A comprehensive, consistent and systematic mathematical model of PEM fuel cells
International Nuclear Information System (INIS)
Baschuk, J.J.; Li Xianguo
2009-01-01
This paper presents a comprehensive, consistent and systematic mathematical model for PEM fuel cells that can be used as the general formulation for the simulation and analysis of PEM fuel cells. As an illustration, the model is applied to an isothermal, steady state, two-dimensional PEM fuel cell. Water is assumed to be in either the gas phase or as a liquid phase in the pores of the polymer electrolyte. The model includes the transport of gas in the gas flow channels, electrode backing and catalyst layers; the transport of water and hydronium in the polymer electrolyte of the catalyst and polymer electrolyte layers; and the transport of electrical current in the solid phase. Water and ion transport in the polymer electrolyte was modeled using the generalized Stefan-Maxwell equations, based on non-equilibrium thermodynamics. Model simulations show that the bulk, convective gas velocity facilitates hydrogen transport from the gas flow channels to the anode catalyst layers, but inhibits oxygen transport. While some of the water required by the anode is supplied by the water produced in the cathode, the majority of water must be supplied by the anode gas phase, making operation with fully humidified reactants necessary. The length of the gas flow channel has a significant effect on the current production of the PEM fuel cell, with a longer channel length having a lower performance relative to a shorter channel length. This lower performance is caused by a greater variation in water content within the longer channel length
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
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.
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…
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Consistent model driven architecture
Niepostyn, Stanisław J.
2015-09-01
The goal of the MDA is to produce software systems from abstract models in a way where human interaction is restricted to a minimum. These abstract models are based on the UML language. However, the semantics of UML models is defined in a natural language. Subsequently the verification of consistency of these diagrams is needed in order to identify errors in requirements at the early stage of the development process. The verification of consistency is difficult due to a semi-formal nature of UML diagrams. We propose automatic verification of consistency of the series of UML diagrams originating from abstract models implemented with our consistency rules. This Consistent Model Driven Architecture approach enables us to generate automatically complete workflow applications from consistent and complete models developed from abstract models (e.g. Business Context Diagram). Therefore, our method can be used to check practicability (feasibility) of software architecture models.
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…
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 Modeling Using MATLAB
National Research Council Canada - National Science Library
Phillips, Donovan
1998-01-01
.... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...
Mathematical modelling of membrane separation
DEFF Research Database (Denmark)
Vinther, Frank
This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...
Mathematical Modelling Approach in Mathematics Education
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
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
STP: A mathematically and physically consistent library of steam properties
International Nuclear Information System (INIS)
Aguilar, F.; Hutter, A.C.; Tuttle, P.G.
1982-01-01
A new FORTRAN library of subroutines has been developed from the fundamental equation of Keenan et al. to evaluate a large set of water properties including derivatives such as sound speed and isothermal compressibility. The STP library uses the true saturation envelope of the Keenan et al. fundamental equation. The evaluation of the true envelope by a continuation method is explained. This envelope, along with other design features, imparts an exceptionally high degree of thermodynamic and mathematical consistency to the STP library, even at the critical point. Accuracy and smoothness, library self-consistency, and designed user convenience make the STP library a reliable and versatile water property package
MATHEMATICAL MODEL MANIPULATOR ROBOTS
Directory of Open Access Journals (Sweden)
O. N. Krakhmalev
2015-12-01
Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.
Developing mathematical modelling competence
DEFF Research Database (Denmark)
Blomhøj, Morten; Jensen, Tomas Højgaard
2003-01-01
In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....
Mathematical modelling techniques
Aris, Rutherford
1995-01-01
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
Mathematical modelling of metabolism
DEFF Research Database (Denmark)
Gombert, Andreas Karoly; Nielsen, Jens
2000-01-01
Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...
Principles of mathematical modeling
Dym, Clive
2004-01-01
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Mathematical models in radiogeochronology
International Nuclear Information System (INIS)
Abril, J.M.; Garcia Leon, M.
1991-01-01
The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)
Concepts of mathematical modeling
Meyer, Walter J
2004-01-01
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec
Mathematical Modeling: A Structured Process
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Toward a consistent model for glass dissolution
International Nuclear Information System (INIS)
Strachan, D.M.; McGrail, B.P.; Bourcier, W.L.
1994-01-01
Understanding the process of glass dissolution in aqueous media has advanced significantly over the last 10 years through the efforts of many scientists around the world. Mathematical models describing the glass dissolution process have also advanced from simple empirical functions to structured models based on fundamental principles of physics, chemistry, and thermodynamics. Although borosilicate glass has been selected as the waste form for disposal of high-level wastes in at least 5 countries, there is no international consensus on the fundamental methodology for modeling glass dissolution that could be used in assessing the long term performance of waste glasses in a geologic repository setting. Each repository program is developing their own model and supporting experimental data. In this paper, we critically evaluate a selected set of these structured models and show that a consistent methodology for modeling glass dissolution processes is available. We also propose a strategy for a future coordinated effort to obtain the model input parameters that are needed for long-term performance assessments of glass in a geologic repository. (author) 4 figs., tabs., 75 refs
Mathematical models of hysteresis
International Nuclear Information System (INIS)
1998-01-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above
Mathematical models of hysteresis
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-08-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
Consistent ranking of volatility models
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Lunde, Asger
2006-01-01
We show that the empirical ranking of volatility models can be inconsistent for the true ranking if the evaluation is based on a proxy for the population measure of volatility. For example, the substitution of a squared return for the conditional variance in the evaluation of ARCH-type models can...... variance in out-of-sample evaluations rather than the squared return. We derive the theoretical results in a general framework that is not specific to the comparison of volatility models. Similar problems can arise in comparisons of forecasting models whenever the predicted variable is a latent variable....
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.
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…
Modeling interdisciplinary activities involving Mathematics
DEFF Research Database (Denmark)
Iversen, Steffen Møllegaard
2006-01-01
In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
A Primer for Mathematical Modeling
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
International Nuclear Information System (INIS)
Castillo M, J.A.; Pimentel P, A.E.
2000-01-01
This work presents the results to define the adult egg viability behavior (VHA) of two species, Drosophila melanogaster and D. simulans obtained with the mathematical model proposed, as well as the respective curves. The data are the VHA result of both species coming from the vicinity of the Laguna Verde Nuclear Power plant (CNLV) comprise a 10 years collect period starting from 1987 until 1997. Each collect includes four series of data which are the VHA result obtained after treatment with 0, 4, 6 and 8 Gy of gamma rays. (Author)
Mathematical modeling with multidisciplinary applications
Yang, Xin-She
2013-01-01
Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Mathematical Modelling of Predatory Prokaryotes
Wilkinson, Michael H.F.
2006-01-01
Predator–prey models have a long history in mathematical modelling of ecosystem dynamics and evolution. In this chapter an introduction to the methodology of mathematical modelling is given, with emphasis on microbial predator–prey systems, followed by a description of variants of the basic
Mathematical problems in meteorological modelling
Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella
2016-01-01
This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...
From virtual clustering analysis to self-consistent clustering analysis: a mathematical study
Tang, Shaoqiang; Zhang, Lei; Liu, Wing Kam
2018-03-01
In this paper, we propose a new homogenization algorithm, virtual clustering analysis (VCA), as well as provide a mathematical framework for the recently proposed self-consistent clustering analysis (SCA) (Liu et al. in Comput Methods Appl Mech Eng 306:319-341, 2016). In the mathematical theory, we clarify the key assumptions and ideas of VCA and SCA, and derive the continuous and discrete Lippmann-Schwinger equations. Based on a key postulation of "once response similarly, always response similarly", clustering is performed in an offline stage by machine learning techniques (k-means and SOM), and facilitates substantial reduction of computational complexity in an online predictive stage. The clear mathematical setup allows for the first time a convergence study of clustering refinement in one space dimension. Convergence is proved rigorously, and found to be of second order from numerical investigations. Furthermore, we propose to suitably enlarge the domain in VCA, such that the boundary terms may be neglected in the Lippmann-Schwinger equation, by virtue of the Saint-Venant's principle. In contrast, they were not obtained in the original SCA paper, and we discover these terms may well be responsible for the numerical dependency on the choice of reference material property. Since VCA enhances the accuracy by overcoming the modeling error, and reduce the numerical cost by avoiding an outer loop iteration for attaining the material property consistency in SCA, its efficiency is expected even higher than the recently proposed SCA algorithm.
Mathematical Modeling and Computational Thinking
Sanford, John F.; Naidu, Jaideep T.
2017-01-01
The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Explorations in Elementary Mathematical Modeling
Shahin, Mazen
2010-01-01
In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
Modeling and Testing Legacy Data Consistency Requirements
DEFF Research Database (Denmark)
Nytun, J. P.; Jensen, Christian Søndergaard
2003-01-01
An increasing number of data sources are available on the Internet, many of which offer semantically overlapping data, but based on different schemas, or models. While it is often of interest to integrate such data sources, the lack of consistency among them makes this integration difficult....... This paper addresses the need for new techniques that enable the modeling and consistency checking for legacy data sources. Specifically, the paper contributes to the development of a framework that enables consistency testing of data coming from different types of data sources. The vehicle is UML and its...... accompanying XMI. The paper presents techniques for modeling consistency requirements using OCL and other UML modeling elements: it studies how models that describe the required consistencies among instances of legacy models can be designed in standard UML tools that support XMI. The paper also considers...
Consistency of the MLE under mixture models
Chen, Jiahua
2016-01-01
The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many researchers ignore the precise conditions required on the mixture model. An incorrect claim of consistency can lead to false conclusions even if the mixture model under investigation seems well behaved. Under a finite normal mixture model, for instance, the consis...
Mathematical Modelling Plant Signalling Networks
Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.
2013-01-01
methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more
Parallel Boltzmann machines : a mathematical model
Zwietering, P.J.; Aarts, E.H.L.
1991-01-01
A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a
Consistent spectroscopy for a extended gauge model
International Nuclear Information System (INIS)
Oliveira Neto, G. de.
1990-11-01
The consistent spectroscopy was obtained with a Lagrangian constructed with vector fields with a U(1) group extended symmetry. As consistent spectroscopy is understood the determination of quantum physical properties described by the model in an manner independent from the possible parametrizations adopted in their description. (L.C.J.A.)
Mathematical Modeling of Diverse Phenomena
Howard, J. C.
1979-01-01
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
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.
Consistent Stochastic Modelling of Meteocean Design Parameters
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Sterndorff, M. J.
2000-01-01
Consistent stochastic models of metocean design parameters and their directional dependencies are essential for reliability assessment of offshore structures. In this paper a stochastic model for the annual maximum values of the significant wave height, and the associated wind velocity, current...
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
The Spectrum of Mathematical Models.
Karplus, Walter J.
1983-01-01
Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.
1985-06-01
This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)
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.
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…
Consistent Estimation of Partition Markov Models
Directory of Open Access Journals (Sweden)
Jesús E. García
2017-04-01
Full Text Available The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns.
Financial model calibration using consistency hints.
Abu-Mostafa, Y S
2001-01-01
We introduce a technique for forcing the calibration of a financial model to produce valid parameters. The technique is based on learning from hints. It converts simple curve fitting into genuine calibration, where broad conclusions can be inferred from parameter values. The technique augments the error function of curve fitting with consistency hint error functions based on the Kullback-Leibler distance. We introduce an efficient EM-type optimization algorithm tailored to this technique. We also introduce other consistency hints, and balance their weights using canonical errors. We calibrate the correlated multifactor Vasicek model of interest rates, and apply it successfully to Japanese Yen swaps market and US dollar yield market.
Self-consistent asset pricing models
Malevergne, Y.; Sornette, D.
2007-08-01
We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alphas and betas of the factor model are unobservable. Self-consistency leads to renormalized betas with zero effective alphas, which are observable with standard OLS regressions. When the conditions derived from internal consistency are not met, the model is necessarily incomplete, which means that some sources of risk cannot be replicated (or hedged) by a portfolio of stocks traded on the market, even for infinite economies. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value αi at the origin between an asset i's return and the proxy's return. Self-consistency also introduces “orthogonality” and “normality” conditions linking the betas, alphas (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from January 1990 to February 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Assuming that the CAPM holds with the self-consistency condition, the OLS method automatically obeys the resulting orthogonality and normality conditions and therefore provides a simple way to self-consistently assess the parameters of the model by using proxy portfolios made only of the assets which are used in the CAPM regressions. Finally, the factor decomposition with the
Mathematical and physical models and radiobiology
International Nuclear Information System (INIS)
Lokajicek, M.
1980-01-01
The hit theory of the mechanism of biological radiation effects in the cell is discussed with respect to radiotherapy. The mechanisms of biological effects and of intracellular recovery, the cumulative radiation effect and the cumulative biological effect in fractionated irradiation are described. The benefit is shown of consistent application of mathematical and physical models in radiobiology and radiotherapy. (J.P.)
Mathematical model on Alzheimer's disease.
Hao, Wenrui; Friedman, Avner
2016-11-18
Alzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. AD is characterized by the presence of two types of neuropathological hallmarks: extracellular plaques consisting of amyloid β-peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins. The disease affects 5 million people in the United States and 44 million world-wide. Currently there is no drug that can cure, stop or even slow the progression of the disease. If no cure is found, by 2050 the number of alzheimer's patients in the U.S. will reach 15 million and the cost of caring for them will exceed $ 1 trillion annually. The present paper develops a mathematical model of AD that includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. The model is represented by a system of partial differential equations. The model is used to simulate the effect of drugs that either failed in clinical trials, or are currently in clinical trials. Based on these simulations it is suggested that combined therapy with TNF- α inhibitor and anti amyloid β could yield significant efficacy in slowing the progression of AD.
Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics
Wickstrom, Megan H.
2017-01-01
This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Khusna, H.; Heryaningsih, N. Y.
2018-01-01
The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.
Consistent biokinetic models for the actinide elements
International Nuclear Information System (INIS)
Leggett, R.W.
2001-01-01
The biokinetic models for Th, Np, Pu, Am and Cm currently recommended by the International Commission on Radiological Protection (ICRP) were developed within a generic framework that depicts gradual burial of skeletal activity in bone volume, depicts recycling of activity released to blood and links excretion to retention and translocation of activity. For other actinide elements such as Ac, Pa, Bk, Cf and Es, the ICRP still uses simplistic retention models that assign all skeletal activity to bone surface and depicts one-directional flow of activity from blood to long-term depositories to excreta. This mixture of updated and older models in ICRP documents has led to inconsistencies in dose estimates and interpretation of bioassay for radionuclides with reasonably similar biokinetics. This paper proposes new biokinetic models for Ac, Pa, Bk, Cf and Es that are consistent with the updated models for Th, Np, Pu, Am and Cm. The proposed models are developed within the ICRP's generic model framework for bone-surface-seeking radionuclides, and an effort has been made to develop parameter values that are consistent with results of comparative biokinetic data on the different actinide elements. (author)
Using Covariation Reasoning to Support Mathematical Modeling
Jacobson, Erik
2014-01-01
For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...
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…
Thermodynamically consistent model calibration in chemical kinetics
Directory of Open Access Journals (Sweden)
Goutsias John
2011-05-01
Full Text Available Abstract Background The dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function. Results We introduce a thermodynamically consistent model calibration (TCMC method that can be effectively used to provide thermodynamically feasible values for the parameters of an open biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from http://www.cis.jhu.edu/~goutsias/CSS lab/software.html. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database. Conclusions TCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new
Thermodynamically consistent mesoscopic model of the ferro/paramagnetic transition
Czech Academy of Sciences Publication Activity Database
Benešová, Barbora; Kružík, Martin; Roubíček, Tomáš
2013-01-01
Roč. 64, Č. 1 (2013), s. 1-28 ISSN 0044-2275 R&D Projects: GA AV ČR IAA100750802; GA ČR GA106/09/1573; GA ČR GAP201/10/0357 Grant - others:GA ČR(CZ) GA106/08/1397; GA MŠk(CZ) LC06052 Program:GA; LC Institutional support: RVO:67985556 Keywords : ferro-para-magnetism * evolution * thermodynamics Subject RIV: BA - General Mathematics; BA - General Mathematics (UT-L) Impact factor: 1.214, year: 2013 http://library.utia.cas.cz/separaty/2012/MTR/kruzik-thermodynamically consistent mesoscopic model of the ferro-paramagnetic transition.pdf
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.
1985-01-01
This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments
Wind tunnel modeling of roadways: Comparison with mathematical models
International Nuclear Information System (INIS)
Heidorn, K.; Davies, A.E.; Murphy, M.C.
1991-01-01
The assessment of air quality impacts from roadways is a major concern to urban planners. In order to assess future road and building configurations, a number of techniques have been developed including mathematical models, which simulate traffic emissions and atmospheric dispersion through a series of mathematical relationships and physical models. The latter models simulate emissions and dispersion through scaling of these processes in a wind tunnel. Two roadway mathematical models, HIWAY-2 and CALINE-4, were applied to a proposed development in a large urban area. Physical modeling procedures developed by Rowan Williams Davies and Irwin Inc. (RWDI) in the form of line source simulators were also applied, and the resulting carbon monoxide concentrations were compared. The results indicated a factor of two agreement between the mathematical and physical models. The physical model, however, reacted to change in building massing and configuration. The mathematical models did not, since no provision for such changes was included in the mathematical models. In general, the RWDI model resulted in higher concentrations than either HIWAY-2 or CALINE-4. Where there was underprediction, it was often due to shielding of the receptor by surrounding buildings. Comparison of these three models with the CALTRANS Tracer Dispersion Experiment showed good results although concentrations were consistently underpredicted
Mathematical Modeling in the Undergraduate Curriculum
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
Teachers' Conceptions of Mathematical Modeling
Gould, Heather
2013-01-01
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Mathematical modelling in economic processes.
Directory of Open Access Journals (Sweden)
L.V. Kravtsova
2008-06-01
Full Text Available In article are considered a number of methods of mathematical modelling of economic processes and opportunities of use of spreadsheets Excel for reception of the optimum decision of tasks or calculation of financial operations with the help of the built-in functions.
Mathematical modeling of biological processes
Friedman, Avner
2014-01-01
This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.
Self-consistent model of confinement
International Nuclear Information System (INIS)
Swift, A.R.
1988-01-01
A model of the large-spatial-distance, zero--three-momentum, limit of QCD is developed from the hypothesis that there is an infrared singularity. Single quarks and gluons do not propagate because they have infinite energy after renormalization. The Hamiltonian formulation of the path integral is used to quantize QCD with physical, nonpropagating fields. Perturbation theory in the infrared limit is simplified by the absence of self-energy insertions and by the suppression of large classes of diagrams due to vanishing propagators. Remaining terms in the perturbation series are resummed to produce a set of nonlinear, renormalizable integral equations which fix both the confining interaction and the physical propagators. Solutions demonstrate the self-consistency of the concepts of an infrared singularity and nonpropagating fields. The Wilson loop is calculated to provide a general proof of confinement. Bethe-Salpeter equations for quark-antiquark pairs and for two gluons have finite-energy solutions in the color-singlet channel. The choice of gauge is addressed in detail. Large classes of corrections to the model are discussed and shown to support self-consistency
Mathematical modelling in solid mechanics
Sofonea, Mircea; Steigmann, David
2017-01-01
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...
Mathematical modeling of rainwater runoff over catchment surface ...
African Journals Online (AJOL)
The subject of an article is the mathematical modeling of the rainwater runoff along the surface catchment taking account the transport of pollution which permeates into the water flow from a porous media of soil at the certain areas of this surface. The developed mathematical model consists of two types of equations: the ...
Constraint theory multidimensional mathematical model management
Friedman, George J
2017-01-01
Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...
Exploring Yellowstone National Park with Mathematical Modeling
Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia
2017-01-01
Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…
Strategies to Support Students' Mathematical Modeling
Jung, Hyunyi
2015-01-01
An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…
Mathematical Modeling in the High School Curriculum
Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary
2016-01-01
In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…
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.
Consistent three-equation model for thin films
Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul
2017-11-01
Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.
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 Model of Age Aggression
Golovinski, P. A.
2013-01-01
We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...
Mathematical modeling of cancer metabolism.
Medina, Miguel Ángel
2018-04-01
Systemic approaches are needed and useful for the study of the very complex issue of cancer. Modeling has a central position in these systemic approaches. Metabolic reprogramming is nowadays acknowledged as an essential hallmark of cancer. Mathematical modeling could contribute to a better understanding of cancer metabolic reprogramming and to identify new potential ways of therapeutic intervention. Herein, I review several alternative approaches to metabolic modeling and their current and future impact in oncology. Copyright © 2018 Elsevier B.V. All rights reserved.
Mathematical models of granular matter
Mariano, Paolo; Giovine, Pasquale
2008-01-01
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
Summer Camp of Mathematical Modeling in China
Tian, Xiaoxi; Xie, Jinxing
2013-01-01
The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…
Continuum mechanics the birthplace of mathematical models
Allen, Myron B
2015-01-01
Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer. This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe
Mathematical modeling of laser lipolysis
Directory of Open Access Journals (Sweden)
Reynaud Jean
2008-02-01
Full Text Available Abstract Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc. The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s give similar skin surface temperature (max: 41°C. These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction
Mathematical Modeling in Combustion Science
Takeno, Tadao
1988-01-01
An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.
Mathematical models of bipolar disorder
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
mathematical models for estimating radio channels utilization
African Journals Online (AJOL)
2017-08-08
Aug 8, 2017 ... Mathematical models for radio channels utilization assessment by real-time flows transfer in ... data transmission networks application having dynamic topology ..... Journal of Applied Mathematics and Statistics, 56(2): 85–90.
Mathematical models in medicine: Diseases and epidemics
International Nuclear Information System (INIS)
Witten, M.
1987-01-01
This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling
Mathematical Modelling Plant Signalling Networks
Muraro, D.
2013-01-01
During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.
Mathematical modeling of reciprocating pump
International Nuclear Information System (INIS)
Lee, Jong Kyeom; Jung, Jun Ki; Chai, Jang Bom; Lee, Jin Woo
2015-01-01
A new mathematical model is presented for the analysis and diagnosis of a high-pressure reciprocating pump system with three cylinders. The kinematic and hydrodynamic behaviors of the pump system are represented by the piston displacements, volume flow rates and pressures in its components, which are expressed as functions of the crankshaft angle. The flow interaction among the three cylinders, which was overlooked in the previous models, is considered in this model and its effect on the cylinder pressure profiles is investigated. The tuning parameters in the mathematical model are selected, and their values are adjusted to match the simulated and measured cylinder pressure profiles in each cylinder in a normal state. The damage parameter is selected in an abnormal state, and its value is adjusted to match the simulated and ensured pressure profiles under the condition of leakage in a valve. The value of the damage parameter over 300 cycles is calculated, and its probability density function is obtained for diagnosis and prognosis on the basis of the probabilistic feature of valve leakage.
Explorations in Elementary Mathematical Modeling
Directory of Open Access Journals (Sweden)
Mazen Shahin
2010-06-01
Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.
Developing consistent pronunciation models for phonemic variants
CSIR Research Space (South Africa)
Davel, M
2006-09-01
Full Text Available Pronunciation lexicons often contain pronunciation variants. This can create two problems: It can be difficult to define these variants in an internally consistent way and it can also be difficult to extract generalised grapheme-to-phoneme rule sets...
Reflexion and control mathematical models
Novikov, Dmitry A
2014-01-01
This book is dedicated to modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games that describe the gametheoretical interaction of agents making decisions based on a hierarchy of beliefs regarding (1) essential parameters (informational reflexion), (2) decision principles used by opponents (strategic reflexion), (3) beliefs about beliefs, and so on. Informational and reflexive equilibria in reflexive games generalize a series of well-known equilibrium concepts in noncooperative games and models of collective behavior. These models allow posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, in military applications, etc. (the interested reader will find in the book over 30 examples of possible applications in these fields) and describing uniformly many psychological/sociological phenomena connected with reflexion, viz., implicit control, informational control via the mass media, re...
Analytic Intermodel Consistent Modeling of Volumetric Human Lung Dynamics.
