tissue...
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.
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.
Advanced mathematical study and the development of conditional reasoning skills.
Attridge, Nina; Inglis, Matthew
2013-01-01
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.
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...
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Mathematical modeling of tornadoes and squall storms
Directory of Open Access Journals (Sweden)
Sergey A. Arsen’yev
2011-04-01
Full Text Available Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running perturbation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave (soliton; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.
Mathematical 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,...
Mathematical model for bone mineralization
Directory of Open Access Journals (Sweden)
Svetlana V Komarova
2015-08-01
Full Text Available Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly non-linear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...... studies have considered data sets with just one behavioral variable such as email communication. The Social Fabric interdisciplinary research project is an attempt to collect a more complete data set on human behavior by providing 1000 smartphones with pre-installed data collection software to students...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived...
Computacional-representantional model of mathematics (crmmath)
Toro Carvajal, Luis Alberto
2016-01-01
This paper presents the so-called computational representational model of mathematics (MCRMATH), its theoretical importance for mathematics education and its relation with the use of technology tools in mathematics teaching. To do this, from a cognitive point of view, we conduct a research study of representations and we explain the computational-representational model of mind (CRMM).
Mathematical modeling courses for Media technology students
DEFF Research Database (Denmark)
Timcenko, Olga
2009-01-01
This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematical...... Modeling on 6th semester being the latest addition. Some of the reasoning behind curriculum development, lessons learned and remaining issues are presented and discussed. ...
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.
Advanced structural equation modeling issues and techniques
Marcoulides, George A
2013-01-01
By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.
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...
Mineral potential mapping with mathematical geological models
Porwal, A.K.
2006-01-01
Mathematical geological models are being increasingly used by natural resources delineation and planning agencies for mapping areas of mineral potential in order to optimize land use in accordance with socio-economic needs of the society. However, a key problem in spatial-mathematical-model-based mi
Mathematical 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…
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 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.
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
2016-01-01
Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.
Mathematical modelling of scour: A review
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2007-01-01
A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers/piles and pipeli......A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...
Mathematical modeling in soil science
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
A Seminar in Mathematical Model-Building.
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
Applications of mathematical models of road cycling
Dahmen, Thorsten; Saupe, Dietmar; Wolf, Stefan
2012-01-01
This contribution discusses several use cases of mathematical models for road cycling. A mechanical model for the pedaling forces is the basis for an accurate indoor ergometer simulation of road cycling on real-world tracks. Together with a simple physiological model for the exertion of the athlete as a function of his/her accumulated power output, an optimal riding strategy for time trials on mountain ascents is computed. A combination of the two models leads to a mathematical optimization p...
The mathematics of cancer: integrating quantitative models.
Altrock, Philipp M; Liu, Lin L; Michor, Franziska
2015-12-01
Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.
Mathematical models in biology bringing mathematics to life
Ferraro, Maria; Guarracino, Mario
2015-01-01
This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...
A mathematical model of symmetry based on mathematical definition
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
A mathematical model of symmetry based on mathematical definition
Institute of Scientific and Technical Information of China (English)
刘玉生; 杨将新; 吴昭同; 高曙明
2002-01-01
Tolerance is imperative for seamless integration of CAD/CAM(Computer Aided Disignd/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance beeanse of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarify: ( 1 ) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements ; after which, the mathematical models of syrmmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis.
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 ...
Study of Photovoltaic Cells Engineering Mathematical Model
Zhou, Jun; Yu, Zhengping; Lu, Zhengyi; Li, Chenhui; Zhang, Ruilan
2016-11-01
The characteristic curve of photovoltaic cells is the theoretical basis of PV Power, which simplifies the existing mathematical model, eventually, obtains a mathematical model used in engineering. The characteristic curve of photovoltaic cells contains both exponential and logarithmic calculation. The exponential and logarithmic spread out through Taylor series, which includes only four arithmetic and use single chip microcontroller as the control center. The result shows that: the use of single chip microcontroller for calculating exponential and logarithmic functions, simplifies mathematical model of PV curve, also can meet the specific conditions’ requirement for engineering applications.
Mathematical modeling a chemical engineer's perspective
Rutherford, Aris
1999-01-01
Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus
Mathematical modeling in biomedical imaging
2009-01-01
This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
Mathematical Modeling of Chemical Stoichiometry
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
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.
Trude Nilsen; Carl Angell; Liv Sissel Grønmo
2013-01-01
As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal) on the application of mathematics in physics education compared with the research related to the c...
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...
Applied mathematics: Models, Discretizations, and Solvers
Institute of Scientific and Technical Information of China (English)
D.E. Keyes
2007-01-01
@@ Computational plasma physicists inherit decades of developments in mathematical models, numerical algorithms, computer architecture, and software engineering, whose recent coming together marks the beginning of a new era of large-scale simulation.
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
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
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.
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…
Organisation for Economic Cooperation and Development, Paris (France).
The purposes of this volume are to report a survey of current practice in the construction and use of mathematical models for the education sector: to identify the most important technical and substantive problems confronting the model-building effort; and to bridge the gap between the advancing research pursuit of model-building and the lagging…
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...
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…
Controllability, Observability, and Stability of Mathematical Models
Iggidr, Abderrahman
2004-01-01
International audience; This article presents an overview of three fundamental concepts in Mathematical System Theory: controllability, stability and observability. These properties play a prominent role in the study of mathematical models and in the understanding of their behavior. They constitute the main research subject in Control Theory. Historically the tools and techniques of Automatic Control have been developed for artificial engineering systems but nowadays they are more and more ap...
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...
On the mathematical modeling of aeolian saltation
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Sørensen, Michael
1983-01-01
The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...
Mathematical Model of the Jet Engine Fuel System
Klimko, Marek
2015-05-01
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.
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 Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
properties of those spatial mathematical representations are also discussed, especially in view of providing a formal justification for the fact that geomagnetic field models can indeed be constructed from ground-based and satellite-born observations, provided those reasonably approximate the ideal situation......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered...
Mathematical 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
Directory of Open Access Journals (Sweden)
Robert Steven Wallis
2016-05-01
Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.
Interfacial Fluid Mechanics A Mathematical Modeling Approach
Ajaev, Vladimir S
2012-01-01
Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail. Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also: Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...
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 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 modeling of complex noise barriers
Energy Technology Data Exchange (ETDEWEB)
Hayek, S.I.
1982-01-01
Mathematical modeling of the noise reduction efficiency of highway noise barriers depends on the shape and absorptivity of the barrier, the influence of the impedance of the ground under the receiver, the atmospheric conditions as well as traffic details. The mathematical model for a barrier's noise reduction requires the knowledge of point-to-point acoustic diffraction models. In many instances, the shape of the barrier is simple; such as thin wall (edge), sharp wedge, and cylindrically topped berms. However, new designs of more efficient barriers have been investigated recently.
About a mathematical model of market
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
Mathematical model of electrotaxis in osteoblastic cells
Vanegas-Acosta, J.C.; Garzón-Alvarado, D.A.; Zwamborn, A.P.M.
2012-01-01
Electrotaxis is the cell migration in the presence of an electric field (EF). This migration is parallel to the EF vector and overrides chemical migration cues. In this paper we introduce a mathematical model for the electrotaxis in osteoblastic cells. The model is evaluated using different EF stren
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models b
Mathematical models of cell self-organization
Directory of Open Access Journals (Sweden)
Benoît Perthame
2011-04-01
More recently nonlinear hyperbolic and kinetic models also have been used to describe the phenomena at a smaller scale. We explain here some motivations for ‘microscopic’ descriptions, the mathematical difficulties arising in their analysis and how kinetic models can help in understanding the unity of these descriptions.
A mathematical model of forgetting and amnesia
Murre, J.M.J.; Chessa, A.G.; Meeter, M.
2013-01-01
We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in strengt
Mathematical human modelling for impact loading
Happee, R.; Hoof, J.F.A.M. van; Lange, R. de
2001-01-01
Mathematical modeling of the human body is widely used for automotive crash-safety research and design. Simulations have contributed to a reduction of injury numbers by optimization of vehicle structures and restraint systems. Currently, such simulations are largely performed using occupant models b
Mathematical 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 Modeling of Viral Zoonoses in Wildlife
2011-01-01
Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed.
Sullivan, A L
2007-01-01
In recent years, advances in computational power and spatial data analysis (GIS, remote sensing, etc) have led to an increase in attempts to model the spread and behvaiour of wildland fires across the landscape. This series of review papers endeavours to critically and comprehensively review all types of surface fire spread models developed since 1990. This paper reviews models of a simulation or mathematical analogue nature. Most simulation models are implementations of existing empirical or quasi-empirical models and their primary function is to convert these generally one dimensional models to two dimensions and then propagate a fire perimeter across a modelled landscape. Mathematical analogue models are those that are based on some mathematical conceit (rather than a physical representation of fire spread) that coincidentally simulates the spread of fire. Other papers in the series review models of an physical or quasi-physical nature and empirical or quasi-empirical nature. Many models are extensions or ...
Molecular modeling: An open invitation for applied mathematics
Mezey, Paul G.
2013-10-01
Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.
A mathematical model for Neanderthal extinction
Flores, J C
1997-01-01
A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion) is also discussed nevertheless, extinction of Neanderthal seems unavoidable. Numerical analysis of travelling wave solution (fronts) comfirms the extinction. The wave-front-velocity is estimated from linear analysis and numerical simulations confirm this estimation. We conjecture a mathematical formulation for the principle of exclusion between competitive interacting species (Gause).
On the mathematical modeling of memristors
Radwan, Ahmed G.
2012-10-06
Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.
Dynamics of mathematical models in biology bringing mathematics to life
Zazzu, Valeria; Guarracino, Mario
2016-01-01
This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...
Mathematical 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
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 ...
The (mathematical modelling process in biosciences
Directory of Open Access Journals (Sweden)
Nestor V. Torres
2015-12-01
Full Text Available In this communication we introduce a general framework and discussion on the role of models and the modelling process within the scientific activity in the biosciences realm. The objective is sum up the common procedure during the formalization and analysis of a biological problem under the foundations of Systems Biology, which approach the study of biological systems as a whole.We begin by presenting the definitions of (biological system and model. Particular attention is given to the meaning of mathematical model within the context of the biology. Then, we present the modelization and analysis process of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model.All along this presentation the main features and shortcomings of the process are developed together with a set of rules that could help in the modelling endeavour of any biological system. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that the modelling are currently posing to the current biology.
Mathematical System Theory and System Modeling
1980-01-01
Choosing models related effectively to the questions to be addressed is a central issue in the craft of systems analysis. Since the mathematical description the analyst chooses constrains the types of issues he candeal with, it is important for these models to be selected so as to yield limitations that are acceptable in view of the questions the systems analysis seeks to answer. In this paper, the author gives an overview of the central issues affecting the question of model choice. To ...
Mathematical Modelling of Bridges with SAP2000
Maraž, Miha
2006-01-01
The present work describes a relatively new programme module, which is enhanced in the recently released versions of SAP2000 software. The new module, called Bridge Modeler, is intended for simple, parametric mathematical modelling of bridges. The modelling procedure is explained on a test case through the steps of a user-friendly Bridge Wizard. For each step, we described the basic principles and the application possibilities as well as some limitations. We also explained two types of analys...
Identification of the noise using mathematical modelling
Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav
2016-03-01
In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today's computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.
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 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)
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.
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
Some observations on the interdigitation of advances in medical science and mathematics.
Glamore, Michael James; West, James L; O'leary, James Patrick
2013-12-01
The immense advancement of our understanding of disease processes has not been a uniform progression related to the passage of time. Advances have been made in "lurches" and "catches" since the advent of the written word. There has been a remarkable interdependency between such advances in medicine and advances in mathematics that has proved beneficial to both. This work explores some of these critical relationships and documents how the individuals involved contributed to advances in each.
Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling
Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan
2012-01-01
The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…
Causal Bayes Model of Mathematical Competence in Kindergarten
Directory of Open Access Journals (Sweden)
Božidar Tepeš
2016-06-01
Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.
Structured Mathematical Modeling of Industrial Boiler
Directory of Open Access Journals (Sweden)
Abdullah Nur Aziz
2014-04-01
Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.
Structured Mathematical Modeling of Industrial Boiler
Abdullah Nur Aziz; Yul Yunazwin Nazaruddin; Parsaulian Siregar; Yazid Bindar
2014-01-01
As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. T...
Mathematical modeling of rewarming after cold therapy.
Avet, L M
1978-07-01
Statistical methods are presented for fitting mathematical models to skin temperature data. Three types of regression curves, namely, linear regression (Y = A + BX), second-degree regression (Y = A + BX + CX2), and asymptotic regression (Y = alpha + betapx), are discussed as possible models for the rewarming process following cold therapy. The data for fitting the curves consists of back surface temperature (degrees C) corresponding to various times after cold pack treatment (19 degrees C, administered for 20 minutes) was terminated.
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.
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.
Advanced Skills for Chapter 1 Mathematics: Estimation. Workshop Leader's Guide.
Advanced Technology, Inc., Indianapolis, IN.
This Workshop Leader's Guide contains step-by-step procedures for preparing, organizing, and presenting 1-hour and 3-hour workshops on estimation in mathematics. It was designed to assist Technical Assistance Center staff members and other inservice providers in conducting successful workshops on estimation in mathematics for administrators,…
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 for Preservice Teachers: A Problem from Anesthesiology.
Lingefjard, Thomas
2002-01-01
Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…
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 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.
Advanced modelling of optical coherence tomography systems
DEFF Research Database (Denmark)
Andersen, Peter E.; Thrane, L.; Yura, H.T.;
2004-01-01
Analytical and numerical models for describing and understanding the light propagation in samples imaged by optical coherence tomography (OCT) systems are presented. An analytical model for calculating the OCT signal based on the extended Huygens–Fresnel principle valid both for the single...... and multiple scattering regimes is reviewed. An advanced Monte Carlo model for calculating the OCT signal is also reviewed, and the validity of this model is shown through a mathematical proof based on the extended Huygens–Fresnel principle. Moreover, for the first time the model is verified experimentally....... From the analytical model, an algorithm for enhancing OCT images is developed; the so-called true-reflection algorithm in which the OCT signal may be corrected for the attenuation caused by scattering. For the first time, the algorithm is demonstrated by using the Monte Carlo model as a numerical...
