Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

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...

Teaching Mathematical Modeling in Mathematics Education

Science.gov (United States)

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…

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...

Rival approaches to mathematical modelling in immunology

Science.gov (United States)

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 HIV prevention measures including pre-exposure prophylaxis on HIV incidence in South Korea.

Science.gov (United States)

Kim, Sun Bean; Yoon, Myoungho; Ku, Nam Su; Kim, Min Hyung; Song, Je Eun; Ahn, Jin Young; Jeong, Su Jin; Kim, Changsoo; Kwon, Hee-Dae; Lee, Jeehyun; Smith, Davey M; Choi, Jun Yong

2014-01-01

Multiple prevention measures have the possibility of impacting HIV incidence in South Korea, including early diagnosis, early treatment, and pre-exposure prophylaxis (PrEP). We investigated how each of these interventions could impact the local HIV epidemic, especially among men who have sex with men (MSM), who have become the major risk group in South Korea. A mathematical model was used to estimate the effects of each these interventions on the HIV epidemic in South Korea over the next 40 years, as compared to the current situation. We constructed a mathematical model of HIV infection among MSM in South Korea, dividing the MSM population into seven groups, and simulated the effects of early antiretroviral therapy (ART), early diagnosis, PrEP, and combination interventions on the incidence and prevalence of HIV infection, as compared to the current situation that would be expected without any new prevention measures. Overall, the model suggested that the most effective prevention measure would be PrEP. Even though PrEP effectiveness could be lessened by increased unsafe sex behavior, PrEP use was still more beneficial than the current situation. In the model, early diagnosis of HIV infection was also effectively decreased HIV incidence. However, early ART did not show considerable effectiveness. As expected, it would be most effective if all interventions (PrEP, early diagnosis and early treatment) were implemented together. This model suggests that PrEP and early diagnosis could be a very effective way to reduce HIV incidence in South Korea among MSM.

Mathematical modelling techniques

CERN Document Server

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

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

Science.gov (United States)

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…

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

Science.gov (United States)

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 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 modeling of biological processes

CERN Document Server

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.

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 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 models in marketing a collection of abstracts

CERN Document Server

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 modeling for novel cancer drug discovery and development.

Science.gov (United States)

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 models in biology bringing mathematics to life

CERN Document Server

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: A Structured Process

Science.gov (United States)

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…

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

Science.gov (United States)

Karatas, Ilhan

2014-01-01

This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

Science.gov (United States)

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 model of compact type evaporator

Science.gov (United States)

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.

Interfacial Fluid Mechanics A Mathematical Modeling Approach

CERN Document Server

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...

Finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.

Mathematical Modelling 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.

The 24-Hour Mathematical Modeling Challenge

Science.gov (United States)

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 Models of Elementary Mathematics Learning and Performance. Final Report.

Science.gov (United States)

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…

Mathematical problems in meteorological modelling

CERN Document Server

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...

A mathematical approach to research problems of science and technology theoretical basis and developments in mathematical modeling

CERN Document Server

Ei, Shin-ichiro; Koiso, Miyuki; Ochiai, Hiroyuki; Okada, Kanzo; Saito, Shingo; Shirai, Tomoyuki

2014-01-01

This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

Science.gov (United States)

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…

Modelling as a foundation for academic forming in mathematics education

NARCIS (Netherlands)

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

Mathematical modeling and optimization of complex structures

CERN Document Server

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...

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

Science.gov (United States)

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Mathematical modeling with multidisciplinary applications

CERN Document Server

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

A Primer for Mathematical Modeling

Science.gov (United States)

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…

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

Science.gov (United States)

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

Mathematical 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 Modeling: Challenging the Figured Worlds of Elementary Mathematics

Science.gov (United States)

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

Science.gov (United States)

Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

2014-01-01

This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

Mathematical 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 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

Methods of mathematical modelling continuous systems and differential equations

CERN Document Server

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 in the Undergraduate Curriculum

Science.gov (United States)

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

Science.gov (United States)

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 and numerical foundations of turbulence models and applications

CERN Document Server

Chacón Rebollo, Tomás

2014-01-01

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering, and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation, and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics,...

Mathematical Modelling of Predatory Prokaryotes

NARCIS (Netherlands)

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

A mathematical model

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)

The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

Science.gov (United States)

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.

Mathematical Modeling: A Bridge to STEM Education

Science.gov (United States)

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…

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 Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

Science.gov (United States)

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Mathematical modeling of efficient protocols to control glioma growth.

Science.gov (United States)

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.

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.

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.

An Interdisciplinary Approach to Designing Online Learning: Fostering Pre-Service Mathematics Teachers' Capabilities in Mathematical Modelling

Science.gov (United States)

Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian

2018-01-01

In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

Workshop on Advanced Modelling in Mathematical Finance : in Honour of Ernst Eberlein

CERN Document Server

Papapantoleon, Antonis

2016-01-01

This Festschrift resulted from a workshop on “Advanced Modelling in Mathematical Finance” held in honour of Ernst Eberlein’s 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein’s long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.

International Conference on Applied Mathematics, Modeling and Computational Science & Annual meeting of the Canadian Applied and Industrial Mathematics

CERN Document Server

Bélair, Jacques; Kunze, Herb; Makarov, Roman; Melnik, Roderick; Spiteri, Raymond J

2016-01-01

Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science a...

A stream-based mathematical model for distributed information processing systems - SysLab system model

OpenAIRE

Klein, Cornel; Rumpe, Bernhard; Broy, Manfred

2014-01-01

In the SysLab project we develop a software engineering method based on a mathematical foundation. The SysLab system model serves as an abstract mathematical model for information systems and their components. It is used to formalize the semantics of all used description techniques such as object diagrams state automata sequence charts or data-flow diagrams. Based on the requirements for such a reference model, we define the system model including its different views and their relationships.

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

DEFF Research Database (Denmark)

Verotta, Davide; Haagensen, Janus Anders Juul; Spormann, Alfred M.

2017-01-01

Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data...... in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided...... to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We...

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.

Modeling Achievement in Mathematics: The Role of Learner and Learning Environment Characteristics

Science.gov (United States)

Nasser-Abu Alhija, Fadia; Amasha, Marcel

2012-01-01

This study examined a structural model of mathematics achievement among Druze 8th graders in Israel. The model integrates 2 psychosocial theories: goal theory and social learning theory. Variables in the model included gender, father's and mother's education, classroom mastery and performance goal orientation, mathematics self-efficacy and…

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

Directory of Open Access Journals (Sweden)

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.

The role of mathematical models in the optimization of radiopharmaceutical therapy

International Nuclear Information System (INIS)

Divgi, C.

2001-01-01

Mathematical models have been used in radiopharmaceutical therapy for over five decades. These have served to determine the amount of radioactivity required to treat disease, as in the therapy of hyperthyroidism with iodine-131, or, more frequently, to determine the largest amount of radioactivity that can be safely administered. Mathematical models are especially useful in the determination of fractionated radiopharmaceutical therapy. This review will briefly outline the historical development and current utility of mathematical models in radiopharmaceutical therapy, including thyroid disorders and radioimmunotherapy; and describe the potential of modeling in fractionated therapy. The extended application of such models to currently used radiopharmaceutical therapy based on indices of body mass or surface area, to alleviate toxicity and increase radiation dose to tumour, will be proposed. Finally, future applications of mathematical models in radiopharmaceutical therapy will be outlined. (author)

MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM

Directory of Open Access Journals (Sweden)

Olha Sushchenko

2017-07-01

Full Text Available Purpose: The paper deals with the mathematical description of the gimballed attitude and heading reference systems, which can be applied in design of strategic precision navigation systems. The main goal is to created mathematical description taking into consideration the necessity to use different navigations operating modes of this class of navigation systems. To provide the high accuracy the indirect control is used when the position of the gimballed platform is controlled by signals of gyroscopic devices, which are corrected using accelerometer’s signals. Methods: To solve the given problem the methods of the classical theoretical mechanics, gyro theory, and inertial navigation are used. Results: The full mathematical model of the gimballed attitude and heading reference system is derived including descriptions of different operating modes. The mathematical models of the system Expressions for control and correction moments in the different modes are represented. The simulation results are given. Conclusions: The represented results prove efficiency of the proposed models. Developed mathematical models can be useful for design of navigation systems of the wide class of moving vehicles.

Mathematical 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 Computational Thinking

Science.gov (United States)

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…

Summer Camp of Mathematical Modeling in China

Science.gov (United States)

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…

Strategies to Support Students' Mathematical Modeling

Science.gov (United States)

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…

Explorations in Elementary Mathematical Modeling

Science.gov (United States)

Shahin, Mazen

2010-01-01

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

Mathematical Modeling of Diverse Phenomena

Science.gov (United States)

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.

Effectiveness of discovery learning model on mathematical problem solving

Science.gov (United States)

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.

Undergraduate Students' Perceptions of the Mathematics Courses Included in the Primary School Teacher Education Program

Science.gov (United States)

Serin, Mehmet Koray; Incikabi, Semahat

2017-01-01

Mathematics educators have reported on many issues regarding students' mathematical education, particularly students who received mathematics education at different departments such as engineering, science or primary school, including their difficulties with mathematical concepts, their understanding of and preferences for mathematical concepts.…

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 models of human cerebellar development in the fetal period.

Science.gov (United States)

Dudek, Krzysztof; Nowakowska-Kotas, Marta; Kędzia, Alicja

2018-04-01

The evaluation of cerebellar growth in the fetal period forms a part of a widely used examination to identify any features of abnormalities in early stages of human development. It is well known that the development of anatomical structures, including the cerebellum, does not always follow a linear model of growth. The aim of the study was to analyse a variety of mathematical models of human cerebellar development in fetal life to determine their adequacy. The study comprised 101 fetuses (48 males and 53 females) between the 15th and 28th weeks of fetal life. The cerebellum was exposed and measurements of the vermis and hemispheres were performed, together with statistical analyses. The mathematical model parameters of fetal growth were assessed for crown-rump length (CRL) increases, transverse cerebellar diameter and ventrodorsal dimensions of the cerebellar vermis in the transverse plane, and rostrocaudal dimensions of the cerebellar vermis and hemispheres in the frontal plane. A variety of mathematical models were applied, including linear and non-linear functions. Taking into consideration the variance between models and measurements, as well as correlation parameters, the exponential and Gompertz models proved to be the most suitable for modelling cerebellar growth in the second and third trimesters of pregnancy. However, the linear model gave a satisfactory approximation of cerebellar growth, especially in older fetuses. The proposed models of fetal cerebellar growth constructed on the basis of anatomical examination and objective mathematical calculations could be useful in the estimation of fetal development. © 2018 Anatomical Society.