Ilegbusi, Olusegun; Seyfi, Behnaz; Neylon, John; Santhanam, Anand P
2015-10-01
Human lung undergoes breathing-induced deformation in the form of inhalation and exhalation. Modeling the dynamics is numerically complicated by the lack of information on lung elastic behavior and fluid-structure interactions between air and the tissue. A mathematical method is developed to integrate deformation results from a deformable image registration (DIR) and physics-based modeling approaches in order to represent consistent volumetric lung dynamics. The computational fluid dynamics (CFD) simulation assumes the lung is a poro-elastic medium with spatially distributed elastic property. Simulation is performed on a 3D lung geometry reconstructed from four-dimensional computed tomography (4DCT) dataset of a human subject. The heterogeneous Young's modulus (YM) is estimated from a linear elastic deformation model with the same lung geometry and 4D lung DIR. The deformation obtained from the CFD is then coupled with the displacement obtained from the 4D lung DIR by means of the Tikhonov regularization (TR) algorithm. The numerical results include 4DCT registration, CFD, and optimal displacement data which collectively provide consistent estimate of the volumetric lung dynamics. The fusion method is validated by comparing the optimal displacement with the results obtained from the 4DCT registration.
Mathematical models in biological discovery
Walter, Charles
1977-01-01
When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...
Mathematical models of viscous friction
Buttà, Paolo; Marchioro, Carlo
2015-01-01
In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...
Mathematical study of mixing models
International Nuclear Information System (INIS)
Lagoutiere, F.; Despres, B.
1999-01-01
This report presents the construction and the study of a class of models that describe the behavior of compressible and non-reactive Eulerian fluid mixtures. Mixture models can have two different applications. Either they are used to describe physical mixtures, in the case of a true zone of extensive mixing (but then this modelization is incomplete and must be considered only as a point of departure for the elaboration of models of mixtures actually relevant). Either they are used to solve the problem of the numerical mixture. This problem appears during the discretization of an interface which separates fluids having laws of different state: the zone of numerical mixing is the set of meshes which cover the interface. The attention is focused on numerical mixtures, for which the hypothesis of non-miscibility (physics) will bring two equations (the sixth and the eighth of the system). It is important to emphasize that even in the case of the only numerical mixture, the presence in one and same place (same mesh) of several fluids have to be taken into account. This will be formalized by the possibility for mass fractions to take all values between 0 and 1. This is not at odds with the equations that derive from the hypothesis of non-miscibility. One way of looking at things is to consider that there are two scales of observation: the physical scale at which one observes the separation of fluids, and the numerical scale, given by the fineness of the mesh, to which a mixture appears. In this work, mixtures are considered from the mathematical angle (both in the elaboration phase and during their study). In particular, Chapter 5 shows a result of model degeneration for a non-extended mixing zone (case of an interface): this justifies the use of models in the case of numerical mixing. All these models are based on the classical model of non-viscous compressible fluids recalled in Chapter 2. In Chapter 3, the central point of the elaboration of the class of models is
Consistent Alignment of World Embedding Models
2017-03-02
propose a solution that aligns variations of the same model (or different models) in a joint low-dimensional la- tent space leveraging carefully...representations of linguistic enti- ties, most often referred to as embeddings. This includes techniques that rely on matrix factoriza- tion (Levy & Goldberg ...higher, the variation is much higher as well. As we increase the size of the neighborhood, or improve the quality of our sample by only picking the most
Mathematical modeling courses for Media technology students
DEFF Research Database (Denmark)
Timcenko, Olga
2009-01-01
This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...
Specific Type of Knowledge Map: Mathematical Model
Milan, Houška; Martina, Beránková
2005-01-01
The article deals with relationships between mathematical models and knowledge maps. The goal of the article is to suggest how to use the mathematical model as a knowledge map and/or as a part (esp. the inference mechanism) of the knowledge system. The results are demonstrated on the case study, when the knowledge from a story is expressed by mathematical model. The model is used for both knowledge warehousing and inferencing new artificially derived knowledge.
Self-consistent modelling of ICRH
International Nuclear Information System (INIS)
Hellsten, T.; Hedin, J.; Johnson, T.; Laxaaback, M.; Tennfors, E.
2001-01-01
The performance of ICRH is often sensitive to the shape of the high energy part of the distribution functions of the resonating species. This requires self-consistent calculations of the distribution functions and the wave-field. In addition to the wave-particle interactions and Coulomb collisions the effects of the finite orbit width and the RF-induced spatial transport are found to be important. The inward drift dominates in general even for a symmetric toroidal wave spectrum in the centre of the plasma. An inward drift does not necessarily produce a more peaked heating profile. On the contrary, for low concentrations of hydrogen minority in deuterium plasmas it can even give rise to broader profiles. (author)
String consistency for unified model building
International Nuclear Information System (INIS)
Chaudhuri, S.; Chung, S.W.; Hockney, G.; Lykken, J.
1995-01-01
We explore the use of real fermionization as a test case for understanding how specific features of phenomenological interest in the low-energy effective superpotential are realized in exact solutions to heterotic superstring theory. We present pedagogic examples of models which realize SO(10) as a level two current algebra on the world-sheet, and discuss in general how higher level current algebras can be realized in the tensor product of simple constituent conformal field theories. We describe formal developments necessary to compute couplings in models built using real fermionization. This allows us to isolate cases of spin structures where the standard prescription for real fermionization may break down. (orig.)
REPFLO model evaluation, physical and numerical consistency
International Nuclear Information System (INIS)
Wilson, R.N.; Holland, D.H.
1978-11-01
This report contains a description of some suggested changes and an evaluation of the REPFLO computer code, which models ground-water flow and nuclear-waste migration in and about a nuclear-waste repository. The discussion contained in the main body of the report is supplemented by a flow chart, presented in the Appendix of this report. The suggested changes are of four kinds: (1) technical changes to make the code compatible with a wider variety of digital computer systems; (2) changes to fill gaps in the computer code, due to missing proprietary subroutines; (3) changes to (a) correct programming errors, (b) correct logical flaws, and (c) remove unnecessary complexity; and (4) changes in the computer code logical structure to make REPFLO a more viable model from the physical point of view
Mathematical modeling of drug dissolution.
Siepmann, J; Siepmann, F
2013-08-30
The dissolution of a drug administered in the solid state is a pre-requisite for efficient subsequent transport within the human body. This is because only dissolved drug molecules/ions/atoms are able to diffuse, e.g. through living tissue. Thus, generally major barriers, including the mucosa of the gastro intestinal tract, can only be crossed after dissolution. Consequently, the process of dissolution is of fundamental importance for the bioavailability and, hence, therapeutic efficacy of various pharmaco-treatments. Poor aqueous solubility and/or very low dissolution rates potentially lead to insufficient availability at the site of action and, hence, failure of the treatment in vivo, despite a potentially ideal chemical structure of the drug to interact with its target site. Different physical phenomena are involved in the process of drug dissolution in an aqueous body fluid, namely the wetting of the particle's surface, breakdown of solid state bonds, solvation, diffusion through the liquid unstirred boundary layer surrounding the particle as well as convection in the surrounding bulk fluid. Appropriate mathematical equations can be used to quantify these mass transport steps, and more or less complex theories can be developed to describe the resulting drug dissolution kinetics. This article gives an overview on the current state of the art of modeling drug dissolution and points out the assumptions the different theories are based on. Various practical examples are given in order to illustrate the benefits of such models. This review is not restricted to mathematical theories considering drugs exhibiting poor aqueous solubility and/or low dissolution rates, but also addresses models quantifying drug release from controlled release dosage forms, in which the process of drug dissolution plays a major role. Copyright © 2013 Elsevier B.V. All rights reserved.
Consistency test of the standard model
International Nuclear Information System (INIS)
Pawlowski, M.; Raczka, R.
1997-01-01
If the 'Higgs mass' is not the physical mass of a real particle but rather an effective ultraviolet cutoff then a process energy dependence of this cutoff must be admitted. Precision data from at least two energy scale experimental points are necessary to test this hypothesis. The first set of precision data is provided by the Z-boson peak experiments. We argue that the second set can be given by 10-20 GeV e + e - colliders. We pay attention to the special role of tau polarization experiments that can be sensitive to the 'Higgs mass' for a sample of ∼ 10 8 produced tau pairs. We argue that such a study may be regarded as a negative selfconsistency test of the Standard Model and of most of its extensions
Mathematical models for plant-herbivore interactions
Feng, Zhilan; DeAngelis, Donald L.
2017-01-01
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.
Surface EXAFS - A mathematical model
International Nuclear Information System (INIS)
Bateman, J.E.
2002-01-01
Extended X-ray absorption fine structure (EXAFS) studies are a powerful technique for studying the chemical environment of specific atoms in a molecular or solid matrix. The study of the surface layers of 'thick' materials introduces special problems due to the different escape depths of the various primary and secondary emission products which follow X-ray absorption. The processes are governed by the properties of the emitted fluorescent photons or electrons and of the material. Their interactions can easily destroy the linear relation between the detected signal and the absorption cross-section. Also affected are the probe depth within the surface and the background superimposed on the detected emission signal. A general mathematical model of the escape processes is developed which permits the optimisation of the detection modality (X-rays or electrons) and the experimental variables to suit the composition of any given surface under study
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
at the Technical University of Denmark. The data set includes face-to-face interaction (Bluetooth), communication (calls and texts), mobility (GPS), social network (Facebook), and general background information including a psychological profile (questionnaire). This thesis presents my work on the Social Fabric...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived....... Evidence is provided, which implies that the asymmetry is caused by a self-enhancement in the initiation dynamics. These results have implications for the formation of social networks and the dynamics of the links. It is shown that the Big Five Inventory (BFI) representing a psychological profile only...
Large scale Bayesian nuclear data evaluation with consistent model defects
International Nuclear Information System (INIS)
Schnabel, G
2015-01-01
Monte Carlo sampling schemes of available evaluation methods. The second improvement concerns Bayesian evaluation methods based on a certain simplification of the nuclear model. These methods were restricted to the consistent evaluation of tens of thousands of observables. In this thesis, a new evaluation scheme has been developed, which is mathematically equivalent to existing methods, but allows the consistent evaluation of dozens of millions of observables. The new scheme is suited for the implementation as a database application. The realization of such an application with public access can help to accelerate the production of reliable nuclear data sets. Furthermore, in combination with the novel treatment of model deficiencies, problems of the model and the experimental data can be tracked down without user interaction. This feature can foster the development of nuclear models with high predictive power. (author) [de
Leading Undergraduate Research Projects in Mathematical Modeling
Seshaiyer, Padmanabhan
2017-01-01
In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…
Scaffolding Mathematical Modelling with a Solution Plan
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
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…
Handayani, I.; Januar, R. L.; Purwanto, S. E.
2018-01-01
This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.
Students’ mathematical learning in modelling activities
DEFF Research Database (Denmark)
Kjeldsen, Tinne Hoff; Blomhøj, Morten
2013-01-01
Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts i...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....
Rival approaches to mathematical modelling in immunology
Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.
2007-08-01
In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.
Mathematical modeling of tornadoes and squall storms
Directory of Open Access Journals (Sweden)
Sergey A. Arsen’yev
2011-04-01
Full Text Available Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running perturbation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave (soliton; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.
MATHEMATICAL MODEL OF GRAIN MICRONIZATION
Directory of Open Access Journals (Sweden)
V. A. Afanas’ev
2014-01-01
Full Text Available Summary. During micronisation grain moisture evaporates mainly in decreasing drying rate period. Grain layer located on the surface of the conveyor micronisers will be regarded as horizontal plate. Due to the fact that the micronisation process the surface of the grain evaporates little moisture (within 2-7 % is assumed constant plate thickness. Because in the process of micronization grain structure is changing, in order to achieve an exact solution of the equations necessary to take into account changes thermophysical, optical and others. Equation of heat transfer is necessary to add a term that is responsible for the infrared heating. Because of the small thickness of the grain, neglecting the processes occurring at the edge of the grain, that is actually consider the problem of an infinite plate. To check the adequacy of the mathematical model of the process of micronisation of wheat grain moisture content must be comparable to the function of time, obtained by solving the system of equations with the measured experimental data of experience. Numerical solution of a system of equations for the period of decreasing drying rate is feasible with the help of the Maple 14, substituting the values of the constants in the system. Calculation of the average relative error does not exceed 7- 10 %, and shows a good agreement between the calculated data and the experimental values.
The prediction of epidemics through mathematical modeling.
Schaus, Catherine
2014-01-01
Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.
A mathematical model for iodine kinetics
International Nuclear Information System (INIS)
Silva, E.A.T. da.
1976-01-01
A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case [pt
Mathematical Modeling Applied to Maritime Security
Center for Homeland Defense and Security
2010-01-01
Center for Homeland Defense and Security, OUT OF THE CLASSROOM Download the paper: Layered Defense: Modeling Terrorist Transfer Threat Networks and Optimizing Network Risk Reduction” Students in Ted Lewis’ Critical Infrastructure Protection course are taught how mathematic modeling can provide...
Lowe, James; Carter, Merilyn; Cooper, Tom
2018-01-01
Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…
Identification of Chemical Reactor Plant’s Mathematical Model
Pyakullya, Boris Ivanovich; Kladiev, Sergey Nikolaevich
2015-01-01
This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.
Identification of Chemical Reactor Plant’s Mathematical Model
Directory of Open Access Journals (Sweden)
Pyakillya Boris
2015-01-01
Full Text Available This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.
A thermodynamically consistent model of shape-memory alloys
Czech Academy of Sciences Publication Activity Database
Benešová, Barbora
2011-01-01
Roč. 11, č. 1 (2011), s. 355-356 ISSN 1617-7061 R&D Projects: GA ČR GAP201/10/0357 Institutional research plan: CEZ:AV0Z20760514 Keywords : slape memory alloys * model based on relaxation * thermomechanic coupling Subject RIV: BA - General Mathematics http://onlinelibrary.wiley.com/doi/10.1002/pamm.201110169/abstract
Alkhateeb, Haitham M
2004-06-01
The Arabic translation of the Mathematics Teaching Efficacy Beliefs was completed by 144 undergraduate students (M age=20.6) in Jordan. The findings support the internal reliability of the Arabic translation of the Mathematics Teaching Efficacy Beliefs as well as its construct validity.
Mathematical models in biology bringing mathematics to life
Ferraro, Maria; Guarracino, Mario
2015-01-01
This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...
Mathematical 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.
Precipitation of metal sulphides using gaseous hydrogen sulphide: mathematical modelling
Al Tarazi, M.Y.M.; Heesink, Albertus B.M.; Versteeg, Geert
2004-01-01
A mathematical model has been developed that describes the precipitation of metal sulffides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use
Precipitation of metal sulphides using gaseous hydrogen sulphide : mathematical modelling
Tarazi, Mousa Al-; Heesink, A. Bert M.; Versteeg, Geert F.
2004-01-01
A mathematical model has been developed that describes the precipitation of metal sulphides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use
Mathematical modelling of scour: A review
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2007-01-01
A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...
Mathematical modeling a chemical engineer's perspective
Rutherford, Aris
1999-01-01
Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus
Mathematical modeling of a process the rolling delivery
Stepanov, Mikhail A.; Korolev, Andrey A.
2018-03-01
An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...
Mathematical Modelling of Intraretinal Oxygen Partial Pressure
African Journals Online (AJOL)
Erah
The system of non-linear differential equations was solved numerically using Runge-kutta. Nystroms method. ... artery occlusion. Keywords: Mathematical modeling, Intraretinal oxygen pressure, Retinal capillaries, Oxygen ..... Mass transfer,.
Cooking Potatoes: Experimentation and Mathematical Modeling.
Chen, Xiao Dong
2002-01-01
Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)
А mathematical model study of suspended monorail
Viktor GUTAREVYCH
2012-01-01
The mathematical model of suspended monorail track with allowance for elastic strain which occurs during movement of the monorail carriage was developed. Standard forms for single span and double span of suspended monorail sections were established.
А mathematical model study of suspended monorail
Directory of Open Access Journals (Sweden)
Viktor GUTAREVYCH
2012-01-01
Full Text Available The mathematical model of suspended monorail track with allowance for elastic strain which occurs during movement of the monorail carriage was developed. Standard forms for single span and double span of suspended monorail sections were established.
Mathematical Modeling of Circadian/Performance Countermeasures
National Aeronautics and Space Administration — We developed and refined our current mathematical model of circadian rhythms to incorporate melatonin as a marker rhythm. We used an existing physiologically based...
short communication mathematical modelling for magnetite
African Journals Online (AJOL)
Preferred Customer
The present research focuses to develop mathematical model for the ..... Staler, M.J. The Principle of Ion Exchange Technology, Butterworth-Heinemann: Boston; ... Don, W.G. Perry's Chemical Engineering Hand Book, 7th ed., McGraw-Hill:.
Mathematical Modeling Approaches in Plant Metabolomics.
Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas
2018-01-01
The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
2017-01-01
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
Modelling Mathematical Reasoning in Physics Education
Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche
2012-04-01
Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers
Thrasher, Emily Plunkett
2016-01-01
The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
Zbiek, Rose Mary; Conner, Annamarie
2006-01-01
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…
A mathematical model for postirradiation immunity
International Nuclear Information System (INIS)
Smirnova, O.A.
1988-01-01
A mathematical model of autoimmune processes in exposed mammals was developed. In terms of this model a study was made of the dependence of the autoimmunity kinetics on radiation dose and radiosensitivity of autologous tissues. The model simulates the experimentally observed dynamics of autoimmune diseases
Mathematical model of three winding auto transformer
International Nuclear Information System (INIS)
Volcko, V.; Eleschova, Z.; Belan, A.; Janiga, P.
2012-01-01
This article deals with the design of mathematical model of three-winding auto transformer for steady state analyses. The article is focused on model simplicity for the purposes of the use in complex transmission systems and authenticity of the model taking into account different types of step-voltage regulator. (Authors)
Mathematical Modelling of Intraretinal Oxygen Partial Pressure ...
African Journals Online (AJOL)
Purpose: The aim of our present work is to develop a simple steady state model for intraretinal oxygen partial pressure distribution and to investigate the effect of various model parameters on the partial pressure distribution under adapted conditions of light and darkness.. Method: A simple eight-layered mathematical model ...
Potential of mathematical modeling in fruit quality
African Journals Online (AJOL)
ONOS
2010-01-18
Jan 18, 2010 ... successful mathematical model, the modeler needs to chose what .... equations. In the SUCROS models, the rate of CO2 assimilation is .... insect ecology. ... García y García A, Ingram KT, Hatch U, Hoogenboom G, Jones JW,.
Edwin Musdi
2016-01-01
This research aims to develop a mathematics instructional model based realistic mathematics education (RME) to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characterist...
Mathematical models and accuracy of radioisotope gauges
International Nuclear Information System (INIS)
Urbanski, P.
1989-01-01
Mathematical expressions relating the variance and mean value of the intrinsic error with the parameters of one and multi-dimensional mathematical models of radioisotope gauges are given. Variance of the intrinsic error at the model's output is considered as a sum of the variances of the random error which is created in the first stages of the measuring chain and the random error of calibration procedure. The mean value of the intrinsic error (systematic error) appears always for nonlinear models. It was found that the optimal model of calibration procedure not always corresponds to the minimal value of the intrinsic error. The derived expressions are applied for the assessment of the mathematical models of some of the existing gauges (radioisotope belt weigher, XRF analyzer and coating thickness gauge). 7 refs., 5 figs., 1 tab. (author)
Mathematical model of glucose-insulin homeostasis in healthy rats.
Lombarte, Mercedes; Lupo, Maela; Campetelli, German; Basualdo, Marta; Rigalli, Alfredo
2013-10-01
According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat. Copyright © 2013 Elsevier Inc. All rights reserved.
Effectiveness of discovery learning model on mathematical problem solving
Herdiana, Yunita; Wahyudin, Sispiyati, Ririn
2017-08-01
This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.
Mathematical Models of Issue Voting
小林, 良彰
2009-01-01
1. Introduction2. An Examination of the Expected Utility Model3. An Examination of the Minimax Regret Model4. An Examination of the Diametros Model5. An Examination of the Revised Diametros Model6. An Examination of the Party Coalition Model7. The Construction and Examination of the Diametros ll Model8. Conclusion
An upper limb mathematical model of an oil palm harvester
Tumit, N. P.; Rambely, A. S.; BMT, Shamsul; Shahriman A., B.; Ng Y., G.; Deros, B. M.; Zailina, H.; Goh, Y. M.; Arumugam, Manohar; Ismail, I. A.; Abdul Hafiz A., R.
2014-09-01
The main purpose of this article is to develop a mathematical model of human body during harvesting via Kane's method. In this paper, a 2-D closed-kinematic biomechanical model that represents a harvesting movement is developed. The model of six segments consisted of upper right arm, right forearm, harvesting equipment, left forearm, upper left arm, and upper part of trunk. Finally, the inverse dynamic equations are represented in matrix form.
Mathematical modeling and optimization of complex structures
Repin, Sergey; Tuovinen, Tero
2016-01-01
This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include: * Computer simulation methods in mechanics, physics, and biology; * Variational problems and methods; minimiz...
Mathematical Models of Tuberculosis Reactivation and Relapse
Directory of Open Access Journals (Sweden)
Robert Steven Wallis
2016-05-01
Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Interfacial Fluid Mechanics A Mathematical Modeling Approach
Ajaev, Vladimir S
2012-01-01
Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail. Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also: Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...
Mathematical models and methods for planet Earth
Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta
2014-01-01
In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.
Mathematical modelling of two-phase flows
International Nuclear Information System (INIS)
Komen, E.M.J.; Stoop, P.M.
1992-11-01
A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs
Mathematical Modeling: Are Prior Experiences Important?
Czocher, Jennifer A.; Moss, Diana L.
2017-01-01
Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…
Uncertainty and Complexity in Mathematical Modeling
Cannon, Susan O.; Sanders, Mark
2017-01-01
Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…
A mathematical model of embodied consciousness
Rudrauf, D.; Bennequin, D.; Granic, I.; Landini, G.; Friston, K.; Williford, K.
2017-01-01
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM
Mathematical model of the reactor coolant pump
International Nuclear Information System (INIS)
Kozuh, M.
1989-01-01
The mathematical model of reactor coolant pump is described in this paper. It is based on correlations for centrifugal reactor coolant pumps. This code is one of the elements needed for the simulation of the whole NPP primary system. In subroutine developed according to this model we tried in every possible detail to incorporate plant specific data for Krsko NPP. (author)
A mathematical model of forgetting and amnesia
Murre, J.M.J.; Chessa, A.G.; Meeter, M.
2013-01-01
We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models
A mathematical model of brain glucose homeostasis
Directory of Open Access Journals (Sweden)
Kimura Hidenori
2009-11-01
Full Text Available Abstract Background The physiological fact that a stable level of brain glucose is more important than that of blood glucose suggests that the ultimate goal of the glucose-insulin-glucagon (GIG regulatory system may be homeostasis of glucose concentration in the brain rather than in the circulation. Methods In order to demonstrate the relationship between brain glucose homeostasis and blood hyperglycemia in diabetes, a brain-oriented mathematical model was developed by considering the brain as the controlled object while the remaining body as the actuator. After approximating the body compartmentally, the concentration dynamics of glucose, as well as those of insulin and glucagon, are described in each compartment. The brain-endocrine crosstalk, which regulates blood glucose level for brain glucose homeostasis together with the peripheral interactions among glucose, insulin and glucagon, is modeled as a proportional feedback control of brain glucose. Correlated to the brain, long-term effects of psychological stress and effects of blood-brain-barrier (BBB adaptation to dysglycemia on the generation of hyperglycemia are also taken into account in the model. Results It is shown that simulation profiles obtained from the model are qualitatively or partially quantitatively consistent with clinical data, concerning the GIG regulatory system responses to bolus glucose, stepwise and continuous glucose infusion. Simulations also revealed that both stress and BBB adaptation contribute to the generation of hyperglycemia. Conclusion Simulations of the model of a healthy person under long-term severe stress demonstrated that feedback control of brain glucose concentration results in elevation of blood glucose level. In this paper, we try to suggest that hyperglycemia in diabetes may be a normal outcome of brain glucose homeostasis.