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)
Nabb, Keith A.
2013-01-01
The research literature has made calls for greater coherence and consistency with regard to the meaning and use of the term advanced mathematical thinking (AMT) in mathematics education (Artigue, Batanero, & Kent, 2007; Selden & Selden, 2005). Educators and researchers agree that students should be engaged in AMT but it is unclear…
Proceedings: Workshop on Advanced Mathematics and Computer Science for Power Systems Analysis
Energy Technology Data Exchange (ETDEWEB)
None
1991-08-01
EPRI's Office of Exploratory Research sponsors a series of workshops that explore how to apply recent advances in mathematics and computer science to the problems of the electric utility industry. In this workshop, participants identified research objectives that may significantly improve the mathematical methods and computer architecture currently used for power system analysis.
Origins of the brain networks for advanced mathematics in expert mathematicians.
Amalric, Marie; Dehaene, Stanislas
2016-05-03
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.
Mathematical Modeling of an Automobile Damper
Directory of Open Access Journals (Sweden)
N. B. Kate, T. A. Jadhav
2013-10-01
Full Text Available - In an automotive industry, to reduce product development time and increase quality of product, it is essential to reduce the number of physical prototypes and rely more on precise & reliable design for the final design of vehicles. This paper presents a mathematical model for the damping force of the hydraulic shock absorber which is implemented to analyse the shock absorbers mounting brackets attached to the vehicle structure. Physical testing results indicate that the considered shock absorber’s mathematical model is reliable and can be used to calculate the durability target life of mounting brackets. Thus this presented methodology can be utilized as an effective way to reduce time and cost in design and development of automotive components.
Mathematical modelling of the lower urinary tract.
Paya, Antonio Soriano; Fernandez, Daniel Ruiz; Gil, David; Garcia Chamizo, Juan Manuel; Perez, Francisco Macia
2013-03-01
The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.
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.
A Mathematical Model for Suppression Subtractive Hybridization
2002-01-01
Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assess...
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.
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)
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.
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.
Study on mathematical model of steam coal blending
Institute of Scientific and Technical Information of China (English)
高洪阁; 李白英; 刘泽常; 尹增德
2002-01-01
It is necessary to set up a new mathematical model of steam coal blending instead of the old model. Indexes such as moisture content, ash content, volatile matter, sulfur content and heating value in the new mathematical model have linear relation. The new mathematical model can also predict ash-fusion temperature precisely by considering coal ash ratio in steam coal blending, therefore it is possible to obtain linear relation of ash-fusion temperature between single coal and steam coal blending. The new mathematical model can improve precision of steam coal blending and perfect the old mathematical model of steam coal blending.
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
Mathematical analysis of a muscle architecture model.
Navallas, Javier; Malanda, Armando; Gila, Luis; Rodríguez, Javier; Rodríguez, Ignacio
2009-01-01
Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area; and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition, a considerable 'edge effect' is present in the outer zone of the muscle cross-section, making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size.
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
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...
Advanced Applications for Underwater Acoustic Modeling
Directory of Open Access Journals (Sweden)
Paul C. Etter
2012-01-01
Full Text Available Changes in the ocean soundscape have been driven by anthropogenic activity (e.g., naval-sonar systems, seismic-exploration activity, maritime shipping and windfarm development and by natural factors (e.g., climate change and ocean acidification. New regulatory initiatives have placed additional restrictions on uses of sound in the ocean: mitigation of marine-mammal endangerment is now an integral consideration in acoustic-system design and operation. Modeling tools traditionally used in underwater acoustics have undergone a necessary transformation to respond to the rapidly changing requirements imposed by this new soundscape. Advanced modeling techniques now include forward and inverse applications, integrated-modeling approaches, nonintrusive measurements, and novel processing methods. A 32-year baseline inventory of modeling techniques has been updated to reflect these new developments including the basic mathematics and references to the key literature. Charts have been provided to guide soundscape practitioners to the most efficient modeling techniques for any given application.
Mathematical models of human african trypanosomiasis epidemiology.
Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul
2015-03-01
Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.
The mathematical modeling revolution in extractive metallurgy
Szekely, Julian
1988-08-01
A brief review is presented of the current state of extractive metallurgy, and it is shown that it is still a significant part of the national economy. Then a definition is given of mathematical models, and the general philosophy of modeling is discussed, together with the cost of models, hardware, and software options. Several illustrative examples are given, drawn from aluminum electrolysis, flash smelting, tundish operations, and plasma systems. The paper is concluded with the future modeling tasks facing us; these include the more widespread applications of models to represent both existing and new processing operations. It is stressed that models can play a major role in developing a holistic approach to metals and materials processing, where the primary extraction and refining operations are combined with the final processing steps.
Mathematical Modelling of Tyndall Star Initiation
Harvey, Peter; Katz, Richard F; Lacey, Andrew A
2015-01-01
The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid/liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface, and it leads to an interesting class of codimension-2 free boundary problems.
Mathematical Model of the Processoof Pearlite Austenitization
Directory of Open Access Journals (Sweden)
Olejarczyk-Wożeńska I.
2014-10-01
Full Text Available The paper presents a mathematical model of the pearlite - austenite transformation. The description of this process uses the diffusion mechanism which takes place between the plates of ferrite and cementite (pearlite as well as austenite. The process of austenite growth was described by means of a system of differential equations solved with the use of the finite difference method. The developed model was implemented in the environment of Delphi 4. The proprietary program allows for the calculation of the rate and time of the transformation at an assumed temperature as well as to determine the TTT diagram for the assigned temperature range.
A mathematical model of 'Pride and Prejudice'.
Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro
2014-04-01
A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
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...
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 Modelling of Immune Response in Tissues
Directory of Open Access Journals (Sweden)
B. Su
2009-01-01
Full Text Available We have developed a spatial–temporal mathematical model (PDE to capture fundamental aspects of the immune response to antigen. We have considered terms that broadly describe intercellular communication, cell movement, and effector function (activation or inhibition. The PDE model is robust to variation in antigen load and it can account for (1 antigen recognition, (2 an innate immune response, (3 an adaptive immune response, (4 the elimination of antigen and subsequent resolution of the immune response or (5 equilibrium of the immune response to the presence of persistent antigen (chronic infection and the formation of a granuloma.
MATHEMATICAL MODEL OF THE MICROBIAL FLOODING
Institute of Scientific and Technical Information of China (English)
Lei Guang-lun; Zhang Zhong-zhi; Chen Yue-ming
2003-01-01
On the basis of growth kinetics of microorganism and the principle of material balance, equations were derived to describe microbial growth, nutrient consumption, metabolites production and their transport in formation. The changes in porosity, permeability, oil viscosity and capillary force were also described as the main facturs of microbial flooding. For reservoirs with black oil properties, three-dimensional three-phase mathematical models with the cosidaration of multi-microbial components were established to depict microbial flooding oil. With this model, calculated results are in good agreement with experimental data.
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond
2010-01-01
This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical neuroimaging data...... sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative influence...
A mathematical model on Acquired Immunodeficiency Syndrome
Directory of Open Access Journals (Sweden)
Buddhadeo Mahato
2014-10-01
Full Text Available A mathematical model SEIA (susceptible-exposed-infectious-AIDS infected with vertical transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the world is currently facing. Even with anti-retroviral therapies (ART, many resource-constrained countries are unable to meet the treatment needs of their infected populations. We consider a function of number of AIDS cases in a community with an inverse relation. A stated theorem with proof and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number R0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R0⩽1 and unstable if R0>1. Finally, numerical simulations are presented to illustrate the results.
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 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 modelling of risk reduction in reinsurance
Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.
2017-01-01
The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.
Mathematical Modeling of Diaphragm Pneumatic Motors
Directory of Open Access Journals (Sweden)
Fojtášek Kamil
2014-03-01
Full Text Available Pneumatic diaphragm motors belong to the group of motors with elastic working parts. This part is usually made of rubber with a textile insert and it is deformed under the pressure of a compressed air or from the external mass load. This is resulting in a final working effect. In this type of motors are in contact two different elastic environments – the compressed air and the esaltic part. These motors are mainly the low-stroke and working with relatively large forces. This paper presents mathematical modeling static properties of diaphragm motors.
Mathematical modeling of diesel fuel hydrotreating
Tataurshikov, A.; Ivanchina, E.; Krivtcova, N.; Krivtsov, E.; Syskina, A.
2015-11-01
Hydrotreating of the diesel fraction with the high initial sulfur content of 1,4 mass% is carried out in the flow-through laboratory setup with the industrial GKD-202 catalyst at various process temperature. On the basis of the experimental data the regularities of the hydrogenation reactions are revealed, and the formalized scheme of sulfur-containing components (sulfides, benzothiophenes, and dibenzothiophenes) transformations is made. The mathematical model of hydrotreating process is developed, the constant values for the reaction rate of hydrodesulfurization of the specified components are calculated.
Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi
2016-09-01
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record
A mathematical model of aortic aneurysm formation
Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai
2017-01-01
Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412
Comparison of Different Mathematical Models of Cavitation
Directory of Open Access Journals (Sweden)
Dorota HOMA
2014-12-01
Full Text Available Cavitation occurs during the flow when local pressure drops to the saturation pressure according to the temperature of the flow. It includes both evaporation and condensation of the vapor bubbles, which occur alternately with high frequency. Cavitation can be very dangerous, especially for pumps, because it leads to break of flow continuity, noise, vibration, erosion of blades and change in pump’s characteristics. Therefore it is very important for pump designers and users to avoid working in cavitation conditions. Simulation of flow can be very useful in that and can indicate if there is risk of cavitating flow occurrence. As this is a multiphase flow and quite complicated phenomena, there are a few mathematical models describing it. The aim of this paper is to make a short review of them and describe their approach to model cavitation. It is desirable to know differences between them to model this phenomenon properly.
A MATHEMATICAL MODEL OF RESERVOIR SEDIMENTATION
Institute of Scientific and Technical Information of China (English)
HUANG Jinchi
2001-01-01
Reliable quantitative estimation of bed aggradation or degradation is important for river-training and water management projects. With the development of water resources, sediment problems associated with a dam are becoming more severe. This paper describes some special problems in mathematical model for calculation of degradation and aggradation in a reservoir. The main efforts of this study are on the treatment of some physical processes of fine sediment transport (＜0.05 mm). Problems in a reservoir are obviously different from a natural stream, such as the turbid current flow, orifice sediment flushing;and the initiation and consolidation of cohesive sediment deposition. The case of Liujiaxia Reservoir,which is located in the upper reaches of the Yellow River, is employed to verify the model. The results show that the model is applicable in the evaluation of an engineering planing with plenty of fine sediment movement.
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.
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.
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Building Mathematics Achievement Models in Four Countries Using TIMSS 2003
Wang, Ze; Osterlind, Steven J.; Bergin, David A.
2012-01-01
Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries…
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
Building a Two Axes Process Model of Understanding Mathematics
Koyama, Masataka
1993-01-01
The purpose of this study is to make clear what kind of characteristics a model of understanding mathematics should have so as to be useful and effective in mathematics education. The models of understanding presented in preceding papers are classified into two large categories, i. e. "aspect model" and "process model". Focusing on the process of understanding mathematics, reflective thinking plays an important role to develop children's understanding, or to progress children's thinking from ...
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...
International Conference on Recent Advances in Mathematical Biology, Analysis and Applications
Saleem, M; Srivastava, H; Khan, Mumtaz; Merajuddin, M
2016-01-01
The book contains recent developments and contemporary research in mathematical analysis and in its application to problems arising from the biological and physical sciences. The book is of interest to readers who wish to learn of new research in such topics as linear and nonlinear analysis, mathematical biology and ecology, dynamical systems, graph theory, variational analysis and inequalities, functional analysis, differential and difference equations, partial differential equations, approximation theory, and chaos. All papers were prepared by participants at the International Conference on Recent Advances in Mathematical Biology, Analysis and Applications (ICMBAA-2015) held during 4–6 June 2015 in Aligarh, India. A focal theme of the conference was the application of mathematics to the biological sciences and on current research in areas of theoretical mathematical analysis that can be used as sophisticated tools for the study of scientific problems. The conference provided researchers, academicians and ...
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
Laser interaction with biological material mathematical modeling
Kulikov, Kirill
2014-01-01
This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.
Mathematical Models and Methods for Living Systems
Chaplain, Mark; Pugliese, Andrea
2016-01-01
The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods. Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Knowledge Map: Mathematical Model and Dynamic Behaviors
Institute of Scientific and Technical Information of China (English)
Hai Zhuge; Xiang-Feng Luo
2005-01-01
Knowledge representation and reasoning is a key issue of the Knowledge Grid. This paper proposes a Knowledge Map (KM) model for representing and reasoning causal knowledge as an overlay in the Knowledge Grid. It extends Fuzzy Cognitive Maps (FCMs) to represent and reason not only simple cause-effect relations, but also time-delay causal relations, conditional probabilistic causal relations and sequential relations. The mathematical model and dynamic behaviors of KM are presented. Experiments show that, under certain conditions, the dynamic behaviors of KM can translate between different states. Knowing this condition, experts can control or modify the constructed KM while its dynamic behaviors do not accord with their expectation. Simulations and applications show that KM is more powerful and natural than FCM in emulating real world.
Mathematics Teacher Education: A Model from Crimea.
Ferrucci, Beverly J.; Evans, Richard C.
1993-01-01
Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)
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).
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.
Mathematical modeling of normal pharyngeal bolus transport: a preliminary study.