Mathematical modeling a chemical engineer's perspective

CERN Document Server

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

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

Science.gov (United States)

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…

Specific Type of Knowledge Map: Mathematical Model

OpenAIRE

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.

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

Science.gov (United States)

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…

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

Science.gov (United States)

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…

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

Science.gov (United States)

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.

Mathematical Modelling as a Professional Task

Science.gov (United States)

Frejd, Peter; Bergsten, Christer

2016-01-01

Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…

Mathematical 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.

Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach.

Science.gov (United States)

Campitelli, Guillermo; Gerrans, Paul

2014-04-01

We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research.

Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

Science.gov (United States)

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…

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...

Using Covariation Reasoning to Support Mathematical Modeling

Science.gov (United States)

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…

Engaging Students in Mathematical Modeling through Service-Learning

Science.gov (United States)

Carducci, Olivia M.

2014-01-01

I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…

The many faces of the mathematical modeling cycle

NARCIS (Netherlands)

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

ABOUT THE RELEVANCE AND METHODOLOGY ASPECTS OF TEACHING THE MATHEMATICAL MODELING TO PEDAGOGICAL STUDENTS

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2014-01-01

Full Text Available The paper substantiates the need for profile training in mathematical modeling for pedagogical students, caused by the total penetration of mathematics into different sciences, including the humanities; fast development of the information communications technologies; and growing importance of mathematical modeling, combining the informal scientific and formal mathematical languages with the unique opportunities of computer programming. The author singles out the reasons for mastering and using the mathematical apparatus by teaches in every discipline. Indeed, among all the modern mathematical methods and ideas, mathematical modeling retains its priority in all professional spheres. Therefore, the discipline of “Mathematical Modeling” can play an important role in integrating different components of specialists training in various profiles. By mastering the basics of mathematical modeling, students acquire skills of methodological thinking; learn the principles of analysis, synthesis, generalization of ideas and methods in different disciplines and scientific spheres; and achieve general culture competences. In conclusion, the author recommends incorporating the “Methods of Profile Training in Mathematical Modeling” into the pedagogical magistracy curricula. 

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)

Mathematical modelling a case studies approach

CERN Document Server

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 modelling in engineering: A proposal to introduce linear algebra concepts

Directory of Open Access Journals (Sweden)

Andrea Dorila Cárcamo

2016-03-01

Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts:  span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.

Engaging Elementary Students in the Creative Process of Mathematizing Their World through Mathematical Modeling

Directory of Open Access Journals (Sweden)

Jennifer M. Suh

2017-06-01

Full Text Available This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1 How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2 What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.

Mathematical physiology

CERN Document Server

Sneyd, James

2009-01-01

There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...

Mathematical Modeling in the High School Curriculum

Science.gov (United States)

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 Approaches in Plant Metabolomics.

Science.gov (United States)

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.

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....

The role of mathematics in politics as an issue for mathematics teaching

DEFF Research Database (Denmark)

Sánchez, Mario; Blomhøj, Morten

2010-01-01

This paper presents analyses of some examples of mathematical models used in the Mexican society of today. We seek to justify why and illustrate how such examples can be included in mathematics teaching and in teacher education.......This paper presents analyses of some examples of mathematical models used in the Mexican society of today. We seek to justify why and illustrate how such examples can be included in mathematics teaching and in teacher education....

Fun with maths: exploring implications of mathematical models for malaria eradication.

Science.gov (United States)

Eckhoff, Philip A; Bever, Caitlin A; Gerardin, Jaline; Wenger, Edward A

2014-12-11

Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches. These examples include the time to eradication, the impact of vaccine efficacy and coverage, drug programs and the effects of duration of infections and delays to treatment, and the influence of seasonality and migration coupling on disease fadeout. An excessively simple structure can miss key results, but simple mathematical approaches can still achieve key results for eradication strategy and define areas for investigation by more complex models.

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

Science.gov (United States)

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 modeling of sleep state dynamics in a rodent model of shift work

Directory of Open Access Journals (Sweden)

Michael J. Rempe

2018-06-01

Full Text Available Millions of people worldwide are required to work when their physiology is tuned for sleep. By forcing wakefulness out of the body’s normal schedule, shift workers face numerous adverse health consequences, including gastrointestinal problems, sleep problems, and higher rates of some diseases, including cancers. Recent studies have developed protocols to simulate shift work in rodents with the intention of assessing the effects of night-shift work on subsequent sleep (Grønli et al., 2017. These studies have already provided important contributions to the understanding of the metabolic consequences of shift work (Arble et al., 2015; Marti et al., 2016; Opperhuizen et al., 2015 and sleep-wake-specific impacts of night-shift work (Grønli et al., 2017. However, our understanding of the causal mechanisms underlying night-shift-related sleep disturbances is limited. In order to advance toward a mechanistic understanding of sleep disruption in shift work, we model these data with two different approaches. First we apply a simple homeostatic model to quantify differences in the rates at which sleep need, as measured by slow wave activity during slow wave sleep (SWS rises and falls. Second, we develop a simple and novel mathematical model of rodent sleep and use it to investigate the timing of sleep in a simulated shift work protocol (Grønli et al., 2017. This mathematical framework includes the circadian and homeostatic processes of the two-process model, but additionally incorporates a stochastic process to model the polyphasic nature of rodent sleep. By changing only the time at which the rodents are forced to be awake, the model reproduces some key experimental results from the previous study, including correct proportions of time spent in each stage of sleep as a function of circadian time and the differences in total wake time and SWS bout durations in the rodents representing night-shift workers and those representing day-shift workers

Mathematical finance theory review and exercises from binomial model to risk measures

CERN Document Server

Gianin, Emanuela Rosazza

2013-01-01

The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.

Nonconvex Model of Material Growth: Mathematical Theory

Science.gov (United States)

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.

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

A Mathematical Model of Marine Diesel Engine Speed Control System

Science.gov (United States)

Sinha, Rajendra Prasad; Balaji, Rajoo

2018-02-01

Diesel engine is inherently an unstable machine and requires a reliable control system to regulate its speed for safe and efficient operation. Also, the diesel engine may operate at fixed or variable speeds depending upon user's needs and accordingly the speed control system should have essential features to fulfil these requirements. This paper proposes a mathematical model of a marine diesel engine speed control system with droop governing function. The mathematical model includes static and dynamic characteristics of the control loop components. Model of static characteristic of the rotating fly weights speed sensing element provides an insight into the speed droop features of the speed controller. Because of big size and large time delay, the turbo charged diesel engine is represented as a first order system or sometimes even simplified to a pure integrator with constant gain which is considered acceptable in control literature. The proposed model is mathematically less complex and quick to use for preliminary analysis of the diesel engine speed controller performance.

Exploring Yellowstone National Park with Mathematical Modeling

Science.gov (United States)

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…

Mathematical models from the collections of universities and museums : photograph volume and commentary

CERN Document Server

2017-01-01

This book presents beautiful photos of mathematical models of geometric surfaces made from a variety of materials including plaster, metal, paper, wood, and string. The construction of these models at the time (of Felix Klein and others) was not an end in itself, but was accompanied by mathematical research especially in the field of algebraic geometry. The models were used to illustrate the mathematical objects defined by abstract formulas, either as equations or parameterizations. In the second part of the book, the models are explained by experts in the field of geometry. This book is a reprint thirty years after the original publication in 1986 with a new preface by Gert-Martin Greuel. The models have a timeless appeal and a historical value. The Editor Prof. Dr. Gerd Fischer, Department of Mathematics, Technical University of Munich.

PENGEMBANGAN MODEL COMPREHENSIVE MATHEMATICS INSTRUCTION (CMI DALAM MEMBANGUN KEMAMPUAN MATHEMATICAL THINKING SISWA

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

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Science.gov (United States)

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

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...

Teaching Mathematical Modelling for Earth Sciences via Case Studies

Science.gov (United States)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Mathematical manipulative models: in defense of "beanbag biology".

Science.gov (United States)

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.

A mathematical model of the accumulation of radionuclides by oysters (C. virginica) aquacultured in the effluent of a nuclear power reactor to include major biological parameters

International Nuclear Information System (INIS)

Hess, C.T.; Smith, C.W.; Price, A.H.

1977-01-01

The uptake, accumulation and loss of radionuclides by the American oyster (C. virginica) aquacultured in the effluent of a nuclear power reactor has been measured monthly for 3 yr at four field stations in the Montsweag Estuary of the Sheepscot River and at a control station in the nearby Damariscotta River Estuary, southern central coastal Maine, U.S.A. A mathematical model for the time variation of the specific activity of the oysters has been developed to include the physical half-lives of the various radionuclides, the biological half-lives of the various radionuclides (biological depuration), the water temperature (oyster hibernation) and shell growth. The resulting first order linear differential equation incorporating these phenomena is driven by the liquid radionuclide effluent release of the Maine Yankee Nuclear Reactor. Comparison of the monthly measurements of the specific activity for 58 Co, 60 Co, 54 Mn, 134 Cs and 137 Cs in oysters with model calculations show close agreement over all ranges of variation observed. A special feature of this mathematical model is its ability to describe the non-chemostatic field situation. (author)

Assessment of Primary 5 Students' Mathematical Modelling Competencies

Science.gov (United States)

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…

Mathematics for energy

International Nuclear Information System (INIS)

Snow, D.R.

1975-01-01

This paper provides mathematicians and other persons interested in energy problems with some ideas of the kinds of mathematics being applied and a few ideas for further investigation both in the relevant mathematics and in mathematical modeling. This paper is not meant to be an extensive bibliography on the subject, but references are provided. The Conference emphasized large scale and economic considerations related to energy rather than specific technologies, but additional mathematical problems arising in current and future technologies are suggested. Several of the papers dealt with linear programming models of large scale systems related to energy. These included economic models, policy models, energy sector models for supply and demand and environmental concerns. One of the economic models utilized variational techniques including such things as the Hamiltonian, the Euler-Lagrange differential equation, transversality and natural boundary conditions

A mathematical model of steam-drum dynamics

International Nuclear Information System (INIS)

Moeck, E.O.; Hinds, H.W.