High-performance speech recognition using consistency modeling
Digalakis, Vassilios; Murveit, Hy; Monaco, Peter; Neumeyer, Leo; Sankar, Ananth
1994-12-01
The goal of SRI's consistency modeling project is to improve the raw acoustic modeling component of SRI's DECIPHER speech recognition system and develop consistency modeling technology. Consistency modeling aims to reduce the number of improper independence assumptions used in traditional speech recognition algorithms so that the resulting speech recognition hypotheses are more self-consistent and, therefore, more accurate. At the initial stages of this effort, SRI focused on developing the appropriate base technologies for consistency modeling. We first developed the Progressive Search technology that allowed us to perform large-vocabulary continuous speech recognition (LVCSR) experiments. Since its conception and development at SRI, this technique has been adopted by most laboratories, including other ARPA contracting sites, doing research on LVSR. Another goal of the consistency modeling project is to attack difficult modeling problems, when there is a mismatch between the training and testing phases. Such mismatches may include outlier speakers, different microphones and additive noise. We were able to either develop new, or transfer and evaluate existing, technologies that adapted our baseline genonic HMM recognizer to such difficult conditions.
Mathematical models of information and stochastic systems
Kornreich, Philipp
2008-01-01
From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t
On the mathematical modeling of memristors
Radwan, Ahmed G.
2012-10-06
Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.
Dynamics of mathematical models in biology bringing mathematics to life
Zazzu, Valeria; Guarracino, Mario
2016-01-01
This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...
FEMME, a flexible environment for mathematically modelling the environment
Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.
2002-01-01
A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model
Mathematical Modelling of Unmanned Aerial Vehicles
Directory of Open Access Journals (Sweden)
Saeed Sarwar
2013-04-01
Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV
Mathematical modelling of unmanned aerial vehicles
International Nuclear Information System (INIS)
Sarwar, S.; Rehman, S.U.
2013-01-01
UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)
Mathematical model for spreading dynamics of social network worms
International Nuclear Information System (INIS)
Sun, Xin; Liu, Yan-Heng; Han, Jia-Wei; Liu, Xue-Jie; Li, Bin; Li, Jin
2012-01-01
In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks
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 ...
Use of mathematical modeling in nuclear measurements projects
International Nuclear Information System (INIS)
Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.
2011-01-01
Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)
A consistent modelling methodology for secondary settling tanks in wastewater treatment.
Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar
2011-03-01
The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.
Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling
Karali, Diren; Durmus, Soner
2015-01-01
The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…
Mathematical modelling a case studies approach
Illner, Reinhard; McCollum, Samantha; Roode, Thea van
2004-01-01
Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; oth...
Mathematical model of compact type evaporator
Borovička, Martin; Hyhlík, Tomáš
2018-06-01
In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.
The (Mathematical) Modeling Process in Biosciences.
Torres, Nestor V; Santos, Guido
2015-01-01
In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.
On the mathematical modeling of aeolian saltation
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Sørensen, Michael
1983-01-01
The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...... on aeolian saltation. This comparison points out the necessity of discriminating between pure and real saltation. -Authors...
Mathematical Modeling Projects: Success for All Students
Shelton, Therese
2018-01-01
Mathematical modeling allows flexibility for a project-based experience. We share details of our regular capstone course, successful for virtually 100% of our math majors for almost two decades. Our research-like approach in this course accommodates a variety of student backgrounds and interests, and has produced some award-winning student…
ECONOMIC AND MATHEMATICAL MODELING INNOVATION SYSTEMS
Directory of Open Access Journals (Sweden)
D.V. Makarov
2014-06-01
Full Text Available The paper presents one of the mathematical tools for modeling innovation processes. With the help of Kondratieff long waves can define innovation cycles. However, complexity of the innovation system implies a qualitative description. The article describes the problems of this area of research.
Mathematical modeling of optical glazing performance
Nijnatten, van P.A.; Wittwer, V.; Granqvist, C.G.; Lampert, C.M.
1994-01-01
Mathematical modelling can be a powerful tool in the design and optimalization of glazing. By calculation, the specifications of a glazing design and the optimal design parameters can be predicted without building costly prototypes first. Furthermore, properties which are difficult to measure, like
Description of a comprehensive mathematical model
DEFF Research Database (Denmark)
Li, Xiyan; Yin, Chungen
2017-01-01
Biomass gasification is still a promising technology after over 30 years’ research and development and has success only in a few niche markets. In this paper, a comprehensive mathematical model for biomass particle gasification is developed within a generic particle framework, assuming the feed...
Introduction to mathematical models and methods
Energy Technology Data Exchange (ETDEWEB)
Siddiqi, A. H.; Manchanda, P. [Gautam Budha University, Gautam Budh Nagar-201310 (India); Department of Mathematics, Guru Nanak Dev University, Amritsar (India)
2012-07-17
Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.
Standard Model Vacuum Stability and Weyl Consistency Conditions
DEFF Research Database (Denmark)
Antipin, Oleg; Gillioz, Marc; Krog, Jens
2013-01-01
At high energy the standard model possesses conformal symmetry at the classical level. This is reflected at the quantum level by relations between the different beta functions of the model. These relations are known as the Weyl consistency conditions. We show that it is possible to satisfy them...... order by order in perturbation theory, provided that a suitable coupling constant counting scheme is used. As a direct phenomenological application, we study the stability of the standard model vacuum at high energies and compare with previous computations violating the Weyl consistency conditions....
Consistency and Reconciliation Model In Regional Development Planning
Directory of Open Access Journals (Sweden)
Dina Suryawati
2016-10-01
Full Text Available The aim of this study was to identify the problems and determine the conceptual model of regional development planning. Regional development planning is a systemic, complex and unstructured process. Therefore, this study used soft systems methodology to outline unstructured issues with a structured approach. The conceptual models that were successfully constructed in this study are a model of consistency and a model of reconciliation. Regional development planning is a process that is well-integrated with central planning and inter-regional planning documents. Integration and consistency of regional planning documents are very important in order to achieve the development goals that have been set. On the other hand, the process of development planning in the region involves technocratic system, that is, both top-down and bottom-up system of participation. Both must be balanced, do not overlap and do not dominate each other. regional, development, planning, consistency, reconciliation
Mathematical modeling models, analysis and applications
Banerjee, Sandip
2014-01-01
""…the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. … it may be well used as a valuable source of interesting examples as well as complementary reading in a number of courses.""-Svitlana P. Rogovchenko, Zentralblatt MATH 1298
Mathematical Modeling of Loop Heat Pipes
Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.
1998-01-01
The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.
Optimization and mathematical modeling in computer architecture
Sankaralingam, Karu; Nowatzki, Tony
2013-01-01
In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t
Modeling life the mathematics of biological systems
Garfinkel, Alan; Guo, Yina
2017-01-01
From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)
1996-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
Mathematical modeling of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H Y; Perez-Tello, M; Riihilahti, K M [Utah Univ., Salt Lake City, UT (United States)
1997-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
Mathematical modelling of fracture hydrology
International Nuclear Information System (INIS)
Rae, J.; Hodgkinson, D.P.; Robinson, P.C.; Herbert, A.W.
1984-04-01
This progress report contains notes on three aspects of hydrological modelling. Work on hydrodynamic dispersion in fractured media has been extended to transverse dispersion. Further work has been done on diffusion into the rock matrix and its effect on solute transport. The program NAMSOL has been used for the MIRAGE code comparison exercise being organised by Atkins R and D. (author)
Modeling a Consistent Behavior of PLC-Sensors
Directory of Open Access Journals (Sweden)
E. V. Kuzmin
2014-01-01
Full Text Available The article extends the cycle of papers dedicated to programming and verificatoin of PLC-programs by LTL-specification. This approach provides the availability of correctness analysis of PLC-programs by the model checking method.The model checking method needs to construct a finite model of a PLC program. For successful verification of required properties it is important to take into consideration that not all combinations of input signals from the sensors can occur while PLC works with a control object. This fact requires more advertence to the construction of the PLC-program model.In this paper we propose to describe a consistent behavior of sensors by three groups of LTL-formulas. They will affect the program model, approximating it to the actual behavior of the PLC program. The idea of LTL-requirements is shown by an example.A PLC program is a description of reactions on input signals from sensors, switches and buttons. In constructing a PLC-program model, the approach to modeling a consistent behavior of PLC sensors allows to focus on modeling precisely these reactions without an extension of the program model by additional structures for realization of a realistic behavior of sensors. The consistent behavior of sensors is taken into account only at the stage of checking a conformity of the programming model to required properties, i. e. a property satisfaction proof for the constructed model occurs with the condition that the model contains only such executions of the program that comply with the consistent behavior of sensors.
Mathematical Models of Breast and Ovarian Cancers
Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron
2016-01-01
Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061
MATHEMATICAL MODEL FOR RIVERBOAT DYNAMICS
Directory of Open Access Journals (Sweden)
Aleksander Grm
2017-01-01
Full Text Available Present work describes a simple dynamical model for riverboat motion based on the square drag law. Air and water interactions with the boat are determined from aerodynamic coefficients. CFX simulations were performed with fully developed turbulent flow to determine boat aerodynamic coefficients for an arbitrary angle of attack for the air and water portions separately. The effect of wave resistance is negligible compared to other forces. Boat movement analysis considers only two-dimensional motion, therefore only six aerodynamics coefficients are required. The proposed model is solved and used to determine the critical environmental parameters (wind and current under which river navigation can be conducted safely. Boat simulator was tested in a single area on the Ljubljanica river and estimated critical wind velocity.
Mathematical modelling of flooding at Magela Creek
International Nuclear Information System (INIS)
Vardavas, I.
1989-01-01
The extent and frequency of the flooding at Magela Creek can be predicted from a mathematical/computer model describing the hydrological phases of surface runoff. Surface runoff involves complex water transfer processes over very inhomogeneous terrain. A simple mathematical model of these has been developed which includes the interception of rainfall by the plant canopy, evapotranspiration, infiltration of surface water into the soil, the storage of water in surface depressions, and overland and subsurface water flow. The rainfall-runoff model has then been incorporated into a more complex computer model to predict the amount of water that enters and leaves the Magela Creek flood plain, downstream of the mine. 2 figs., ills
Structured Mathematical Modeling of Industrial Boiler
Directory of Open Access Journals (Sweden)
Abdullah Nur Aziz
2014-04-01
Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.
Diagnosing a Strong-Fault Model by Conflict and Consistency.
Zhang, Wenfeng; Zhao, Qi; Zhao, Hongbo; Zhou, Gan; Feng, Wenquan
2018-03-29
The diagnosis method for a weak-fault model with only normal behaviors of each component has evolved over decades. However, many systems now demand a strong-fault models, the fault modes of which have specific behaviors as well. It is difficult to diagnose a strong-fault model due to its non-monotonicity. Currently, diagnosis methods usually employ conflicts to isolate possible fault and the process can be expedited when some observed output is consistent with the model's prediction where the consistency indicates probably normal components. This paper solves the problem of efficiently diagnosing a strong-fault model by proposing a novel Logic-based Truth Maintenance System (LTMS) with two search approaches based on conflict and consistency. At the beginning, the original a strong-fault model is encoded by Boolean variables and converted into Conjunctive Normal Form (CNF). Then the proposed LTMS is employed to reason over CNF and find multiple minimal conflicts and maximal consistencies when there exists fault. The search approaches offer the best candidate efficiency based on the reasoning result until the diagnosis results are obtained. The completeness, coverage, correctness and complexity of the proposals are analyzed theoretically to show their strength and weakness. Finally, the proposed approaches are demonstrated by applying them to a real-world domain-the heat control unit of a spacecraft-where the proposed methods are significantly better than best first and conflict directly with A* search methods.
Consistent Partial Least Squares Path Modeling via Regularization.
Jung, Sunho; Park, JaeHong
2018-01-01
Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.
Structured Mathematical Modeling of Industrial Boiler
Aziz, Abdullah Nur; Nazaruddin, Yul Yunazwin; Siregar, Parsaulian; Bindar, Yazid
2014-01-01
As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. T...
Mathematical modelling of the decomposition of explosives
International Nuclear Information System (INIS)
Smirnov, Lev P
2010-01-01
Studies on mathematical modelling of the molecular and supramolecular structures of explosives and the elementary steps and overall processes of their decomposition are analyzed. Investigations on the modelling of combustion and detonation taking into account the decomposition of explosives are also considered. It is shown that solution of problems related to the decomposition kinetics of explosives requires the use of a complex strategy based on the methods and concepts of chemical physics, solid state physics and theoretical chemistry instead of empirical approach.
Models and structures: mathematical physics
International Nuclear Information System (INIS)
2003-01-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems
Geboy, Nicholas J.; Engle, Mark A.; Hower, James C.
2013-01-01
Several standard methods require coal to be ashed prior to geochemical analysis. Researchers, however, are commonly interested in the compositional nature of the whole-coal, not its ash. Coal geochemical data for any given sample can, therefore, be reported in the ash basis on which it is analyzed or the whole-coal basis to which the ash basis data are back calculated. Basic univariate (mean, variance, distribution, etc.) and bivariate (correlation coefficients, etc.) measures of the same suite of samples can be very different depending which reporting basis the researcher uses. These differences are not real, but an artifact resulting from the compositional nature of most geochemical data. The technical term for this artifact is subcompositional incoherence. Since compositional data are forced to a constant sum, such as 100% or 1,000,000 ppm, they possess curvilinear properties which make the Euclidean principles on which most statistical tests rely inappropriate, leading to erroneous results. Applying the isometric logratio (ilr) transformation to compositional data allows them to be represented in Euclidean space and evaluated using traditional tests without fear of producing mathematically inconsistent results. When applied to coal geochemical data, the issues related to differences between the two reporting bases are resolved as demonstrated in this paper using major oxide and trace metal data from the Pennsylvanian-age Pond Creek coal of eastern Kentucky, USA. Following ilr transformation, univariate statistics, such as mean and variance, still differ between the ash basis and whole-coal basis, but in predictable and calculated manners. Further, the stability between two different components, a bivariate measure, is identical, regardless of the reporting basis. The application of ilr transformations addresses both the erroneous results of Euclidean-based measurements on compositional data as well as the inconsistencies observed on coal geochemical data
Consistent partnership formation: application to a sexually transmitted disease model.
Artzrouni, Marc; Deuchert, Eva
2012-02-01
We apply a consistent sexual partnership formation model which hinges on the assumption that one gender's choices drives the process (male or female dominant model). The other gender's behavior is imputed. The model is fitted to UK sexual behavior data and applied to a simple incidence model of HSV-2. With a male dominant model (which assumes accurate male reports on numbers of partners) the modeled incidences of HSV-2 are 77% higher for men and 50% higher for women than with a female dominant model (which assumes accurate female reports). Although highly stylized, our simple incidence model sheds light on the inconsistent results one can obtain with misreported data on sexual activity and age preferences. Copyright © 2011 Elsevier Inc. All rights reserved.
Diagnosing a Strong-Fault Model by Conflict and Consistency
Directory of Open Access Journals (Sweden)
Wenfeng Zhang
2018-03-01
Full Text Available The diagnosis method for a weak-fault model with only normal behaviors of each component has evolved over decades. However, many systems now demand a strong-fault models, the fault modes of which have specific behaviors as well. It is difficult to diagnose a strong-fault model due to its non-monotonicity. Currently, diagnosis methods usually employ conflicts to isolate possible fault and the process can be expedited when some observed output is consistent with the model’s prediction where the consistency indicates probably normal components. This paper solves the problem of efficiently diagnosing a strong-fault model by proposing a novel Logic-based Truth Maintenance System (LTMS with two search approaches based on conflict and consistency. At the beginning, the original a strong-fault model is encoded by Boolean variables and converted into Conjunctive Normal Form (CNF. Then the proposed LTMS is employed to reason over CNF and find multiple minimal conflicts and maximal consistencies when there exists fault. The search approaches offer the best candidate efficiency based on the reasoning result until the diagnosis results are obtained. The completeness, coverage, correctness and complexity of the proposals are analyzed theoretically to show their strength and weakness. Finally, the proposed approaches are demonstrated by applying them to a real-world domain—the heat control unit of a spacecraft—where the proposed methods are significantly better than best first and conflict directly with A* search methods.
Mathematical modelling of tissue formation in chondrocyte filter cultures.
Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J
2011-12-17
In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.
mathematical modelling of atmospheric dispersion of pollutants
International Nuclear Information System (INIS)
Mohamed, M.E.
2002-01-01
the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established
Mathematical models of natural gas consumption
International Nuclear Information System (INIS)
Sabo, Kristian; Scitovski, Rudolf; Vazler, Ivan; Zekic-Susac, Marijana
2011-01-01
In this paper we consider the problem of natural gas consumption hourly forecast on the basis of hourly movement of temperature and natural gas consumption in the preceding period. There are various methods and approaches for solving this problem in the literature. Some mathematical models with linear and nonlinear model functions relating to natural gas consumption forecast with the past natural gas consumption data, temperature data and temperature forecast data are mentioned. The methods are tested on concrete examples referring to temperature and natural gas consumption for the area of the city of Osijek (Croatia) from the beginning of the year 2008. The results show that most acceptable forecast is provided by mathematical models in which natural gas consumption and temperature are related explicitly.
Electrorheological fluids modeling and mathematical theory
Růžička, Michael
2000-01-01
This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.
Consistent Conformal Extensions of the Standard Model arXiv
Loebbert, Florian; Plefka, Jan
The question of whether classically conformal modifications of the standard model are consistent with experimental obervations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework for the study of the effective potential of the resulting multi-scalar standard model extensions. This approach relies on the assumption of the ordinary loop hierarchy $\\lambda_\\text{s} \\sim g^2_\\text{g}$ of scalar and gauge couplings. On the other hand, Andreassen, Frost and Schwartz recently argued that in the (single-scalar) standard model, gauge invariant results require the consistent scaling $\\lambda_\\text{s} \\sim g^4_\\text{g}$. In the present paper we contrast these two hierarchy assumptions and illustrate the differences in the phenomenological predictions of minimal conformal extensions of the standard model.
The Conceptualization of the Mathematical Modelling Process in Technology-Aided Environment
Hidiroglu, Çaglar Naci; Güzel, Esra Bukova
2017-01-01
The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…
Final Report Fermionic Symmetries and Self consistent Shell Model
International Nuclear Information System (INIS)
Zamick, Larry
2008-01-01
In this final report in the field of theoretical nuclear physics we note important accomplishments.We were confronted with 'anomoulous' magnetic moments by the experimetalists and were able to expain them. We found unexpected partial dynamical symmetries--completely unknown before, and were able to a large extent to expain them. The importance of a self consistent shell model was emphasized.
CONSISTENCY UNDER SAMPLING OF EXPONENTIAL RANDOM GRAPH MODELS.
Shalizi, Cosma Rohilla; Rinaldo, Alessandro
2013-04-01
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the data consists only of a sampled sub-network. Parameters for the whole network, which is what is of interest, are estimated by applying the model to the sub-network. This assumes that the model is consistent under sampling , or, in terms of the theory of stochastic processes, that it defines a projective family. Focusing on the popular class of exponential random graph models (ERGMs), we show that this apparently trivial condition is in fact violated by many popular and scientifically appealing models, and that satisfying it drastically limits ERGM's expressive power. These results are actually special cases of more general results about exponential families of dependent random variables, which we also prove. Using such results, we offer easily checked conditions for the consistency of maximum likelihood estimation in ERGMs, and discuss some possible constructive responses.
Сontrol systems using mathematical models of technological objects ...
African Journals Online (AJOL)
Сontrol systems using mathematical models of technological objects in the control loop. ... Journal of Fundamental and Applied Sciences ... Such mathematical models make it possible to specify the optimal operating modes of the considered ...
Building Mathematical Models of Simple Harmonic and Damped Motion.
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
Vibratory gyroscopes : identification of mathematical model from test data
CSIR Research Space (South Africa)
Shatalov, MY
2007-05-01
Full Text Available Simple mathematical model of vibratory gyroscopes imperfections is formulated, which includes anisotropic damping and variation of mass-stiffness parameters and their harmonics. The method of identification of parameters of the mathematical model...
Mathematical Modelling of Surfactant Self-assembly at Interfaces
Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.
2015-01-01
© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary
Self-consistent mean-field models for nuclear structure
International Nuclear Information System (INIS)
Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard
2003-01-01
The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications
Detection and quantification of flow consistency in business process models
DEFF Research Database (Denmark)
Burattin, Andrea; Bernstein, Vered; Neurauter, Manuel
2017-01-01
, to show how such features can be quantified into computational metrics, which are applicable to business process models. We focus on one particular feature, consistency of flow direction, and show the challenges that arise when transforming it into a precise metric. We propose three different metrics......Business process models abstract complex business processes by representing them as graphical models. Their layout, as determined by the modeler, may have an effect when these models are used. However, this effect is currently not fully understood. In order to systematically study this effect......, a basic set of measurable key visual features is proposed, depicting the layout properties that are meaningful to the human user. The aim of this research is thus twofold: first, to empirically identify key visual features of business process models which are perceived as meaningful to the user and second...
A consistent transported PDF model for treating differential molecular diffusion
Wang, Haifeng; Zhang, Pei
2016-11-01
Differential molecular diffusion is a fundamentally significant phenomenon in all multi-component turbulent reacting or non-reacting flows caused by the different rates of molecular diffusion of energy and species concentrations. In the transported probability density function (PDF) method, the differential molecular diffusion can be treated by using a mean drift model developed by McDermott and Pope. This model correctly accounts for the differential molecular diffusion in the scalar mean transport and yields a correct DNS limit of the scalar variance production. The model, however, misses the molecular diffusion term in the scalar variance transport equation, which yields an inconsistent prediction of the scalar variance in the transported PDF method. In this work, a new model is introduced to remedy this problem that can yield a consistent scalar variance prediction. The model formulation along with its numerical implementation is discussed, and the model validation is conducted in a turbulent mixing layer problem.
Consistency checks in beam emission modeling for neutral beam injectors
International Nuclear Information System (INIS)
Punyapu, Bharathi; Vattipalle, Prahlad; Sharma, Sanjeev Kumar; Baruah, Ujjwal Kumar; Crowley, Brendan
2015-01-01
In positive neutral beam systems, the beam parameters such as ion species fractions, power fractions and beam divergence are routinely measured using Doppler shifted beam emission spectrum. The accuracy with which these parameters are estimated depend on the accuracy of the atomic modeling involved in these estimations. In this work, an effective procedure to check the consistency of the beam emission modeling in neutral beam injectors is proposed. As a first consistency check, at a constant beam voltage and current, the intensity of the beam emission spectrum is measured by varying the pressure in the neutralizer. Then, the scaling of measured intensity of un-shifted (target) and Doppler shifted intensities (projectile) of the beam emission spectrum at these pressure values are studied. If the un-shifted component scales with pressure, then the intensity of this component will be used as a second consistency check on the beam emission modeling. As a further check, the modeled beam fractions and emission cross sections of projectile and target are used to predict the intensity of the un-shifted component and then compared with the value of measured target intensity. An agreement between the predicted and measured target intensities provide the degree of discrepancy in the beam emission modeling. In order to test this methodology, a systematic analysis of Doppler shift spectroscopy data obtained on the JET neutral beam test stand data was carried out
Simplified models for dark matter face their consistent completions
Energy Technology Data Exchange (ETDEWEB)
Gonçalves, Dorival; Machado, Pedro A. N.; No, Jose Miguel
2017-03-01
Simplified dark matter models have been recently advocated as a powerful tool to exploit the complementarity between dark matter direct detection, indirect detection and LHC experimental probes. Focusing on pseudoscalar mediators between the dark and visible sectors, we show that the simplified dark matter model phenomenology departs significantly from that of consistent ${SU(2)_{\\mathrm{L}} \\times U(1)_{\\mathrm{Y}}}$ gauge invariant completions. We discuss the key physics simplified models fail to capture, and its impact on LHC searches. Notably, we show that resonant mono-Z searches provide competitive sensitivities to standard mono-jet analyses at $13$ TeV LHC.
SOME TRENDS IN MATHEMATICAL MODELING FOR BIOTECHNOLOGY
Directory of Open Access Journals (Sweden)
O. M. Klyuchko
2018-02-01
Full Text Available The purpose of present research is to demonstrate some trends of development of modeling methods for biotechnology according to contemporary achievements in science and technique. At the beginning the general approaches are outlined, some types of classifications of modeling methods are observed. The role of mathematic methods modeling for biotechnology in present époque of information computer technologies intensive development is studied and appropriate scheme of interrelation of all these spheres is proposed. Further case studies are suggested: some mathematic models in three different spaces (1D, 2D, 3D models are described for processes in living objects of different levels of hierarchic organization. In course of this the main attention was paid to some processes modeling in neurons as well as in their aggregates of different forms, including glioma cell masses (1D, 2D, 3D brain processes models. Starting from the models that have only theoretical importance for today, we describe at the end a model which application may be important for the practice. The work was done after the analysis of approximately 250 current publications in fields of biotechnology, including the authors’ original works.