Chang, M W; Rosendall, B; Finlayson, B A
1998-07-01
Dysphagia (difficulty in swallowing) is a common clinical symptom associated with many diseases, such as stroke, multiple sclerosis, neuromuscular diseases, and cancer. Its complications include choking, aspiration, malnutrition, cachexia, and dehydration. The goal in dysphagia management is to provide adequate nutrition and hydration while minimizing the risk of choking and aspiration. It is important to advance the individual toward oral feeding in a timely manner to enhance the recovery of swallowing function and preserve the quality of life. Current clinical assessments of dysphagia are limited in providing adequate guidelines for oral feeding. Mathematical modeling of the fluid dynamics of pharyngeal bolus transport provides a unique opportunity for studying the physiology and pathophysiology of swallowing. Finite element analysis (FEA) is a special case of computational fluid dynamics (CFD). In CFD, the flow of a fluid in a space is modeled by covering the space with a grid and predicting how the fluid moves from grid point to grid point. FEA is capable of solving problems with complex geometries and free surfaces. A preliminary pharyngeal model has been constructed using FEA. This model incorporates literature-reported, normal, anatomical data with time-dependent pharyngeal/upper esophageal sphincter (UES) wall motion obtained from videofluorography (VFG). This time-dependent wall motion can be implemented as a moving boundary condition in the model. Clinical kinematic data can be digitized from VFG studies to construct and test the mathematical model. The preliminary model demonstrates the feasibility of modeling pharyngeal bolus transport, which, to our knowledge, has not been attempted before. This model also addresses the need and the potential for CFD in understanding the physiology and pathophysiology of the pharyngeal phase of swallowing. Improvements of the model are underway. Combining the model with individualized clinical data should potentially
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...
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 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.
Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.
Scharf, John; And Others
This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…
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...
A Mathematical Model of Cigarette Smoldering Process
Directory of Open Access Journals (Sweden)
Chen P
2014-12-01
Full Text Available A mathematical model for a smoldering cigarette has been proposed. In the analysis of the cigarette combustion and pyrolysis processes, a receding burning front is defined, which has a constant temperature (~450 °C and divides the cigarette into two zones, the burning zone and the pyrolysis zone. The char combustion processes in the burning zone and the pyrolysis of virgin tobacco and evaporation of water in the pyrolysis zone are included in the model. The hot gases flow from the burning zone, are assumed to go out as sidestream smoke during smoldering. The internal heat transport is characterized by effective thermal conductivities in each zone. Thermal conduction of cigarette paper and convective and radiative heat transfer at the outer surface were also considered. The governing partial differential equations were solved using an integral method. Model predictions of smoldering speed as well as temperature and density profiles in the pyrolysis zone for different kinds of cigarettes were found to agree with the experimental data. The model also predicts the coal length and the maximum coal temperatures during smoldering conditions. The model provides a relatively fast and efficient way to simulate the cigarette burning processes. It offers a practical tool for exploring important parameters for cigarette smoldering processes, such as tobacco components, properties of cigarette paper, and heat generation in the burning zone and its dependence on the mass burn rate.
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
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
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.
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?
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 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 modelling on instability of shear fault
Institute of Scientific and Technical Information of China (English)
范天佑
1996-01-01
A study on mathematical modelling on instability of fault is reported.The fracture mechanics and fracture dynamics as a basis of the discussion,and the method of complex variable function (including the conformal mapping and approximate conformal mapping) are employed,and some analytic solutions of the problem in closed form are found.The fault body concept is emphasized and the characteristic size of fault body is introduced.The effect of finite size of the fault body and the effect of the fault propagating speed (especially the effect of the high speed) and their influence on the fault instability are discussed.These results further explain the low-stress drop phenomena observed in earthquake source.
Mathematical Modelling of the Heald Shaft
Directory of Open Access Journals (Sweden)
Bílek Martin
2016-12-01
Full Text Available The manufacturers of weaving equipment recently endeavour to minimise the necessary designing plays in the weaving loom mechanisms. One of the mechanisms most exposed to stress is the shedding motion that defines the held-shaft stroke. Its end part is the heald shaft. The heald shaft constitutes a problematic assembly of the shedding motion. The design employed presently is characterised by dynamic impact loading caused by designing play in the suspension of healds into the heald shaft. During weaving cycle, the healds fly between the main beams of the heald shaft, producing a considerable force pulse. This paper is concerned with the description of dynamic behaviour of the existing design on the basis of mathematical modelling and verification of obtained results by means of experimental analysis.
Some Mathematical Models for ELM Signal
XIE, Hua-sheng
2012-01-01
There is no wide accepted theory for ELM (Edge Localized Mode) yet. Some fusion people feel that we may never get a final theory for ELM and H-mode, since which are too complicated (also related to the unsolved turbulence problem) and with at least three time scales. The only way out is using models. (This is analogous to that we believe quantum mechanics can explain chemistry and biology, but no one can calculate DNA structure from Schrodinger equation directly.) This manuscript gives some possible mathematical approaches to it. I should declare that these are just math toys for me yet. They may inspire to good understandings of ELM and H-mode, may not. Useful or useless, I don't know. One need not take too much care of it. Just for fun and enjoying different interesting ideas.
Mathematical 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
The Use of Models in Teaching Proof by Mathematical Induction
Ron, Gila; Dreyfus, Tommy
2004-01-01
Proof by mathematical induction is known to be conceptually difficult for high school students. This paper presents results from interviews with six experienced high school teachers, concerning the use of models in teaching mathematical induction. Along with creative and adequate use of models, we found explanations, models and examples that…
Mathematical modeling of endovenous laser treatment (ELT
Directory of Open Access Journals (Sweden)
Wassmer Benjamin
2006-04-01
Full Text Available Abstract Background and objectives Endovenous laser treatment (ELT has been recently proposed as an alternative in the treatment of reflux of the Great Saphenous Vein (GSV and Small Saphenous Vein (SSV. Successful ELT depends on the selection of optimal parameters required to achieve an optimal vein damage while avoiding side effects. Mathematical modeling of ELT could provide a better understanding of the ELT process and could determine the optimal dosage as a function of vein diameter. Study design/materials and methods The model is based on calculations describing the light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma Inc., Arlington, MA, USA. Damage to the vein wall for CW and single shot energy was calculated for 3 and 5 mm vein diameters. In pulsed mode, the pullback distance (3, 5 and 7 mm was considered. For CW mode simulation, the pullback speed (1, 2, 3 mm/s was the variable. The total dose was expressed as joules per centimeter in order to perform comparison to results already reported in clinical studies. Results In pulsed mode, for a 3 mm vein diameter, irrespective of the pullback distance (2, 5 or 7 mm, a minimum fluence of 15 J/cm is required to obtain a permanent damage of the intima. For a 5 mm vein diameter, 50 J/cm (15W-2s is required. In continuous mode, for a 3 mm and 5 mm vein diameter, respectively 65 J/cm and 100 J/cm are required to obtain a permanent damage of the vessel wall. Finally, the use of different wavelengths (810 nm or 980 nm played only a minor influence on these results. Discussion and conclusion The parameters
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
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.
Mathematical Modeling Social Responsibility for Dynamic Organizations
Directory of Open Access Journals (Sweden)
Farzaneh Chavoshbashi
2012-03-01
Full Text Available Dynamic organizations as accountable organizations, for transparency and accountability to its stakeholders to stakeholders for their toward performance there should express their commitment to social responsibility are through their values and ensure that this commitment throughout the organization are now and thus will have a social responsibility for their mutual benefit, so there is more and more coherent in their ethical approach takes advantage and the community and stakeholders and the organization will have better performance and strengths. Because of interest in social responsibility, in this paper dynamic model is presented for Corporate Social Responsibility of Bionic organization. Model presented a new model is inspired by chaos theory and natural systems theory based on bifurcation in creation to be all natural systems, realizing the value of responsibility as one of the fundamental values of social and institutional development that the relationship between business and work environment in the global market economy and range will be specified. First Social Responsibility factors identified, then experts and scholars determine the weight of the components and technical coefficient for modeling and paired comparison has been done using MATLAB mathematical Software.
Mathematical Model for the Mineralization of Bone
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
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...
System and mathematical modeling of quadrotor dynamics
Goodman, Jacob M.; Kim, Jinho; Gadsden, S. Andrew; Wilkerson, Stephen A.
2015-05-01
Unmanned aerial systems (UAS) are becoming increasingly visible in our daily lives; and range in operation from search and rescue, monitoring hazardous environments, and to the delivery of goods. One of the most popular UAS are based on a quad-rotor design. These are typically small devices that rely on four propellers for lift and movement. Quad-rotors are inherently unstable, and rely on advanced control methodologies to keep them operating safely and behaving in a predictable and desirable manner. The control of these devices can be enhanced and improved by making use of an accurate dynamic model. In this paper, we examine a simple quadrotor model, and note some of the additional dynamic considerations that were left out. We then compare simulation results of the simple model with that of another comprehensive model.
Ma, Xin
2001-01-01
Using six waves of data (Grades 7 through 12) from the Longitudinal Study of American Youth (LSAY), this study investigated the effects of expectation and influence of students, peers, teachers, and parents on participation in advanced mathematics. Results of survival analysis indicated a significant decline in participation rate in the transition from Grades 11 to 12. Students with higher future expectation were more likely to participate in advanced mathematics. Peer influence and teacher expectation did not have strong effects, and the effect of student future expectation was independent of peer and teacher effects. The effect of parent expectation and parent college plan for children were strong, and in their presence, the effect of student future expectation declined. Mathematics achievement and attitude toward mathematics were the most important factors affecting participation in advanced mathematics. With control over achievement and attitude, (a) the effect of student future expectation declined, (b) the effects of peer influence and teacher expectation disappeared, and (c) the effects of parent expectation and parent college plan for children were reduced. Copyright 2001 Academic Press.
Mathematical Models for Immunology: Current State of the Art and Future Research Directions
Raluca EFTIMIE; Gillard, Joseph J.; Cantrell, Doreen A.
2016-01-01
The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range...
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.
Grinstead, Mary L.
2013-01-01
This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…
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
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.
Mathematics Problem Solving: A More Advanced Skill for Chapter 1. Workshop Leader's Guide.
Advanced Technology, Inc., Indianapolis, IN.
This guide is designed to assist inservice providers in conducting successful workshops for teachers, administrators, and others associated with Chapter 1 mathematics programs. It contains step-by-step procedures for preparing, organizing, and presenting the workshop. Included in this guide are: (1) an advanced planner, which includes a detailed…
Science and Mathematics Advanced Placement Exams: Growth and Achievement over Time
Judson, Eugene
2017-01-01
Rapid growth of Advanced Placement (AP) exams in the last 2 decades has been paralleled by national enthusiasm to promote availability and rigor of science, technology, engineering, and mathematics (STEM). Trends were examined in STEM AP to evaluate and compare growth and achievement. Analysis included individual STEM subjects and disaggregation…
Application of Mathematical Modeling Activities in Costarican High School Education
Directory of Open Access Journals (Sweden)
Karen Porras-Lizano
2015-01-01
Full Text Available This paper describes the experience gained in implementing mathematical modeling activities as a methodological strategy in teaching issues such as proportions, with a group of eighth year of an academic-day-school, located in the province of San Jose, Costa Rica in 2012. Different techniques for gathering information were applied, such as participant observation and questionnaires. Among the relevant results are the cyclical development of mathematical thinking of students in the stages of mathematical modeling (description, manipulation, prediction and validation for solving the problem; developing of teamwork skills; and appreciation of mathematics as a useful and effective discipline. To resolve the activities proposed in this study, social interactions such as sharing information, thoughts and ideas, were generated, stimulating the zone of proximal development of the participating students. Likewise, the mathematical modeling activities allowed students to have a positive role in mathematics classes, stimulating, in turn, a different attitude compared to regular classes.
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…
Mathematics Teacher TPACK Standards and Development Model
Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis
2009-01-01
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…
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…
Mathematical Modelling Research in Turkey: A Content Analysis Study
Çelik, H. Coskun
2017-01-01
The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…
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.
Simple mathematical models of gene regulatory dynamics
Mackey, Michael C; Tyran-Kamińska, Marta; Zeron, Eduardo S
2016-01-01
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduat...
Mathematical model I. Electron and quantum mechanics
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical model I. Electron and quantum mechanics
Directory of Open Access Journals (Sweden)
Nitin Ramchandra Gadre
2011-03-01
Full Text Available The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
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.
Study on advancement of in vivo counting using mathematical simulation
Kinase, S
2003-01-01
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 m...
Mathematical Modeling of Photochemical Air Pollution.
McRae, Gregory John
Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations. The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms. Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF(,6)) tracer experiments. Conventional models are employed for neutral and stable conditions. A new formulation for gaseous deposition fluxes
A mathematical model of a computational problem solving system
Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan
2015-05-01
This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.
MATHEMATICAL MODELING OF AC ELECTRIC POINT MOTOR
Directory of Open Access Journals (Sweden)
S. YU. Buryak
2014-03-01
Full Text Available Purpose. In order to ensure reliability, security, and the most important the continuity of the transportation process, it is necessary to develop, implement, and then improve the automated methods of diagnostic mechanisms, devices and rail transport systems. Only systems that operate in real time mode and transmit data on the instantaneous state of the control objects can timely detect any faults and thus provide additional time for their correction by railway employees. Turnouts are one of the most important and responsible components, and therefore require the development and implementation of such diagnostics system.Methodology. Achieving the goal of monitoring and control of railway automation objects in real time is possible only with the use of an automated process of the objects state diagnosing. For this we need to know the diagnostic features of a control object, which determine its state at any given time. The most rational way of remote diagnostics is the shape and current spectrum analysis that flows in the power circuits of railway automatics. Turnouts include electric motors, which are powered by electric circuits, and the shape of the current curve depends on both the condition of the electric motor, and the conditions of the turnout maintenance. Findings. For the research and analysis of AC electric point motor it was developed its mathematical model. The calculation of parameters and interdependencies between the main factors affecting the operation of the asynchronous machine was conducted. The results of the model operation in the form of time dependences of the waveform curves of current on the load on engine shaft were obtained. Originality. During simulation the model of AC electric point motor, which satisfies the conditions of adequacy was built. Practical value. On the basis of the constructed model we can study the AC motor in various mode of operation, record and analyze current curve, as a response to various changes
Mathematical modeling of biomass fuels formation process.
Gaska, Krzysztof; Wandrasz, Andrzej J
2008-01-01
The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task.