1976-12-01

Mathematical equations describing the dynamic behaviour of pressure, water mass, etc. in a steam drum are derived from basic principles. The resultant model includes such effects as steam superheating and water subcooling as well as spontaneous flashing of liquid and condensation of vapour. Experimental data from a pressurizer are adequately predicted by the model. The pressure rise following a turbine trip can be predicted by the isentropic-compression model but not by the thermodynamic-equilibrium model. The equations are individually linearized and implemented on an analog computer in such a way that their non-linear behaviour is retained for small-perturbation studies. (author)

Mathematical modeling and computational intelligence in engineering applications

CERN Document Server

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.

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

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.

Continuum mechanics the birthplace of mathematical models

CERN Document Server

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

Modelling and Optimizing Mathematics Learning in Children

Science.gov (United States)

Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

2013-01-01

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

Mathematical modeling of a process the rolling delivery

Science.gov (United States)

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.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

Science.gov (United States)

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.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches.

Science.gov (United States)

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks

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

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

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.

Model answers in pure mathematics for a-level students

CERN Document Server

Pratt, GA; Schofield, C W

1967-01-01

Model Answers in Pure Mathematics for A-Level Students provides a set of solutions that indicate what is required and expected in an Advanced Level examination in Pure Mathematics. This book serves as a guide to the length of answer required, layout of the solution, and methods of selecting the best approach to any particular type of math problem. This compilation intends to supplement, not replace, the normal textbook and provides a varied selection of questions for practice in addition to the worked solutions. The subjects covered in this text include algebra, trigonometry, coordinate geomet

An introduction to mathematical modeling a course in mechanics

CERN Document Server

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...

Mathematics of flexible risers including pressure and internal flow affects

Energy Technology Data Exchange (ETDEWEB)

Seyed, F.B. (John Brown Engineers and Constructors Ltd., London (GB)); Patel, M.H. (University Coll., London (GB). Dept. of Mechanical Engineering)

1992-01-01

Derivations are presented for calculation of pressure and internal flow induced forces on flexible risers and other curved pipes using a mathematically rigorous approach. Approximate and exact methods are presented for calculation of pressure forces on straight and curved pipes in two dimensions. The mathematical identity of these equations with those for effective tension is illustrated. The force arising from the flow of an internal fluid of constant density is then calculated and combined with those for pressure forces in derivation of the catenary equations including pressure and internal flow terms. It is shown that internal flow contributes a new term to the expression for effective tension. These governing equations are then reduced for the specific cases of simple catenary, steep-S, lazy-S, steep-wave and lazy-wave risers. In each case, the solution method has been presented and the governing equilibrium and geometric compatability conditions cited. (author).

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)

Leading Undergraduate Research Projects in Mathematical Modeling

Science.gov (United States)

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

Science.gov (United States)

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…

Development of a revised mathematical model of the gastrointestinal tract

International Nuclear Information System (INIS)

Barker, A.

1991-01-01

The objectives of this research are as follows. First, to incorporate new biological data into a revised mathematical adult gastrointestinal tract model that includes: ingestion in both liquid and solid forms; consideration of absorption in the stomach, small intestine, ascending colon, transverse colon or not at all; gender and age of the adult; and whether the adult is a smoker or not. Next, to create a computer program in basic language for calculating residence times in each anatomical section of the GI tract for commonly used radionuclides. Also, to compare and contrast the new model with the ICRP 30 GI tract model in terms of physiological concepts, mathematical concepts, and revised residence times for several commonly used radionuclides. Finally, to determine whether the new model is sufficiently better than the current model to warrant its use as a replacement for the Eve model

Modeling interdisciplinary activities involving Mathematics

DEFF Research Database (Denmark)

Iversen, Steffen Møllegaard

2006-01-01

In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...

The Spectrum of Mathematical Models.

Science.gov (United States)

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 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.

Development of a Multidisciplinary Middle School Mathematics Infusion Model

Science.gov (United States)

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…

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

Science.gov (United States)

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.

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

Science.gov (United States)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

A Simple Mathematical Model for Standard Model of Elementary Particles and Extension Thereof

Science.gov (United States)

Sinha, Ashok

2016-03-01

An algebraically (and geometrically) simple model representing the masses of the elementary particles in terms of the interaction (strong, weak, electromagnetic) constants is developed, including the Higgs bosons. The predicted Higgs boson mass is identical to that discovered by LHC experimental programs; while possibility of additional Higgs bosons (and their masses) is indicated. The model can be analyzed to explain and resolve many puzzles of particle physics and cosmology including the neutrino masses and mixing; origin of the proton mass and the mass-difference between the proton and the neutron; the big bang and cosmological Inflation; the Hubble expansion; etc. A novel interpretation of the model in terms of quaternion and rotation in the six-dimensional space of the elementary particle interaction-space - or, equivalently, in six-dimensional spacetime - is presented. Interrelations among particle masses are derived theoretically. A new approach for defining the interaction parameters leading to an elegant and symmetrical diagram is delineated. Generalization of the model to include supersymmetry is illustrated without recourse to complex mathematical formulation and free from any ambiguity. This Abstract represents some results of the Author's Independent Theoretical Research in Particle Physics, with possible connection to the Superstring Theory. However, only very elementary mathematics and physics is used in my presentation.

Mathematical modeling of CANDU-PHWR

Energy Technology Data Exchange (ETDEWEB)

Gaber, F.A.; Aly, R.A.; El-Shal, A.O. [Atomic Energy Authority, Cairo (Egypt)

2001-07-01

The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR) system. This study involved mathematical modeling of CANDU PHWR major system components and the developments of software to study the thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique.The integrated CANDU-PHWR model includes the neutronic, reactivity, fuel channel heat transfer, piping and the preheater type U-tube steam generator (PUTSG). The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and reactivity feed back due to the changes in fuel temperature and coolant temperature. The complex operation of the preheater type U-tube steam generator (PUTSG) is represented by a non-linear dynamic model using a state variable, moving boundary and lumped parameter techniques. The secondary side of the PUTSG model has six separate lumps including a preheater region, a lower boiling section, a mixing region, a riser, a chimmeny section, and a down-corner. The tube side of PUTSG has three main thermal zones. The PUTSG model is based on conservation of mass, energy and momentum relation-ships. The CANDU-PHWR integrated model are coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)

A mathematical model of insulin resistance in Parkinson's disease.

Science.gov (United States)

Braatz, Elise M; Coleman, Randolph A

2015-06-01

This paper introduces a mathematical model representing the biochemical interactions between insulin signaling and Parkinson's disease. The model can be used to examine the changes that occur over the course of the disease as well as identify which processes would be the most effective targets for treatment. The model is mathematized using biochemical systems theory (BST). It incorporates a treatment strategy that includes several experimental drugs along with current treatments. In the past, BST models of neurodegeneration have used power law analysis and simulation (PLAS) to model the system. This paper recommends the use of MATLAB instead. MATLAB allows for more flexibility in both the model itself and in data analysis. Previous BST analyses of neurodegeneration began treatment at disease onset. As shown in this model, the outcomes of delayed, realistic treatment and full treatment at disease onset are significantly different. The delayed treatment strategy is an important development in BST modeling of neurodegeneration. It emphasizes the importance of early diagnosis, and allows for a more accurate representation of disease and treatment interactions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Mathematical models for therapeutic approaches to control HIV disease transmission

CERN Document Server

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...

Models of the Structure of Some Rule-Governed Mathematical Behaviors.

Science.gov (United States)

Bergan, John R.

1981-01-01

This study investigated the extent to which various latent class models adequately described elementary rule-governed mathematical behaviors. Children were given a fraction concepts test. Results supported the adoption of a set of three-class models including a mastery class, a nonmastery class, and a transitional class to describe the data.…

Mathematical Modelling of Surfactant Self-assembly at Interfaces

KAUST Repository

Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary

Mathematical modelling of plant transients in the PWR for simulator purposes

International Nuclear Information System (INIS)

Hartel, K.

1984-01-01

This chapter presents the results of the testing of anticipated and abnormal plant transients in pressurized water reactors (PWRs) of the type WWER 440 by means of the numerical simulation of 32 different, stationary and nonstationary, operational regimes. Topics considered include the formation of the PWR mathematical model, the physical approximation of the reactor core, the structure of the reactor core model, a mathematical approximation of the reactor model, the selection of numerical methods, and a computerized simulation system. The necessity of a PWR simulator in Czechoslovakia is justified by the present status and the outlook for the further development of the Czechoslovak nuclear power complex

a Discrete Mathematical Model to Simulate Malware Spreading

Science.gov (United States)

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.

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)

Improving science and mathematics education with computational modelling in interactive engagement environments

Science.gov (United States)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.

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 Modelling Plant Signalling Networks

KAUST Repository

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

Developing Teaching Material Based on Realistic Mathematics Andoriented to the Mathematical Reasoning and Mathematical Communication

OpenAIRE

Habsah, Fitria

2017-01-01

This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental cla...

Modelling the Intention to Use Technology for Teaching Mathematics among Pre-Service Teachers in Serbia

Science.gov (United States)

Teo, Timothy; Milutinovic, Verica

2015-01-01

This study aims to examine the variables that influence Serbian pre-service teachers' intention to use technology to teach mathematics. Using the technology acceptance model (TAM) as the framework, we developed a research model to include subjective norm, knowledge of mathematics, and facilitating conditions as external variables to the TAM. In…

APPLYING PROFESSIONALLY ORIENTED PROBLEMS OF MATHEMATICAL MODELING IN TEACHING STUDENTS OF ENGINEERING DEPARTMENTS

Directory of Open Access Journals (Sweden)

Natal’ya Yur’evna Gorbunova

2017-06-01

Full Text Available We described several aspects of organizing student research work, as well as solving a number of mathematical modeling problems: professionally-oriented, multi-stage, etc. We underlined the importance of their economic content. Samples of using such problems in teaching Mathematics at agricultural university were given. Several questions connected with information material selection and peculiarities of research problems application were described. Purpose. The author aims to show the possibility and necessity of using professionally-oriented problems of mathematical modeling in teaching Mathematics at agricultural university. The subject of analysis is including such problems into educational process. Methodology. The main research method is dialectical method of obtaining knowledge of finding approaches to selection, writing and using mathematical modeling and professionally-oriented problems in educational process; the methodology is study of these methods of obtaining knowledge. Results. As a result of analysis of literature, students opinions, observation of students work, and taking into account personal teaching experience, it is possible to make conclusion about importance of using mathematical modeling problems, as it helps to systemize theoretical knowledge, apply it to practice, raise students study motivation in engineering sphere. Practical implications. Results of the research can be of interest for teachers of Mathematics in preparing Bachelor and Master students of engineering departments of agricultural university both for theoretical research and for modernization of study courses.