Mathematical models for photovoltaic solar panel simulation
Energy Technology Data Exchange (ETDEWEB)
Santos, Jose Airton A. dos; Gnoatto, Estor; Fischborn, Marcos; Kavanagh, Edward [Universidade Tecnologica Federal do Parana (UTFPR), Medianeira, PR (Brazil)], Emails: airton@utfpr.edu.br, gnoatto@utfpr.edu.br, fisch@utfpr.edu.br, kavanagh@utfpr.edu.br
2008-07-01
A photovoltaic generator is subject to several variations of solar intensity, ambient temperature or load, that change your point of operation. This way, your behavior should be analyzed by such alterations, to optimize your operation. The present work sought to simulate a photovoltaic generator, of polycrystalline silicon, by characteristics supplied by the manufacturer, and to compare the results of two mathematical models with obtained values of field, in the city of Cascavel, for a period of one year. (author)
Nonconvex Model of Material Growth: Mathematical Theory
Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.
2018-06-01
The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.
Consistency of the tachyon warm inflationary universe models
International Nuclear Information System (INIS)
Zhang, Xiao-Min; Zhu, Jian-Yang
2014-01-01
This study concerns the consistency of the tachyon warm inflationary models. A linear stability analysis is performed to find the slow-roll conditions, characterized by the potential slow-roll (PSR) parameters, for the existence of a tachyon warm inflationary attractor in the system. The PSR parameters in the tachyon warm inflationary models are redefined. Two cases, an exponential potential and an inverse power-law potential, are studied, when the dissipative coefficient Γ = Γ 0 and Γ = Γ(φ), respectively. A crucial condition is obtained for a tachyon warm inflationary model characterized by the Hubble slow-roll (HSR) parameter ε H , and the condition is extendable to some other inflationary models as well. A proper number of e-folds is obtained in both cases of the tachyon warm inflation, in contrast to existing works. It is also found that a constant dissipative coefficient (Γ = Γ 0 ) is usually not a suitable assumption for a warm inflationary model
The many faces of the mathematical modeling cycle
Perrenet, J.C.; Zwaneveld, B.
2012-01-01
In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been
Simple mathematical models of symmetry breaking. Application to particle physics
International Nuclear Information System (INIS)
Michel, L.
1976-01-01
Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)
Modeling self-consistent multi-class dynamic traffic flow
Cho, Hsun-Jung; Lo, Shih-Ching
2002-09-01
In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.
Detection and quantification of flow consistency in business process models.
Burattin, Andrea; Bernstein, Vered; Neurauter, Manuel; Soffer, Pnina; Weber, Barbara
2018-01-01
Business process models abstract complex business processes by representing them as graphical models. Their layout, as determined by the modeler, may have an effect when these models are used. However, this effect is currently not fully understood. In order to systematically study this effect, a basic set of measurable key visual features is proposed, depicting the layout properties that are meaningful to the human user. The aim of this research is thus twofold: first, to empirically identify key visual features of business process models which are perceived as meaningful to the user and second, to show how such features can be quantified into computational metrics, which are applicable to business process models. We focus on one particular feature, consistency of flow direction, and show the challenges that arise when transforming it into a precise metric. We propose three different metrics addressing these challenges, each following a different view of flow consistency. We then report the results of an empirical evaluation, which indicates which metric is more effective in predicting the human perception of this feature. Moreover, two other automatic evaluations describing the performance and the computational capabilities of our metrics are reported as well.
Consistency Across Standards or Standards in a New Business Model
Russo, Dane M.
2010-01-01
Presentation topics include: standards in a changing business model, the new National Space Policy is driving change, a new paradigm for human spaceflight, consistency across standards, the purpose of standards, danger of over-prescriptive standards, a balance is needed (between prescriptive and general standards), enabling versus inhibiting, characteristics of success-oriented standards, characteristics of success-oriented standards, and conclusions. Additional slides include NASA Procedural Requirements 8705.2B identifies human rating standards and requirements, draft health and medical standards for human rating, what's been done, government oversight models, examples of consistency from anthropometry, examples of inconsistency from air quality and appendices of government and non-governmental human factors standards.
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.
Self-consistent approach for neutral community models with speciation
Haegeman, Bart; Etienne, Rampal S.
2010-03-01
Hubbell’s neutral model provides a rich theoretical framework to study ecological communities. By incorporating both ecological and evolutionary time scales, it allows us to investigate how communities are shaped by speciation processes. The speciation model in the basic neutral model is particularly simple, describing speciation as a point-mutation event in a birth of a single individual. The stationary species abundance distribution of the basic model, which can be solved exactly, fits empirical data of distributions of species’ abundances surprisingly well. More realistic speciation models have been proposed such as the random-fission model in which new species appear by splitting up existing species. However, no analytical solution is available for these models, impeding quantitative comparison with data. Here, we present a self-consistent approximation method for neutral community models with various speciation modes, including random fission. We derive explicit formulas for the stationary species abundance distribution, which agree very well with simulations. We expect that our approximation method will be useful to study other speciation processes in neutral community models as well.
Consistent Partial Least Squares Path Modeling via Regularization
Directory of Open Access Journals (Sweden)
Sunho Jung
2018-02-01
Full Text Available Partial least squares (PLS path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc, designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.
A Consistent Pricing Model for Index Options and Volatility Derivatives
DEFF Research Database (Denmark)
Kokholm, Thomas
to be priced consistently, while allowing for jumps in volatility and returns. An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for volatility derivatives, such as VIX options, as well as efficient numerical methods for pricing of European options...... on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across...
A Consistent Pricing Model for Index Options and Volatility Derivatives
DEFF Research Database (Denmark)
Cont, Rama; Kokholm, Thomas
2013-01-01
to be priced consistently, while allowing for jumps in volatility and returns. An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for volatility derivatives, such as VIX options, as well as efficient numerical methods for pricing of European options...... on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across...
Spectrally-consistent regularization modeling of turbulent natural convection flows
International Nuclear Information System (INIS)
Trias, F Xavier; Gorobets, Andrey; Oliva, Assensi; Verstappen, Roel
2012-01-01
The incompressible Navier-Stokes equations constitute an excellent mathematical modelization of turbulence. Unfortunately, attempts at performing direct simulations are limited to relatively low-Reynolds numbers because of the almost numberless small scales produced by the non-linear convective term. Alternatively, a dynamically less complex formulation is proposed here. Namely, regularizations of the Navier-Stokes equations that preserve the symmetry and conservation properties exactly. To do so, both convective and diffusive terms are altered in the same vein. In this way, the convective production of small scales is effectively restrained whereas the modified diffusive term introduces a hyperviscosity effect and consequently enhances the destruction of small scales. In practice, the only additional ingredient is a self-adjoint linear filter whose local filter length is determined from the requirement that vortex-stretching must stop at the smallest grid scale. In the present work, the performance of the above-mentioned recent improvements is assessed through application to turbulent natural convection flows by means of comparison with DNS reference data.
A Consistent Pricing Model for Index Options and Volatility Derivatives
DEFF Research Database (Denmark)
Cont, Rama; Kokholm, Thomas
observed properties of variance swap dynamics and allows for jumps in volatility and returns. An affine specification using L´evy processes as building blocks leads to analytically tractable pricing formulas for options on variance swaps as well as efficient numerical methods for pricing of European......We propose and study a flexible modeling framework for the joint dynamics of an index and a set of forward variance swap rates written on this index, allowing options on forward variance swaps and options on the underlying index to be priced consistently. Our model reproduces various empirically...... options on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options...
Laser filamentation mathematical methods and models
Lorin, Emmanuel; Moloney, Jerome
2016-01-01
This book is focused on the nonlinear theoretical and mathematical problems associated with ultrafast intense laser pulse propagation in gases and in particular, in air. With the aim of understanding the physics of filamentation in gases, solids, the atmosphere, and even biological tissue, specialists in nonlinear optics and filamentation from both physics and mathematics attempt to rigorously derive and analyze relevant non-perturbative models. Modern laser technology allows the generation of ultrafast (few cycle) laser pulses, with intensities exceeding the internal electric field in atoms and molecules (E=5x109 V/cm or intensity I = 3.5 x 1016 Watts/cm2 ). The interaction of such pulses with atoms and molecules leads to new, highly nonlinear nonperturbative regimes, where new physical phenomena, such as High Harmonic Generation (HHG), occur, and from which the shortest (attosecond - the natural time scale of the electron) pulses have been created. One of the major experimental discoveries in this nonlinear...
Thermoregulation in premature infants: A mathematical model.
Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen
2016-12-01
In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright Â© 2016 Elsevier Ltd. All rights reserved.
Mathematical models for atmospheric pollutants. Final report
International Nuclear Information System (INIS)
Drake, R.L.; Barrager, S.M.
1979-08-01
The present and likely future roles of mathematical modeling in air quality decisions are described. The discussion emphasizes models and air pathway processes rather than the chemical and physical behavior of specific anthropogenic emissions. Summarized are the characteristics of various types of models used in the decision-making processes. Specific model subclasses are recommended for use in making air quality decisions that have site-specific, regional, national, or global impacts. The types of exposure and damage models that are currently used to predict the effects of air pollutants on humans, other animals, plants, ecosystems, property, and materials are described. The aesthetic effects of odor and visibility and the impact of pollutants on weather and climate are also addressed. Technical details of air pollution meteorology, chemical and physical properties of air pollutants, solution techniques, and air quality models are discussed in four appendices bound in separate volumes
Mathematical modeling of CANDU-PHWR
Energy Technology Data Exchange (ETDEWEB)
Gaber, F.A.; Aly, R.A.; El-Shal, A.O. [Atomic Energy Authority, Cairo (Egypt)
2003-07-01
The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR). This study involved mathematical modeling of CANDU-PHWR to study its thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique. The reactor model includes the neutronic, reactivity, and fuel channel heat transfer. The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and the reactivity feed back due to the changes in the fuel temperature and coolant temperature. The CANDU-PHWR model was coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative influence...... be carefully selected, so that the model and its visualization enhance our ability to interpret the brain. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...
Mathematical modeling and visualization of functional neuroimages
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup
This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular analysis tools within the neuroimaging community. Such methods...... neuroimaging data sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative...... be carefully selected, so that the model and its visualization enhance our ability to interpret brain function. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...
Mathematical methods and models in composites
Mantic, Vladislav
2014-01-01
This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics cover
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London...
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.
Chancroid transmission dynamics: a mathematical modeling approach.
Bhunu, C P; Mushayabasa, S
2011-12-01
Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.
Directory of Open Access Journals (Sweden)
Dinh An Nguyen
2012-07-01
Full Text Available Many of the Proton Exchange Membrane Fuel Cell (PEMFC models proposed in the literature consist of mathematical equations. However, they are not adequately practical for simulating power systems. The proposed model takes into account phenomena such as activation polarization, ohmic polarization, double layer capacitance and mass transport effects present in a PEM fuel cell. Using electrical analogies and a mathematical modeling of PEMFC, the circuit model is established. To evaluate the effectiveness of the circuit model, its static and dynamic performances under load step changes are simulated and compared to the numerical results obtained by solving the mathematical model. Finally, the applicability of our model is demonstrated by simulating a practical system.
An introduction to mathematical modeling of infectious diseases
Li, Michael Y
2018-01-01
This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.
Development of a Consistent and Reproducible Porcine Scald Burn Model
Kempf, Margit; Kimble, Roy; Cuttle, Leila
2016-01-01
There are very few porcine burn models that replicate scald injuries similar to those encountered by children. We have developed a robust porcine burn model capable of creating reproducible scald burns for a wide range of burn conditions. The study was conducted with juvenile Large White pigs, creating replicates of burn combinations; 50°C for 1, 2, 5 and 10 minutes and 60°C, 70°C, 80°C and 90°C for 5 seconds. Visual wound examination, biopsies and Laser Doppler Imaging were performed at 1, 24 hours and at 3 and 7 days post-burn. A consistent water temperature was maintained within the scald device for long durations (49.8 ± 0.1°C when set at 50°C). The macroscopic and histologic appearance was consistent between replicates of burn conditions. For 50°C water, 10 minute duration burns showed significantly deeper tissue injury than all shorter durations at 24 hours post-burn (p ≤ 0.0001), with damage seen to increase until day 3 post-burn. For 5 second duration burns, by day 7 post-burn the 80°C and 90°C scalds had damage detected significantly deeper in the tissue than the 70°C scalds (p ≤ 0.001). A reliable and safe model of porcine scald burn injury has been successfully developed. The novel apparatus with continually refreshed water improves consistency of scald creation for long exposure times. This model allows the pathophysiology of scald burn wound creation and progression to be examined. PMID:27612153
Thermodynamically consistent model of brittle oil shales under overpressure
Izvekov, Oleg
2016-04-01
The concept of dual porosity is a common way for simulation of oil shale production. In the frame of this concept the porous fractured media is considered as superposition of two permeable continua with mass exchange. As a rule the concept doesn't take into account such as the well-known phenomenon as slip along natural fractures, overpressure in low permeability matrix and so on. Overpressure can lead to development of secondary fractures in low permeability matrix in the process of drilling and pressure reduction during production. In this work a new thermodynamically consistent model which generalizes the model of dual porosity is proposed. Particularities of the model are as follows. The set of natural fractures is considered as permeable continuum. Damage mechanics is applied to simulation of secondary fractures development in low permeability matrix. Slip along natural fractures is simulated in the frame of plasticity theory with Drucker-Prager criterion.
Fermentation process diagnosis using a mathematical model
Energy Technology Data Exchange (ETDEWEB)
Yerushalmi, L; Volesky, B; Votruba, J
1988-09-01
Intriguing physiology of a solvent-producing strain of Clostridium acetobutylicum led to the synthesis of a mathematical model of the acetone-butanol fermentation process. The model presented is capable of describing the process dynamics and the culture behavior during a standard and a substandard acetone-butanol fermentation. In addition to the process kinetic parameters, the model includes the culture physiological parameters, such as the cellular membrane permeability and the number of membrane sites for active transport of sugar. Computer process simulation studies for different culture conditions used the model, and quantitatively pointed out the importance of selected culture parameters that characterize the cell membrane behaviour and play an important role in the control of solvent synthesis by the cell. The theoretical predictions by the new model were confirmed by experimental determination of the cellular membrane permeability.
A mathematical model on Acquired Immunodeficiency Syndrome
Directory of Open Access Journals (Sweden)
Buddhadeo Mahato
2014-10-01
Full Text Available A mathematical model SEIA (susceptible-exposed-infectious-AIDS infected with vertical transmission of AIDS epidemic is formulated. AIDS is one of the largest health problems, the world is currently facing. Even with anti-retroviral therapies (ART, many resource-constrained countries are unable to meet the treatment needs of their infected populations. We consider a function of number of AIDS cases in a community with an inverse relation. A stated theorem with proof and an example to illustrate it, is given to find the equilibrium points of the model. The disease-free equilibrium of the model is investigated by finding next generation matrix and basic reproduction number R0 of the model. The disease-free equilibrium of the AIDS model system is locally asymptotically stable if R0⩽1 and unstable if R0>1. Finally, numerical simulations are presented to illustrate the results.
Assessment of Primary 5 Students' Mathematical Modelling Competencies
Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia
2012-01-01
Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…
Development of a Multidisciplinary Middle School Mathematics Infusion Model
Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura
2011-01-01
The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond
2010-01-01
This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…
Mathematical Model for the Control of measles 1*PETER, OJ ...
African Journals Online (AJOL)
PROF HORSFALL
2018-04-16
Apr 16, 2018 ... 5Department of Mathematics/Statistics, Federal University of Technology, Minna, Nigeria ... ABSTRACT: We proposed a mathematical model of measles disease dynamics with vaccination by ...... Equation with application.
Mathematical Modeling in Population Dynamics: The Case of Single ...
African Journals Online (AJOL)
kofimereku
Department of Mathematics, Kwame Nkrumah University of Science and Technology,. Kumasi, Ghana ... The trust of this paper is the application of mathematical models in helping to ..... Statistics and Computing, New York: Wiley. Cox, C.B and ...
A model for cytoplasmic rheology consistent with magnetic twisting cytometry.
Butler, J P; Kelly, S M
1998-01-01
Magnetic twisting cytometry is gaining wide applicability as a tool for the investigation of the rheological properties of cells and the mechanical properties of receptor-cytoskeletal interactions. Current technology involves the application and release of magnetically induced torques on small magnetic particles bound to or inside cells, with measurements of the resulting angular rotation of the particles. The properties of purely elastic or purely viscous materials can be determined by the angular strain and strain rate, respectively. However, the cytoskeleton and its linkage to cell surface receptors display elastic, viscous, and even plastic deformation, and the simultaneous characterization of these properties using only elastic or viscous models is internally inconsistent. Data interpretation is complicated by the fact that in current technology, the applied torques are not constant in time, but decrease as the particles rotate. This paper describes an internally consistent model consisting of a parallel viscoelastic element in series with a parallel viscoelastic element, and one approach to quantitative parameter evaluation. The unified model reproduces all essential features seen in data obtained from a wide variety of cell populations, and contains the pure elastic, viscoelastic, and viscous cases as subsets.
A self-consistent model of an isothermal tokamak
McNamara, Steven; Lilley, Matthew
2014-10-01
Continued progress in liquid lithium coating technologies have made the development of a beam driven tokamak with minimal edge recycling a feasibly possibility. Such devices are characterised by improved confinement due to their inherent stability and the suppression of thermal conduction. Particle and energy confinement become intrinsically linked and the plasma thermal energy content is governed by the injected beam. A self-consistent model of a purely beam fuelled isothermal tokamak is presented, including calculations of the density profile, bulk species temperature ratios and the fusion output. Stability considerations constrain the operating parameters and regions of stable operation are identified and their suitability to potential reactor applications discussed.
Mean-field theory and self-consistent dynamo modeling
International Nuclear Information System (INIS)
Yoshizawa, Akira; Yokoi, Nobumitsu
2001-12-01
Mean-field theory of dynamo is discussed with emphasis on the statistical formulation of turbulence effects on the magnetohydrodynamic equations and the construction of a self-consistent dynamo model. The dynamo mechanism is sought in the combination of the turbulent residual-helicity and cross-helicity effects. On the basis of this mechanism, discussions are made on the generation of planetary magnetic fields such as geomagnetic field and sunspots and on the occurrence of flow by magnetic fields in planetary and fusion phenomena. (author)
Mathematical Modelling of Involute Spur Gears Manufactured by Rack Cutter
Directory of Open Access Journals (Sweden)
Tufan Gürkan YILMAZ
2016-05-01
Full Text Available In this study, mathematical modelling of asymmetric involute spur gears was situated in by Litvin approach. In this context, firstly, mathematical expressions of rack cutter which manufacture asymmetric involute spur gear, then mathematical expression of asymmetric involute spur gear were obtained by using differential geometry, coordinate transformation and gear theory. Mathematical expressions were modelled in MATLAB and output files including points of involute spur gear’s teeth were designed automatically thanks to macros.
Mathematical Modeling of Extinction of Inhomogeneous Populations
Karev, G.P.; Kareva, I.
2016-01-01
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117
A Mathematical Model of Cardiovascular Response to Dynamic Exercise
National Research Council Canada - National Science Library
Magosso, E
2001-01-01
A mathematical model of cardiovascular response to dynamic exercise is presented, The model includes the pulsating heart, the systemic and pulmonary, circulation, a functional description of muscle...
Mathematical model of the Amazon Stirling engine
Energy Technology Data Exchange (ETDEWEB)
Vidal Medina, Juan Ricardo [Universidad Autonoma de Occidente (Colombia)], e-mail: jrvidal@uao.edu.co; Cobasa, Vladimir Melian; Silva, Electo [Universidade Federal de Itajuba, MG (Brazil)], e-mail: vlad@unifei.edu.br
2010-07-01
The Excellency Group in Thermoelectric and Distributed Generation (NEST, for its acronym in Portuguese) at the Federal University of Itajuba, has designed a Stirling engine prototype to provide electricity to isolated regions of Brazil. The engine was designed to operate with residual biomass from timber process. This paper presents mathematical models of heat exchangers (hot, cold and regenerator) integrated into second order adiabatic models. The general model takes into account the pressure drop losses, hysteresis and internal losses. The results of power output, engine efficiency, optimal velocity of the exhaust gases and the influence of dead volume in engine efficiency are presented in this paper. The objective of this modeling is to propose improvements to the manufactured engine design. (author)
A self-consistent spin-diffusion model for micromagnetics
Abert, Claas; Ruggeri, Michele; Bruckner, Florian; Vogler, Christoph; Manchon, Aurelien; Praetorius, Dirk; Suess, Dieter
2016-01-01
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
Self-consistent modeling of amorphous silicon devices
International Nuclear Information System (INIS)
Hack, M.
1987-01-01
The authors developed a computer model to describe the steady-state behaviour of a range of amorphous silicon devices. It is based on the complete set of transport equations and takes into account the important role played by the continuous distribution of localized states in the mobility gap of amorphous silicon. Using one set of parameters they have been able to self-consistently simulate the current-voltage characteristics of p-i-n (or n-i-p) solar cells under illumination, the dark behaviour of field-effect transistors, p-i-n diodes and n-i-n diodes in both the ohmic and space charge limited regimes. This model also describes the steady-state photoconductivity of amorphous silicon, in particular, its dependence on temperature, doping and illumination intensity
A self-consistent spin-diffusion model for micromagnetics
Abert, Claas
2016-12-17
We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.
Biological-Mathematical Modeling of Chronic Toxicity.
1981-07-22
34Mathematical Model of Uptake and Distribution," Uptake and Distribution of Anesthetic Agents, E. M. Papper and R. J. Kitz (Editors, McGraw-Hill Book Co., Inc...distribution, In: Papper , E.M. and Kltz, R.J.(eds.) Uptake and distribution of anesthetic agents, McGraw- Hill, New York, p. 72 3. Plpleson, W.W...1963) Quantitative prediction of anesthetic concentrations. In: Papper , E.M. and Kitz, R.J. (eds.) Uptake and distribution of anesthetic agents, McGraw
Mathematical Modeling of Diaphragm Pneumatic Motors
Directory of Open Access Journals (Sweden)
Fojtášek Kamil
2014-03-01
Full Text Available Pneumatic diaphragm motors belong to the group of motors with elastic working parts. This part is usually made of rubber with a textile insert and it is deformed under the pressure of a compressed air or from the external mass load. This is resulting in a final working effect. In this type of motors are in contact two different elastic environments – the compressed air and the esaltic part. These motors are mainly the low-stroke and working with relatively large forces. This paper presents mathematical modeling static properties of diaphragm motors.
A mathematical model of Chagas disease transmission
Hidayat, Dayat; Nugraha, Edwin Setiawan; Nuraini, Nuning
2018-03-01
Chagas disease is a parasitic infection caused by protozoan Trypanosoma cruzi which is transmitted to human by insects of the subfamily Triatominae, including Rhodnius prolixus. This disease is a major problem in several countries of Latin America. A mathematical model of Chagas disease with separate vector reservoir and a neighboring human resident is constructed. The basic reproductive ratio is obtained and stability analysis of the equilibria is shown. We also performed sensitivity populations dynamics of infected humans and infected insects based on migration rate, carrying capacity, and infection rate parameters. Our findings showed that the dynamics of the infected human and insect is mostly affected by carrying capacity insect in the settlement.
Modellus: Learning Physics with Mathematical Modelling
Teodoro, Vitor
Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations
Self-consistent modeling of electron cyclotron resonance ion sources
International Nuclear Information System (INIS)
Girard, A.; Hitz, D.; Melin, G.; Serebrennikov, K.; Lecot, C.