Proceedings: Workshop on advanced mathematics and computer science for power systems analysis
Energy Technology Data Exchange (ETDEWEB)
Esselman, W.H.; Iveson, R.H. (Electric Power Research Inst., Palo Alto, CA (United States))
1991-08-01
The Mathematics and Computer Workshop on Power System Analysis was held February 21--22, 1989, in Palo Alto, California. The workshop was the first in a series sponsored by EPRI's Office of Exploratory Research as part of its effort to develop ways in which recent advances in mathematics and computer science can be applied to the problems of the electric utility industry. The purpose of this workshop was to identify research objectives in the field of advanced computational algorithms needed for the application of advanced parallel processing architecture to problems of power system control and operation. Approximately 35 participants heard six presentations on power flow problems, transient stability, power system control, electromagnetic transients, user-machine interfaces, and database management. In the discussions that followed, participants identified five areas warranting further investigation: system load flow analysis, transient power and voltage analysis, structural instability and bifurcation, control systems design, and proximity to instability. 63 refs.
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...
Garcia-Santillan, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe
2016-01-01
Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of technology modified the educational process, thus generating a meaningful impact as presented by studies carried out by Galbraith and Haines (2000). They d...
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.
Formation, characterization and mathematical modeling of the aerobic granular sludge
Energy Technology Data Exchange (ETDEWEB)
Ni, Bing-Jie [Queensland Univ., Brisbane, QLD (Australia). Advanced Water Management Centre
2013-07-01
Reports on successful aerobic granulation of sludge in pilot-scale reactor for treatment of low-strength municipal wastewater and identifies the key factors responsible for this process. Develops comprehensive models for sludge granulation, microbial interactions and microbial products formation to provide insights into the dynamics of all the soluble and solid components in aerobic granular sludge system. Demonstrates accelerated start-up and optimization of the anaerobic ammonia oxidation process by seeding the reactor with aerobic granules. Aerobic granular sludge technology will play an important role as an innovative technology alternative to the present activated sludge process in industrial and municipal wastewater treatment in the near future. Intended to fill the gaps in the studies of aerobic granular sludge, this thesis comprehensively investigates the formation, characterization and mathematical modeling of aerobic granular sludge, through integrating the process engineering tools and advanced molecular microbiology. The research results of this thesis contributed significantly to the advance of understanding and optimization of the bacterial granulation processes, the next generation of technology for cost-effective biological wastewater treatment.
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)
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 for nanotube bundle oscillators
Thamwattana, Ngamta; Cox, Barry J.; Hill, James M.
2009-07-01
This paper investigates the mechanics of a gigahertz oscillator comprising a nanotube oscillating within the centre of a uniform concentric ring or bundle of nanotubes. The study is also extended to the oscillation of a fullerene inside a nanotube bundle. In particular, certain fullerene-nanotube bundle oscillators are studied, namely C60-carbon nanotube bundle, C60-boron nitride nanotube bundle, B36N36-carbon nanotube bundle and B36N36-boron nitride nanotube bundle. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the fullerene and the nanotube bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques which provides considerable insight into the underlying mechanisms. The paper presents a synopsis of the major results derived in detail by the present authors in [1, 2].
A basic mathematical and numerical model for gas injection
Molenaar, J.
1996-01-01
In this paper we discuss a mathematical model for gas storage processes. In addition we outline an approach for numerical simulations. The focus is on model assumptions and limitations with respect to the software to be developed.
Generalized Mathematical Model for Hot Rolling Process of Plate
Institute of Scientific and Technical Information of China (English)
Zhenshan CUI; Bingye XU
2003-01-01
A generalized mathematical model is developed to predict the changes of temperature, rolling pressure, strain,strain rate, and austenite grain size for plate hot rolling and cooling processes. The model is established mainly by incorporating analytical an
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.
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
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
Directory of Open Access Journals (Sweden)
Universidade Estadual do Oeste do Paraná
2012-12-01
Full Text Available This paper presents an analysis of scientific communications published in the IV Mathematical Modeling National Conference (CNMEM in the Brazilian abbreviation, which took place in 2005. The analysis consists of a meta-analytical and content qualitative approach, aided by the software Atlas T.i. The data collected was originated in the above mentioned conference which is the first of the three which will be analyzed in the study that aims to unveil the research on Mathematical Modeling in Brazil. The categories established in this paper and which will be interpreted are: a Meta-study on Mathematics Modeling; b Modeling application; c Articulation between Modeling and other theories, and d Modeling and teachers education.
Economic mathematical methods and forecasting models
K. Karpovska-Skoryk
2000-01-01
In the article the questions of the expert system, based on the fuzzy mathematics, are discussed. It is pointed out that usage of such a system for medical insurance in the conditions of the Ukrainian economy is very convenient.
Energy Technology Data Exchange (ETDEWEB)
Zhou Tao [Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)]. E-mail: zhoutao@mail.tsinghua.edu.cn; Wang Zenghui [Department of Engineering Mechanics, Tsinghua University, Beijing 100084 (China); Yang Ruichang [Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)
2005-10-01
Experiment data got from onset of nucleate boiling (ONB) in natural circulation is analyzed using unascertained mathematics. Unitary mathematics model of the relation between the temperature and onset of nucleate boiling is built up to analysis ONB. Multiple unascertained mathematics models are also built up with the onset of natural circulation boiling equation based on the experiment. Unascertained mathematics makes that affirmative results are a range of numbers that reflect the fluctuation of experiment data more truly. The fluctuating value with the distribution function F(x) is the feature of unascertained mathematics model and can express fluctuating experimental data. Real status can be actually described through using unascertained mathematics. Thus, for calculation of ONB point, the description of unascertained mathematics model is more precise than common mathematics model. Based on the unascertained mathematics, a new ONB model is developed, which is important for advanced reactor safety analysis. It is conceivable that the unascertained mathematics could be applied to many other two-phase measurements as well.
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.
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.
Typhoid transmission: a historical perspective on mathematical model development.
Bakach, Iurii; Just, Matthew R; Gambhir, Manoj; Fung, Isaac Chun-Hai
2015-11-01
Mathematical models of typhoid transmission were first developed nearly half a century ago. To facilitate a better understanding of the historical development of this field, we reviewed mathematical models of typhoid and summarized their structures and limitations. Eleven models, published in 1971 to 2014, were reviewed. While models of typhoid vaccination are well developed, we highlight the need to better incorporate water, sanitation and hygiene interventions into models of typhoid and other foodborne and waterborne diseases. Mathematical modeling is a powerful tool to test and compare different intervention strategies which is important in the world of limited resources. By working collaboratively, epidemiologists and mathematicians should build better mathematical models of typhoid transmission, including pharmaceutical and non-pharmaceutical interventions, which will be useful in epidemiological and public health practice.
Mathematical 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.
Teaching Writing and Communication in a Mathematical Modeling Course
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
Mathematical Modeling of the Vacuum Circulation Refining Processof Molten Steel
Institute of Scientific and Technical Information of China (English)
魏季和
2003-01-01
The available studies in the literature on mathematical modeling of the vacuum circulation (RH) refining process of molten steel have briefly been reviewed. The latest advances obtained by the author with his research group have been Summarized. On the basis of the mass and momentum balances in the system, a new mathematical model for decarburization and degassing during the RH and RH-KTB refining processes of molten steel was proposed and developed. The refining roles of the three reaction sites, i.e. the up-snorkel zone, the droplet group and steel bath in the vacuum vessel, were considered in the model. It was assumed that the mass transfer of reactive components in the molten steel is the rate control step of the refining reactions. And the friction losses and drags of flows in the snorkels and vacuum vessel were all counted. The model was applied to the refining of molten steel in a multifunction RH degasser of 90 t capacity. The decarburization and degassing processes in the degasser under the RH and RH-KTB operating condi-tions were modeled and analyzed using this model. Besides, proceeded from the two-resistance mass transfer theory and the mass bal-ance of sulphur in the system, a kinetic model for the desulphurization by powder injection and blowing in the RH refining of molten steel was developed. Modeling and predictions of the process of injecting and blowing the lime based powder flux under assumed oper-ating modes with the different initial contents of sulphur and amounts of powder injected and blown in a RH degasser of 300 t capacity were carried out using the model. It was demonstrated that for the RH and RH-KTB refining processes, and the desulphurization by powder injection and blowing in the RH refining, the results predicted by the models were all in good agreement respectively with data from industrial experiments and practice. These models may be expected to offer some useful information and a reliable basis for de-termining and optimizing
Physical vs. Mathematical Models in Rock Mechanics
Morozov, I. B.; Deng, W.
2013-12-01
One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an
Wright, Vince
2014-01-01
Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…
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.
Deductive Nomological Model and Mathematics: Making Dissatisfaction more Satisfactory
Directory of Open Access Journals (Sweden)
Daniele Molinini
2014-06-01
Full Text Available The discussion on mathematical explanation has inherited the same sense of dissatisfaction that philosophers of science expressed, in the context of scientific explanation, towards the deductive-nomological model. This model is regarded as unable to cover cases of bona fide mathematical explanations and, furthermore, it is largely ignored in the relevant literature. Surprisingly, the reasons for this ostracism are not sufficiently manifest. In this paper I explore a possible extension of the model to the case of mathematical explanations and I claim that there are at least two reasons to judge the deductive-nomological picture of explanation as inadequate in that context.
Mathematical Model of Extrinsic Blood Coagulation Cascade Dynamic System
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The blood coagulation system is very important to life. This paper presents a mathematical blood coagulation model for the extrinsic pathway. This model simulates clotting factor VIII, which plays an important role in the coagulation mechanism. The mathematical model is used to study the equilibrium stability, orbit structure, attractors and global stability behavior, with conclusions in accordance with the physiological phenomena. Moreover, the results provide information about blood related illnesses, which can be used for further study of the coagulation mechanism.
The 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.
Mathematical modeling of urea transport in the kidney.
Layton, Anita T
2014-01-01
Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.
Advanced Mirror & Modelling Technology Development
Effinger, Michael; Stahl, H. Philip; Abplanalp, Laura; Maffett, Steven; Egerman, Robert; Eng, Ron; Arnold, William; Mosier, Gary; Blaurock, Carl
2014-01-01
The 2020 Decadal technology survey is starting in 2018. Technology on the shelf at that time will help guide selection to future low risk and low cost missions. The Advanced Mirror Technology Development (AMTD) team has identified development priorities based on science goals and engineering requirements for Ultraviolet Optical near-Infrared (UVOIR) missions in order to contribute to the selection process. One key development identified was lightweight mirror fabrication and testing. A monolithic, stacked, deep core mirror was fused and replicated twice to achieve the desired radius of curvature. It was subsequently successfully polished and tested. A recently awarded second phase to the AMTD project will develop larger mirrors to demonstrate the lateral scaling of the deep core mirror technology. Another key development was rapid modeling for the mirror. One model focused on generating optical and structural model results in minutes instead of months. Many variables could be accounted for regarding the core, face plate and back structure details. A portion of a spacecraft model was also developed. The spacecraft model incorporated direct integration to transform optical path difference to Point Spread Function (PSF) and between PSF to modulation transfer function. The second phase to the project will take the results of the rapid mirror modeler and integrate them into the rapid spacecraft modeler.
Mathematics of tsunami: modelling and identification
Krivorotko, Olga; Kabanikhin, Sergey
2015-04-01
Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of
Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors
Directory of Open Access Journals (Sweden)
Zoran Benić
2016-01-01
Full Text Available Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton’s second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.
Mathematical Modelling for Micropiles Embedded in Salt Rock
Directory of Open Access Journals (Sweden)
Rădan (Toader Georgiana
2016-03-01
Full Text Available This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.
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-
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.
Key Concept Mathematics and Management Science Models
Macbeth, Thomas G.; Dery, George C.
1973-01-01
The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)
Mathematical Model of Silicon Oxidation in Microelectronics
Directory of Open Access Journals (Sweden)
V. A. Bondarev
2006-01-01
Full Text Available The paper involves analytical solutions and formulae for determination of the oxide film thickness in the silicon oxidation while using nitride mask. Calculations are based on solutions of a three-dimensional diffusion equation and new mathematical functions that are firstly defined by the author. Suitable analytical and numerical solutions based on the diffusion equation have not yet been obtained
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.
A Local Mathematical Model for EPR-Experiments
Philipp, W.; Hess, K.
2002-01-01
In this paper we give a detailed and simplified version of our original mathematical model published first in the Proceedings of the National Academy of Science. We hope that this will clarify some misinterpretations of our original paper.
Mathematical 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.
The Mathematical Concept of Set and the 'Collection' Model.
Fischbein, Efraim; Baltsan, Madlen
1999-01-01
Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)
A practical course in differential equations and mathematical modeling
Ibragimov , Nail H
2009-01-01
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame
A mathematical look at a physical power prediction model
DEFF Research Database (Denmark)
Landberg, L.
1998-01-01
This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...
Mathematical Modeling of Neuro-Vascular Coupling in Rat Cerebellum
DEFF Research Database (Denmark)
Rasmussen, Tina
measured field potential is used as an indicator of neuronal activity, and the cortical blood flow is measured by means of laser-Doppler flowmetry. Using system identification methods, these measurements have been used to construct and validate parametric mathematical models of the neuro-vascular system....... Mathematical arguments as well as hypotheses about the physiological system have been used to construct the models.......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...
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.
The mathematical model realization algorithm of high voltage cable
2006-01-01
At mathematical model realization algorithm is very important to know the account order of necessary relations and how it presents. Depending of loads or signal sources connection in selected points of mathematical model its very important to know as to make the equations in this point that it was possible to determine all unknown variables in this point. The number of equations which describe this point must to coincide with number of unknown variables, and matrix which describes factor...
Mathematical and computational modeling in biology at multiple scales
Tuszynski, Jack A; Winter, Philip; White, Diana; Tseng, Chih-Yuan; Sahu, Kamlesh K.; Gentile, Francesco; Spasevska, Ivana; Omar, Sara Ibrahim; Nayebi, Niloofar; Churchill, Cassandra DM; Klobukowski, Mariusz; El-Magd, Rabab M Abou
2014-01-01
A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields f...
Mathematical modeling of a V-stack piezoelectric aileron actuation
Directory of Open Access Journals (Sweden)
Ioan URSU
2016-12-01
Full Text Available The article presents a mathematical modeling of aileron actuation that uses piezo V-shaped stacks. The aim of the actuation is the increasing of flutter speed in the context of a control law, in order to widen the flight envelope. In this way the main advantage of such a piezo actuator, the bandwidth is exploited. The mathematical model is obtained based on free body diagrams, and the numerical simulations allow a preliminary sizing of the actuator.
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...
Some Aspects of Mathematical Model of Collaborative Learning
Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu
2012-01-01
There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…
Mathematical 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
Mathematical model of a moment-less arch.