Ways of Thinking, Ways of Seeing Mathematical and other Modelling in Engineering and Technology

CERN Document Server

Dillon, Chris

2012-01-01

This fascinating book examines some of the characteristics of technological/engineering models that are likely to be unfamiliar to those who are interested primarily in the history and philosophy of science and mathematics, and which differentiate technological models from scientific and mathematical ones. Themes that will be highlighted include: • the role of language: the models developed for engineering design have resulted in new ways of talking about technological systems • communities of practice: related to the previous point, particular engineering communities have particular ways of sharing and developing knowledge • graphical (re)presentation: engineers have developed many ways of reducing quite complex mathematical models to more simple representations • reification: highly abstract mathematical models are turned into ‘objects’ that can be manipulated almost like components of a physical system • machines: not only the currently ubiquitous digital computer, but also older analogue dev...

Understanding Experimental LCMV Infection of Mice: The Role of Mathematical Models

Directory of Open Access Journals (Sweden)

Gennady Bocharov

2015-01-01

Full Text Available Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations should be tightly linked to a fundamental step called “coordinatization” (Hermann Weyl, that is, the definition of observables, parameters, and structures that enable the link with a biological phenotype. In this review, we analyse the mathematical modelling approaches to LCMV infection in mice that resulted in quantification of some fundamental parameters of the CTL-mediated virus control including the rates of T cell turnover, infected target cell elimination, and precursor frequencies. We show how the modelling approaches can be implemented to address diverse aspects of immune system functioning under normal conditions and in response to LCMV and, importantly, make quantitative predictions of the outcomes of immune system perturbations. This may highlight the notion that data-driven applications of meaningful mathematical models in infection biology remain a challenge.

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

Science.gov (United States)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The

FEMME, a flexible environment for mathematically modelling the environment

NARCIS (Netherlands)

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 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 Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa

Directory of Open Access Journals (Sweden)

Amira Rachah

2015-01-01

it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method.

Developing calculus textbook model that supported with GeoGebra to enhancing students’ mathematical problem solving and mathematical representation

Science.gov (United States)

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.

Understanding post-operative temperature drop in cardiac surgery: a mathematical model

NARCIS (Netherlands)

Tindall, M. J.; Peletier, M. A.; Severens, N. M. W.; Veldman, D. J.; de Mol, B. A. J. M.

2008-01-01

A mathematical model is presented to understand heat transfer processes during the cooling and re-warming of patients during cardiac surgery. Our compartmental model is able to account for many of the qualitative features observed in the cooling of various regions of the body including the central

Mathematical modelling in solid mechanics

CERN Document Server

Sofonea, Mircea; Steigmann, David

2017-01-01

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...

Mathematical Models of 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.

Correlation of spacecraft thermal mathematical models to reference data

Science.gov (United States)

Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier

2018-03-01

Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

Exploring the Relationship between Mathematical Modelling and Classroom Discourse

Science.gov (United States)

Redmond, Trevor; Sheehy, Joanne; Brown, Raymond

2010-01-01

This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…

A new mathematical model of gastrointestinal transit incorporating age- and gender-dependent physiological parameters

International Nuclear Information System (INIS)

Stubbs, J.B.

1992-01-01

As part of the revision by the International Commission on Radiological Protection (ICRP) of its report on Reference Man, an extensive review of the literature regarding anatomy and morphology of the gastrointestinal (GI) tract has been completed. Data on age- and gender-dependent GI physiology and motility may be included in the proposed ICRP report. A new mathematical model describing the transit of substances through the GI tract as well as the absorption and secretion of material in the GI tract has been developed. This mathematical description of GI tract kinetics utilizes more physiologically accurate transit processes than the mathematically simple, but nonphysiological, GI tract model that was used in ICRP Report 30. The proposed model uses a combination of zero- and first-order kinetics to describe motility. Some of the physiological parameters that the new model accounts for include sex, age, pathophysiological condition and meal phase (solid versus liquid). A computer algorithm, written in BASIC, based on this new model has been derived and results are compared to those of the ICRP-30 model

Modellus: Learning Physics with Mathematical Modelling

Science.gov (United States)

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

The irradiance and temperature dependent mathematical model for estimation of photovoltaic panel performances

International Nuclear Information System (INIS)

Barukčić, M.; Ćorluka, V.; Miklošević, K.

2015-01-01

Highlights: • The temperature and irradiance dependent model for the I–V curve estimation is presented. • The purely mathematical model based on the analysis of the I–V curve shape is presented. • The model includes the Gompertz function with temperature and irradiance dependent parameters. • The input data are extracted from the data sheet I–V curves. - Abstract: The temperature and irradiance dependent mathematical model for photovoltaic panel performances estimation is proposed in the paper. The base of the model is the mathematical function of the photovoltaic panel current–voltage curve. The model of the current–voltage curve is based on the sigmoid function with temperature and irradiance dependent parameters. The temperature and irradiance dependencies of the parameters are proposed in the form of analytic functions. The constant parameters are involved in the analytical functions. The constant parameters need to be estimated to get the temperature and irradiance dependent current–voltage curve. The mathematical model contains 12 constant parameters and they are estimated by using the evolutionary algorithm. The optimization problem is defined for this purpose. The optimization problem objective function is based on estimated and extracted (measured) current and voltage values. The current and voltage values are extracted from current–voltage curves given in datasheet of the photovoltaic panels. The new procedure for estimation of open circuit voltage value at any temperature and irradiance is proposed in the model. The performance of the proposed mathematical model is presented for three different photovoltaic panel technologies. The simulation results indicate that the proposed mathematical model is acceptable for estimation of temperature and irradiance dependent current–voltage curve and photovoltaic panel performances within temperature and irradiance ranges

PREFACE: Physics-Based Mathematical Models for Nanotechnology

Science.gov (United States)

Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten

2008-03-01

stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines

On the mathematical modeling of memristors

KAUST Repository

Radwan, Ahmed G.

2012-10-06

Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2010-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2014-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

Directory of Open Access Journals (Sweden)

Zoran Benić

2016-01-01

Full Text Available Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton’s second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.

Mathematical Modeling of Loop Heat Pipes

Science.gov (United States)

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.

Mathematical Modelling Plant Signalling Networks

KAUST Repository

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.

Building Mathematical Models of Simple Harmonic and Damped Motion.

Science.gov (United States)

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)

Simple mathematical models of symmetry breaking. Application to particle physics

International Nuclear Information System (INIS)

Michel, L.

1976-01-01

Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)

Mathematical 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 ...

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.

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. 

Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics

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Cecilia Noecker

2015-03-01

Full Text Available Upon infection of a new host, human immunodeficiency virus (HIV replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV. First, we found that the mode of virus production by infected cells (budding vs. bursting has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

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Morten Andersen

Full Text Available The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

Mathematical models of human behavior

DEFF Research Database (Denmark)

Møllgaard, Anders Edsberg

at the Technical University of Denmark. The data set includes face-to-face interaction (Bluetooth), communication (calls and texts), mobility (GPS), social network (Facebook), and general background information including a psychological profile (questionnaire). This thesis presents my work on the Social Fabric...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived....... Evidence is provided, which implies that the asymmetry is caused by a self-enhancement in the initiation dynamics. These results have implications for the formation of social networks and the dynamics of the links. It is shown that the Big Five Inventory (BFI) representing a psychological profile only...

Mathematical Modeling of Hybrid Electrical Engineering Systems

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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

iSTEM: Promoting Fifth Graders' Mathematical Modeling

Science.gov (United States)

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…

Qualitative mathematics for the social sciences mathematical models for research on cultural dynamics

CERN Document Server

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

Applied Mathematics, Modelling and Computational Science

CERN Document Server

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 ...

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 ...

The Relationship between Big Data and Mathematical Modeling: A Discussion in a Mathematical Education Scenario

Science.gov (United States)

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…

The High Level Mathematical Models in Calculating Aircraft Gas Turbine Engine Parameters

Directory of Open Access Journals (Sweden)

Yu. A. Ezrokhi

2017-01-01

Full Text Available The article describes high-level mathematical models developed to solve special problems arising at later stages of design with regard to calculation of the aircraft gas turbine engine (GTE under real operating conditions. The use of blade row mathematics models, as well as mathematical models of a higher level, including 2D and 3D description of the working process in the engine units and components, makes it possible to determine parameters and characteristics of the aircraft engine under conditions significantly different from the calculated ones.The paper considers application of mathematical modelling methods (MMM for solving a wide range of practical problems, such as forcing the engine by injection of water into the flowing part, estimate of the thermal instability effect on the GTE characteristics, simulation of engine start-up and windmill starting condition, etc. It shows that the MMM use, when optimizing the laws of the compressor stator control, as well as supplying cooling air to the hot turbine components in the motor system, can significantly improve the integral traction and economic characteristics of the engine in terms of its gas-dynamic stability, reliability and resource.It ought to bear in mind that blade row mathematical models of the engine are designed to solve purely "motor" problems and do not replace the existing models of various complexity levels used in calculation and design of compressors and turbines, because in “quality” a description of the working processes in these units is inevitably inferior to such specialized models.It is shown that the choice of the mathematical modelling level of an aircraft engine for solving a particular problem arising in its designing and computational study is to a large extent a compromise problem. Despite the significantly higher "resolution" and information ability the motor mathematical models containing 2D and 3D approaches to the calculation of flow in blade machine

Prospective Mathematics Teachers' Opinions about Mathematical Modeling Method and Applicability of This Method

Science.gov (United States)

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…

Mathematical modelling of the process of quality control of construction products

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Pogorelov Vadim

2017-01-01

Full Text Available The study presents the results of years of research in the field of quality management of industrial production construction production, based on mathematical modelling techniques, process and results of implementing the developed programme of monitoring and quality control in the production process of the enterprise. The aim of this work is the presentation of scientific community of the practical results of mathematical modelling in application programs. In the course of the research addressed the description of the applied mathematical models, views, practical results of its application in the applied field to assess quality control. The authors used this mathematical model in practice. The article presents the results of applying this model. The authors developed the experimental software management and quality assessment by using mathematical modeling methods. The authors continue research in this direction to improve the diagnostic systems and quality management systems based on mathematical modeling methods prognostic and diagnostic processes.

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 ...