2004-01-01
In order to predict the performances of electron cyclotron resonance ion source (ECRIS), it is necessary to perfectly model the different parts of these sources: (i) magnetic configuration; (ii) plasma characteristics; (iii) extraction system. The magnetic configuration is easily calculated via commercial codes; different codes also simulate the ion extraction, either in two dimension, or even in three dimension (to take into account the shape of the plasma at the extraction influenced by the hexapole). However the characteristics of the plasma are not always mastered. This article describes the self-consistent modeling of ECRIS: we have developed a code which takes into account the most important construction parameters: the size of the plasma (length, diameter), the mirror ratio and axial magnetic profile, whether a biased probe is installed or not. These input parameters are used to feed a self-consistent code, which calculates the characteristics of the plasma: electron density and energy, charge state distribution, plasma potential. The code is briefly described, and some of its most interesting results are presented. Comparisons are made between the calculations and the results obtained experimentally
Self-consistent modeling of electron cyclotron resonance ion sources
Girard, A.; Hitz, D.; Melin, G.; Serebrennikov, K.; Lécot, C.
2004-05-01
In order to predict the performances of electron cyclotron resonance ion source (ECRIS), it is necessary to perfectly model the different parts of these sources: (i) magnetic configuration; (ii) plasma characteristics; (iii) extraction system. The magnetic configuration is easily calculated via commercial codes; different codes also simulate the ion extraction, either in two dimension, or even in three dimension (to take into account the shape of the plasma at the extraction influenced by the hexapole). However the characteristics of the plasma are not always mastered. This article describes the self-consistent modeling of ECRIS: we have developed a code which takes into account the most important construction parameters: the size of the plasma (length, diameter), the mirror ratio and axial magnetic profile, whether a biased probe is installed or not. These input parameters are used to feed a self-consistent code, which calculates the characteristics of the plasma: electron density and energy, charge state distribution, plasma potential. The code is briefly described, and some of its most interesting results are presented. Comparisons are made between the calculations and the results obtained experimentally.
Mathematical modeling of infectious disease dynamics
Siettos, Constantinos I.; Russo, Lucia
2013-01-01
Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814
A self-consistent upward leader propagation model
International Nuclear Information System (INIS)
Becerra, Marley; Cooray, Vernon
2006-01-01
The knowledge of the initiation and propagation of an upward moving connecting leader in the presence of a downward moving lightning stepped leader is a must in the determination of the lateral attraction distance of a lightning flash by any grounded structure. Even though different models that simulate this phenomenon are available in the literature, they do not take into account the latest developments in the physics of leader discharges. The leader model proposed here simulates the advancement of positive upward leaders by appealing to the presently understood physics of that process. The model properly simulates the upward continuous progression of the positive connecting leaders from its inception to the final connection with the downward stepped leader (final jump). Thus, the main physical properties of upward leaders, namely the charge per unit length, the injected current, the channel gradient and the leader velocity are self-consistently obtained. The obtained results are compared with an altitude triggered lightning experiment and there is good agreement between the model predictions and the measured leader current and the experimentally inferred spatial and temporal location of the final jump. It is also found that the usual assumption of constant charge per unit length, based on laboratory experiments, is not valid for lightning upward connecting leaders
A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis
Czech Academy of Sciences Publication Activity Database
Kaltenbacher, B.; Krejčí, Pavel
2016-01-01
Roč. 96, č. 7 (2016), s. 874-891 ISSN 0044-2267 R&D Projects: GA ČR(CZ) GA15-12227S Institutional support: RVO:67985840 Keywords : piezoelectricity * hysteresis * ferroelasticity Subject RIV: BA - General Mathematics Impact factor: 1.332, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/zamm.201400292/abstract
A thermodynamically consistent phenomenological model for ferroelectric and ferroelastic hysteresis
Czech Academy of Sciences Publication Activity Database
Kaltenbacher, B.; Krejčí, Pavel
2016-01-01
Roč. 96, č. 7 (2016), s. 874-891 ISSN 0044-2267 R&D Projects: GA ČR(CZ) GA15-12227S Institutional support: RVO:67985840 Keywords : piezoelectric ity * hysteresis * ferroelasticity Subject RIV: BA - General Mathematics Impact factor: 1.332, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/zamm.201400292/abstract
Comparison of Different Mathematical Models of Cavitation
Directory of Open Access Journals (Sweden)
Dorota HOMA
2014-12-01
Full Text Available Cavitation occurs during the flow when local pressure drops to the saturation pressure according to the temperature of the flow. It includes both evaporation and condensation of the vapor bubbles, which occur alternately with high frequency. Cavitation can be very dangerous, especially for pumps, because it leads to break of flow continuity, noise, vibration, erosion of blades and change in pump’s characteristics. Therefore it is very important for pump designers and users to avoid working in cavitation conditions. Simulation of flow can be very useful in that and can indicate if there is risk of cavitating flow occurrence. As this is a multiphase flow and quite complicated phenomena, there are a few mathematical models describing it. The aim of this paper is to make a short review of them and describe their approach to model cavitation. It is desirable to know differences between them to model this phenomenon properly.
Mathematical modeling of CANDU-PHWR
Energy Technology Data Exchange (ETDEWEB)
Gaber, F.A.; Aly, R.A.; El-Shal, A.O. [Atomic Energy Authority, Cairo (Egypt)
2001-07-01
The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR) system. This study involved mathematical modeling of CANDU PHWR major system components and the developments of software to study the thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique.The integrated CANDU-PHWR model includes the neutronic, reactivity, fuel channel heat transfer, piping and the preheater type U-tube steam generator (PUTSG). The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and reactivity feed back due to the changes in fuel temperature and coolant temperature. The complex operation of the preheater type U-tube steam generator (PUTSG) is represented by a non-linear dynamic model using a state variable, moving boundary and lumped parameter techniques. The secondary side of the PUTSG model has six separate lumps including a preheater region, a lower boiling section, a mixing region, a riser, a chimmeny section, and a down-corner. The tube side of PUTSG has three main thermal zones. The PUTSG model is based on conservation of mass, energy and momentum relation-ships. The CANDU-PHWR integrated model are coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)
Dalla Vecchia, Rodrigo
2015-01-01
This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…
Mathematical modelling of the growth of human fetus anatomical structures.
Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech
2017-09-01
The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.
Mathematical Modeling of 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
Mathematical model of highways network optimization
Sakhapov, R. L.; Nikolaeva, R. V.; Gatiyatullin, M. H.; Makhmutov, M. M.
2017-12-01
The article deals with the issue of highways network design. Studies show that the main requirement from road transport for the road network is to ensure the realization of all the transport links served by it, with the least possible cost. The goal of optimizing the network of highways is to increase the efficiency of transport. It is necessary to take into account a large number of factors that make it difficult to quantify and qualify their impact on the road network. In this paper, we propose building an optimal variant for locating the road network on the basis of a mathematical model. The article defines the criteria for optimality and objective functions that reflect the requirements for the road network. The most fully satisfying condition for optimality is the minimization of road and transport costs. We adopted this indicator as a criterion of optimality in the economic-mathematical model of a network of highways. Studies have shown that each offset point in the optimal binding road network is associated with all other corresponding points in the directions providing the least financial costs necessary to move passengers and cargo from this point to the other corresponding points. The article presents general principles for constructing an optimal network of roads.
Classical and Quantum Consistency of the DGP Model
Nicolis, A; Nicolis, Alberto; Rattazzi, Riccardo
2004-01-01
We study the Dvali-Gabadadze-Porrati model by the method of the boundary effective action. The truncation of this action to the bending mode \\pi consistently describes physics in a wide range of regimes both at the classical and at the quantum level. The Vainshtein effect, which restores agreement with precise tests of general relativity, follows straightforwardly. We give a simple and general proof of stability, i.e. absence of ghosts in the fluctuations, valid for most of the relevant cases, like for instance the spherical source in asymptotically flat space. However we confirm that around certain interesting self-accelerating cosmological solutions there is a ghost. We consider the issue of quantum corrections. Around flat space \\pi becomes strongly coupled below a macroscopic length of 1000 km, thus impairing the predictivity of the model. Indeed the tower of higher dimensional operators which is expected by a generic UV completion of the model limits predictivity at even larger length scales. We outline ...
Modelling as a foundation for academic forming in mathematics education
Perrenet, J.C.; Morsche, ter H.G.
2004-01-01
The Bachelor curriculum of Applied Mathematics in Eindhoven includes a series of modelling projects where pairs of students solve mathematical problems posed in non-mathematical language. Communication skills training is integrated with this track. Recently a new course has been added. The students
Self-Consistent Dynamical Model of the Broad Line Region
Energy Technology Data Exchange (ETDEWEB)
Czerny, Bozena [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland); Li, Yan-Rong [Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing (China); Sredzinska, Justyna; Hryniewicz, Krzysztof [Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw (Poland); Panda, Swayam [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland); Copernicus Astronomical Center, Polish Academy of Sciences, Warsaw (Poland); Wildy, Conor [Center for Theoretical Physics, Polish Academy of Sciences, Warsaw (Poland); Karas, Vladimir, E-mail: bcz@cft.edu.pl [Astronomical Institute, Czech Academy of Sciences, Prague (Czech Republic)
2017-06-22
We develop a self-consistent description of the Broad Line Region based on the concept of a failed wind powered by radiation pressure acting on a dusty accretion disk atmosphere in Keplerian motion. The material raised high above the disk is illuminated, dust evaporates, and the matter falls back toward the disk. This material is the source of emission lines. The model predicts the inner and outer radius of the region, the cloud dynamics under the dust radiation pressure and, subsequently, the gravitational field of the central black hole, which results in asymmetry between the rise and fall. Knowledge of the dynamics allows us to predict the shapes of the emission lines as functions of the basic parameters of an active nucleus: black hole mass, accretion rate, black hole spin (or accretion efficiency) and the viewing angle with respect to the symmetry axis. Here we show preliminary results based on analytical approximations to the cloud motion.
Self-Consistent Dynamical Model of the Broad Line Region
Directory of Open Access Journals (Sweden)
Bozena Czerny
2017-06-01
Full Text Available We develop a self-consistent description of the Broad Line Region based on the concept of a failed wind powered by radiation pressure acting on a dusty accretion disk atmosphere in Keplerian motion. The material raised high above the disk is illuminated, dust evaporates, and the matter falls back toward the disk. This material is the source of emission lines. The model predicts the inner and outer radius of the region, the cloud dynamics under the dust radiation pressure and, subsequently, the gravitational field of the central black hole, which results in asymmetry between the rise and fall. Knowledge of the dynamics allows us to predict the shapes of the emission lines as functions of the basic parameters of an active nucleus: black hole mass, accretion rate, black hole spin (or accretion efficiency and the viewing angle with respect to the symmetry axis. Here we show preliminary results based on analytical approximations to the cloud motion.
Consistent constraints on the Standard Model Effective Field Theory
International Nuclear Information System (INIS)
Berthier, Laure; Trott, Michael
2016-01-01
We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, Λ≳ 3 TeV. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an S,T analysis is modified by the theory errors we include as an illustrative example.
Ma, Xin; Ma, Lingling
2004-04-01
In this study, the authors introduced a multivariate multilevel model to estimate the consistency among students and schools in the rates of growth between mathematics and science achievement during the entire middle and high school years with data from the Longitudinal Study of American Youth (LSAY). There was no evident consistency in the rates of growth between mathematics and science achievement among students, and this inconsistency was not much influenced by student characteristics and school characteristics. However, there was evident consistency in the average rates of growth between mathematics and science achievement among schools, and this consistency was influenced by student characteristics and school characteristics. Major school-level variables associated with parental involvement did not show any significant impacts on consistency among either students or schools. Results call for educational policies that promote collaboration between mathematics and science departments or teachers.
Creation of Consistent Burn Wounds: A Rat Model
Directory of Open Access Journals (Sweden)
Elijah Zhengyang Cai
2014-07-01
Full Text Available Background Burn infliction techniques are poorly described in rat models. An accurate study can only be achieved with wounds that are uniform in size and depth. We describe a simple reproducible method for creating consistent burn wounds in rats. Methods Ten male Sprague-Dawley rats were anesthetized and dorsum shaved. A 100 g cylindrical stainless-steel rod (1 cm diameter was heated to 100℃ in boiling water. Temperature was monitored using a thermocouple. We performed two consecutive toe-pinch tests on different limbs to assess the depth of sedation. Burn infliction was limited to the loin. The skin was pulled upwards, away from the underlying viscera, creating a flat surface. The rod rested on its own weight for 5, 10, and 20 seconds at three different sites on each rat. Wounds were evaluated for size, morphology and depth. Results Average wound size was 0.9957 cm2 (standard deviation [SD] 0.1845 (n=30. Wounds created with duration of 5 seconds were pale, with an indistinct margin of erythema. Wounds of 10 and 20 seconds were well-defined, uniformly brown with a rim of erythema. Average depths of tissue damage were 1.30 mm (SD 0.424, 2.35 mm (SD 0.071, and 2.60 mm (SD 0.283 for duration of 5, 10, 20 seconds respectively. Burn duration of 5 seconds resulted in full-thickness damage. Burn duration of 10 seconds and 20 seconds resulted in full-thickness damage, involving subjacent skeletal muscle. Conclusions This is a simple reproducible method for creating burn wounds consistent in size and depth in a rat burn model.
Mathematical models for therapeutic approaches to control HIV disease transmission
Roy, Priti Kumar
2015-01-01
The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...
Mathematical modeling of a thermovoltaic cell
White, Ralph E.; Kawanami, Makoto
1992-01-01
A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.
Description of mathematical models and computer programs
International Nuclear Information System (INIS)
1977-01-01
The paper gives a description of mathematical models and computer programs for analysing possible strategies for spent fuel management, with emphasis on economic analysis. The computer programs developed, describe the material flows, facility construction schedules, capital investment schedules and operating costs for the facilities used in managing the spent fuel. The computer programs use a combination of simulation and optimization procedures for the economic analyses. Many of the fuel cycle steps (such as spent fuel discharges, storage at the reactor, and transport to the RFCC) are described in physical and economic terms through simulation modeling, while others (such as reprocessing plant size and commissioning schedules, interim storage facility commissioning schedules etc.) are subjected to economic optimization procedures to determine the approximate lowest-cost plans from among the available feasible alternatives
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Mathematical Model of Cytomegalovirus (CMV) Disease
Sriningsih, R.; Subhan, M.; Nasution, M. L.
2018-04-01
The article formed the mathematical model of cytomegalovirus (CMV) disease. Cytomegalovirus (CMV) is a type of herpes virus. This virus is actually not dangerous, but if the body's immune weakens the virus can cause serious problems for health and even can cause death. This virus is also susceptible to infect pregnant women. In addition, the baby may also be infected through the placenta. If this is experienced early in pregnancy, it will increase the risk of miscarriage. If the baby is born, it can cause disability in the baby. The model is formed by determining its variables and parameters based on assumptions. The goal is to analyze the dynamics of cytomegalovirus (CMV) disease spread.
Laser interaction with biological material mathematical modeling
Kulikov, Kirill
2014-01-01
This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.
Mathematical Models and Methods for Living Systems
Chaplain, Mark; Pugliese, Andrea
2016-01-01
The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods. Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.
Missing the Promise of Mathematical Modeling
Meyer, Dan
2015-01-01
The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…
Mathematics Teacher Education: A Model from Crimea.
Ferrucci, Beverly J.; Evans, Richard C.
1993-01-01
Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)
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.
A Mathematical Model for Cisplatin Cellular Pharmacodynamics
Directory of Open Access Journals (Sweden)
Ardith W. El-Kareh
2003-03-01
Full Text Available A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours. The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.
Rudolph, Lee
2012-01-01
In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, in
Topologically Consistent Models for Efficient Big Geo-Spatio Data Distribution
Jahn, M. W.; Bradley, P. E.; Doori, M. Al; Breunig, M.
2017-10-01
Geo-spatio-temporal topology models are likely to become a key concept to check the consistency of 3D (spatial space) and 4D (spatial + temporal space) models for emerging GIS applications such as subsurface reservoir modelling or the simulation of energy and water supply of mega or smart cities. Furthermore, the data management for complex models consisting of big geo-spatial data is a challenge for GIS and geo-database research. General challenges, concepts, and techniques of big geo-spatial data management are presented. In this paper we introduce a sound mathematical approach for a topologically consistent geo-spatio-temporal model based on the concept of the incidence graph. We redesign DB4GeO, our service-based geo-spatio-temporal database architecture, on the way to the parallel management of massive geo-spatial data. Approaches for a new geo-spatio-temporal and object model of DB4GeO meeting the requirements of big geo-spatial data are discussed in detail. Finally, a conclusion and outlook on our future research are given on the way to support the processing of geo-analytics and -simulations in a parallel and distributed system environment.
Mathematical modeling of acid-base physiology.
Occhipinti, Rossana; Boron, Walter F
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3(-), [Formula: see text] ) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3(-) influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. Copyright © 2015 Elsevier Ltd. All rights reserved.
Self-consistent imbedding and the ellipsoidal model model for porous rocks
International Nuclear Information System (INIS)
Korringa, J.; Brown, R.J.S.; Thompson, D.D.; Runge, R.J.
1979-01-01
Equations are obtained for the effective elastic moduli for a model of an isotropic, heterogeneous, porous medium. The mathematical model used for computation is abstract in that it is not simply a rigorous computation for a composite medium of some idealized geometry, although the computation contains individual steps which are just that. Both the solid part and pore space are represented by ellipsoidal or spherical 'grains' or 'pores' of various sizes and shapes. The strain of each grain, caused by external forces applied to the medium, is calculated in a self-consistent imbedding (SCI) approximation, which replaces the true surrounding of any given grain or pore by an isotropic medium defined by the effective moduli to be computed. The ellipsoidal nature of the shapes allows us to use Eshelby's theoretical treatment of a single ellipsoidal inclusion in an infiinte homogeneous medium. Results are compared with the literature, and discrepancies are found with all published accounts of this problem. Deviations from the work of Wu, of Walsh, and of O'Connell and Budiansky are attributed to a substitution made by these authors which though an identity for the exact quantities involved, is only approximate in the SCI calculation. This reduces the validity of the equations to first-order effects only. Differences with the results of Kuster and Toksoez are attributed to the fact that the computation of these authors is not self-consistent in the sense used here. A result seems to be the stiffening of the medium as if the pores are held apart. For spherical grains and pores, their calculated moduli are those given by the Hashin-Shtrikman upper bounds. Our calculation reproduces, in the case of spheres, an early result of Budiansky. An additional feature of our work is that the algebra is simpler than in earlier work. We also incorporate into the theory the possibility that fluid-filled pores are interconnected
Directory of Open Access Journals (Sweden)
Edwin Musdi
2016-02-01
Full Text Available This research aims to develop a mathematics instructional model based realistic mathematics education (RME to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.
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).
Directory of Open Access Journals (Sweden)
Jennifer M. Suh
2017-06-01
Full Text Available This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1 How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2 What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.
Linear models in the mathematics of uncertainty
Mordeson, John N; Clark, Terry D; Pham, Alex; Redmond, Michael A
2013-01-01
The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data is difficult to measure and an assumption of randomness and/or statistical validity is questionable. We apply our methods to real world issues in international relations such as nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and fail...
Mathematical problems in modeling artificial heart
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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.
Moreno Chaparro, Nicolas; Nunes, Suzana Pereira; Calo, Victor M.
2015-01-01
considerations we explicitly account for the correlation between beads in fine-grained DPD models and consistently represent the effect of these correlations in a reduced model, in a practical and simple fashion via power laws and the consistent scaling
Consistent phase-change modeling for CO2-based heat mining operation
DEFF Research Database (Denmark)
Singh, Ashok Kumar; Veje, Christian
2017-01-01
The accuracy of mathematical modeling of phase-change phenomena is limited if a simple, less accurate equation of state completes the governing partial differential equation. However, fluid properties (such as density, dynamic viscosity and compressibility) and saturation state are calculated using...... a highly accurate, complex equation of state. This leads to unstable and inaccurate simulation as the equation of state and governing partial differential equations are mutually inconsistent. In this study, the volume-translated Peng–Robinson equation of state was used with emphasis to model the liquid......–gas phase transition with more accuracy and consistency. Calculation of fluid properties and saturation state were based on the volume translated Peng–Robinson equation of state and results verified. The present model has been applied to a scenario to simulate a CO2-based heat mining process. In this paper...
The use of mathematical models in teaching wastewater treatment engineering
DEFF Research Database (Denmark)
Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.
2002-01-01
Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...... efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available....
Mathematical modeling of wiped-film evaporators
International Nuclear Information System (INIS)
Sommerfeld, J.T.
1976-05-01
A mathematical model and associated computer program were developed to simulate the steady-state operation of wiped-film evaporators for the concentration of typical waste solutions produced at the Savannah River Plant. In this model, which treats either a horizontal or a vertical wiped-film evaporator as a plug-flow device with no backmixing, three fundamental phenomena are described: sensible heating of the waste solution, vaporization of water, and crystallization of solids from solution. Physical property data were coded into the computer program, which performs the calculations of this model. Physical properties of typical waste solutions and of the heating steam, generally as analytical functions of temperature, were obtained from published data or derived by regression analysis of tabulated or graphical data. Preliminary results from tests of the Savannah River Laboratory semiworks wiped-film evaporators were used to select a correlation for the inside film heat transfer coefficient. This model should be a useful aid in the specification, operation, and control of the full-scale wiped-film evaporators proposed for application under plant conditions. In particular, it should be of value in the development and analysis of feed-forward control schemes for the plant units. Also, this model can be readily adapted, with only minor changes, to simulate the operation of wiped-film evaporators for other conceivable applications, such as the concentration of acid wastes
Mathematical modeling of diphtheria transmission in Thailand.
Sornbundit, Kan; Triampo, Wannapong; Modchang, Charin
2017-08-01
In this work, a mathematical model for describing diphtheria transmission in Thailand is proposed. Based on the course of diphtheria infection, the population is divided into 8 epidemiological classes, namely, susceptible, symptomatic infectious, asymptomatic infectious, carrier with full natural-acquired immunity, carrier with partial natural-acquired immunity, individual with full vaccine-induced immunity, and individual with partial vaccine-induced immunity. Parameter values in the model were either directly obtained from the literature, estimated from available data, or estimated by means of sensitivity analysis. Numerical solutions show that our model can correctly describe the decreasing trend of diphtheria cases in Thailand during the years 1977-2014. Furthermore, despite Thailand having high DTP vaccine coverage, our model predicts that there will be diphtheria outbreaks after the year 2014 due to waning immunity. Our model also suggests that providing booster doses to some susceptible individuals and those with partial immunity every 10 years is a potential way to inhibit future diphtheria outbreaks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mathematical models for indoor radon prediction
International Nuclear Information System (INIS)
Malanca, A.; Pessina, V.; Dallara, G.
1995-01-01
It is known that the indoor radon (Rn) concentration can be predicted by means of mathematical models. The simplest model relies on two variables only: the Rn source strength and the air exchange rate. In the Lawrence Berkeley Laboratory (LBL) model several environmental parameters are combined into a complex equation; besides, a correlation between the ventilation rate and the Rn entry rate from the soil is admitted. The measurements were carried out using activated carbon canisters. Seventy-five measurements of Rn concentrations were made inside two rooms placed on the second floor of a building block. One of the rooms had a single-glazed window whereas the other room had a double pane window. During three different experimental protocols, the mean Rn concentration was always higher into the room with a double-glazed window. That behavior can be accounted for by the simplest model. A further set of 450 Rn measurements was collected inside a ground-floor room with a grounding well in it. This trend maybe accounted for by the LBL model
Mathematical foundations of the dendritic growth models.
Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos
2007-11-01
At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.
Mathematical modeling of alcohol distillation columns
Directory of Open Access Journals (Sweden)
Ones Osney Pérez
2011-04-01
Full Text Available New evaluation modules are proposed to extend the scope of a modular simulator oriented to the sugar cane industry, called STA 4.0, in a way that it can be used to carry out x calculation and analysis in ethanol distilleries. Calculation modules were developed for the simulation of the columns that are combined in the distillation area. Mathematical models were supported on materials and energy balances, equilibrium relations and thermodynamic properties of the ethanol-water system. Ponchon-Savarit method was used for the evaluation of the theoretical stages in the columns. A comparison between the results using Ponchon- Savarit method and those obtained applying McCabe-Thiele method was done for a distillation column. These calculation modules for ethanol distilleries were applied to a real case for validation.
Mathematical Modeling of the Origins of Life
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Mathematical modeling in mechanics of heterogeneous media
International Nuclear Information System (INIS)
Fedorov, A.V.; Fomin, V.M.