Lewis, W J
2016-06-01
This paper presents a mathematical model for predicting the geometrical shapes of rigid, two-pin, moment-less arches of constant cross section. The advancement of this work lies in the inclusion of arch self-weight and the ability to produce moment-less arch forms for any span/rise ratio, and any ratio of uniformly distributed load per unit span, w, to uniformly distributed arch weight per unit arch length, q. The model is used to derive the shapes of two classical 'moment-less' arch forms: parabolic and catenary, prior to demonstrating a general case, not restricted by the unrealistic load assumptions (absence of q, in the case of a parabolic form, or no w, in the case of a catenary arch). Using the same value of span/rise ratio, and w/q>1, the behaviour of the moment-less and parabolic arches under permanent loading, (w+q), is analysed. Results show the former to be developing much lower stresses than its parabolic rival, even when there are relatively small differences in the two geometries; for a medium span/rise ratio of 4 and w/q=2, differences in the parabolic and moment-less arch geometries would, in practical terms, be viewed as insignificant, but the stresses in them are different.
浅谈高等数学在中学数学中的两个应用%Application of Advanced Mathematics in Secondary Mathematics
Institute of Scientific and Technical Information of China (English)
王跃华
2012-01-01
通过对行列式在因式分解中的应用和导数在解不等式中的应用的探究,揭示了现代数学观点下如何沟通高等数学与中学数学的联系.%By researching the application of determinant in factoring and derivative in inequality,the communication between advanced mathematics and secondary mathematics is studied under the view of modern mathematics.
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Michelsen, Claus
2015-01-01
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…
The development of mathematical creativity through model-eliciting activities
Directory of Open Access Journals (Sweden)
Helena M. Wessels
2012-03-01
Full Text Available The ability to think creatively and solve problems is regarded as crucial for economic and personal success. The traditional approach in classrooms is not conducive to mathematical creativity, and prospective teachers should be exposed to alternative problem solving activities through which mathematical knowledge, competencies and creativity can be developed. Research studies have pointed out the possibilities and successes of a modelling approach in which complex, open problems or model-eliciting problems are used to develop meaningful mathematical knowledge and prepare learners for everyday life, as well as for tertiary studies and their occupations. Model-eliciting activities (MEAs do not only develop mathematical knowledge, but also creativity. Five hundred and one preservice Foundation Phase teachers completed different model-eliciting activities (MEAs in a longitudinal project over a period of two years. The purpose was to develop and consolidate their own mathematical knowledge, and at the same time develop creativity and modelling competencies. The ultimate purpose of the project is to prepare preservice teachers to use mathematical modelling to develop creativity in young children aged six to nine. Through solving MEAs learners also build and consolidate their mathematical knowledge and improve their own problem-solving abilities. A framework with four criteria for the identification of creativity was successfully used to evaluate levels of creativity in the solutions offered to the MEAs. Preservice teachers’ final models displayed reasonably consistent levels of creativity regarding the four criteria. Their willingness to solve MEAs and create multiple, original and useful – therefore creative – solutions also increased over the period of their exposure to modelling tasks.
Mathematical Modeling of the Induced Mutation Process in Bacterial Cells
Belov, Oleg V.; Krasavin, Evgeny A.; Parkhomenko, Alexander Yu.
2010-01-01
A mathematical model of the ultraviolet (UV) irradiation-induced mutation process in bacterial cells Escherichia coli is developed. Using mathematical approaches, the whole chain of events is tracked from a cell exposure to the damaging factor to mutation formation in the DNA chain. An account of the key special features of the regulation of this genetic network allows predicting the effects induced by the cell exposure to certain UV energy fluence.
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.
Application of Mathematic Idea in Tleaching of Advanced Mathematic%论数学思想方法在高数教学中的应用
Institute of Scientific and Technical Information of China (English)
李志海
2011-01-01
With the deepening of education reform, the application of mathematic idea in teaching of advanced mathematic attracts more and more attention of educators. This paper describes the concept of mathematical thinking and the important position and critical role in teaching of higher mathematics and points out the problems that should pay attention to in mathematic idea in teaching of advanced mathematic from the current reality of higher education.%随着教育改革的不断深入,教学思想方法在高等数学教学中的应用越来越受到教育工作者的重视.本文阐述了数学思想方法的概念及其在高等数学教学中的重要地位和关键作用,并从目前高等教育的现实出发,提出了在高等数学教学中渗透数学思想方法应注意的问题.
Mathematical models to characterize early epidemic growth: A review
Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile
2016-09-01
There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.
An evaluation of mathematical models for predicting skin permeability.
Lian, Guoping; Chen, Longjian; Han, Lujia
2008-01-01
A number of mathematical models have been proposed for predicting skin permeability, mostly empirical and very few are deterministic. Early empirical models use simple lipophilicity parameters. The recent trend is to use more complicated molecular structure descriptors. There has been much debate on which models best predict skin permeability. This article evaluates various mathematical models using a comprehensive experimental dataset of skin permeability for 124 chemical compounds compiled from various sources. Of the seven models compared, the deterministic model of Mitragotri gives the best prediction. The simple quantitative structure permeability relationships (QSPR) model of Potts and Guy gives the second best prediction. The two models have many features in common. Both assume the lipid matrix as the pathway of transdermal permeation. Both use octanol-water partition coefficient and molecular size. Even the mathematical formulae are similar. All other empirical QSPR models that use more complicated molecular structure descriptors fail to provide satisfactory prediction. The molecular structure descriptors in the more complicated QSPR models are empirically related to skin permeation. The mechanism on how these descriptors affect transdermal permeation is not clear. Mathematically it is an ill-defined approach to use many colinearly related parameters rather than fewer independent parameters in multi-linear regression.
Mathematical model of layered metallurgical furnaces and units
Shvydkiy, V. S.; Spirin, N. A.; Lavrov, V. V.
2016-09-01
The basic approaches to mathematical modeling of the layered steel furnaces and units are considered. It is noted that the particular importance have the knowledge about the mechanisms and physical nature of processes of the charge column movement and the gas flow in the moving layer, as well as regularities of development of heat- and mass-transfer in them. The statement and mathematical description of the problem solution targeting the potential gas flow in the layered unit of an arbitrary profile are presented. On the basis of the proposed mathematical model the software implementation of information-modeling system of BF gas dynamics is carried out. The results of the computer modeling of BF non-isothermal gas dynamics with regard to the cohesion zone, gas dynamics of the combustion zone and calculation of hot-blast stoves are provided
What Is Known about Elementary Grades Mathematical Modelling
Directory of Open Access Journals (Sweden)
Micah S. Stohlmann
2016-01-01
Full Text Available Mathematical modelling has often been emphasized at the secondary level, but more research is needed at the elementary level. This paper serves to summarize what is known about elementary mathematical modelling to guide future research. A targeted and general literature search was conducted and studies were summarized based on five categories: content of mathematical modelling intervention, assessment data collected, unit of analysis studied, population, and effectiveness. It was found that there were three main units of analysis into which the studies could be categorized: representational and conceptual competence, models created, and student beliefs. The main findings from each of these units of analysis are discussed along with future research that is needed.
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
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.
Analysis of mathematical model for micromechanical vibratory wheel gyroscope
Institute of Scientific and Technical Information of China (English)
LUO Yue-sheng; FAN Chong-jin; TAN Zhen-fan
2003-01-01
By the sketch of structure of MVWG,the working laws of this kind of gyroscope were explained.To the aid of Euler′s Dynamics Equation,a mathematical model of the gyroscope was constructed,and then by the basic working laws of MVWG the model was simplified.Under the conditions of the three axial direction rotations and general rotation,the mathematical model was resolved.And finally by the solutions, the working laws of the gyroscope, the working disparity among all sorts of gyrations and the influences from the gyrations in the axial directions were analysed.
Solutions manual to accompany finite mathematics models and applications
Morris, Carla C
2015-01-01
A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr
Mathematical 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 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.
MATHEMATIC MODEL FOR SITY BUS SCHEDULING IN YOGYAKARTA
Directory of Open Access Journals (Sweden)
Sahid Sahid
2016-05-01
Full Text Available Various methods can be used to construct a mathematical model of the transportation problems. One model that can be used is a linear model. Several studies have used a linear model to get the schedule and the optimal route of bus trips. This research will build a mathematical model of a city bus transportation problems in DIY using linear models. Linear model is built to get the condition density city bus passengers on shifts respectively that morning, noon, and evening. After finding a suitable model, applied to the bus passengers data in Yogyakarta. From these results it can be seen the optimum conditions in terms of density, because the condition of the city bus at this time that quiet enthusiasts. Besides, the optimum density at each shift in the morning is 11 passengers, 10 passengers during the day, and evening 9 passengers. Keywords: transportation problems, the linear model, the optimal route, density
Analysis of rear end impact using mathematical human modelling
Happee, R.; Meijer, R.; Horst, M.J. van der; Ono, K.; Yamazaki, K.
2000-01-01
At TNO an omni-directional mathematical human body model has been developed. Until now this human model has been validated for frontal and lateral loading using response data of volunteer and post mortem human subject (PMHS) sled tests. For rearward loading it has been validated for high speed impac
Precipitation of metal sulphides using gaseous hydrogen sulphide : mathematical modelling
Tarazi, Mousa Al-; Heesink, A. Bert M.; Versteeg, Geert F.
2004-01-01
A mathematical model has been developed that describes the precipitation of metal sulphides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use
Use of mathematical modeling in nuclear measurements projects
Energy Technology Data Exchange (ETDEWEB)
Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A. [AREVA/CANBERRA Nuclear Measurements Business Unit, Saint Quentin-en-Yvelines 78182 (France); Chany, P. [AREVA/BE Nuclear Sites Value Development AREVA NC Marcoule, BP 76170, 30206 Bagnols Sur Ceze (France); Devita, A. [AREVA/BE MELOX, BP 124, 30206 Bagnols Sur Ceze (France)
2011-07-01
Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)
Metaphors and Models in Translation between College and Workplace Mathematics
Williams, Julian; Wake, Geoff
2007-01-01
We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…
Applicability of mathematical modeling to problems of environmental physiology
White, Ronald J.; Lujan, Barbara F.; Leonard, Joel I.; Srinivasan, R. Srini
1988-01-01
The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.
Invention software support by integrating function and mathematical modeling
Chechurin, L.S.; Wits, W.W.; Bakker, H.M.
2015-01-01
New idea generation is imperative for successful product innovation and technology development. This paper presents the development of a novel type of invention support software. The support tool integrates both function modeling and mathematical modeling, thereby enabling quantitative analyses on a
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…
Mathematical modeling of steel fiber concrete under dynamic impact
Belov, N. N.; Yugov, N. T.; Kopanitsa, D. G.; Kopanitsa, G. D.; Yugov, A. A.; Shashkov, V. V.
2015-01-01
This paper introduces a continuum mechanics mathematical model that describes the processes of deformation and destruction of steel-fiber-concrete under a shock wave impact. A computer modeling method was applied to study the processes of shock wave impact of a steel cylindrical rod and concrete and steel fiber concrete plates. The impact speeds were within 100-500 m/s.
Mathematical and computational modeling simulation of solar drying Systems
Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...
Mathematically Modeling Parameters Influencing Surface Roughness in CNC Milling
Directory of Open Access Journals (Sweden)
Engin Nas
2012-01-01
Full Text Available In this study, steel AISI 1050 is subjected to process of face milling in CNC milling machine and such parameters as cutting speed, feed rate, cutting tip, depth of cut influencing the surface roughness are investigated experimentally. Four different experiments are conducted by creating different combinations for parameters. In conducted experiments, cutting tools, which are coated by PVD method used in forcing steel and spheroidal graphite cast iron are used. Surface roughness values, which are obtained by using specified parameters with cutting tools, are measured and correlation between measured surface roughness values and parameters is modeled mathematically by using curve fitting algorithm. Mathematical models are evaluated according to coefficients of determination (R2 and the most ideal one is suggested for theoretical works. Mathematical models, which are proposed for each experiment, are estipulated.
Random curds as mathematical models of fractal rhythm in architecture
Directory of Open Access Journals (Sweden)
Ćirović Ivana
2014-01-01
Full Text Available The author Carl Bovill has suggested and described a method for generating rhythm in architecture with the help of random curds, as they are the mathematical models of unpredictable and uneven groupings which he recognizes in natural shapes and in natural processes. He specified the rhythm generated in this way as the fractal rhythm. Random curds can be generated by a simple process of curdling, as suggested by B. Mandelbrot. This paper examines the way in which the choice of probability for every stage or level of the curdling process, and the number of stages in the procedure of curdling, affect the characteristics of the obtained fractal object as a potential mathematical model of rhythm in the design process. At the same time, this paper examines the characteristics of rhythm in architecture which determine whether the obtained fractal object will be accepted as an appropriate mathematical model of the observed rhythm.
Mathematical 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.
Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration
Warwick, Jon
2015-01-01
This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…
Mathematical Models for Room Air Distribution - Addendum
DEFF Research Database (Denmark)
Nielsen, Peter V.
1982-01-01
A number of different models on the air distribution in rooms are introduced. This includes the throw model, a model on penetration length of a cold wall jet and a model for maximum velocity in the dimensioning of an air distribution system in highly loaded rooms and shows that the amount of heat...
Mathematical Models for Room Air Distribution
DEFF Research Database (Denmark)
Nielsen, Peter V.
1982-01-01
A number of different models on the air distribution in rooms are introduced. This includes the throw model, a model on penetration length of a cold wall jet and a model for maximum velocity in the dimensioning of an air distribution system in highly loaded rooms and shows that the amount of heat...
Mathematically modelling proportions of Japanese populations by industry
Hirata, Yoshito
2016-10-01
I propose a mathematical model for temporal changes of proportions for industrial sectors. I prove that the model keeps the proportions for the primary, the secondary, and the tertiary sectors between 0 and 100% and preserves their total as 100%. The model fits the Japanese historical data between 1950 and 2005 for the population proportions by industry very well. The model also predicts that the proportion for the secondary industry becomes negligible and becomes less than 1% at least around 2080.