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

Science.gov (United States)

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…

Ethnophysics, Mathematical Modeling, Geometry... All in the same Manzuá

Directory of Open Access Journals (Sweden)

Ednilson Sergio Ramalho de Souza

2013-06-01

Full Text Available The objective this is paper is to show partial results of research for project of doctorate whose intention is to analyze the Ethnophysics of the amazon fisherman end to develop innovative didactic resources for the conceptual approach in Physics and Mathematics in the classroom of the high school and higher education in environment of Mathematical Modeling. The research question was: How the build the Manzuá can contextualize lessons of Physics and Mathematics in high school? The methodology used was ethnographicresearch. The theoretical foundations were Ethnomathematics (D’AMBROSIO, 2008, Mental Models (JONHSON-LAIRD, 1983, Mathematical Modeling (CHAVES e ESPÍRITO SANTO, 2008 end Conceptual Field ((VERGNAUD, 2007. The initial results suggest which the traditional physical knowledge is strongly related to mental models formed in function long years practice in the construction of the Manzuá end the operational invariants take part in the mental models. The situations lived during the construction of the Manzuá can base situations-problem in the classes of Physics and Mathematics in environment of Mathematical Modeling. We can, therefore, develop didactics resources that relate the traditional knowledge to the school knowledge

The enhancement of mathematical analogical reasoning ability of university students through concept attainment model

Science.gov (United States)

Angraini, L. M.; Kusumah, Y. S.; Dahlan, J. A.

2018-05-01

This study aims to see the enhancement of mathematical analogical reasoning ability of the university students through concept attainment model learning based on overall and Prior Mathematical Knowledge (PMK) and interaction of both. Quasi experiments with the design of this experimental-controlled equivalent group involved 54 of second semester students at the one of State Islamic University. The instrument used is pretest-postest. Kolmogorov-Smirnov test, Levene test, t test, two-way ANOVA test were used to analyse the data. The result of this study includes: (1) The enhancement of the mathematical analogical reasoning ability of the students who gets the learning of concept attainment model is better than the enhancement of the mathematical analogical reasoning ability of the students who gets the conventional learning as a whole and based on PMK; (2) There is no interaction between the learning that is used and PMK on enhancing mathematical analogical reasoning ability.

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 and computational prediction of cancer drug resistance.

Science.gov (United States)

Sun, Xiaoqiang; Hu, Bin

2017-06-23

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of

BioModels: expanding horizons to include more modelling approaches and formats.

Science.gov (United States)

Glont, Mihai; Nguyen, Tung V N; Graesslin, Martin; Hälke, Robert; Ali, Raza; Schramm, Jochen; Wimalaratne, Sarala M; Kothamachu, Varun B; Rodriguez, Nicolas; Swat, Maciej J; Eils, Jurgen; Eils, Roland; Laibe, Camille; Malik-Sheriff, Rahuman S; Chelliah, Vijayalakshmi; Le Novère, Nicolas; Hermjakob, Henning

2018-01-04

BioModels serves as a central repository of mathematical models representing biological processes. It offers a platform to make mathematical models easily shareable across the systems modelling community, thereby supporting model reuse. To facilitate hosting a broader range of model formats derived from diverse modelling approaches and tools, a new infrastructure for BioModels has been developed that is available at http://www.ebi.ac.uk/biomodels. This new system allows submitting and sharing of a wide range of models with improved support for formats other than SBML. It also offers a version-control backed environment in which authors and curators can work collaboratively to curate models. This article summarises the features available in the current system and discusses the potential benefit they offer to the users over the previous system. In summary, the new portal broadens the scope of models accepted in BioModels and supports collaborative model curation which is crucial for model reproducibility and sharing. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

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)

Molecular modeling: An open invitation for applied mathematics

Science.gov (United States)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

Fundamentals of Cryobiology Physical Phenomena and Mathematical Models

CERN Document Server

Zhmakin, Alexander I

2009-01-01

The book gives a summary of the state-of-the-art of cryobiology and its applications. The accent is on the underlying physical phenomena, which are common in such opposite applications as cryosurgery and cryoconservation, and the corresponding mathematical models, including numerical ones. The treatment of some more special issues is moved to the appendices. The glossary contains definitions and explanations of the major entities. All the topics considered are well referenced. The book is useful to both biologists and physicits of different level including practioners and graduate students.

Application of mathematical modeling in sustained release delivery systems.

Science.gov (United States)

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.

A fuzzy mathematics model for radioactive waste characterization by process knowledge

International Nuclear Information System (INIS)

Smith, M.; Stevens, S.; Elam, K.; Vrba, J.

1994-01-01

Fuzzy mathematics and fuzzy logic are means for making decisions that can integrate complicated combinations of hard and soft factors and produce mathematically validated results that can be independently verified. In this particular application, several sources of information regarding the waste stream have been compiled, including facility operating records, other waste generated from the facility in the past, laboratory analysis results, and interviews with facility personnel. A fuzzy mathematics model is used to interrelate these various sources of information and arrive at a defensible estimate of the contaminant concentration in the final waste product. The model accounts for the separate process knowledge-based contaminant concentrations by providing a weighted averaging technique to incorporate information from the various sources. Reliability estimates are provided for each of the component pieces of information and combined using the model into an estimate that provides a near-probabilistic value for contaminant concentration. The speadsheet accounts for the estimated uncertainty in the concentration on the basis of open-quotes reliability curves,close quotes which are derived from personal process knowledge as well as limited independent measurements

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 swirled flows in industrial applications

Science.gov (United States)

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.

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

Modelling and applications in mathematics education the 14th ICMI study

CERN Document Server

Galbraith, Peter L; Niss, Mogens

2007-01-01

The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.

The mathematical model of thread unrolling from a bobbin

Directory of Open Access Journals (Sweden)

S. M. Tenenbaum

2014-01-01

solving of ordinary differential equation.III. Mathematical modelIn this section the detailed description of proposed mathematical model based on conventional spring-mass model is given.The major feature of this model is that on the every integration step all nodes divided into three groups: nodes on the bobbin (linked – their motion is completely determined by the bobbin rotation; free nodes – descended from the bobbin and not neighboring nodes on the bobbin; boundary nodes - descended from the bobbin neighboring nodes on the bobbin.For each nodes group the right parts of equations of motions are different. In these equations the additional corrections are included that result in reducing the impact of discretization on simulation results. These corrections are: equations of motion for boundary nodes eliminate unphysical reaction components, resulting from discretization; when a node descends from the bobbin its velocity vector turns following motion of already descended nodes, thus simulating the thread bending of very small radius at the point of thread descending.IV. Numerical experimentThe developed mathematical model is tested using the simplified problem of two-blades rotary solar sail deploying from the «BMSTU-Sail» project [2].The calculations demonstrated that the proposed mathematical model satisfies the law of conservation of angular momentum. It is also shown that calculation results are almost independent on the utility parameters of mathematical model (e.g. damping coefficient of nodes relative oscillations.V. ConclusionMajor conclusions in this paper are: proposed mathematical model satisfies the law of conservation of angular momentum that indirectly confirms its correctness; the transverse thread motion is almost independent on the damping and stiffness coefficients, therefore they can be adjusted for calculation stability without accuracy loss; based on proposed mathematical model of unrolling a thread from a bobbin the

Hybrid modelling framework by using mathematics-based and information-based methods

International Nuclear Information System (INIS)

Ghaboussi, J; Kim, J; Elnashai, A

2010-01-01

Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.

Mathematics of epidemics on networks from exact to approximate models

CERN Document Server

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 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.

Mathematical modeling in wound healing, bone regeneration and tissue engineering.

Science.gov (United States)

Geris, Liesbet; Gerisch, Alf; Schugart, Richard C

2010-12-01

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.

Mathematical 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

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Mazen Shahin

2010-06-01

Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.

Mathematical modeling and the two-phase constitutive equations

International Nuclear Information System (INIS)

Boure, J.A.

1975-01-01

The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr

Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors

Science.gov (United States)

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…

Use of mathematical modelling in electron beam processing: A guidebook

International Nuclear Information System (INIS)

2010-01-01

The use of electron beam irradiation for industrial applications, like the sterilization of medical devices or cross-linking of polymers, has a long and successful track record and has proven itself to be a key technology. Emerging fields, including environmental applications of ionizing radiation, the sterilization of complex medical and pharmaceutical products or advanced material treatment, require the design and control of even more complex irradiators and irradiation processes. Mathematical models can aid the design process, for example by calculating absorbed dose distributions in a product, long before any prototype is built. They support process qualification through impact assessment of process variable uncertainties, and can be an indispensable teaching tool for technologists in training in the use of radiation processing. The IAEA, through various mechanisms, including its technical cooperation programme, coordinated research projects, technical meetings, guidelines and training materials, is promoting the use of radiation technologies to minimize the effects of harmful contaminants and develop value added products originating from low cost natural and human made raw materials. The need to publish a guidebook on the use of mathematical modelling for design processes in the electron beam treatment of materials was identified through the increased interest of radiation processing laboratories in Member States and as a result of recommendations from several IAEA expert meetings. In response, the IAEA has prepared this report using the services of an expert in the field. This publication should serve as both a guidebook and introductory tutorial for the use of mathematical modelling (using mostly Monte Carlo methods) in electron beam processing. The emphasis of this guide is on industrial irradiation methodologies with a strong reference to existing literature and applicable standards. Its target audience is readers who have a basic understanding of electron

Achilles and the tortoise: Some caveats to mathematical modeling in biology.

Science.gov (United States)

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.

Mathematical model for temperature change of a journal bearing

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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.

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.

Mathematical psychology.

Science.gov (United States)

Batchelder, William H

2010-09-01

Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

Application of computer mathematical modeling in nuclear well-logging industry

International Nuclear Information System (INIS)

Cai Shaohui

1994-01-01

Nuclear well logging techniques have made rapid progress since the first well log calibration facility (the API pits) was dedicated in 1959. Then came the first computer mathematical model in the late 70's. Mathematical modeling can now minimize design and experiment time, as well as provide new information and idea on tool design, environmental effects and result interpretation. The author gives a brief review on the achievements of mathematical modeling on nuclear logging problems

Mathematical Modeling Applied to Maritime Security

OpenAIRE

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...

Authenticity of Mathematical Modeling

Science.gov (United States)

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…

How to Introduce Mathematic Modeling in Industrial Design Education

NARCIS (Netherlands)

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

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

Science.gov (United States)

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…

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

Science.gov (United States)

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

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.