1991-01-01
The paper reviews the work carried out at the Department of Multi-Phase Media Mechanics of the Institute of Theoretical and Applied Mechanics of the Siberian Division of the USSR Academy of Sciences. It deals with mathematical models for the flow of gas mixtures and solid particles that account for phase transitions and chemical reactions. This work is concerned with the problems of construction of laws of conservation, determination of the type of equations of heterogeneous media mechanics, structure of shock waves, and combined discontinuities in mixtures. The theory of ideal and nonideal detonation in suspension of matter in gases is discussed. Self-similar flows of gas mixtures and responding particles, as well as the problem of breakup of discontinuity for suspension of matter in gases, is studied. 42 refs
Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors
Rash, Agnes M.; Zurbach, E. Peter
2004-01-01
The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…
Akgün, Levent
2015-01-01
The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…
Noise in restaurants: levels and mathematical model.
To, Wai Ming; Chung, Andy
2014-01-01
Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Noise in restaurants: Levels and mathematical model
Directory of Open Access Journals (Sweden)
Wai Ming To
2014-01-01
Full Text Available Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (Leq,1-h was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.
Ganusov, Vitaly V
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.
Strong inference in mathematical modeling: a method for robust science in the 21st century
Directory of Open Access Journals (Sweden)
Vitaly V. Ganusov
2016-07-01
Full Text Available While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers [1], the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions and data. Following the principle of strong inference for experimental sciences proposed by Platt [2], I suggest ``strong inference in mathematical modeling'' as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are 1 to develop multiple alternative models for the phenomenon in question; 2 to compare the models with available experimental data and to determine which of the models are not consistent with the data; 3 to determine reasons why rejected models failed to explain the data, and 4 to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the 21st century.
Mathematical modeling plasma transport in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Quiang, Ji [Univ. of Illinois, Urbana-Champaign, IL (United States)
1997-01-01
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10^{20}/m^{3} with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%.
Mathematical modeling plasma transport in tokamaks
International Nuclear Information System (INIS)
Quiang, Ji
1995-01-01
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10 20 /m 3 with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%
Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2016-01-01
This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.
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
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century
Ganusov, Vitaly V.
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750
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...
A mathematical model of crevice and pitting corrosion
International Nuclear Information System (INIS)
Sharland, S.M.; Tasker, P.W.
1985-09-01
A predictive and self-consistent mathematical model incorporating the electrochemical, chemical and ionic migration processes characterising crevice and pitting corrosion is described. The model predicts full details of the steady-state solution chemistry and electrode kinetics (and hence metal penetration rates) within the corrosion cavities as functions of the many parameters on which these depend such as external electrode potential and crevice dimensions. The crevice is modelled as a parallel-sided slot filled with a dilute sodium chloride solution. Corrosion in both one and two directions is considered. The model includes a solid hydroxide precipitation reaction and assesses the effect on the corrosion rates of consequent changes in the chemical and physical environment within the crevice. A time stepping method is developed for the study of the progression of the corrosion with a precipitation reaction included and is applied to a restricted range of parameters. The applicability of this method is justified in relation to the physical and mathematical approximations made during the construction of the model. (author)
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
Joutsenlahti, Jorma; Kulju, Pirjo
2017-01-01
The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…
Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe
2016-01-01
Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…
On Mathematical Modeling Of Quantum Systems
International Nuclear Information System (INIS)
Achuthan, P.; Narayanankutty, Karuppath
2009-01-01
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Mathematical Models of Cardiac Pacemaking Function
Li, Pan; Lines, Glenn T.; Maleckar, Mary M.; Tveito, Aslak
2013-10-01
Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.
Manual on mathematical models in isotope hydrogeology
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-10-01
Methodologies based on the use of naturally occurring isotopes are, at present, an integral part of studies being undertaken for water resources assessment and management. Quantitative evaluations based on the temporal and/or spatial distribution of different isotopic species in hydrological systems require conceptual mathematical formulations. Different types of model can be employed depending on the nature of the hydrological system under investigation, the amount and type of data available, and the required accuracy of the parameter to be estimated. This manual provides an overview of the basic concepts of existing modelling approaches, procedures for their application to different hydrological systems, their limitations and data requirements. Guidance in their practical applications, illustrative case studies and information on existing PC software are also included. While the subject matter of isotope transport modelling and improved quantitative evaluations through natural isotopes in water sciences is still at the development stage, this manual summarizes the methodologies available at present, to assist the practitioner in the proper use within the framework of ongoing isotope hydrological field studies. In view of the widespread use of isotope methods in groundwater hydrology, the methodologies covered in the manual are directed towards hydrogeological applications, although most of the conceptual formulations presented would generally be valid. Refs, figs, tabs.
Mathematical Models of Cardiac Pacemaking Function
Directory of Open Access Journals (Sweden)
Pan eLi
2013-10-01
Full Text Available Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.
Manual on mathematical models in isotope hydrogeology
International Nuclear Information System (INIS)
1996-10-01
Methodologies based on the use of naturally occurring isotopes are, at present, an integral part of studies being undertaken for water resources assessment and management. Quantitative evaluations based on the temporal and/or spatial distribution of different isotopic species in hydrological systems require conceptual mathematical formulations. Different types of model can be employed depending on the nature of the hydrological system under investigation, the amount and type of data available, and the required accuracy of the parameter to be estimated. This manual provides an overview of the basic concepts of existing modelling approaches, procedures for their application to different hydrological systems, their limitations and data requirements. Guidance in their practical applications, illustrative case studies and information on existing PC software are also included. While the subject matter of isotope transport modelling and improved quantitative evaluations through natural isotopes in water sciences is still at the development stage, this manual summarizes the methodologies available at present, to assist the practitioner in the proper use within the framework of ongoing isotope hydrological field studies. In view of the widespread use of isotope methods in groundwater hydrology, the methodologies covered in the manual are directed towards hydrogeological applications, although most of the conceptual formulations presented would generally be valid. Refs, figs, tabs
Ocular hemodynamics and glaucoma: the role of mathematical modeling.
Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A
2013-01-01
To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.
Logistics of Mathematical Modeling-Focused Projects
Harwood, R. Corban
2018-01-01
This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical…
Modelling Mathematical Argumentation: The Importance of Qualification
Inglis, Matthew; Mejia-Ramos, Juan; Simpson, Adrian
2007-01-01
In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…
Self-consistent Modeling of Elastic Anisotropy in Shale
Kanitpanyacharoen, W.; Wenk, H.; Matthies, S.; Vasin, R.
2012-12-01
Elastic anisotropy in clay-rich sedimentary rocks has increasingly received attention because of significance for prospecting of petroleum deposits, as well as seals in the context of nuclear waste and CO2 sequestration. The orientation of component minerals and pores/fractures is a critical factor that influences elastic anisotropy. In this study, we investigate lattice and shape preferred orientation (LPO and SPO) of three shales from the North Sea in UK, the Qusaiba Formation in Saudi Arabia, and the Officer Basin in Australia (referred to as N1, Qu3, and L1905, respectively) to calculate elastic properties and compare them with experimental results. Synchrotron hard X-ray diffraction and microtomography experiments were performed to quantify LPO, weight proportions, and three-dimensional SPO of constituent minerals and pores. Our preliminary results show that the degree of LPO and total amount of clays are highest in Qu3 (3.3-6.5 m.r.d and 74vol%), moderately high in N1 (2.4-5.6 m.r.d. and 70vol%), and lowest in L1905 (2.3-2.5 m.r.d. and 42vol%). In addition, porosity in Qu3 is as low as 2% while it is up to 6% in L1605 and 8% in N1, respectively. Based on this information and single crystal elastic properties of mineral components, we apply a self-consistent averaging method to calculate macroscopic elastic properties and corresponding seismic velocities for different shales. The elastic model is then compared with measured acoustic velocities on the same samples. The P-wave velocities measured from Qu3 (4.1-5.3 km/s, 26.3%Ani.) are faster than those obtained from L1905 (3.9-4.7 km/s, 18.6%Ani.) and N1 (3.6-4.3 km/s, 17.7%Ani.). By making adjustments for pore structure (aspect ratio) and single crystal elastic properties of clay minerals, a good agreement between our calculation and the ultrasonic measurement is obtained.
Mathematical models and algorithms for the computer program 'WOLF'
International Nuclear Information System (INIS)
Halbach, K.
1975-12-01
The computer program FLOW finds the nonrelativistic self- consistent set of two-dimensional ion trajectories and electric fields (including space charges from ions and electrons) for a given set of initial and boundary conditions for the particles and fields. The combination of FLOW with the optimization code PISA gives the program WOLF, which finds the shape of the emitter which is consistent with the plasma forming it, and in addition varies physical characteristics such as electrode position, shapes, and potentials so that some performance characteristics are optimized. The motivation for developing these programs was the desire to design optimum ion source extractor/accelerator systems in a systematic fashion. The purpose of this report is to explain and derive the mathematical models and algorithms which approximate the real physical processes. It serves primarily to document the computer programs. 10 figures
Mathematical Modeling of Tuberculosis Granuloma Activation
Directory of Open Access Journals (Sweden)
Steve M. Ruggiero
2017-12-01
Full Text Available Tuberculosis (TB is one of the most common infectious diseases worldwide. It is estimated that one-third of the world’s population is infected with TB. Most have the latent stage of the disease that can later transition to active TB disease. TB is spread by aerosol droplets containing Mycobacterium tuberculosis (Mtb. Mtb bacteria enter through the respiratory system and are attacked by the immune system in the lungs. The bacteria are clustered and contained by macrophages into cellular aggregates called granulomas. These granulomas can hold the bacteria dormant for long periods of time in latent TB. The bacteria can be perturbed from latency to active TB disease in a process called granuloma activation when the granulomas are compromised by other immune response events in a host, such as HIV, cancer, or aging. Dysregulation of matrix metalloproteinase 1 (MMP-1 has been recently implicated in granuloma activation through experimental studies, but the mechanism is not well understood. Animal and human studies currently cannot probe the dynamics of activation, so a computational model is developed to fill this gap. This dynamic mathematical model focuses specifically on the latent to active transition after the initial immune response has successfully formed a granuloma. Bacterial leakage from latent granulomas is successfully simulated in response to the MMP-1 dynamics under several scenarios for granuloma activation.
A mathematical model of forgetting and amnesia
Directory of Open Access Journals (Sweden)
Jaap M. J. Murre
2013-02-01
Full Text Available We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time-scales share two fundamental properties: (1 representations in a store decline in strength (2 while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i the temporal gradient of retrograde amnesia (Ribot's Law, (ii forgetting curves with and without anterograde amnesia, and (iii learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff's Disease, Alzheimer's Dementia, Huntington's Disease, and other disorders.
Simple mathematical models of gene regulatory dynamics
Mackey, Michael C; Tyran-Kamińska, Marta; Zeron, Eduardo S
2016-01-01
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduat...
Mathematical modeling of the mixing zone for getting bimetallic compound
Energy Technology Data Exchange (ETDEWEB)
Kim, Stanislav L. [Institute of Applied Mechanics, Ural Branch, Izhevsk (Russian Federation)
2011-07-01
A mathematical model of the formation of atomic bonds in metals and alloys, based on the electrostatic interaction between the outer electron shells of atoms of chemical elements. Key words: mathematical model, the interatomic bonds, the electron shell of atoms, the potential, the electron density, bimetallic compound.
iSTEM: Promoting Fifth Graders' Mathematical Modeling
Yanik, H. Bahadir; Karabas, Celil
2014-01-01
Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…
PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE
Directory of Open Access Journals (Sweden)
N. V. Andrianov
2006-01-01
Full Text Available The analysis of the mathematical models which can be used at optimization of the control system of the enterprise organizational structure is presented. The new approach to the mathematical modeling of the enterprise organizational structure, based on using of temporary characteristics of the control blocks working, is formulated
How to Introduce Mathematic Modeling in Industrial Design Education
Langereis, G.R.; Hu, J.; Feijs, L.M.G.; Stillmann, G.A.; Kaiser, G.; Blum, W.B.; Brown, J.P.
2013-01-01
With competency based learning in a project driven environment, we are facing a different perspective of how students perceive mathematical modelling. In this chapter, a model is proposed where conventional education is seen as a process from mathematics to design, while competency driven approaches
Mathematical Modelling Research in Turkey: A Content Analysis Study
Çelik, H. Coskun
2017-01-01
The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…
An Integrated Approach to Mathematical Modeling: A Classroom Study.
Doerr, Helen M.
Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…
Mathematical modeling of dissolved oxygen in fish ponds ...
African Journals Online (AJOL)
Mathematical modeling of dissolved oxygen in fish ponds. WJS Mwegoha, ME Kaseva, SMM Sabai. Abstract. A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide and chemical oxygen demand (COD) on Dissolved Oxygen (DO) in fish ponds. The effects ...
Achilles and the tortoise: Some caveats to mathematical modeling in biology.
Gilbert, Scott F
2018-01-31
Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.
Incorporating neurophysiological concepts in mathematical thermoregulation models
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
Genetic demographic networks: Mathematical model and applications.
Kimmel, Marek; Wojdyła, Tomasz
2016-10-01
Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise
MATHEMATICAL MODELING OF AC ELECTRIC POINT MOTOR
Directory of Open Access Journals (Sweden)
S. YU. Buryak
2014-03-01
Full Text Available Purpose. In order to ensure reliability, security, and the most important the continuity of the transportation process, it is necessary to develop, implement, and then improve the automated methods of diagnostic mechanisms, devices and rail transport systems. Only systems that operate in real time mode and transmit data on the instantaneous state of the control objects can timely detect any faults and thus provide additional time for their correction by railway employees. Turnouts are one of the most important and responsible components, and therefore require the development and implementation of such diagnostics system.Methodology. Achieving the goal of monitoring and control of railway automation objects in real time is possible only with the use of an automated process of the objects state diagnosing. For this we need to know the diagnostic features of a control object, which determine its state at any given time. The most rational way of remote diagnostics is the shape and current spectrum analysis that flows in the power circuits of railway automatics. Turnouts include electric motors, which are powered by electric circuits, and the shape of the current curve depends on both the condition of the electric motor, and the conditions of the turnout maintenance. Findings. For the research and analysis of AC electric point motor it was developed its mathematical model. The calculation of parameters and interdependencies between the main factors affecting the operation of the asynchronous machine was conducted. The results of the model operation in the form of time dependences of the waveform curves of current on the load on engine shaft were obtained. Originality. During simulation the model of AC electric point motor, which satisfies the conditions of adequacy was built. Practical value. On the basis of the constructed model we can study the AC motor in various mode of operation, record and analyze current curve, as a response to various changes
Mathematical modeling of biomass fuels formation process
International Nuclear Information System (INIS)
Gaska, Krzysztof; Wandrasz, Andrzej J.
2008-01-01
The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task
Self-consistent modelling of resonant tunnelling structures
DEFF Research Database (Denmark)
Fiig, T.; Jauho, A.P.
1992-01-01
We report a comprehensive study of the effects of self-consistency on the I-V-characteristics of resonant tunnelling structures. The calculational method is based on a simultaneous solution of the effective-mass Schrödinger equation and the Poisson equation, and the current is evaluated...... applied voltages and carrier densities at the emitter-barrier interface. We include the two-dimensional accumulation layer charge and the quantum well charge in our self-consistent scheme. We discuss the evaluation of the current contribution originating from the two-dimensional accumulation layer charges......, and our qualitative estimates seem consistent with recent experimental studies. The intrinsic bistability of resonant tunnelling diodes is analyzed within several different approximation schemes....
Self-consistent approach for neutral community models with speciation
Haegeman, Bart; Etienne, Rampal S.
Hubbell's neutral model provides a rich theoretical framework to study ecological communities. By incorporating both ecological and evolutionary time scales, it allows us to investigate how communities are shaped by speciation processes. The speciation model in the basic neutral model is
Exotic nuclei in self-consistent mean-field models
International Nuclear Information System (INIS)
Bender, M.; Rutz, K.; Buervenich, T.; Reinhard, P.-G.; Maruhn, J. A.; Greiner, W.
1999-01-01
We discuss two widely used nuclear mean-field models, the relativistic mean-field model and the (nonrelativistic) Skyrme-Hartree-Fock model, and their capability to describe exotic nuclei with emphasis on neutron-rich tin isotopes and superheavy nuclei. (c) 1999 American Institute of Physics
Mathematics of epidemics on networks from exact to approximate models
Kiss, István Z; Simon, Péter L
2017-01-01
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...
Mathematical models in marketing a collection of abstracts
Funke, Ursula H
1976-01-01
Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...
Mathematical model of radon activity measurements
Energy Technology Data Exchange (ETDEWEB)
Paschuk, Sergei A.; Correa, Janine N.; Kappke, Jaqueline; Zambianchi, Pedro, E-mail: sergei@utfpr.edu.br, E-mail: janine_nicolosi@hotmail.com [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Denyak, Valeriy, E-mail: denyak@gmail.com [Instituto de Pesquisa Pele Pequeno Principe, Curitiba, PR (Brazil)
2015-07-01
Present work describes a mathematical model that quantifies the time dependent amount of {sup 222}Rn and {sup 220}Rn altogether and their activities within an ionization chamber as, for example, AlphaGUARD, which is used to measure activity concentration of Rn in soil gas. The differential equations take into account tree main processes, namely: the injection of Rn into the cavity of detector by the air pump including the effect of the traveling time Rn takes to reach the chamber; Rn release by the air exiting the chamber; and radioactive decay of Rn within the chamber. Developed code quantifies the activity of {sup 222}Rn and {sup 220}Rn isotopes separately. Following the standard methodology to measure Rn activity in soil gas, the air pump usually is turned off over a period of time in order to avoid the influx of Rn into the chamber. Since {sup 220}Rn has a short half-life time, approximately 56s, the model shows that after 7 minutes the activity concentration of this isotope is null. Consequently, the measured activity refers to {sup 222}Rn, only. Furthermore, the model also addresses the activity of {sup 220}Rn and {sup 222}Rn progeny, which being metals represent potential risk of ionization chamber contamination that could increase the background of further measurements. Some preliminary comparison of experimental data and theoretical calculations is presented. Obtained transient and steady-state solutions could be used for planning of Rn in soil gas measurements as well as for accuracy assessment of obtained results together with efficiency evaluation of chosen measurements procedure. (author)
Perspectives on instructor modeling in mathematics teacher education
Brown, Cassondra
2009-01-01
Teachers' instructional practices are greatly shaped by their own learning experiences as students in K-12 and college classrooms, which for most teachers was traditional, teacher-centered instruction. One of the challenges facing mathematics education reform is that, traditional teaching is in contrast to reform student- centered instruction. If teachers learn from their experiences as mathematics students, mathematics teacher educators are encouraged to model practices they would like teach...
Data driven mathematical models for policy making
Nannyonga, Betty
2011-01-01
This thesis consists of two papers. 1. Betty Nannyonga, D.J.T. Sumpter, J.Y.T. Mugisha and L.S. Luboobi: The Dynamics,causes and possible prevention of Hepaititis E outbreaks. 2. Betty Nannyonga, D.J.T. Sumpter, andStam Nicolis: A dynamical systems approach tosocial and economic development. The first paper deals with a deterministic approach of modelling a Hepatitis E outbreak whenmalaria is endemic in a population. We design three models based on the epidemiology ofHepatitis E, malaria, and...
Quantum Gravity Mathematical Models and Experimental Bounds
Fauser, Bertfried; Zeidler, Eberhard
2007-01-01
The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...
Symmetrization of mathematical model of charge transport in semiconductors
Directory of Open Access Journals (Sweden)
Alexander M. Blokhin
2002-11-01
Full Text Available A mathematical model of charge transport in semiconductors is considered. The model is a quasilinear system of differential equations. A problem of finding an additional entropy conservation law and system symmetrization are solved.
Is the island universe model consistent with observations?
Piao, Yun-Song
2005-01-01
We study the island universe model, in which initially the universe is in a cosmological constant sea, then the local quantum fluctuations violating the null energy condition create the islands of matter, some of which might corresponds to our observable universe. We examine the possibility that the island universe model is regarded as an alternative scenario of the origin of observable universe.
The mathematics of models for climatology and environment. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Ildefonso Diaz, J. [ed.] [Universidad Complutense de Madrid (Spain). Facultad de Ciencas Matematicas
1997-12-31
This book presents a coherent survey of modelling in climatology and the environment and the mathematical treatment of those problems. It is divided into 4 parts containing a total of 16 chapters. Parts I, II and III are devoted to general models and part IV to models related to some local problems. Most of the mathematical models considered here involve systems of nonlinear partial differential equations.
Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent
2017-01-01
The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...
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.
Thermodynamically consistent description of criticality in models of correlated electrons
Czech Academy of Sciences Publication Activity Database
Janiš, Václav; Kauch, Anna; Pokorný, Vladislav
2017-01-01
Roč. 95, č. 4 (2017), s. 1-14, č. článku 045108. ISSN 2469-9950 R&D Projects: GA ČR GA15-14259S Institutional support: RVO:68378271 Keywords : conserving approximations * Anderson model * Hubbard model * parquet equations Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Condensed matter physics (including formerly solid state physics, supercond.) Impact factor: 3.836, year: 2016
Consistent Evolution of Software Artifacts and Non-Functional Models
2014-11-14
induce bad software performance)? 15. SUBJECT TERMS EOARD, Nano particles, Photo-Acoustic Sensors, Model-Driven Engineering ( MDE ), Software Performance...Università degli Studi dell’Aquila, Via Vetoio, 67100 L’Aquila, Italy Email: vittorio.cortellessa@univaq.it Web : http: // www. di. univaq. it/ cortelle/ Phone...Model-Driven Engineering ( MDE ), Software Performance Engineering (SPE), Change Propagation, Performance Antipatterns. For sake of readability of the
Mathematical modeling and computational intelligence in engineering applications
Silva Neto, Antônio José da; Silva, Geraldo Nunes
2016-01-01
This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.
Mathematical Model of Nicholson’s Experiment
Directory of Open Access Journals (Sweden)
Sergey D. Glyzin
2017-01-01
Full Text Available Considered is a mathematical model of insects population dynamics, and an attempt is made to explain classical experimental results of Nicholson with its help. In the first section of the paper Nicholson’s experiment is described and dynamic equations for its modeling are chosen. A priori estimates for model parameters can be made more precise by means of local analysis of the dynamical system, that is carried out in the second section. For parameter values found there the stability loss of the problem equilibrium of the leads to the bifurcation of a stable two-dimensional torus. Numerical simulations based on the estimates from the second section allows to explain the classical Nicholson’s experiment, whose detailed theoretical substantiation is given in the last section. There for an atrractor of the system the largest Lyapunov exponent is computed. The nature of this exponent change allows to additionally narrow the area of model parameters search. Justification of this experiment was made possible only due to the combination of analytical and numerical methods in studying equations of insects population dynamics. At the same time, the analytical approach made it possible to perform numerical analysis in a rather narrow region of the parameter space. It is not possible to get into this area, based only on general considerations.
Mathematical manipulative models: in defense of "beanbag biology".
Jungck, John R; Gaff, Holly; Weisstein, Anton E
2010-01-01
Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.
Technological geological and mathematical models of petroleum stratum
International Nuclear Information System (INIS)
Zhumagulov, B.T.; Monakhov, V.N.
1997-01-01
The comparative analysis of different mathematical methods of petroleum stratum, the limit of their applicability and hydrodynamical analysis of numerical calculation's results is carried out. The problem of adaptation of the mathematical models and the identification of petroleum stratum parameters are considered. (author)
Mathematical Modeling, Sense Making, and the Common Core State Standards
Schoenfeld, Alan H.
2013-01-01
On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…
Teaching Writing and Communication in a Mathematical Modeling Course
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
Phase models of galaxies consisting of disk and halo
International Nuclear Information System (INIS)
Osipkov, L.P.; Kutuzov, S.A.
1987-01-01
A method of finding the phase density of a two-component model of mass distribution is developed. The equipotential surfaces and the potential law are given. The equipotentials are lenslike surfaces with a sharp edge in the equatorial plane, which provides the existence of an imbedded thin disk in halo. The equidensity surfaces of the halo coincide with the equipotentials. Phase models for the halo and the disk are constructed separately on the basis of spatial and surface mass densities by solving the corresponding integral equations. In particular the models for the halo with finite dimensions can be constructed. The even part of the phase density in respect to velocities is only found. For the halo it depends on the energy integral as a single argument
Phase models of galaxies consisting of a disk and halo
International Nuclear Information System (INIS)
Osipkov, L.P.; Kutuzov, S.A.