Modeling eBook acceptance: A study on mathematics teachers
Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad
2014-12-01
The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
influence of model regularization parameter choices on the model generalization, the reliability of the spatial brain patterns extracted from the analysis model, and the ability of the model to identify relevant brain networks defining the underlying neural encoding of the experiment. We show that known...... parts of brain networks can be overlooked in pursuing maximization of prediction accuracy. This supports the view that the quality of spatial patterns extracted from models cannot be assessed purely by focusing on prediction accuracy. Our results instead suggest that model regularization parameters must...
Mathematical modelling in the computer-aided process planning
Mitin, S.; Bochkarev, P.
2016-04-01
This paper presents new approaches to organization of manufacturing preparation and mathematical models related to development of the computer-aided multi product process planning (CAMPP) system. CAMPP system has some peculiarities compared to the existing computer-aided process planning (CAPP) systems: fully formalized developing of the machining operations; a capacity to create and to formalize the interrelationships among design, process planning and process implementation; procedures for consideration of the real manufacturing conditions. The paper describes the structure of the CAMPP system and shows the mathematical models and methods to formalize the design procedures.
Mathematical models of magnetite desliming for automated quality control systems
Olevska, Yu.; Mishchenko, V.; Olevskyi, V.
2016-10-01
The aim of the study is to provide multifactor mathematical models suitable for use in automatic control systems of desliming process. For this purpose we described the motion of a two-phase environment regard to the shape the desliming machine and technological parameters of the enrichment process. We created the method for preparation of dependences of the enrichment process quality from the technological and design parameters. To automate the process we constructed mathematical models to justify intensive technological modes and optimal parameters for design of desliming machine.
Mass Extinction in a Simple Mathematical Biological Model
Tokita, K; Tokita, Kei; Yasutomi, Ayumu
1997-01-01
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system initially has a large number of species ( diversity). The extinction dynamics shows several significant features such as a power law in basin size distribution, induction time, etc. The present theory can be a mathematical foundation of the species-area effect in the paleontologic theory for mass extinction.
A mathematical look at a physical power prediction model
Energy Technology Data Exchange (ETDEWEB)
Landberg, L. [Riso National Lab., Roskilde (Denmark)
1997-12-31
This paper takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations, and to give guidelines as to where the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.
Directory of Open Access Journals (Sweden)
Kansuporn eSriyudthsak
2016-05-01
Full Text Available The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.
MATHEMATICAL MODELING OF ORANGE SEED DRYING KINETICS
Directory of Open Access Journals (Sweden)
Daniele Penteado Rosa
2015-06-01
Full Text Available Drying of orange seeds representing waste products from juice processing was studied in the temperatures of 40, 50, 60 and 70 °C and drying velocities of 0.6, 1.0 and 1.4 m/s. Experimental drying kinetics of orange seeds were obtained using a convective air forced dryer. Three thin-layer models: Page model, Lewis model, and the Henderson-Pabis model and the diffusive model were used to predict the drying curves. The Henderson-Pabis and the diffusive models show the best fitting performance and statistical evaluations. Moreover, the temperature dependence on the effective diffusivity followed an Arrhenius relationship, and the activation energies ranging from 16.174 to 16.842 kJ/mol
Mathematical modeling of the human knee joint
Energy Technology Data Exchange (ETDEWEB)
Ricafort, Juliet [Univ. of Southern California, Los Angeles, CA (United States). Dept. of Biomedical Engineering
1996-05-01
A model was developed to determine the forces exerted by several flexor and extensor muscles of the human knee under static conditions. The following muscles were studied: the gastrocnemius, biceps femoris, semitendinosus, semimembranosus, and the set of quadricep muscles. The tibia and fibula were each modeled as rigid bodies; muscles were modeled by their functional lines of action in space. Assumptions based on previous data were used to resolve the indeterminacy.
Incorporating neurophysiological concepts in mathematical thermoregulation models
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR physiology.
Mathematical analysis and numerical simulation of a model of morphogenesis.
Muñoz, Ana I; Tello, José Ignacio
2011-10-01
We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters.
A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy.
Li, Xuefang; Xu, Jian-Xin
2016-10-07
Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon-γ (IFN-γ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013). The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model.
Mathematical Modelling of Laser/Material Interactions.
1983-11-25
translated to the model input. Even an experimental mode print can also be digitalised for the model. In trying to describe high order modes matliematically...4. Mazumder J. Steen W.M. "Welding of Ti 6al - 4V by continuous wave CO2 laser". Metal construction Sept. 1980 pp423 - 427. 5. Kogelnik H, Li.T Proc
A Mathematical model of copper corrosion
Clarelli, Fabrizio; Natalini, Roberto
2012-01-01
A new partial differential model for monitoring and detecting copper corrosion products (mainly brochantite and cuprite) is proposed to provide predictive tools suitable for describing the evolution of damage induced on bronze specimens by sulfur dioxide (SO_2) pollution. This model is characterized by the movement of a double free boundary. Numerical simulations show a nice agreement with experimental result.
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.
Undergraduate Research: Mathematical Modeling of Mortgages
Choi, Youngna; Spero, Steven
2010-01-01
In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current…
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.
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
Physical and Mathematical Modeling in Experimental Papers.
Möbius, Wolfram; Laan, Liedewij
2015-12-17
An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations.
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...
Mathematical Model of Lifetime Duration at Insulation of Electrical Machines
Directory of Open Access Journals (Sweden)
Mihaela Răduca
2009-10-01
Full Text Available Abstract. This paper present a mathematical model of lifetime duration at hydro generator stator winding insulation when at hydro generator can be appear the damage regimes. The estimation to make by take of the programming and non-programming revisions, through the introduction and correlation of the new defined notions.
A Mathematical Model of the Great Solar Eclipse of 1991.
Lamb, John Jr.
1991-01-01
An activity that shows how mathematics can be used to model events in the real world is described. A way to calculate the area of the sun covered by the moon during a partial eclipse is presented. A computer program that will determine the coverage percentage is also included. (KR)
Mathematical modeling of the aerodynamic characteristics in flight dynamics
Tobak, M.; Chapman, G. T.; Schiff, L. B.
1984-01-01
Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.
A Mathematical Model for HIV Drug-Resistance
Faedo, Ivan; Raimundo, Silvia Martorano; Venturino, Ezio
2010-09-01
In this paper we present a mathematical model of the transmission of HIV infection here the individuals receive antiretroviral drugs but may not respond to treatment. In such case the latter can be changed to a different therapy, and individuals may or may not respond also to this second set of drugs.
Optlang: An algebraic modeling language for mathematical optimization
DEFF Research Database (Denmark)
Jensen, Kristian; Cardoso, Joao; Sonnenschein, Nikolaus
2016-01-01
Optlang is a Python package implementing a modeling language for solving mathematical optimization problems, i.e., maximizing or minimizing an objective function over a set of variables subject to a number of constraints. It provides a common native Python interface to a series of optimization...
Mathematical Modelling and Experimental Analysis of Early Age Concrete
DEFF Research Database (Denmark)
Hauggaard-Nielsen, Anders Boe
1997-01-01
The report deals with mathematical models for concrete at early age. In the hardening process chemical reactions take place and the concrete skeleton is created. The processes changes the moisture content and produces heat. The associated temperature rise gives expansion of the material which may...
Mathematical Model For Engineering Analysis And Optimization
Sobieski, Jaroslaw
1992-01-01
Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.
Mathematical modelling of paper degradation in books
Nimmo, A J
2015-01-01
Paper cannot be prevented from degrading and does not necessarily degrade uniformly across its volume. It has been established that as paper degrades, VOCs (Volatile Organic Compounds) are produced. This body of work studies paper degradation with respect to the role VOCs play. The thesis investigates how a VOC a ecting the paper's acidity can in turn a ect the degradation rate and through modelling the VOC concentration pro le, the degradation pro le is found. To create the model from a chem...
Frejd, Peter
2014-01-01
The relevance of using mathematics in and for out-of-school activities is one main argument for teaching mathematics in education. Mathematical modelling is considered as a bridge between the mathematics learned and taught in schools and the mathematics used at the workplace and in society and it is also a central notion in the present Swedish mathematical syllabus for upper secondary school. This doctoral thesis reports on students’, teachers’ and modelling experts’ experiences of, learning,...
Mathematical modeling of polymer electrolyte fuel cells
Sousa, Ruy; Gonzalez, Ernesto R.
Fuel cells with a polymer electrolyte membrane have been receiving more and more attention. Modeling plays an important role in the development of fuel cells. In this paper, the state-of-the-art regarding modeling of fuel cells with a polymer electrolyte membrane is reviewed. Modeling has allowed detailed studies concerning the development of these cells, e.g. in discussing the electrocatalysis of the reactions and the design of water-management schemes to cope with membrane dehydration. Two-dimensional models have been used to represent reality, but three-dimensional models can cope with some important additional aspects. Consideration of two-phase transport in the air cathode of a proton exchange membrane fuel cell seems to be very appropriate. Most fuel cells use hydrogen as a fuel. Besides safety concerns, there are problems associated with production, storage and distribution of this fuel. Methanol, as a liquid fuel, can be the solution to these problems and direct methanol fuel cells (DMFCs) are attractive for several applications. Mass transport is a factor that may limit the performance of the cell. Adsorption steps may be coupled to Tafel kinetics to describe methanol oxidation and methanol crossover must also be taken into account. Extending the two-phase approach to the DMFC modeling is a recent, important point.
Mathematical Existence Results for the Doi-Edwards Polymer Model
Chupin, Laurent
2017-01-01
In this paper, we present some mathematical results on the Doi-Edwards model describing the dynamics of flexible polymers in melts and concentrated solutions. This model, developed in the late 1970s, has been used and extensively tested in modeling and simulation of polymer flows. From a mathematical point of view, the Doi-Edwards model consists in a strong coupling between the Navier-Stokes equations and a highly nonlinear constitutive law. The aim of this article is to provide a rigorous proof of the well-posedness of the Doi-Edwards model, namely that it has a unique regular solution. We also prove, which is generally much more difficult for flows of viscoelastic type, that the solution is global in time in the two dimensional case, without any restriction on the smallness of the data.
Mathematical modeling of a convective textile drying process
Directory of Open Access Journals (Sweden)
G. Johann
2014-12-01
Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.
Mathematical Model of Hot Metal Desulfurization by Powder Injection
Directory of Open Access Journals (Sweden)
Yolanda Cepeda Rodríguez
2012-01-01
Full Text Available Although there have been a numerous number of studies on mathematical model of hot metal desulfurization by deep injection of calcium carbide, the research field as a whole is not well integrated. This paper presents a model that takes into account the kinetics, thermodynamics, and transport processes to predict the sulfur levels in the hot metal throughout a blow. The model could be utilized to assess the influence of the treatment temperature, rate of injection, gas flow rate, and initial concentration of sulfur on the desulfurization kinetics. In the second part of this paper an analysis of the industrial data for injection of calcium carbide using this model is described. From a mathematical model that describes the characteristics of a system, it is possible to predict the behavior of the variables involved in the process, resulting in savings of time and money. Discretization is realized through the finite difference method combined with interpolation in the border domain by Taylor series.
Mathematical modeling/problem solving in global oxygen transport.
Farrell, Kevin; Hill, Andrew; Dent, Leon; Nguyen, Minh Ly
2009-08-01
A simplified approach to mathematical modeling/problem solving in global oxygen transport is presented. In addition to standard oxygen transport formulae, it uses the S-Factor and a mathematical relationship relating SvO(2) to the ratio DO(2)/VO(2). This method allows the determination or specification of SvO(2), PvO(2), P(50), and systemic shunting in the context of this simplified approach. Heretofore this has not been possible. With this approach, essentially all clinical problems in global oxygen transport can be dealt with. This is illustrated by the broad scope of the five problems presented.
Mathematical model for corundum single crystal growth by Verneuil method
Grzymkowski, Radosław; Mochnacki, Bohdan; Suchy, Józef
1983-05-01
A mathematical model which is an attempt to describe the complex process of monocrystallization by the Verneuil method is presented. The problem has been solved through the method of finite differences and at the same time making use of a certain modification of the mathematical description of Stefan's problem called the the alternating phase truncation method [9]. The elaborated algorithm and the examples of solutions given at the end of the present study point at the usefulness of the presented method of numerical simulation for modern designing and controlling the processes of crystal production.
Mathematical Modeling of Column-Base Connections under Monotonic Loading
Directory of Open Access Journals (Sweden)
Gholamreza Abdollahzadeh
2014-12-01
Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.
Mathematical Model of Piston Ring Sealing in Combustion Engine
Directory of Open Access Journals (Sweden)
Koszałka Grzegorz
2015-01-01
Full Text Available This paper presents a mathematical model of piston-rings-cylinder sealing (TPC of a combustion engine. The developed model is an itegrated model of gas flow through gaps in TPC unit, displacements and twisting motions of piston rings in ring grooves as well as generation of oil film between ring face surfaces and cylinder liner. Thermal deformations and wear of TPC unit elements as well as heat exchange between flowing gas and surrounding walls, were taken into account in the model. The paper contains descriptions of: assumptions used for developing the model, the model itself, its numerical solution as well as its computer application for carrying out simulation tests.
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 models of decision making and learning].
Ito, Makoto; Doya, Kenji
2008-07-01
Computational models of reinforcement learning have recently been applied to analysis of brain imaging and neural recording data to identity neural correlates of specific processes of decision making, such as valuation of action candidates and parameters of value learning. However, for such model-based analysis paradigms, selecting an appropriate model is crucial. In this study we analyze the process of choice learning in rats using stochastic rewards. We show that "Q-learning," which is a standard reinforcement learning algorithm, does not adequately reflect the features of choice behaviors. Thus, we propose a generalized reinforcement learning (GRL) algorithm that incorporates the negative reward effect of reward loss and forgetting of values of actions not chosen. Using the Bayesian estimation method for time-varying parameters, we demonstrated that the GRL algorithm can predict an animal's choice behaviors as efficiently as the best Markov model. The results suggest the usefulness of the GRL for the model-based analysis of neural processes involved in decision making.
Three dimensional mathematical model of tooth for finite element analysis
Directory of Open Access Journals (Sweden)
Puškar Tatjana
2010-01-01
Full Text Available Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body into simple geometric bodies (cylinder, cone, pyramid,.... Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
Mathematical and Numerical Modeling in Maritime Geomechanics
Directory of Open Access Journals (Sweden)
Miguel Martín Stickle
2012-04-01
Full Text Available A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,... combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the overning equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism.