Mathematical models of ABE fermentation: review and analysis.

Science.gov (United States)

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.

Mathematical modeling of drug dissolution.

Science.gov (United States)

Siepmann, J; Siepmann, F

2013-08-30

The dissolution of a drug administered in the solid state is a pre-requisite for efficient subsequent transport within the human body. This is because only dissolved drug molecules/ions/atoms are able to diffuse, e.g. through living tissue. Thus, generally major barriers, including the mucosa of the gastro intestinal tract, can only be crossed after dissolution. Consequently, the process of dissolution is of fundamental importance for the bioavailability and, hence, therapeutic efficacy of various pharmaco-treatments. Poor aqueous solubility and/or very low dissolution rates potentially lead to insufficient availability at the site of action and, hence, failure of the treatment in vivo, despite a potentially ideal chemical structure of the drug to interact with its target site. Different physical phenomena are involved in the process of drug dissolution in an aqueous body fluid, namely the wetting of the particle's surface, breakdown of solid state bonds, solvation, diffusion through the liquid unstirred boundary layer surrounding the particle as well as convection in the surrounding bulk fluid. Appropriate mathematical equations can be used to quantify these mass transport steps, and more or less complex theories can be developed to describe the resulting drug dissolution kinetics. This article gives an overview on the current state of the art of modeling drug dissolution and points out the assumptions the different theories are based on. Various practical examples are given in order to illustrate the benefits of such models. This review is not restricted to mathematical theories considering drugs exhibiting poor aqueous solubility and/or low dissolution rates, but also addresses models quantifying drug release from controlled release dosage forms, in which the process of drug dissolution plays a major role. Copyright © 2013 Elsevier B.V. All rights reserved.

Mathematical Modelling for Micropiles Embedded in Salt Rock

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Rădan (Toader Georgiana

2016-03-01

Full Text Available This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

Science.gov (United States)

Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

2018-04-01

Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

Perspectives on instructor modeling in mathematics teacher education

OpenAIRE

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...

Mathematical modeling and simulation of nanopore blocking by precipitation

KAUST Repository

Wolfram, M-T

2010-10-29

High surface charges of polymer pore walls and applied electric fields can lead to the formation and subsequent dissolution of precipitates in nanopores. These precipitates block the pore, leading to current fluctuations. We present an extended Poisson-Nernst-Planck system which includes chemical reactions of precipitation and dissolution. We discuss the mathematical modeling and present 2D numerical simulations. © 2010 IOP Publishing Ltd.

Solving cross-disciplinary problems by mathematical modelling

Science.gov (United States)

Panfilov, D. A.; Romanchikov, V. V.; Krupin, K. N.

2018-03-01

The article deals with the creation of a human tibia 3D model by means of “Autodesk Revit-2016” PC based on tomogram data. The model was imported into “Lira- SAPR2013 R4” software system. To assess the possibility of education and the nature of bone fracture (and their visualization), the Finite Element Analysis (FEA) method was used. The geometric parameters of the BBK model corresponded to the physical parameters of the individual. The compact plate different thickness is modeled by rigidity properties of the finite elements in accordance with the parameters on the roentgenogram. The BBK model included parameters of the outer compact plate and the spongy substance having a more developed structure of the epiphysic region. In the “Lira-SAPR2013 R4” software system, mathematical modeling of the traumatic effect was carried out and the analysis of the stress-strain state of the finite element model of the tibia was made to assess fracture conditions.

A REFINED MATHEMATICAL MODEL OF MULTIPHYSICS PROCESSES FOR MAGNETIC PULSE TREATMENT OF MATERIALS

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E.I. Baida

2015-04-01

Full Text Available Introduction. The complexity of the theoretical description of the magnetic pulse treatment of the material is in the mutual coupled processes of electromagnetic and thermal fields with plastic deformation of the material and processes in an electrical circuit. The paper deals with the combined transient mathematical model of the system of equations of the electromagnetic field, theory of elasticity, thermal conductivity and electrical circuit. Purpose. Research and testing of the developed mathematical model and assess the impact of various parameters on the process of deformation of the work piece. Methodology. Investigation of nonlinear mathematical model is carried out by the finite element method using a special software package. Results. The resulting solution of the transient mathematical model allows studying the influence of parameters of the circuit, the speed and the characteristics of the material to plastic deformation and heating of the work piece, which allows to select the optimum process parameters. Originality. This is an integrated approach to the development of a mathematical model, which includes the electromagnetic field equations, the theory of elasticity, thermal conductivity and electrical circuit equations with a storage capacitor. Conclusions. A comprehensive mathematical model and its solution are obtained. It is established a small effect of heating temperature on the amount of strain. Currents caused by movement of the work piece must be taken into account in the calculations. Inertial forces significantly affect the nature of the deformation. During the deformation it is necessary to consider the nonlinearity of elasticity modulus. Thermal deformation of the work piece is much less mechanical strain and opposite in sign to them, but the surface temperature stresses due to the high temperature gradient equal to 20 % of the yield strength of the work piece.

Improving ability mathematic literacy, self-efficacy and reducing mathematical anxiety with learning Treffinger model at senior high school students

Directory of Open Access Journals (Sweden)

Hafizh Nizham

2017-12-01

Full Text Available This study is a Quasi Experimental study with the design of The Pretest-Post-Test Non-Equivalent Group Design. Population in this research is all student of class X SHS in South Jakarta. Sampling is done by purposive sampling, to obtain an experimental class and control class. In the experimental class, students learn with Treffinger learning model and control, class learning with conventional learning. This study is also to examine the differences of self-efficacy improvement and students literacy skills, and decreased students' mathematical anxiety. Also, this study also examines the relevance of early mathematical abilities (high, medium, low with improving students' math literacy skills. The instrument used in this research is literacy skill test, self-efficacy scale, mathematical anxiety scale, observation sheet, and student interview. Data were analyzed by t-test, one-way ANOVA, and two lines. From the results of the data, it is found that: (1 The improvement of literacy ability of students who are learned with Treffinger model learning is not significantly higher than students who learn with conventional. (2 The self-efficacy of students who learning with the Treffinger model learning  is better than the student that is learning by conventional. (3 The mathematical anxiety of students learning with Treffinger model learning reduces better than students learning with conventional. (4 There is a difference in the improvement of students' mathematical literacy skills learning by learning the Treffinger model and students learning with conventional learning based on early mathematical abilities. (5 Student response to Treffinger model learning is better than students learning with conventional learning. Therefore, learning model Treffinger can be an alternative model of learning to improve students' mathematical literacy skills, and self-efficacy students, and able to reduce mathematical anxiety.

An Integrated Approach to Mathematical Modeling: A Classroom Study.

Science.gov (United States)

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…

DigitalHuman (DH): An Integrative Mathematical Model ofHuman Physiology

Science.gov (United States)

Hester, Robert L.; Summers, Richard L.; lIescu, Radu; Esters, Joyee; Coleman, Thomas G.

2010-01-01

Mathematical models and simulation are important tools in discovering the key causal relationships governing physiological processes and improving medical intervention when physiological complexity is a central issue. We have developed a model of integrative human physiology called DigitalHuman (DH) consisting of -5000 variables modeling human physiology describing cardiovascular, renal, respiratory, endocrine, neural and metabolic physiology. Users can view time-dependent solutions and interactively introduce perturbations by altering numerical parameters to investigate new hypotheses. The variables, parameters and quantitative relationships as well as all other model details are described in XML text files. All aspects of the model, including the mathematical equations describing the physiological processes are written in XML open source, text-readable files. Model structure is based upon empirical data of physiological responses documented within the peer-reviewed literature. The model can be used to understand proposed physiological mechanisms and physiological interactions that may not be otherwise intUitively evident. Some of the current uses of this model include the analyses of renal control of blood pressure, the central role of the liver in creating and maintaining insulin resistance, and the mechanisms causing orthostatic hypotension in astronauts. Additionally the open source aspect of the modeling environment allows any investigator to add detailed descriptions of human physiology to test new concepts. The model accurately predicts both qualitative and more importantly quantitative changes in clinically and experimentally observed responses. DigitalHuman provides scientists a modeling environment to understand the complex interactions of integrative physiology. This research was supported by.NIH HL 51971, NSF EPSCoR, and NASA

Mathematical models of information and stochastic systems

CERN Document Server

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

Uncertainty and variability in computational and mathematical models of cardiac physiology.

Science.gov (United States)

Mirams, Gary R; Pathmanathan, Pras; Gray, Richard A; Challenor, Peter; Clayton, Richard H

2016-12-01

Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for

Mathematical modelling with case studies using Maple and Matlab

CERN Document Server

Barnes, B

2014-01-01

Introduction to Mathematical ModelingMathematical models An overview of the book Some modeling approaches Modeling for decision makingCompartmental Models Introduction Exponential decay and radioactivity Case study: detecting art forgeries Case study: Pacific rats colonize New Zealand Lake pollution models Case study: Lake Burley Griffin Drug assimilation into the blood Case study: dull, dizzy, or dead? Cascades of compartments First-order linear DEs Equilibrium points and stability Case study: money, money, money makes the world go aroundModels of Single PopulationsExponential growth Density-

Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

Science.gov (United States)

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-01-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

A practical course in differential equations and mathematical modeling

CERN Document Server

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

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

Science.gov (United States)

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina

2018-04-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel , designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel , designed to facilitate the exploration of novel research questions for advanced modelers.

Concentrator optical characterization using computer mathematical modelling and point source testing

Science.gov (United States)

Dennison, E. W.; John, S. L.; Trentelman, G. F.

1984-01-01

The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.

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)

A mathematical framework for agent based models of complex biological networks.

Science.gov (United States)

Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2011-07-01

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.

PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE

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N. V. Andrianov

2006-01-01

Full Text Available The analysis of the mathematical models which can be used at optimization of the control system of the enterprise organizational structure is presented. The new approach to the mathematical modeling of the enterprise organizational structure, based on using of temporary characteristics of the control blocks working, is formulated

Mathematical model for estimating of technical and technological indicators of railway stations operation

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D.M. Kozachenko

2013-06-01

Full Text Available Purpose. The article aims to create a mathematical model of the railway station functioning for the solving of problems of station technology development on the plan-schedule basis. Methodology. The methods of graph theory and object-oriented analysis are used as research methods. The model of the station activity plan-schedule includes a model of technical equipment of the station (plan-schedule net and a model of the station functioning , which are formalized on the basis of parametric graphs. Findings. The presented model is implemented as an application to the graphics package AutoCAD. The software is developed in Visual LISP and Visual Basic. Taking into account that the construction of the plan-schedule is mostly a traditional process of adding, deleting, and modifying of icons, the developed interface is intuitively understandable for a technologist and practically does not require additional training. Originality. A mathematical model was created on the basis of the theory of graphs and object-oriented analysis in order to evaluate the technical and process of railway stations indicators; it is focused on solving problems of technology development of their work. Practical value. The proposed mathematical model is implemented as an application to the graphics package of AutoCAD. The presence of a mathematical model allows carrying out an automatic analysis of the plan-schedule and, thereby, reducing the period of its creation more than twice.