1988-01-01
A method is developed for finding the phase density of a two-component model of a distribution of masses. The equipotential surfaces and potential law are given. The equipotentials are lenslike surfaces with a sharp edge in the equatorial plane, this ensuring the existence of a vanishingly thin embedded disk. The equidensity surfaces of the halo coincide with the equipotentials. Phase models are constructed separately for the halo and for the disk on the basis of the spatial and surface mass densities by the solution of the corresponding integral equations. In particular, models with a halo having finite dimensions can be constructed. For both components, the part of the phase density even with respect to the velocities is found. For the halo, it depends only on the energy integral. Two examples, for which exact solutions are found, are considered
A whole-body mathematical model for intracranial pressure dynamics.
Lakin, William D; Stevens, Scott A; Tranmer, Bruce I; Penar, Paul L
2003-04-01
Most attempts to study intracranial pressure using lumped-parameter models have adopted the classical "Kellie-Monro Doctrine," which considers the intracranial space to be a closed system that is confined within the nearly-rigid skull, conserves mass, and has equal inflow and outflow. The present work revokes this Doctrine and develops a mathematical model for the dynamics of intracranial pressures, volumes, and flows that embeds the intracranial system in extensive whole-body physiology. The new model consistently introduces compartments representing the tissues and vasculature of the extradural portions of the body, including both the thoracic region and the lower extremities. In addition to vascular connections, a spinal-subarachnoid cerebrospinal fluid (CSF) compartment bridges intracranial and extracranial physiology allowing explict buffering of intracranial pressure fluctuations by the spinal theca. The model contains cerebrovascular autoregulation, regulation of systemic vascular pressures by the sympathetic nervous system, regulation of CSF production in the choroid plexus, a lymphatic system, colloid osmotic pressure effects, and realistic descriptions of cardiac output. To validate the model in situations involving normal physiology, the model's response to a realistic pulsatile cardiac output is examined. A well-known experimentally-derived intracranial pressure-volume relationship is recovered by using the model to simulate CSF infusion tests, and the effect on cerebral blood flow of a change in body position is also examined. Cardiac arrest and hemorrhagic shock are simulated to demonstrate the predictive capabilities of the model in pathological conditions.
Mathematical model of melt flow channel granulator
Directory of Open Access Journals (Sweden)
A. A. Kiselev
2016-01-01
Full Text Available Granulation of carbohydrate-vitamin-mineral supplements based on molasses is performed at a high humidity (26 %, so for a stable operation of granulator it is necessary to reveal its melt flow pattern. To describe melt non-isothermal flow in the granulator a mathematical model with following initial equations: continuity equation, motion equation and rheological equation – was developed. The following assumptions were adopted: the melt flow in the granulator is a steady laminar flow; inertial and gravity forces can be ignored; melt is an incompressible fluid; velocity gradient in the flow direction is much smaller than in the transverse direction; the pressure gradient over the cross section of the channel is constant; the flow is hydrodynamically fully developed; effects impact on the channel inlet and outlet may be neglected. Due to the assumptions adopted, it can be considered that in this granulator only velocity components in the x-direction are significant and all the members of the equation with the components and their derivatives with respect to the coordinates y and z can be neglected. The resulting solutions were obtained: the equation for the mean velocity, the equation for determining the volume flow, the formula for calculating of mean time of the melt being in the granulator, the equation for determining the shear stress, the equation for determining the shear rate and the equation for determining the pressure loss. The results of calculations of the equations obtained are in complete agreement with the experimental data; deviation range is 16–19 %. The findings about the melt movement pattern in granulator allowed developing a methodology for calculating a rational design of the granulator molding unit.
Mathematical modeling in wound healing, bone regeneration and tissue engineering.
Geris, Liesbet; Gerisch, Alf; Schugart, Richard C
2010-12-01
The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.
Flood damage: a model for consistent, complete and multipurpose scenarios
Menoni, Scira; Molinari, Daniela; Ballio, Francesco; Minucci, Guido; Mejri, Ouejdane; Atun, Funda; Berni, Nicola; Pandolfo, Claudia
2016-12-01
Effective flood risk mitigation requires the impacts of flood events to be much better and more reliably known than is currently the case. Available post-flood damage assessments usually supply only a partial vision of the consequences of the floods as they typically respond to the specific needs of a particular stakeholder. Consequently, they generally focus (i) on particular items at risk, (ii) on a certain time window after the occurrence of the flood, (iii) on a specific scale of analysis or (iv) on the analysis of damage only, without an investigation of damage mechanisms and root causes. This paper responds to the necessity of a more integrated interpretation of flood events as the base to address the variety of needs arising after a disaster. In particular, a model is supplied to develop multipurpose complete event scenarios. The model organizes available information after the event according to five logical axes. This way post-flood damage assessments can be developed that (i) are multisectoral, (ii) consider physical as well as functional and systemic damage, (iii) address the spatial scales that are relevant for the event at stake depending on the type of damage that has to be analyzed, i.e., direct, functional and systemic, (iv) consider the temporal evolution of damage and finally (v) allow damage mechanisms and root causes to be understood. All the above features are key for the multi-usability of resulting flood scenarios. The model allows, on the one hand, the rationalization of efforts currently implemented in ex post damage assessments, also with the objective of better programming financial resources that will be needed for these types of events in the future. On the other hand, integrated interpretations of flood events are fundamental to adapting and optimizing flood mitigation strategies on the basis of thorough forensic investigation of each event, as corroborated by the implementation of the model in a case study.
A simple mathematical model of society collapse applied to Easter Island
Bologna, M.; Flores, J. C.
2008-02-01
In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society. Based on historical reports, the available primary resources consisted almost exclusively in the trees, then we describe the inhabitants and the resources as an isolated dynamical system. A mathematical, and numerical, analysis about the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters and a demographic curve is presented. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of another extinguished civilization (Copán Maya) confirming the consistency of the adopted model.
Mathematical model of gluconic acid fermentation by Aspergillus niger
Energy Technology Data Exchange (ETDEWEB)
Takamatsu, T.; Shioya, S.; Furuya, T.
1981-11-01
A mathematical model for the study of gluconic acid fermentation by Aspergillus niger has been developed. The model has been deduced from the basic biological concept of multicellular filamentous microorganisms, i.e. cell population balance. It can be used to explain the behaviour of both batch and continuous cultures, even when in a lag phase. A new characteristic, involving the existence of dual equilibrium stages during fermentation, has been predicted using this mathematical model. (Refs. 6).
A Mathematical Model, Implementation and Study of a Swarm System
Varghese, Blesson; McKee, Gerard
2013-01-01
The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to conf...
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.
a Discrete Mathematical Model to Simulate Malware Spreading
Del Rey, A. Martin; Sánchez, G. Rodriguez
2012-10-01
With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.
Dewi, N. R.; Arini, F. Y.
2018-03-01
The main purpose of this research is developing and produces a Calculus textbook model that supported with GeoGebra. This book was designed to enhancing students’ mathematical problem solving and mathematical representation. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 6 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2. The data were analyzed with descriptive statistics. The analysis showed that the Calculus textbook model that supported with GeoGebra, valid and fill up the criteria of practicality.
Kutepov, A L
2015-08-12
Self-consistent solutions of Hedin's equations (HE) for the two-site Hubbard model (HM) have been studied. They have been found for three-point vertices of increasing complexity (Γ = 1 (GW approximation), Γ1 from the first-order perturbation theory, and the exact vertex Γ(E)). Comparison is made between the cases when an additional quasiparticle (QP) approximation for Green's functions is applied during the self-consistent iterative solving of HE and when QP approximation is not applied. The results obtained with the exact vertex are directly related to the present open question-which approximation is more advantageous for future implementations, GW + DMFT or QPGW + DMFT. It is shown that in a regime of strong correlations only the originally proposed GW + DMFT scheme is able to provide reliable results. Vertex corrections based on perturbation theory (PT) systematically improve the GW results when full self-consistency is applied. The application of QP self-consistency combined with PT vertex corrections shows similar problems to the case when the exact vertex is applied combined with QP sc. An analysis of Ward Identity violation is performed for all studied in this work's approximations and its relation to the general accuracy of the schemes used is provided.
Key Concept Mathematics and Management Science Models
Macbeth, Thomas G.; Dery, George C.
1973-01-01
The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)
Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors
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.
On the internal consistency of holographic dark energy models
International Nuclear Information System (INIS)
Horvat, R
2008-01-01
Holographic dark energy (HDE) models, underpinned by an effective quantum field theory (QFT) with a manifest UV/IR connection, have become convincing candidates for providing an explanation of the dark energy in the universe. On the other hand, the maximum number of quantum states that a conventional QFT for a box of size L is capable of describing relates to those boxes which are on the brink of experiencing a sudden collapse to a black hole. Another restriction on the underlying QFT is that the UV cut-off, which cannot be chosen independently of the IR cut-off and therefore becomes a function of time in a cosmological setting, should stay the largest energy scale even in the standard cosmological epochs preceding a dark energy dominated one. We show that, irrespective of whether one deals with the saturated form of HDE or takes a certain degree of non-saturation in the past, the above restrictions cannot be met in a radiation dominated universe, an epoch in the history of the universe which is expected to be perfectly describable within conventional QFT
Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity
Stohlmann, Micah S.
2017-01-01
Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…
Mathematical Modelling for Micropiles Embedded in Salt Rock
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-
Mechanical-mathematical modeling for landslide process
Svalova, V.
2009-04-01
500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.
Schwerdtfeger, Sara
2017-01-01
This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…
Coupling between phosphate and calcium homeostasis: a mathematical model.
Granjon, David; Bonny, Olivier; Edwards, Aurélie
2017-12-01
We developed a mathematical model of calcium (Ca) and phosphate (PO 4 ) homeostasis in the rat to elucidate the hormonal mechanisms that underlie the regulation of Ca and PO 4 balance. The model represents the exchanges of Ca and PO 4 between the intestine, plasma, kidneys, bone, and the intracellular compartment, and the formation of Ca-PO 4 -fetuin-A complexes. It accounts for the regulation of these fluxes by parathyroid hormone (PTH), vitamin D 3 , fibroblast growth factor 23, and Ca 2+ -sensing receptors. Our results suggest that the Ca and PO 4 homeostatic systems are robust enough to handle small perturbations in the production rate of either PTH or vitamin D 3 The model predicts that large perturbations in PTH or vitamin D 3 synthesis have a greater impact on the plasma concentration of Ca 2+ ([Ca 2+ ] p ) than on that of PO 4 ([PO 4 ] p ); due to negative feedback loops, [PO 4 ] p does not consistently increase when the production rate of PTH or vitamin D 3 is decreased. Our results also suggest that, following a large PO 4 infusion, the rapidly exchangeable pool in bone acts as a fast, transient storage PO 4 compartment (on the order of minutes), whereas the intracellular pool is able to store greater amounts of PO 4 over several hours. Moreover, a large PO 4 infusion rapidly lowers [Ca 2+ ] p owing to the formation of CaPO 4 complexes. A large Ca infusion, however, has a small impact on [PO 4 ] p , since a significant fraction of Ca binds to albumin. This mathematical model is the first to include all major regulatory factors of Ca and PO 4 homeostasis. Copyright © 2017 the American Physiological Society.
Mathematical rainfall model for hydrographic demarcation of Manabi ...
African Journals Online (AJOL)
PROMOTING ACCESS TO AFRICAN RESEARCH ... To achieve this objective, the basins of the Hydrographic Demarcation of Manabí ... Keywords: multiple regression; mathematical model; GIS; Hydrology; rainfall. ... HOW TO USE AJOL.
Mathematical models of thermohydraulic disturbance sources in the NPP circuits
International Nuclear Information System (INIS)
Proskuryakov, K.N.
1999-01-01
Methods and means of diagnostics of equipment and processes at NPPs allowing one to substantially increase safety and economic efficiency of nuclear power plant operation are considered. Development of mathematical models, describing the occurrence and propagation of violations is conducted
Mathematical modelling of a farm enterprise value on the ...
African Journals Online (AJOL)
Mathematical modelling of a farm enterprise value on the agricultural market with the ... Subsidies in the EU countries reached 45-50% of the value of commodity output ... This financing gap entailed a number of negative consequences.
Stability Analysis of a Mathematical Model for Onchocerciaisis ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: In this work, we propose a Deterministic Mathematical Model that ... blackflies Center for Disease Control and World ... villages located along fast flowing rivers where the ..... distribution of Blackflies (Simulium Species) in.
Improved Mathematical Models for Particle-Size Distribution Data
African Journals Online (AJOL)
BirukEdimon
School of Civil & Environmental Engineering, Addis Ababa Institute of Technology,. 3. Murray Rix ... two improved mathematical models to describe ... demand further improvement to handle the PSD ... statistics and the range of the optimized.
MATHEMATICAL MODELING OF HEATING AND COOLING OF SAUSAGES
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A. V. Zhuchkov
2013-01-01
Full Text Available In the article the mathematical modeling of the processes of heating and cooling of sausage products in order to define reference characteristics of the processes was carried out. Basic regularities of the processes are graphically shown.
Mathematical and numerical foundations of turbulence models and applications
Chacón Rebollo, Tomás
2014-01-01
With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering, and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation, and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics,...
PREFACE: Physics-Based Mathematical Models for Nanotechnology
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
in the cross-disciplinary research area: low-dimensional semiconductor nanostructures. Since the main properties of two-dimensional heterostructures (such as quantum wells) are now quite well understood, there has been a consistently growing interest in the mathematical physics community to further dimensionality reduction of semiconductor structures. Experimental achievements in realizing one-dimensional and quasi-zero-dimensional heterostructures have opened new opportunities for theory and applications of such low-dimensional semiconductor nanostructures. One of the most important implications of this process has been a critical re-examining of assumptions under which traditional quantum mechanical models have been derived in this field. Indeed, the formation of LDSNs, in particular quantum dots, is a competition between the surface energy in the structure and strain energy. However, current models for bandstructure calculations use quite a simplified analysis of strain relaxation effects, although such effects are in the heart of nanostructure formation. By now, it has been understood that traditional models in this field may not be adequate for modeling realistic objects based on LDSNs due to neglecting many effects that may profoundly influence optoelectronic properties of the nanostructures. Among such effects are electromechanical effects, including strain relaxation, piezoelectric effect, spontaneous polarization, and higher order nonlinear effects. Up to date, major efforts have been concentrated on the analysis of idealized, isolated quantum dots, while a typical self-assembled semiconductor quantum dot nanostructure is an array (or a molecule) of many individual quantum dots sitting on the same `substrate' known as the wetting layer. Each such dot contains several hundred thousand atoms. In order to account for quantum effects accurately in a situation like that, attempts can be made to apply ab initio or atomistic methodologies, but then one would face a
A mathematical look at a physical power prediction model
DEFF Research Database (Denmark)
Landberg, L.
1998-01-01
This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...
2nd Tbilisi-Salerno Workshop on Modeling in Mathematics
Ricci, Paolo; Tavkhelidze, Ilia
2017-01-01
This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling in March 2015. The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such topics as multimodal logic, fractional calculus, special functions, Fourier-like solutions for PDE’s, Rvachev-functions and linear dynamical systems. Special chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula. The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.
A Mathematical Approach to Establishing Constitutive Models for Geomaterials
Directory of Open Access Journals (Sweden)
Guang-hua Yang
2013-01-01
Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.
A practical course in differential equations and mathematical modeling
Ibragimov , Nail H
2009-01-01
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame
Mathematical model of polyethylene pipe bending stress state
Serebrennikov, Anatoly; Serebrennikov, Daniil
2018-03-01
Introduction of new machines and new technologies of polyethylene pipeline installation is usually based on the polyethylene pipe flexibility. It is necessary that existing bending stresses do not lead to an irreversible polyethylene pipe deformation and to violation of its strength characteristics. Derivation of the mathematical model which allows calculating analytically the bending stress level of polyethylene pipes with consideration of nonlinear characteristics is presented below. All analytical calculations made with the mathematical model are experimentally proved and confirmed.
MATHEMATICAL MODELLING OF AIRCRAFT PILOTING PROSSESS UNDER SPECIFIED FLIGHT PATH
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И. Кузнецов
2012-04-01
Full Text Available The author suggests mathematical model of pilot’s activity as follow up system and mathematical methods of pilot’s activity description. The main idea of the model is flight path forming and aircraft stabilization on it during instrument flight. Input of given follow up system is offered to be aircraft deflection from given path observed by pilot by means of sight and output is offered to be pilot’s regulating actions for aircraft stabilization on flight path.
Mathematical modeling of a V-stack piezoelectric aileron actuation
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.
Classical and Weak Solutions for Two Models in Mathematical Finance
Gyulov, Tihomir B.; Valkov, Radoslav L.
2011-12-01
We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.
Mathematical modelling and numerical simulation of oil pollution problems
2015-01-01
Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics, together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems. The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...
Mathematical modelling of non-isothermal venturi scrubbers
Energy Technology Data Exchange (ETDEWEB)
Rahimi, A. [Isfahan Univ., Isfahan (Iran, Islamic Republic of). Dept. of Chemical Engineering; Taheri, M.; Fathikakajahi, J. [Shiraz Univ., Shiraz (Iran, Islamic Republic of). Dept. of Chemical Engineering
2005-06-01
Venturi scrubbers collect gaseous pollutants and particulate matter from industrial exhaust. This air pollution control device is highly efficient, easy to maintain and has a low initial cost. However, the high pressure drop through the device results in a high running cost. The main mechanism for collecting particulates is the inertial impaction of the particles on the droplets, which occurs due to high velocity between the gas stream and droplets. Droplet acceleration and irreversible drag-force which results from this high relative velocity are responsible for the high pressure drop in this type of scrubber. While several attempts have been made to mathematically model particulate removal in Venturi scrubbers, most models do not consider simultaneous heat and mass transfer. This factor is important because most Venturi scrubbers operate under non-isothermal conditions where the inlet gas is humidified in order to cool it before entering the scrubber. For that reason, the authors developed a more realistic model to determine the effects of heat and mass transfer on the particulate removal efficiency of a non-isothermal Venturi type scrubber. The model considers the effect of droplet size distribution and liquid film flow on the walls. It consists of differential equations for energy, momentum and material exchange. Model results were compared with data from experimental studies and industrial facilities. It was concluded that the removal efficiency of the scrubber is influenced by the inlet humidity temperature of the inlet gas. 26 refs., 1 tab., 10 figs.
Thermodynamically Consistent Algorithms for the Solution of Phase-Field Models
Vignal, Philippe
2016-02-11
Phase-field models are emerging as a promising strategy to simulate interfacial phenomena. Rather than tracking interfaces explicitly as done in sharp interface descriptions, these models use a diffuse order parameter to monitor interfaces implicitly. This implicit description, as well as solid physical and mathematical footings, allow phase-field models to overcome problems found by predecessors. Nonetheless, the method has significant drawbacks. The phase-field framework relies on the solution of high-order, nonlinear partial differential equations. Solving these equations entails a considerable computational cost, so finding efficient strategies to handle them is important. Also, standard discretization strategies can many times lead to incorrect solutions. This happens because, for numerical solutions to phase-field equations to be valid, physical conditions such as mass conservation and free energy monotonicity need to be guaranteed. In this work, we focus on the development of thermodynamically consistent algorithms for time integration of phase-field models. The first part of this thesis focuses on an energy-stable numerical strategy developed for the phase-field crystal equation. This model was put forward to model microstructure evolution. The algorithm developed conserves, guarantees energy stability and is second order accurate in time. The second part of the thesis presents two numerical schemes that generalize literature regarding energy-stable methods for conserved and non-conserved phase-field models. The time discretization strategies can conserve mass if needed, are energy-stable, and second order accurate in time. We also develop an adaptive time-stepping strategy, which can be applied to any second-order accurate scheme. This time-adaptive strategy relies on a backward approximation to give an accurate error estimator. The spatial discretization, in both parts, relies on a mixed finite element formulation and isogeometric analysis. The codes are
Directory of Open Access Journals (Sweden)
Wannaree Pansiri
2016-12-01
Full Text Available The objectives of this research were 1 to develop the assessment for learning model of Mathematics for Rajamangala University 2 to study the effectivness of assessment for learning model of Mathematics for Rajamagala University of Technology Rattanakosin. The research target group consisted of 72 students from 3 classes and 3 General Mathematics teachers. The data was gathered from observation, worksheets, achievement test and skill of assessment for learning, questionnaire of the assessment for learning model of Mathematics. The statistics that used in this research were Frequency, Percentage, Mean, Standard Deviation, and Growth Score. The results of this research were 1. The assessment of learning model of Mathematics for Rajamangala University of Technology Rattanakosin consisted of 3 components ; 1. Pre-assessment which consisted of 4 activities ; a Preparation b Teacher development c Design and creation the assessment plan and instrument for assessment and d Creation of the learning experience plan 2. The component for assessment process consisted of 4 steps which were a Identifying the learning objectives and criteria b Identifying the learning experience plan and assessment follow the plan c Learning reflection and giving feedback and d Learner development based on information and improve instruction and 3. Giving feedback component. 2. The effective of assessment for learning model found that most students had good score in concentration, honest, responsibilities, group work, task presentation, worksheets, and doing exercises. The development knowledge of learning and knowledge and skill of assessment for learning of lecturers were fairly good. The opinion to the assessment for learning of learners and assessment for learning model of Mathematics of teachers found that was in a good level.
A mathematical model of sentimental dynamics accounting for marital dissolution.
Rey, José-Manuel
2010-03-31
Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.
A mathematical model of sentimental dynamics accounting for marital dissolution.
Directory of Open Access Journals (Sweden)
José-Manuel Rey
Full Text Available BACKGROUND: Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. METHODOLOGY/PRINCIPAL FINDINGS: Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. CONCLUSIONS/SIGNIFICANCE: These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.
Application of mathematical modeling in sustained release delivery systems.
Grassi, Mario; Grassi, Gabriele
2014-08-01
This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.
Directory of Open Access Journals (Sweden)
Nita Delima
2017-03-01
Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa. Kata Kunci: Comprehensive
Mathematical model for solid fuel combustion in fluidized bed
International Nuclear Information System (INIS)
Kostikj, Zvonimir; Noshpal, Aleksandar
1994-01-01
A mathematical model for computation of the combustion process of solid fuel in fluidized bed is presented in this work. Only the combustor part of the plant (the fluidized bed and the free board) is treated with this model. In that manner, all principal, physical presumption and improvements (upon which this model is based) are given. Finally, the results of the numerical realisation of the mathematical model for combustion of minced straw as well as the results of the experimental investigation of a concrete physical model are presented. (author)
Mathematical modeling of swirled flows in industrial applications
Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.
2018-03-01
Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.
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
A Long-Term Mathematical Model for Mining Industries
International Nuclear Information System (INIS)
Achdou, Yves; Giraud, Pierre-Noel; Lasry, Jean-Michel; Lions, Pierre-Louis
2016-01-01
A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.
A Long-Term Mathematical Model for Mining Industries
Energy Technology Data Exchange (ETDEWEB)
Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France); Giraud, Pierre-Noel [CERNA, Mines ParisTech (France); Lasry, Jean-Michel [Univ. Paris Dauphine (France); Lions, Pierre-Louis [Collège de France (France)
2016-12-15
A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.
Mathematical model for temperature change of a journal bearing
Directory of Open Access Journals (Sweden)
Antunović Ranko
2018-01-01
Full Text Available In this work, a representative mathematical model has been developed, which reliably describes the heating and cooling of a journal bearing as a result of its malfunctioning, and the model has been further confirmed on a test bench. The bearing model was validated by using analytical modeling methods, i. e. the experimental results were compared to the data obtained by analytical calculations. The regression and variance analysis techniques were applied to process the recorded data, to test the mathematical model and to define mathematical functions for the heating/cooling of the journal bearing. This investigation shows that a representative model may reliably indicate the change in the thermal field, which may be a consequence of journal bearing damage.
Saragih, Sahat; Napitupulu, E. Elvis; Fauzi, Amin
2017-01-01
This research aims to develop a student-centered learning model based on local culture and instrument of mathematical higher order thinking of junior high school students in the frame of the 2013-Curriculum in North Sumatra, Indonesia. The subjects of the research are seventh graders which are taken proportionally random consisted of three public…
Fasni, N.; Turmudi, T.; Kusnandi, K.