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
Using Archeological Data to Model Mathematics
Yanik, H. Bahadir; Kurz, Terri L.; Memis, Yasin
2014-01-01
The purpose of this investigation is to describe an implementation of a modeling task using mock data from an ancient archeological find. Students discover the relationship between the height of a person and his or her stride length. Qualitative data from student discussions document thinking and reasoning.
Mathematical Model of Porous Medium Dynamics
Gerschuk, Peotr; Sapozhnikov, Anatoly
1999-06-01
Semiempirical model describing porous material strains under pulse mechanical and thermal loadings is proposed. Porous medium is considered as continuous one but with special form of pressure dependence upon strain. This model takes into account principal features of porous materials behavior which can be observed when the material is strained in dynamic and static experiments ( non-reversibility of large strains, nonconvexity of loading curve). Elastoplastic properties of porous medium, its damages when it is strained and dynamic fracture are also taken into account. Dispersion of unidirectional motion caused by medium heterogeneity (porousness) is taken into acount by introducing the physical viscosity depending upon pores size. It is supposed that at every moment of time pores are in equilibrium with pressure i.e. kinetic of pores collapse is not taken into account. The model is presented by the system of differential equations connecting pressure and energy of porous medium with its strain. These equations close system of equations of motion and continuity which then is integrated numerically. The proposed model has been tested on carbon materials and porous copper . Results of calculation of these materials shock compressing are in satisfactory agreement with experimental data. Results of calculation of thin plate with porous copper layer collision are given as an illustration.
MATHEMATICAL MODELING OF INFRARED MILK PASTEURIZATION
Directory of Open Access Journals (Sweden)
S. T. Antipov
2013-01-01
Full Text Available Based on the model representation of the process of pasteurization of milk infrared patterns of change in temperature of the product in the heating zone with the heat flows of different nature were obtained. The changes in the basic performance of the quartz oscillator during operation were also obtained.
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 Models Light Up Plant Signaling
Chew, Y.H.; Smith, R.W.; Jones, H.J.; Seaton, D.D.; Grima, R.; Halliday, K.J.
2014-01-01
Plants respond to changes in the environment by triggering a suite of regulatory networks that control and synchronize molecular signaling in different tissues, organs, and the whole plant. Molecular studies through genetic and environmental perturbations, particularly in the model plant Arabidopsis
A Cognitive Model of College Mathematics Placement
1989-08-01
study focused on the precalculus -- calculus placement decision. The Cognitive model uses novel, or analysis level, placement test items in an attempt to...relative to the requirements of a precalculus course. Placement test scores may be partitioned to give analysis and non-analysis subtest scores which can...67 5.1.1 1989 Intercorrelations ....................................................................... 67 5.1.2 1989 Precalculus -Calculus
Modeling Students' Mathematics Using Steffe's Fraction Schemes
Norton, Anderson H.; McCloskey, Andrea V.
2008-01-01
Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…
Innovative mathematical modeling in environmental remediation
Energy Technology Data Exchange (ETDEWEB)
Yeh, Gour T. [Taiwan Typhoon and Flood Research Institute (Taiwan); National Central Univ. (Taiwan); Univ. of Central Florida (United States); Gwo, Jin Ping [Nuclear Regulatory Commission (NRC), Rockville, MD (United States); Siegel, Malcolm D. [Sandia National Laboratories, Albuquerque, NM (United States); Li, Ming-Hsu [National Central Univ. (Taiwan); ; Fang, Yilin [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Zhang, Fan [Inst. of Tibetan Plateau Research, Chinese Academy of Sciences (China); Luo, Wensui [Inst. of Tibetan Plateau Research, Chinese Academy of Sciences (China); Yabusaki, Steven B. [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)
2013-05-01
There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g.,Ni, Cr, Co).The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport models
On the treatment of airline travelers in mathematical models.
Directory of Open Access Journals (Sweden)
Michael A Johansson
Full Text Available The global spread of infectious diseases is facilitated by the ability of infected humans to travel thousands of miles in short time spans, rapidly transporting pathogens to distant locations. Mathematical models of the actual and potential spread of specific pathogens can assist public health planning in the case of such an event. Models should generally be parsimonious, but must consider all potentially important components of the system to the greatest extent possible. We demonstrate and discuss important assumptions relative to the parameterization and structural treatment of airline travel in mathematical models. Among other findings, we show that the most common structural treatment of travelers leads to underestimation of the speed of spread and that connecting travel is critical to a realistic spread pattern. Models involving travelers can be improved significantly by relatively simple structural changes but also may require further attention to details of parameterization.
Mathematical modeling of isotope labeling experiments for metabolic flux analysis.
Nargund, Shilpa; Sriram, Ganesh
2014-01-01
Isotope labeling experiments (ILEs) offer a powerful methodology to perform metabolic flux analysis. However, the task of interpreting data from these experiments to evaluate flux values requires significant mathematical modeling skills. Toward this, this chapter provides background information and examples to enable the reader to (1) model metabolic networks, (2) simulate ILEs, and (3) understand the optimization and statistical methods commonly used for flux evaluation. A compartmentalized model of plant glycolysis and pentose phosphate pathway illustrates the reconstruction of a typical metabolic network, whereas a simpler example network illustrates the underlying metabolite and isotopomer balancing techniques. We also discuss the salient features of commonly used flux estimation software 13CFLUX2, Metran, NMR2Flux+, FiatFlux, and OpenFLUX. Furthermore, we briefly discuss methods to improve flux estimates. A graphical checklist at the end of the chapter provides a reader a quick reference to the mathematical modeling concepts and resources.
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 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 modeling of brain tumors: effects of radiotherapy and chemotherapy
Energy Technology Data Exchange (ETDEWEB)
Powathil, G [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Kohandel, M [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Sivaloganathan, S [Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Oza, A [Center for Mathematical Medicine, Fields Institute for Research in Mathematical Sciences, Toronto, Ontario M5T 3J1 (Canada); Milosevic, M [Radiation Medicine Program, Princess Margaret Hospital, and Department of Radiation Oncology, University of Toronto, Toronto, Ontario M5G 2M9 (Canada)
2007-06-07
Gliomas, the most common primary brain tumors, are diffusive and highly invasive. The standard treatment for brain tumors consists of a combination of surgery, radiation therapy and chemotherapy. Over the past few years, mathematical models have been applied to study untreated and treated brain tumors. In an effort to improve treatment strategies, we consider a simple spatio-temporal mathematical model, based on proliferation and diffusion, that incorporates the effects of radiotherapeutic and chemotherapeutic treatments. We study the effects of different schedules of radiation therapy, including fractionated and hyperfractionated external beam radiotherapy, using a generalized linear quadratic (LQ) model. The results are compared with published clinical data. We also discuss the results for combination therapy (radiotherapy plus temozolomide, a new chemotherapy agent), as proposed in recent clinical trials. We use the model to predict optimal sequencing of the postoperative (combination of radiotherapy and adjuvant, neo-adjuvant or concurrent chemotherapy) treatments for brain tumors.
Mathematical 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 modelling of triple arterial stenoses.
Ang, K C; Mazumdar, J
1995-06-01
This paper examines the effects of triple stenoses (ie. three stenoses in series) in a reasonably large artery. The model developed is axi-symmetric and blood is assumed to be a Newtonian fluid. The governing equations are the Navier-Stokes equations and the continuity equation. These equations are solved using the Finite Element Method and the FIDAP computational fluid dynamics (C.F.D.) package. Various combinations of differing degrees of stenosis in the triplet are considered. Pressure drop profiles and streamline plots of the solutions to these models show that the effects of milder stenoses are diminished in the presence of more severe ones. Also, a pressure recovery is observed whenever a mild stenosis follows a more severe stenosis in multiply stenosed arteries.
Novel mathematical neural models for visual attention
DEFF Research Database (Denmark)
Li, Kang
Visual attention has been extensively studied in psychology, but some fundamental questions remain controversial. We focus on two questions in this study. First, we investigate how a neuron in visual cortex responds to multiple stimuli inside the receptive eld, described by either a response...... for the visual attention theories and spiking neuron models for single spike trains. Statistical inference and model selection are performed and various numerical methods are explored. The designed methods also give a framework for neural coding under visual attention theories. We conduct both analysis on real...... system, supported by simulation study. Finally, we present the decoding of multiple temporal stimuli under these visual attention theories, also in a realistic biophysical situation with simulations....
Mathematical 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.
Mathematical models of ecology and evolution
DEFF Research Database (Denmark)
Zhang, Lai
2012-01-01
dynamics but as a trade-o promotes species survival by shortening juvenile delay between birth and the onset of reproduction. Paper II compares the size-spectrum and food-web representations of communities using two traits (body size and habitat location) based unstructured population model of Lotka......) based size-structured population model, that is, interference in foraging, maintenance, survival, and recruitment. Their impacts on the ecology and evolution of size-structured populations and communities are explored. Ecologically, interference aects population demographic properties either negatively...... or positively, depending on the balance between interference induced gain and cost. Evolutionarily, the maturation size is either depressed (interference in foraging and maintenance) or elevated (interference in survival and recruitment) in a monomorphic population environment. Moreover, among the four...
Mathematical modeling and visualization of functional neuroimages
Rasmussen, Peter Mondrup; Hansen, Lars Kai; Madsen, Kristoffer Hougaard
2011-01-01
Denne afhandling præsenterer forskningsresultater omhandlende matematisk modellering indenfor analyse af funktionelle hjernescanningsbilleder. Specifikt fokuserer afhandlingen pa mønster-baserede analysemetoder, som nyligt er blevet populære indenfor hjerneforskning. Ved hjæp af sådanne modelleringsmetoderne forsger forskere at prdiktere en eksperimentelt defineret mental tilstand ud fra hjernescanningsdata. Afhandlingen omhandler emner, der kan inddeles i to dele.Første del undersger hvorled...
Voltammetry: mathematical modelling and Inverse Problem
Koshev, N A; Kuzina, V V
2016-01-01
We propose the fast semi-analytical method of modelling the polarization curves in the voltammetric experiment. The method is based on usage of the special func- tions and shows a big calculation speed and a high accuracy and stability. Low computational needs of the proposed algorithm allow us to state the set of Inverse Problems of voltammetry for the reconstruction of metal ions concentrations or the other parameters of the electrolyte under investigation.
Mathematical modeling of the evolution of a simple biological system
Digital Repository Service at National Institute of Oceanography (India)
Gonsalves, M.J.B.D.; Neetu, S.; Krishnan, K.P.; Attri, K.; LokaBharathi, P.A.
Paula, Goa 403 004, India. Phone: +91 0832 2450624, Fax: +91 0832 2450606, e-mail: mjudith@nio.org Introduction In India, classroom education in biology does not generally include an exercise in which the data can be used to develop models.... This has hampered exposure to quantitative tools in biology, much to the disadvantage of students. The purpose of this note is to report an exercise we carried out to expose traditional biologists educated in India to mathematical modelling of biological...
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.
Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.
Clément, Frédérique
2016-07-01
Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of
A mathematical model of star formation in the Galaxy
Directory of Open Access Journals (Sweden)
M.A. Sharaf
2012-06-01
Full Text Available This paper is generally concerned with star formation in the Galaxy, especially blue stars. Blue stars are the most luminous, massive and the largest in radius. A simple mathematical model of the formation of the stars is established and put in computational algorithm. This algorithm enables us to know more about the formation of the star. Some real and artificial examples had been used to justify this model.
Phase errors elimination in compact digital holoscope (CDH) based on a reasonable mathematical model
Wen, Yongfu; Qu, Weijuan; Cheng, Cheeyuen; Wang, Zhaomin; Asundi, Anand
2015-03-01
In the compact digital holoscope (CDH) measurement process, theoretically, we need to ensure the distances between the reference wave and object wave to the hologram plane exactly match. However, it is not easy to realize in practice due to the human factors. This can lead to a phase error in the reconstruction result. In this paper, the strict theoretical analysis of the wavefront interference is performed to demonstrate the mathematical model of the phase error and then a phase errors elimination method is proposed based on the advanced mathematical model, which has a more explicit physical meaning. Experiments are carried out to verify the performance of the presented method and the results indicate that it is effective and allows the operator can make operation more flexible.
DEFF Research Database (Denmark)
Carugati, Andrea
2002-01-01
has been initiated with the scope of investigating the questions that mathematical modelling technology poses to traditional information systems development projects. Based on the past body of research, this study proposes a framework to guide decision making for managing projects of information......’ skills in the development process. Further observations also indicate that flexibility and adaptability, based on grounded theory, are valuable tools when information systems development involves a new technology.......The advancements in complexity and sophistication of mathematical models for manufacturing scheduling and control and the increase of the ratio power/cost of computers are beginning to provide the manufacturing industry with new software tools to improve production. A Danish action research project...
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 for the EPIC code
Energy Technology Data Exchange (ETDEWEB)
Buchanan, H.L.
1981-06-03
EPIC is a fluid/envelope type computer code designed to study the energetics and dynamics of a high energy, high current electron beam passing through a gas. The code is essentially two dimensional (x, r, t) and assumes an axisymmetric beam whose r.m.s. radius is governed by an envelope model. Electromagnetic fields, background gas chemistry, and gas hydrodynamics (density channel evolution) are all calculated self-consistently as functions of r, x, and t. The code is a collection of five major subroutines, each of which is described in some detail in this report.
A novel mathematical model for controllable near-field electrospinning
Directory of Open Access Journals (Sweden)
Changhai Ru
2014-01-01
Full Text Available Near-field electrospinning (NFES had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
A novel mathematical model for controllable near-field electrospinning
Energy Technology Data Exchange (ETDEWEB)
Ru, Changhai, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [College of Automation, Harbin Engineering University, Harbin 150001 (China); Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Chen, Jie; Shao, Zhushuai [Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Pang, Ming [College of Automation, Harbin Engineering University, Harbin 150001 (China); Luo, Jun, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072 (China)
2014-01-15
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
Mathematical analysis of intermittent gas injection model in oil production
Tasmi, Silvya, D. R.; Pudjo, S.; Leksono, M.; Edy, S.