Mathematics in Nature Modeling Patterns in the Natural World

CERN Document Server

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

Mathematical models to predict rheological parameters of lateritic hydromixtures

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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.

The Comparison of Think Talk Write and Think Pair Share Model with Realistic Mathematics Education Approach Viewed from Mathematical-Logical Intelligence

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Himmatul Afthina

2017-12-01

Full Text Available The aims of this research to determine the effect of Think Talk Write (TTW and Think Pair Share (TPS model with Realistic Mathematics Education (RME approach viewed from mathematical-logical intelligence. This research employed the quasi experimental research. The population of research was all students of the eight graders of junior high school in Karangamyar Regency in academic year 2016/2017. The result of this research shows that (1 TTW with RME approach gave better mathematics achievement than TPS with RME approach, (2 Students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one, (3 In TTW model with RME approach, students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average and low mathematical-logical intelligence gave same mathematics achievement, and  in TPS model with RME approach students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one (4 In each category of  mathematical-logical intelligence, TTW with RME approach and TPS with RME approach gave same mathematics achievement.

Mathematical modeling of physiological systems: an essential tool for discovery.

Science.gov (United States)

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.

Mathematical Models of Breast and Ovarian Cancers

Science.gov (United States)

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

Parallel Boltzmann machines : a mathematical model

NARCIS (Netherlands)

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

Mathematical Modelling Research in Turkey: A Content Analysis Study

Science.gov (United States)

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.…

Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling.

Science.gov (United States)

Barnes, Sean L; Kasaie, Parastu; Anderson, Deverick J; Rubin, Michael

2016-11-01

Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages-such as shorter developmental timelines and opportunities for extensive experimentation-over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship. Infect Control Hosp Epidemiol 2016;1-7.

Constraint theory multidimensional mathematical model management

CERN Document Server

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...

2nd Tbilisi-Salerno Workshop on Modeling in Mathematics

CERN Document Server

Ricci, Paolo; Tavkhelidze, Ilia

2017-01-01

This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling in March 2015. The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such topics as multimodal logic, fractional calculus, special functions, Fourier-like solutions for PDE’s, Rvachev-functions and linear dynamical systems. Special chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula. The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.

A Mathematical Approach to Establishing Constitutive Models for Geomaterials

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Guang-hua Yang

2013-01-01

Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.

Methods and models in mathematical biology deterministic and stochastic approaches

CERN Document Server

Müller, Johannes

2015-01-01

This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and  branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

Mathematical modelling in economic processes.

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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 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 and methods for planet Earth

CERN Document Server

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.

Turbofan engine mathematic model for its static and dynamic characteristics research

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О.Є. Карпов

2004-01-01

Full Text Available  Demands to mathematical model of the turbofan engine are determined in the article. The mathematical model is used for calculations static and dynamic parameters, which are required for estimation of engine technical state in operation. There are the mathematical model of the turbofan engine AИ-25 and the results of calculations static and dynamic parameters at initial condition in the article.

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 Modeling of Circadian/Performance Countermeasures

Data.gov (United States)

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...

A mathematical model of embodied consciousness

NARCIS (Netherlands)

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

Aspects of Mathematical Modelling Applications in Science, Medicine, Economics and Management

CERN Document Server

Hosking, Roger J

2008-01-01

The construction of mathematical models is an essential scientific activity. Mathematics has long been associated with developments in the exact sciences and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in many other fields. The contributors to this book demonstrate the application of mathematics to modern research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.

A Mediation Model to Explain the Role of Mathematics Skills and Probabilistic Reasoning on Statistics Achievement

Science.gov (United States)

Primi, Caterina; Donati, Maria Anna; Chiesi, Francesca

2016-01-01

Among the wide range of factors related to the acquisition of statistical knowledge, competence in basic mathematics, including basic probability, has received much attention. In this study, a mediation model was estimated to derive the total, direct, and indirect effects of mathematical competence on statistics achievement taking into account…

Introduction to mathematical biology modeling, analysis, and simulations

CERN Document Server

Chou, Ching Shan

2016-01-01

This book is based on a one semester course that the authors have been teaching for several years, and includes two sets of case studies. The first includes chemostat models, predator-prey interaction, competition among species, the spread of infectious diseases, and oscillations arising from bifurcations. In developing these topics, readers will also be introduced to the basic theory of ordinary differential equations, and how to work with MATLAB without having any prior programming experience. The second set of case studies were adapted from recent and current research papers to the level of the students. Topics have been selected based on public health interest. This includes the risk of atherosclerosis associated with high cholesterol levels, cancer and immune interactions, cancer therapy, and tuberculosis. Readers will experience how mathematical models and their numerical simulations can provide explanations that guide biological and biomedical research. Considered to be the undergraduate companion to t...

Data-based mathematical modeling of vectorial transport across double-transfected polarized cells.

Science.gov (United States)

Bartholomé, Kilian; Rius, Maria; Letschert, Katrin; Keller, Daniela; Timmer, Jens; Keppler, Dietrich

2007-09-01

Vectorial transport of endogenous small molecules, toxins, and drugs across polarized epithelial cells contributes to their half-life in the organism and to detoxification. To study vectorial transport in a quantitative manner, an in vitro model was used that includes polarized MDCKII cells stably expressing the recombinant human uptake transporter OATP1B3 in their basolateral membrane and the recombinant ATP-driven efflux pump ABCC2 in their apical membrane. These double-transfected cells enabled mathematical modeling of the vectorial transport of the anionic prototype substance bromosulfophthalein (BSP) that has frequently been used to examine hepatobiliary transport. Time-dependent analyses of (3)H-labeled BSP in the basolateral, intracellular, and apical compartments of cells cultured on filter membranes and efflux experiments in cells preloaded with BSP were performed. A mathematical model was fitted to the experimental data. Data-based modeling was optimized by including endogenous transport processes in addition to the recombinant transport proteins. The predominant contributions to the overall vectorial transport of BSP were mediated by OATP1B3 (44%) and ABCC2 (28%). Model comparison predicted a previously unrecognized endogenous basolateral efflux process as a negative contribution to total vectorial transport, amounting to 19%, which is in line with the detection of the basolateral efflux pump Abcc4 in MDCKII cells. Rate-determining steps in the vectorial transport were identified by calculating control coefficients. Data-based mathematical modeling of vectorial transport of BSP as a model substance resulted in a quantitative description of this process and its components. The same systems biology approach may be applied to other cellular systems and to different substances.

Ordinary Mathematical Models in Calculating the Aviation GTE Parameters

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E. A. Khoreva

2017-01-01

Full Text Available The paper presents the analytical review results of the ordinary mathematical models of the operating process used to study aviation GTE parameters and characteristics at all stages of its creation and operation. Considers the mathematical models of the zero and the first level, which are mostly used when solving typical problems in calculating parameters and characteristics of engines.Presents a number of practical problems arising in designing aviation GTE for various applications.The application of mathematical models of the zero-level engine can be quite appropriate when the engine is considered as a component in the aircraft system to estimate its calculated individual flight performance or when modeling the flight cycle of the aircrafts of different purpose.The paper demonstrates that introduction of correction functions into the first-level mathematical models in solving typical problems (influence of the Reynolds number, characteristics deterioration of the units during the overhaul period of engine, as well as influence of the flow inhomogeneity at the inlet because of manufacturing tolerance, etc. enables providing a sufficient engineering estimate accuracy to reflect a realistic operating process in the engine and its elements.

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues.

Science.gov (United States)

Kim, Munju; Gillies, Robert J; Rejniak, Katarzyna A

2013-11-18

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Potential of mathematical modeling in fruit quality

African Journals Online (AJOL)

ONOS

2010-01-18

Jan 18, 2010 ... successful mathematical model, the modeler needs to chose what .... equations. In the SUCROS models, the rate of CO2 assimilation is .... insect ecology. ... García y García A, Ingram KT, Hatch U, Hoogenboom G, Jones JW,.

Mathematical modeling of cancer metabolism.

Science.gov (United States)

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 non-linear phenomena, processes and systems: from molecular scale to planetary atmosphere

CERN Document Server

2013-01-01

This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.

Mathematical models in biological discovery

CERN Document Server

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...

Electrorheological fluids modeling and mathematical theory

CERN Document Server

Růžička, Michael

2000-01-01

This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

Mathematical models of tumour and normal tissue response

International Nuclear Information System (INIS)

Jones, B.; Dale, R.G.; Charing Cross Group of Hospitals, London

1999-01-01

The historical application of mathematics in the natural sciences and in radiotherapy is compared. The various forms of mathematical models and their limitations are discussed. The Linear Quadratic (LQ) model can be modified to include (i) radiobiological parameter changes that occur during fractionated radiotherapy, (ii) situations such as focal forms of radiotherapy, (iii) normal tissue responses, and (iv) to allow for the process of optimization. The inclusion of a variable cell loss factor in the LQ model repopulation term produces a more flexible clonogenic doubling time, which can simulate the phenomenon of 'accelerated repopulation'. Differential calculus can be applied to the LQ model after elimination of the fraction number integers. The optimum dose per fraction (maximum cell kill relative to a given normal tissue fractionation sensitivity) is then estimated from the clonogen doubling times and the radiosensitivity parameters (or α/β ratios). Economic treatment optimization is described. Tumour volume studies during or following teletherapy are used to optimize brachytherapy. The radiation responses of both individual tumours and tumour populations (by random sampling 'Monte-Carlo' techniques from statistical ranges of radiobiological and physical parameters) can be estimated. Computerized preclinical trials can be used to guide choice of dose fractionation scheduling in clinical trials. The potential impact of gene and other biological therapies on the results of radical radiotherapy are testable. New and experimentally testable hypotheses are generated from limited clinical data by exploratory modelling exercises. (orig.)