2017-09-01
This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.
Mathematical modeling of physiological systems: an essential tool for discovery.
Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J
2014-08-28
Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.
Potential of mathematical modeling in fruit quality | Vazquez-Cruz ...
African Journals Online (AJOL)
A review of mathematical modeling applied to fruit quality showed that these models ranged inresolution from simple yield equations to complex representations of processes as respiration, photosynthesis and assimilation of nutrients. The latter models take into account complex genotype environment interactions to ...
Mathematical modelling of dextran filtration through hollow fibre membranes
DEFF Research Database (Denmark)
Vinther, Frank; Pinelo, Manuel; Brøns, Morten
2014-01-01
In this paper we present a mathematical model of an ultrafiltration process. The results of the model are produced using standard numerical techniques with Comsol Multiphysics. The model describes the fluid flow and separation in hollow fibre membranes. The flow of solute and solvent within the h...
Díaz, Verónica; Poblete, Alvaro
2017-07-01
This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.
Mathematical model and simulations of radiation fluxes from buried radionuclides
International Nuclear Information System (INIS)
Ahmad Saat
1999-01-01
A mathematical model and a simple Monte Carlo simulations were developed to predict radiation fluxes from buried radionuclides. The model and simulations were applied to measured (experimental) data. The results of the mathematical model showed good acceptable order of magnitude agreement. A good agreement was also obtained between the simple simulations and the experimental results. Thus, knowing the radionuclide distribution profiles in soil from a core sample, it can be applied to the model or simulations to estimate the radiation fluxes emerging from the soil surface. (author)
Outlooks for mathematical modelling of the glass melting process
Energy Technology Data Exchange (ETDEWEB)
Waal, H. de [TNO Institute of Applied Physics, Delft (Netherlands)
1997-12-31
Mathematical modelling is nowadays a standard tool for major producers of float glass, T.V. glass and fiberglass. Also for container glass furnaces, glass tank modelling proves to be a valuable method to optimize process conditions. Mathematical modelling is no longer just a way to visualize the flow patterns and to provide data on heat transfer. It can also predict glass quality in relation to process parameters, because all chemical and physical phenomena are included in the latest generation of models, based on experimental and theoretical research on these phenomena.
Mathematical model comparing of the multi-level economics systems
Brykalov, S. M.; Kryanev, A. V.
2017-12-01
The mathematical model (scheme) of a multi-level comparison of the economic system, characterized by the system of indices, is worked out. In the mathematical model of the multi-level comparison of the economic systems, the indicators of peer review and forecasting of the economic system under consideration can be used. The model can take into account the uncertainty in the estimated values of the parameters or expert estimations. The model uses the multi-criteria approach based on the Pareto solutions.
Mathematical models for correction of images, obtained at radioisotope scan
International Nuclear Information System (INIS)
Glaz, A.; Lubans, A.
2002-01-01
The images, which obtained at radioisotope scintigraphy, contain distortions. Distortions appear as a result of absorption of radiation by patient's body's tissues. Two mathematical models for reducing of such distortions are proposed. Image obtained by only one gamma camera is used in the first mathematical model. Unfortunately, this model allows processing of the images only in case, when it can be assumed, that the investigated organ has a symmetric form. The images obtained by two gamma cameras are used in the second model. It gives possibility to assume that the investigated organ has non-symmetric form and to acquire more precise results. (authors)
A mathematical model for camera calibration based on straight lines
Directory of Open Access Journals (Sweden)
Antonio M. G. Tommaselli
2005-12-01
Full Text Available In other to facilitate the automation of camera calibration process, a mathematical model using straight lines was developed, which is based on the equivalent planes mathematical model. Parameter estimation of the developed model is achieved by the Least Squares Method with Conditions and Observations. The same method of adjustment was used to implement camera calibration with bundles, which is based on points. Experiments using simulated and real data have shown that the developed model based on straight lines gives results comparable to the conventional method with points. Details concerning the mathematical development of the model and experiments with simulated and real data will be presented and the results with both methods of camera calibration, with straight lines and with points, will be compared.
Consistency in Estimation and Model Selection of Dynamic Panel Data Models with Fixed Effects
Directory of Open Access Journals (Sweden)
Guangjie Li
2015-07-01
Full Text Available We examine the relationship between consistent parameter estimation and model selection for autoregressive panel data models with fixed effects. We find that the transformation of fixed effects proposed by Lancaster (2002 does not necessarily lead to consistent estimation of common parameters when some true exogenous regressors are excluded. We propose a data dependent way to specify the prior of the autoregressive coefficient and argue for comparing different model specifications before parameter estimation. Model selection properties of Bayes factors and Bayesian information criterion (BIC are investigated. When model uncertainty is substantial, we recommend the use of Bayesian Model Averaging to obtain point estimators with lower root mean squared errors (RMSE. We also study the implications of different levels of inclusion probabilities by simulations.
Tsunami evacuation mathematical model for the city of Padang
International Nuclear Information System (INIS)
Kusdiantara, R.; Hadianti, R.; Badri Kusuma, M. S.; Soewono, E.
2012-01-01
Tsunami is a series of wave trains which travels with high speed on the sea surface. This traveling wave is caused by the displacement of a large volume of water after the occurrence of an underwater earthquake or volcano eruptions. The speed of tsunami decreases when it reaches the sea shore along with the increase of its amplitudes. Two large tsunamis had occurred in the last decades in Indonesia with huge casualties and large damages. Indonesian Tsunami Early Warning System has been installed along the west coast of Sumatra. This early warning system will give about 10-15 minutes to evacuate people from high risk regions to the safe areas. Here in this paper, a mathematical model for Tsunami evacuation is presented with the city of Padang as a study case. In the model, the safe areas are chosen from the existing and selected high rise buildings, low risk region with relatively high altitude and (proposed to be built) a flyover ring road. Each gathering points are located in the radius of approximately 1 km from the ring road. The model is formulated as an optimization problem with the total normalized evacuation time as the objective function. The constraints consist of maximum allowable evacuation time in each route, maximum capacity of each safe area, and the number of people to be evacuated. The optimization problem is solved numerically using linear programming method with Matlab. Numerical results are shown for various evacuation scenarios for the city of Padang.
Tsunami evacuation mathematical model for the city of Padang
Energy Technology Data Exchange (ETDEWEB)
Kusdiantara, R.; Hadianti, R.; Badri Kusuma, M. S.; Soewono, E. [Department of Mathematics Institut Teknologi Bandung, Bandung 40132 (Indonesia); Department of Civil Engineering Institut Teknologi Bandung, Bandung 40132 (Indonesia); Department of Mathematics Institut Teknologi Bandung, Bandung 40132 (Indonesia)
2012-05-22
Tsunami is a series of wave trains which travels with high speed on the sea surface. This traveling wave is caused by the displacement of a large volume of water after the occurrence of an underwater earthquake or volcano eruptions. The speed of tsunami decreases when it reaches the sea shore along with the increase of its amplitudes. Two large tsunamis had occurred in the last decades in Indonesia with huge casualties and large damages. Indonesian Tsunami Early Warning System has been installed along the west coast of Sumatra. This early warning system will give about 10-15 minutes to evacuate people from high risk regions to the safe areas. Here in this paper, a mathematical model for Tsunami evacuation is presented with the city of Padang as a study case. In the model, the safe areas are chosen from the existing and selected high rise buildings, low risk region with relatively high altitude and (proposed to be built) a flyover ring road. Each gathering points are located in the radius of approximately 1 km from the ring road. The model is formulated as an optimization problem with the total normalized evacuation time as the objective function. The constraints consist of maximum allowable evacuation time in each route, maximum capacity of each safe area, and the number of people to be evacuated. The optimization problem is solved numerically using linear programming method with Matlab. Numerical results are shown for various evacuation scenarios for the city of Padang.
Mathematical Models of the Sinusoidal Screen Family
Directory of Open Access Journals (Sweden)
Tajana Koren
2011-06-01
Full Text Available In this paper we will define a family of sinusoidal screening elements and explore the possibilities of their application in graphic arts, securities printing and design solutions in photography and typography editing. For this purpose mathematical expressions of sinusoidal families were converted into a Postscript language. The introduction of a random variable results in a countless number of various mutations which cannot be repeated without knowing the programming code itself. The use of the family of screens in protection of securities is thus of great importance. Other possible application of modulated sinusoidal screens is related to the large format color printing. This paper will test the application of sinusoidal screens in vector graphics, pixel graphics and typography. The development of parameters in the sinusoidal screen element algorithms gives new forms defined within screening cells with strict requirements of coverage implementation. Individual solutions include stochastic algorithms, as well as the autonomy of screening forms in regard to multicolor printing channels.
Mathematical models to predict rheological parameters of lateritic hydromixtures
Directory of Open Access Journals (Sweden)
Gabriel Hernández-Ramírez
2017-10-01
Full Text Available The present work had as objective to establish mathematical models that allow the prognosis of the rheological parameters of the lateritic pulp at concentrations of solids from 35% to 48%, temperature of the preheated hydromixture superior to 82 ° C and number of mineral between 3 and 16. Four samples of lateritic pulp were used in the study at different process locations. The results allowed defining that the plastic properties of the lateritic pulp in the conditions of this study conform to the Herschel-Bulkley model for real plastics. In addition, they show that for current operating conditions, even for new situations, UPD mathematical models have a greater ability to predict rheological parameters than least squares mathematical models.
Mathematical modelling and numerical simulation of forces in milling process
Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.
2018-04-01
Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Mathematical modeling for novel cancer drug discovery and development.
Zhang, Ping; Brusic, Vladimir
2014-10-01
Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.
Mathematical modeling of renal hemodynamics in physiology and pathophysiology.
Sgouralis, Ioannis; Layton, Anita T
2015-06-01
In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.
Solutions manual to accompany finite mathematics models and applications
Morris, Carla C
2015-01-01
A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr
MATHEMATICAL MODELLING OF QUAZISTEADY MODE OF BEARING AIR BUFFER FILLING
Directory of Open Access Journals (Sweden)
E. D. Chertov
2014-01-01
Full Text Available Summary. Today the only way to eliminate contact with the product during the manufacturing process is to provide a support surface under its support surface air buffer layer formed due to the expiration of the working environment through holes perforated gas distribution grids forms. There proposed the method of contactless formation of products consisting of composite materials by the means of air buffer in the article. The results of theoretical and experimental investigations of hydro-gas-dynamic processes occurring when casting of organic- mineral composite material onto the bearing air buffer expressed in the form of mathematical description realizing original hypotheses reflected in the choice of transformation algorithm and limiting conditions are presented. On the base of obtained mathematical model the algorithm of calculation of optimum parameters of transporting systems with discretely powered gas buffer is developed. The method of deduction of a semi-finished product on the gas buffer, which allows to level the pressure field under the bearing surface of the deduction object due to the usage of devices of pseudo fluidized granular material in pneumatic chambers is offered. The application of this method allows to eliminate the possibility of contact between the composite material and the working surface of the equipment and also to reduce the cost of production of pneumatic devices, to improve operational characteristics of this equipment. Submitted depending allowed to develop the methodology and implementation of engineering calculation device for non-contact casting composite materials on air buffer, semi-industrial and industrial variants were created and put into production.
Mathematical models of human cerebellar development in the fetal period.
Dudek, Krzysztof; Nowakowska-Kotas, Marta; Kędzia, Alicja
2018-04-01
The evaluation of cerebellar growth in the fetal period forms a part of a widely used examination to identify any features of abnormalities in early stages of human development. It is well known that the development of anatomical structures, including the cerebellum, does not always follow a linear model of growth. The aim of the study was to analyse a variety of mathematical models of human cerebellar development in fetal life to determine their adequacy. The study comprised 101 fetuses (48 males and 53 females) between the 15th and 28th weeks of fetal life. The cerebellum was exposed and measurements of the vermis and hemispheres were performed, together with statistical analyses. The mathematical model parameters of fetal growth were assessed for crown-rump length (CRL) increases, transverse cerebellar diameter and ventrodorsal dimensions of the cerebellar vermis in the transverse plane, and rostrocaudal dimensions of the cerebellar vermis and hemispheres in the frontal plane. A variety of mathematical models were applied, including linear and non-linear functions. Taking into consideration the variance between models and measurements, as well as correlation parameters, the exponential and Gompertz models proved to be the most suitable for modelling cerebellar growth in the second and third trimesters of pregnancy. However, the linear model gave a satisfactory approximation of cerebellar growth, especially in older fetuses. The proposed models of fetal cerebellar growth constructed on the basis of anatomical examination and objective mathematical calculations could be useful in the estimation of fetal development. © 2018 Anatomical Society.
The Relevance of Using Mathematical Models in Macroeconomic Policies Theory
Directory of Open Access Journals (Sweden)
Nora Mihail
2006-11-01
Full Text Available The article presents a look of the principal’s mathematical models – starting with Theil, Hansen and Tinbergen work – and their results used to analysis and design macroeconomic policies. In modeling field changes are very fast in theoretical aspects of modeling the many problems of macroeconomic policies and in using in practice the different political models elaboration. The article points out the problems of static and dynamic theory used in macro-policies modeling.
The Relevance of Using Mathematical Models in Macroeconomic Policies Theory
Directory of Open Access Journals (Sweden)
Nora Mihail
2006-09-01
Full Text Available The article presents a look of the principal’s mathematical models – starting with Theil, Hansen and Tinbergen work – and their results used to analysis and design macroeconomic policies. In modeling field changes are very fast in theoretical aspects of modeling the many problems of macroeconomic policies and in using in practice the different political models elaboration. The article points out the problems of static and dynamic theory used in macro-policies modeling.
Aggregated wind power plant models consisting of IEC wind turbine models
DEFF Research Database (Denmark)
Altin, Müfit; Göksu, Ömer; Hansen, Anca Daniela
2015-01-01
The common practice regarding the modelling of large generation components has been to make use of models representing the performance of the individual components with a required level of accuracy and details. Owing to the rapid increase of wind power plants comprising large number of wind...... turbines, parameters and models to represent each individual wind turbine in detail makes it necessary to develop aggregated wind power plant models considering the simulation time for power system stability studies. In this paper, aggregated wind power plant models consisting of the IEC 61400-27 variable...... speed wind turbine models (type 3 and type 4) with a power plant controller is presented. The performance of the detailed benchmark wind power plant model and the aggregated model are compared by means of simulations for the specified test cases. Consequently, the results are summarized and discussed...
A mathematical model of the growth of uterine myomas.
Chen, C Y; Ward, J P
2014-12-01
Uterine myomas or fibroids are common, benign smooth muscle tumours that can grow to 10 cm or more in diameter and are routinely removed surgically. They are typically slow- growing, well-vascularised, spherical tumours that, on a macro-scale, are a structurally uniform, hard elastic material. We present a multi-phase mathematical model of a fully vascularised myoma growing within a surrounding elastic tissue. Adopting a continuum approach, the model assumes the conservation of mass and momentum of four phases, namely cells/collagen, extracellular fluid, arterial and venous phases. The cell/collagen phase is treated as a poro-elastic material, based on a linear stress-strain relationship, and Darcy's law is applied to describe flow in the extracellular fluid and the two vascular phases. The supply of extracellular fluid is dependent on the capillary flow rate and mean capillary pressure expressed in terms of the arterial and venous pressures. Cell growth and division is limited to the myoma domain and dependent on the local stress in the material. The resulting model consists of a system of nonlinear partial differential equations with two moving boundaries. Numerical solutions of the model successfully reproduce qualitatively the clinically observed three-phase "fast-slow-fast" growth profile that is typical for myomas. The results suggest that this growth profile requires stress-induced resistance to growth by the surrounding tissue and a switch-like cell growth response to stress. Analysis of large-time solutions reveal that while there is a functioning vasculature throughout the myoma, exponential growth results, otherwise power-law growth is predicted. An extensive survey of the effect of parameters on model solutions is also presented, and in particular, the enhanced growth caused by factors such as oestrogen is predicted by the model.
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM
Directory of Open Access Journals (Sweden)
Olha Sushchenko
2017-07-01
Full Text Available Purpose: The paper deals with the mathematical description of the gimballed attitude and heading reference systems, which can be applied in design of strategic precision navigation systems. The main goal is to created mathematical description taking into consideration the necessity to use different navigations operating modes of this class of navigation systems. To provide the high accuracy the indirect control is used when the position of the gimballed platform is controlled by signals of gyroscopic devices, which are corrected using accelerometer’s signals. Methods: To solve the given problem the methods of the classical theoretical mechanics, gyro theory, and inertial navigation are used. Results: The full mathematical model of the gimballed attitude and heading reference system is derived including descriptions of different operating modes. The mathematical models of the system Expressions for control and correction moments in the different modes are represented. The simulation results are given. Conclusions: The represented results prove efficiency of the proposed models. Developed mathematical models can be useful for design of navigation systems of the wide class of moving vehicles.
A mathematical model for the occurrence of historical events
Ohnishi, Teruaki
2017-12-01
A mathematical model was proposed for the frequency distribution of historical inter-event time τ. A basic ingredient was constructed by assuming the significance of a newly occurring historical event depending on the magnitude of a preceding event, the decrease of its significance by oblivion during the successive events, and an independent Poisson process for the occurrence of the event. The frequency distribution of τ was derived by integrating the basic ingredient with respect to all social fields and to all stake holders. The function of such a distribution was revealed as the forms of an exponential type, a power law type or an exponential-with-a-tail type depending on the values of constants appearing in the ingredient. The validity of this model was studied by applying it to the two cases of Modern China and Northern Ireland Troubles, where the τ-distribution varies depending on the different countries interacting with China and on the different stage of history of the Troubles, respectively. This indicates that history is consisted from many components with such different types of τ-distribution, which are the similar situation to the cases of other general human activities.
Mathematical Model for Direct Evaporative Space Cooling Systems ...
African Journals Online (AJOL)
This paper deals with the development of a simple mathematical model for experimental validation of the performance of a small evaporative cooling system in a tropical climate. It also presents the coefficient of convective heat transfer of wide range of temperatures based on existing model. Extensive experiments have ...
Mathematical and computational modeling simulation of solar drying Systems
Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...
Mathematical modelling as basis for efficient enterprise management
Directory of Open Access Journals (Sweden)
Kalmykova Svetlana
2017-01-01
Full Text Available The choice of the most effective HR- management style at the enterprise is based on modeling various socio-economic situations. The article describes the formalization of the managing processes aimed at the interaction between the allocated management subsystems. The mathematical modelling tools are used to determine the time spent on recruiting personnel for key positions in the management hierarchy selection.
Mathematical Analysis of a Model for Human Immunodeficiency ...
African Journals Online (AJOL)
ADOWIE PERE
ABSTRACT: The objective of this paper is to present a mathematical model formulated to investigate the dynamics of human immunodeficiency virus (HIV). The disease free equilibrium of the model was found to be locally and globally asymptotically stable. The endemic equilibrium point exists and it was discovered that the ...
Mathematical models of ABE fermentation: review and analysis.
Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S
2013-12-01
Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.
The Interval Market Model in Mathematical Finance : Game Theoretic Methods
Bernhard, P.; Engwerda, J.C.; Roorda, B.; Schumacher, J.M.; Kolokoltsov, V.; Saint-Pierre, P.; Aubin, J.P.
2013-01-01
Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous
Mathematical Model for Prediction of Flexural Strength of Mound ...
African Journals Online (AJOL)
The mound soil-cement blended proportions were mathematically optimized by using scheffe's approach and the optimization model developed. A computer program predicting the mix proportion for the model was written. The optimal proportion by the program was used prepare beam samples measuring 150mm x 150mm ...
A mathematical model of combustion kinetics of municipal solid ...
African Journals Online (AJOL)
Municipal Solid Waste has become a serious environmental problem troubling many cities. In this paper, a mathematical model of combustion kinetics of municipal solid waste with focus on plastic waste was studied. An analytical solution is obtained for the model. From the numerical simulation, it is observed that the ...
Mathematical model for dissolved oxygen prediction in Cirata ...
African Journals Online (AJOL)
This paper presents the implementation and performance of mathematical model to predict theconcentration of dissolved oxygen in Cirata Reservoir, West Java by using Artificial Neural Network (ANN). The simulation program was created using Visual Studio 2012 C# software with ANN model implemented in it. Prediction ...
A Mathematical Model for Analysis on Ships Collision Avoidance ...
African Journals Online (AJOL)
This study develops a mathematical model for analysis on collision avoidance of ships. The obtained model provides information on the quantitative effect of the ship's engine's response and the applied reversing force on separation distance and stopping abilities of the ships. Appropriate evasive maneuvers require the ...
Mathematical modelling of zirconium salicylate solvent extraction process
International Nuclear Information System (INIS)
Smirnova, N.S.; Evseev, A.M.; Fadeeva, V.I.; Kochetkova, S.K.
1979-01-01
Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built
Mathematical modelling of zirconium salicylate solvent extraction process
Energy Technology Data Exchange (ETDEWEB)
Smirnova, N S; Evseev, A M; Fadeeva, V I; Kochetkova, S K [Moskovskij Gosudarstvennyj Univ. (USSR)
1979-11-01
Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built.
Simple mathematical models for housing allocation to a homeless ...
African Journals Online (AJOL)
We present simple mathematical models for modelling a homeless population and housing allocation. We look at a situation whereby the local authority makes temporary accommodation available for some of the homeless for a while and we examine how this affects the number of families homeless at any given time.
A mathematical model for transducer working at high temperature
International Nuclear Information System (INIS)
Fabre, J.P.
1974-01-01
A mathematical model is proposed for a lithium niobate piezoelectric transducer working at high temperature in liquid sodium. The model proposed suitably described the operation of the high temperature transducer presented; it allows the optimization of the efficiency and band-pass [fr
A theory of drug tolerance and dependence II: the mathematical model.
Peper, Abraham
2004-08-21
The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.
Mathematical model of two-phase flow in accelerator channel
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О.Ф. Нікулін
2010-01-01
Full Text Available The problem of two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in counter jet mill accelerator channel design.
Mathematical Modeling of Biofilm Structures Using COMSTAT Data
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Davide Verotta
2017-01-01
Full Text Available Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data in terms of few parameters and the capability to (i compare different experiments and exposures to different agents, (ii test different hypotheses regarding biofilm growth and interaction with different agents, and (iii simulate arbitrary administrations of agents. The mathematical framework is divided to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We demonstrate the application of (some of the models using confocal microscopy data obtained using the computer program COMSTAT.
Mathematical modeling of efficient protocols to control glioma growth.
Branco, J R; Ferreira, J A; de Oliveira, Paula
2014-09-01
In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. Copyright © 2014 Elsevier Inc. All rights reserved.
Height-Diameter Models for Mixed-Species Forests Consisting of Spruce, Fir, and Beech
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Petráš Rudolf
2014-06-01
Full Text Available Height-diameter models define the general relationship between the tree height and diameter at each growth stage of the forest stand. This paper presents generalized height-diameter models for mixed-species forest stands consisting of Norway spruce (Picea abies Karst., Silver fir (Abies alba L., and European beech (Fagus sylvatica L. from Slovakia. The models were derived using two growth functions from the exponential family: the two-parameter Michailoff and three-parameter Korf functions. Generalized height-diameter functions must normally be constrained to pass through the mean stand diameter and height, and then the final growth model has only one or two parameters to be estimated. These “free” parameters are then expressed over the quadratic mean diameter, height and stand age and the final mathematical form of the model is obtained. The study material included 50 long-term experimental plots located in the Western Carpathians. The plots were established 40-50 years ago and have been repeatedly measured at 5 to 10-year intervals. The dataset includes 7,950 height measurements of spruce, 21,661 of fir and 5,794 of beech. As many as 9 regression models were derived for each species. Although the “goodness of fit” of all models showed that they were generally well suited for the data, the best results were obtained for silver fir. The coefficient of determination ranged from 0.946 to 0.948, RMSE (m was in the interval 1.94-1.97 and the bias (m was -0.031 to 0.063. Although slightly imprecise parameter estimation was established for spruce, the estimations of the regression parameters obtained for beech were quite less precise. The coefficient of determination for beech was 0.854-0.860, RMSE (m 2.67-2.72, and the bias (m ranged from -0.144 to -0.056. The majority of models using Korf’s formula produced slightly better estimations than Michailoff’s, and it proved immaterial which estimated parameter was fixed and which parameters