2016-02-01
Intermittent gas injection is a method to help oil production process. Gas is injected through choke in surface and then gas into tubing. Gas forms three areas in tubing: gas column area, film area and slug area. Gas column is used to propel slug area until surface. A mathematical model of intermittent gas injection is developed in gas column area, film area and slug area. Model is expanding based on mass and momentum conservation. Using assume film thickness constant in tubing, model has been developed by Tasmi et. al. [14]. Model consists of 10 ordinary differential equations. In this paper, assumption of pressure in gas column is uniform. Model consist of 9 ordinary differential equations. Connection of several variables can be obtained from this model. Therefore, dynamics of all variables that affect to intermittent gas lift process can be seen from four equations. To study the behavior of variables can be analyzed numerically and mathematically. In this paper, simple mathematically analysis approach is used to study behavior of the variables. Variables that affect to intermittent gas injection are pressure in upstream valve and in gas column. Pressure in upstream valve will decrease when gas mass in valve greater than gas mass in choke. Dynamic of the pressure in the gas column will decrease and increase depending on pressure in upstream valve.
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.
Institute of Scientific and Technical Information of China (English)
郑博; 唐晓津; 张占柱; 宗保宁
2011-01-01
The fouling mechanisms of membrane in the cross-flow filtration for the slurry Fischer-Tropsch synthesis technology (SFTST) were discussed. The research advances of mathematic modeling in cross-flow filtration for SFTST in literature were reviewed in both three-phase and two-phase systems. Based on different resistances, the models can be divided into blocked resistance, cake resistance and combined resistance. It is supposed that the combined resistance in cross-flow filtration for SFTST will be the further research direction.%分析了浆态床费托合成错流过滤过程中滤膜污染的机理,并分别综述了三相过滤和两相过滤过程中数学模型的研究进展根据阻力不同,将模型分为堵塞阻力模型、滤饼层阻力模型和组合阻力模型.在对现有模型研究总结的基础上,通过对比和分析指出了组合阻力模型是浆态床费托合成错流过滤数学模型研究的方向.
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 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.
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...
Chitera, Nancy
2011-01-01
In this article, the author presents a discussion of how mathematics teacher educators model school mathematics teaching in initial teacher training colleges, as they prepare the student teachers to teach mathematics in multilingual classrooms in Malawi. In particular, the article examines the instructional practices that mathematics teacher…
The Academic Merits of Modelling in Higher Mathematics Education: A Case Study
Perrenet, Jacob; Adan, Ivo
2010-01-01
Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge…
Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification
Directory of Open Access Journals (Sweden)
Grzegorz Mikułowski
2016-01-01
Full Text Available Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA, which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.
Chemical Kinetic Modeling of Advanced Transportation Fuels
Energy Technology Data Exchange (ETDEWEB)
PItz, W J; Westbrook, C K; Herbinet, O
2009-01-20
Development of detailed chemical kinetic models for advanced petroleum-based and nonpetroleum based fuels is a difficult challenge because of the hundreds to thousands of different components in these fuels and because some of these fuels contain components that have not been considered in the past. It is important to develop detailed chemical kinetic models for these fuels since the models can be put into engine simulation codes used for optimizing engine design for maximum efficiency and minimal pollutant emissions. For example, these chemistry-enabled engine codes can be used to optimize combustion chamber shape and fuel injection timing. They also allow insight into how the composition of advanced petroleum-based and non-petroleum based fuels affect engine performance characteristics. Additionally, chemical kinetic models can be used separately to interpret important in-cylinder experimental data and gain insight into advanced engine combustion processes such as HCCI and lean burn engines. The objectives are: (1) Develop detailed chemical kinetic reaction models for components of advanced petroleum-based and non-petroleum based fuels. These fuels models include components from vegetable-oil-derived biodiesel, oil-sand derived fuel, alcohol fuels and other advanced bio-based and alternative fuels. (2) Develop detailed chemical kinetic reaction models for mixtures of non-petroleum and petroleum-based components to represent real fuels and lead to efficient reduced combustion models needed for engine modeling codes. (3) Characterize the role of fuel composition on efficiency and pollutant emissions from practical automotive engines.
Heat-pump-assisted dryer: Pt. 1; Mathematical model
Energy Technology Data Exchange (ETDEWEB)
Pendyala, V.R.; Devotta, S.; Patwardhan, V.S. (National Chemical Lab., Poona (India))
1990-07-01
A mathematical model for an integrated heat-pump-assisted dryer has been developed. The dryer has been modelled considering the heat transfer and simultaneous heat and mass transfer zones. The heat-pump heat exchangers have been modelled by writing the enthalpy balance for differential lengths considering the various zones on the air and working-fluid sides. The compressor has been described by the polytropic compression equation. The model has been used for simulating an existing system using R11 to study the effect of approach velocity of air to the evaporator and of the suction superheat on the specific energy consumption of the heat pump assisted dryer. (author).
Mathematical Model of Piston Ring Sealing in Combustion Engine
Koszałka Grzegorz; Guzik Mirosław
2015-01-01
This paper presents a mathematical model of piston-rings-cylinder sealing (TPC) of a combustion engine. The developed model is an itegrated model of gas flow through gaps in TPC unit, displacements and twisting motions of piston rings in ring grooves as well as generation of oil film between ring face surfaces and cylinder liner. Thermal deformations and wear of TPC unit elements as well as heat exchange between flowing gas and surrounding walls, were taken into account in the model. The pape...
Mathematical modelling of dextran filtration through hollow fibre membranes
DEFF Research Database (Denmark)
Vinther, Frank; Pinelo, Manuel; Brøns, Morten
2014-01-01
In this paper we present a mathematical model of an ultrafiltration process. The results of the model are produced using standard numerical techniques with Comsol Multiphysics. The model describes the fluid flow and separation in hollow fibre membranes. The flow of solute and solvent within...... of the solute permeability the concentration dependent viscosity decreases the volumetric flux through the membrane at high pressures. This effect is due to a very high concentration at the membrane surface. The model is related to experimental data. There is a good qualitative and a reasonable quantitative...
Multiscale mathematical modeling and simulation of cellular dynamical process.
Nakaoka, Shinji
2014-01-01
Epidermal homeostasis is maintained by dynamic interactions among molecules and cells at different spatiotemporal scales. Mathematical modeling and simulation is expected to provide clear understanding and precise description of multiscaleness in tissue homeostasis under systems perspective. We introduce a stochastic process-based description of multiscale dynamics. Agent-based modeling as a framework of multiscale modeling to achieve consistent integration of definitive subsystems is proposed. A newly developed algorithm that particularly aims to perform stochastic simulations of cellular dynamical process is introduced. Finally we review applications of multiscale modeling and quantitative study to important aspects of epidermal and epithelial homeostasis.
Mathematical models with singularities a zoo of singular creatures
Torres, Pedro J
2015-01-01
The book aims to provide an unifying view of a variety (a 'zoo') of mathematical models with some kind of singular nonlinearity, in the sense that it becomes infinite when the state variable approaches a certain point. Up to 11 different concrete models are analyzed in separate chapters. Each chapter starts with a discussion of the basic model and its physical significance. Then the main results and typical proofs are outlined, followed by open problems. Each chapter is closed by a suitable list of references. The book may serve as a guide for researchers interested in the modelling of real world processes.
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 of the growth of human fetus anatomical structures.
Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech
2016-07-08
The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.
Accurate Modeling of Advanced Reflectarrays
DEFF Research Database (Denmark)
Zhou, Min
Analysis and optimization methods for the design of advanced printed re ectarrays have been investigated, and the study is focused on developing an accurate and efficient simulation tool. For the analysis, a good compromise between accuracy and efficiency can be obtained using the spectral domain...... to the POT. The GDOT can optimize for the size as well as the orientation and position of arbitrarily shaped array elements. Both co- and cross-polar radiation can be optimized for multiple frequencies, dual polarization, and several feed illuminations. Several contoured beam reflectarrays have been designed...... using the GDOT to demonstrate its capabilities. To verify the accuracy of the GDOT, two offset contoured beam reflectarrays that radiate a high-gain beam on a European coverage have been designed and manufactured, and subsequently measured at the DTU-ESA Spherical Near-Field Antenna Test Facility...
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 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 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.
Preventing clonal evolutionary processes in cancer: Insights from mathematical models.
Rodriguez-Brenes, Ignacio A; Wodarz, Dominik
2015-07-21
Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.
Directory of Open Access Journals (Sweden)
Esra BUKOVA GÜZEL
2010-05-01
Full Text Available The purpose of this study is to examine the relationships between pre-service mathematics teachers’ achievements in calculus course and their mathematical modelling approaches. This case study has been conducted with twelve pre-service teachers from the Department of Secondary School Mathematics Education who have different academic achievement levels. While the study group has been formed, the mean of five written exams given in Calculus-I course has been taken into account. According to the mean of these exams, four participants have been equally chosen from groups which have higher, average and low achievement. Data have been collected through using mathematical modelling problems. While the problems have been analyzed, the mathematical modelling processes in literature have been taken into account, and a five-step scoring system has been developed by the researchers of the study. The results of study have shown that academic achievement of the pre-service teachers affected their mathematical modelling approaches to some extend. With this study, it has been aimed to provide contribution to the researches the purpose of which is to improve mathematical modelling approaches.
Numerical modeling of advanced materials
Meinders, T.; Perdahcioglu, E.S.; Riel, van M.; Wisselink, H.H.
2007-01-01
The finite element (FE) method is widely used to numerically simulate forming processes. The accuracy of an FE analysis strongly depends on the extent to which a material model can represent the real material behavior. The use of new materials requires complex material models which are able to descr
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)
Information system based on the mathematical model of the EPS
Kalimoldayev, Maksat N.; Abdildayeva, Assel A.; Mamyrbayev, Orken Zh.; Akhmetzhanov, Maksat
2016-11-01
This article discusses the structure of an information system, the mathematical and information models of electric power systems. Currently, the major application areas include system relaying data communication systems and automation, automated dispatching and technological management of electric power facilities, as well as computer-aided calculation of energy resources. Automatic control of excitation (ARV) synchronous machines is one of the most effective ways to ensure the stability of power systems. However, the variety of possible options and modes even in a single grid pose significant obstacles to the development of the best means of ensuring sustainability. Thus, the use of ARVs to ensure stability in some cases may not be sufficient. Therefore, there is a need to develop an information system based on a mathematical model.
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...... in this thesis. The oven was successfully validated against a 10 m tunnel oven. Besides the ability to emulate the baking conditions in a tunnel oven, the new batch oven is designed and constructed for experimental research work. In the design options to follow the product continuously (especially weight...... 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...
Mathematical modeling and simulation of a thermal system
Toropoc, Mirela; Gavrila, Camelia; Frunzulica, Rodica; Toma, Petrica D.
2016-12-01
The aim of the present paper is the conception of a mathematical model and simulation of a system formed by a heatexchanger for domestic hot water preparation, a storage tank for hot water and a radiator, starting from the mathematical equations describing this system and developed using Scilab-Xcos program. The model helps to determine the evolution in time for the hot water temperature, for the return temperature in the primary circuit of the heat exchanger, for the supply temperature in the secondary circuit, the thermal power for heating and for hot water preparation to the consumer respectively. In heating systems, heat-exchangers have an important role and their performances influence the energy efficiency of the systems. In the meantime, it is very important to follow the behavior of such systems in dynamic regimes. Scilab-Xcos program can be utilized to follow the important parameters of the systems in different functioning scenarios.
An inverse problem for a mathematical model of aquaponic agriculture
Bobak, Carly; Kunze, Herb
2017-01-01
Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.
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.
Richardson, Sandra
2009-01-01
This article describes experiences from a professional development project designed to prepare in-service eighth-grade mathematics teachers to develop, explore, and advance technological pedagogical content knowledge (TPCK) in the teaching and learning of Algebra I. This article describes the process of the participating teachers' mathematical…
Modified Mathematical Model For Neutralization System In Stirred Tank Reactor
Directory of Open Access Journals (Sweden)
Ahmmed Saadi Ibrehem
2011-05-01
Full Text Available A modified model for the neutralization process of Stirred Tank Reactors (CSTR reactor is presented in this study. The model accounts for the effect of strong acid [HCL] flowrate and strong base [NaOH] flowrate with the ionic concentrations of [Cl-] and [Na+] on the Ph of the system. In this work, the effect of important reactor parameters such as ionic concentrations and acid and base flowrates on the dynamic behavior of the CSTR is investigated and the behavior of mathematical model is compared with the reported models for the McAvoy model and Jutila model. Moreover, the results of the model are compared with the experimental data in terms of pH dynamic study. A good agreement is observed between our model prediction and the actual plant data. © 2011 BCREC UNDIP. All rights reserved(Received: 1st March 2011, Revised: 28th March 2011; Accepted: 7th April 2011[How to Cite: A.S. Ibrehem. (2011. Modified Mathematical Model For Neutralization System In Stirred Tank Reactor. Bulletin of Chemical Reaction Engineering & Catalysis, 6(1: 47-52. doi:10.9767/bcrec.6.1.825.47-52][How to Link / DOI: http://dx.doi.org/10.9767/bcrec.6.1.825.47-52 || or local: http://ejournal.undip.ac.id/index.php/bcrec/article/view/825 ] | View in
Mathematical modeling of DNA's transcription process for the cancer study
Morales-Peñaloza, A.; Meza-López, C. D.; Godina-Nava, J. J.
2012-10-01
The cancer is a phenomenon caused by an anomaly in the DNA's transcription process, therefore it is necessary to known how such anomaly is generated in order to implement alternative therapies to combat it. We propose to use mathematical modeling to treat the problem. Is implemented a simulation of the process of transcription and are studied the transport properties in the heterogeneous case using nonlinear dynamics.
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.
Mathematical modelling of cell aggregation in liver tissue engineering
Green, John Edward E.
2006-01-01
A promising method for growing functional liver tissue in vitro involves culturing hepatocytes as spheroidal cell aggregates. In this thesis, we develop mathematical models of cell aggregation, and use them to determine how hepatocytes' interactions with the extracellular matrix (ECM) on which they are seeded, and with stellate cells, affect the process. Chapters 2-4 focus on the effect that cell-ECM coupling has on the aggregation process. We use a novel formulation that couples a mechani...