Mathematical model of polyethylene pipe bending stress state

Science.gov (United States)

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 model comparing of the multi-level economics systems

Science.gov (United States)

Brykalov, S. M.; Kryanev, A. V.

2017-12-01

The mathematical model (scheme) of a multi-level comparison of the economic system, characterized by the system of indices, is worked out. In the mathematical model of the multi-level comparison of the economic systems, the indicators of peer review and forecasting of the economic system under consideration can be used. The model can take into account the uncertainty in the estimated values of the parameters or expert estimations. The model uses the multi-criteria approach based on the Pareto solutions.

Mathematical model on Alzheimer's disease.

Science.gov (United States)

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.

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

Science.gov (United States)

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

A mathematical look at a physical power prediction model

DEFF Research Database (Denmark)

Landberg, L.

1998-01-01

This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...

Mathematical 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: Are Prior Experiences Important?

Science.gov (United States)

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…

Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience

Science.gov (United States)

Charpin, J. P. F.; O'Hara, S.; Mackey, D.

2013-01-01

In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…

A Mathematical Model for the Hippocampus: Towards the Understanding of Episodic Memory and Imagination

Science.gov (United States)

Tsuda, I.; Yamaguti, Y.; Kuroda, S.; Fukushima, Y.; Tsukada, M.

How does the brain encode episode? Based on the fact that the hippocampus is responsible for the formation of episodic memory, we have proposed a mathematical model for the hippocampus. Because episodic memory includes a time series of events, an underlying dynamics for the formation of episodic memory is considered to employ an association of memories. David Marr correctly pointed out in his theory of archecortex for a simple memory that the hippocampal CA3 is responsible for the formation of associative memories. However, a conventional mathematical model of associative memory simply guarantees a single association of memory unless a rule for an order of successive association of memories is given. The recent clinical studies in Maguire's group for the patients with the hippocampal lesion show that the patients cannot make a new story, because of the lack of ability of imagining new things. Both episodic memory and imagining things include various common characteristics: imagery, the sense of now, retrieval of semantic information, and narrative structures. Taking into account these findings, we propose a mathematical model of the hippocampus in order to understand the common mechanism of episodic memory and imagination.

Mathematical model of two-phase flow in accelerator channel

Directory of Open Access Journals (Sweden)

О.Ф. Нікулін

2010-01-01

Full Text Available  The problem of  two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in  counter jet mill accelerator channel design.

Comparison of learning models based on mathematics logical intelligence in affective domain

Science.gov (United States)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.

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.

An Equivalent Electrical Circuit Model of Proton Exchange Membrane Fuel Cells Based on Mathematical Modelling

Directory of Open Access Journals (Sweden)

Dinh An Nguyen

2012-07-01

Full Text Available Many of the Proton Exchange Membrane Fuel Cell (PEMFC models proposed in the literature consist of mathematical equations. However, they are not adequately practical for simulating power systems. The proposed model takes into account phenomena such as activation polarization, ohmic polarization, double layer capacitance and mass transport effects present in a PEM fuel cell. Using electrical analogies and a mathematical modeling of PEMFC, the circuit model is established. To evaluate the effectiveness of the circuit model, its static and dynamic performances under load step changes are simulated and compared to the numerical results obtained by solving the mathematical model. Finally, the applicability of our model is demonstrated by simulating a practical system.

Mathematical and numerical models for eddy currents and magnetostatics with selected applications

CERN Document Server

Rappaz, Jacques

2013-01-01

This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problem

Mathematical models used to inform study design or surveillance systems in infectious diseases: a systematic review.

Science.gov (United States)

Herzog, Sereina A; Blaizot, Stéphanie; Hens, Niel

2017-12-18

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals. We searched Ovid Medline and two trial registry platforms (Cochrane, WHO) using search terms related to infection, mathematical model, and study design from the earliest dates to October 2016. Eligible publications and registered trials included mathematical models (compartmental, individual-based, or Markov) which were described and used to inform the design of infectious disease studies. We extracted information about the investigated infection, population, model characteristics, and study design. We identified 28 unique publications but no registered trials. Focusing on compartmental and individual-based models we found 12 observational/surveillance studies and 11 clinical trials. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6). Despite the fact that mathematical models have been advocated to be used at the planning stage of studies or surveillance systems, they are used scarcely. With only one exception, the publications described theoretical studies, hence, not being utilised in real studies.

Mathematical Modeling in Population Dynamics: The Case of Single ...

African Journals Online (AJOL)

kofimereku

Department of Mathematics, Kwame Nkrumah University of Science and Technology,. Kumasi, Ghana ... The trust of this paper is the application of mathematical models in helping to ..... Statistics and Computing, New York: Wiley. Cox, C.B and ...

Mathematical 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 for camera calibration based on straight lines

Directory of Open Access Journals (Sweden)

Antonio M. G. Tommaselli

2005-12-01

Full Text Available In other to facilitate the automation of camera calibration process, a mathematical model using straight lines was developed, which is based on the equivalent planes mathematical model. Parameter estimation of the developed model is achieved by the Least Squares Method with Conditions and Observations. The same method of adjustment was used to implement camera calibration with bundles, which is based on points. Experiments using simulated and real data have shown that the developed model based on straight lines gives results comparable to the conventional method with points. Details concerning the mathematical development of the model and experiments with simulated and real data will be presented and the results with both methods of camera calibration, with straight lines and with points, will be compared.

Mathematical modeling of infectious disease dynamics

Science.gov (United States)

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

Test-and-treat approach to HIV/AIDS: a primer for mathematical modeling.

Science.gov (United States)

Nah, Kyeongah; Nishiura, Hiroshi; Tsuchiya, Naho; Sun, Xiaodan; Asai, Yusuke; Imamura, Akifumi

2017-09-05

The public benefit of test-and-treat has induced a need to justify goodness for the public, and mathematical modeling studies have played a key role in designing and evaluating the test-and-treat strategy for controlling HIV/AIDS. Here we briefly and comprehensively review the essence of contemporary understanding of the test-and-treat policy through mathematical modeling approaches and identify key pitfalls that have been identified to date. While the decrease in HIV incidence is achieved with certain coverages of diagnosis, care and continued treatment, HIV prevalence is not necessarily decreased and sometimes the test-and-treat is accompanied by increased long-term cost of antiretroviral therapy (ART). To confront with the complexity of assessment on this policy, the elimination threshold or the effective reproduction number has been proposed for its use in determining the overall success to anticipate the eventual elimination. Since the publication of original model in 2009, key issues of test-and-treat modeling studies have been identified, including theoretical problems surrounding the sexual partnership network, heterogeneities in the transmission dynamics, and realistic issues of achieving and maintaining high treatment coverage in the most hard-to-reach populations. To explicitly design country-specific control policy, quantitative modeling approaches to each single setting with differing epidemiological context would require multi-disciplinary collaborations among clinicians, public health practitioners, laboratory technologists, epidemiologists and mathematical modelers.

Design based Investigation on Construction of Mathematical Modelling Problems: Example of Financial Content

Directory of Open Access Journals (Sweden)

Melike TURAL SÖNMEZ

2017-12-01

Full Text Available The purpose of this study is to examine the construction of mathematical modelling problems process in the content of financial literacy. It is also aimed to create design proposals for construction of mathematical modelling problems. A design based research method was used in this study. The participants were three seventh grade students, six finance experts and nine mathematics education experts. Data collection tools were transcription of video and tapes group discussions, presentations and worksheets during mathematical modelling activities, and participant experts’ feedback form about mathematical modelling problems. There were three stages in this study. First stage was application of preliminary study. This stage gave information about convenience of problems to grade level, students’ timing for solution of problems, clarity of problems and students’ background about content. In second stage, finance experts commented on convenience of mathematical modelling problems to financial literacy standards. In third stage, mathematics education experts commented on convenience of problems to students’ grade level, mathematical modelling principles and seventh grade mathematics lesson objectives. They also gave suggestion on progress. The frequency value of theme in feedback forms was calculated and experts’ expressions were given as citation. It was given suggestion about stages and application of the design guide

Mathematical 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.

Mathematical model of glucose-insulin homeostasis in healthy rats.

Science.gov (United States)

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.

Modeling eBook acceptance: A study on mathematics teachers

Science.gov (United States)

Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad

2014-12-01

The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.

Mathematical supply-chain modelling: Product analysis of cost and time

International Nuclear Information System (INIS)

Easters, D J

2014-01-01

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management

Mathematical supply-chain modelling: Product analysis of cost and time

Science.gov (United States)

Easters, D. J.

2014-03-01

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management.

Mathematical modeling of flow-injection techniques and their applications for environmental monitoring

International Nuclear Information System (INIS)

Begum, N.N.; Ahmed, J.

2006-01-01

A classification of the existing mathematical models of flow-injection (FI) manifolds based on the main principles on which they are built, have been proposed. Numerous mathematical models of FI systems employing ideas from different scientific areas (e.g. mathematical statistics, chemical engineering, chromatography) have been developed so far. The models have been compared with respect to their predictive power, the complexity of their mathematical treatment, and the requirements for computation time when applied to single-line, multi-channel and conjugated two-line FI systems. It is concluded that the axially dispersed plug flow model deserves special attention because it offers an acceptable compromise between the conflicting requirements for maximal possible mathematical simplicity and maximal possible precision. Applicability of these existing flow-injection models to single-line, multi-channel and conjugated two-line systems for environmental monitoring have been discussed. (author)

short communication mathematical modelling for magnetite

African Journals Online (AJOL)

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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:.

Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.

Science.gov (United States)

Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

2015-07-22

A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.

The prediction of epidemics through mathematical modeling.

Science.gov (United States)

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.

IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS

Directory of Open Access Journals (Sweden)

L. V. Ursulyak

2017-12-01

Full Text Available Purpose. Using scientific publications the paper analyzes the mathematical models developed in Ukraine, CIS countries and abroad for theoretical studies of train dynamics and also shows the urgency of their further improvement. Methodology. Information base of the research was official full-text and abstract databases, scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodological materials of ministries and departments. Analysis of publications on existing mathematical models used to solve a wide range of problems associated with the train dynamics study shows the expediency of their application. Findings. The results of these studies were used in: 1 design of new types of draft gears and air distributors; 2 development of methods for controlling the movement of conventional and connected trains; 3 creation of appropriate process flow diagrams; 4 development of energy-saving methods of train driving; 5 revision of the Construction Codes and Regulations (SNiP ΙΙ-39.76; 6 when selecting the parameters of the autonomous automatic control system, created in DNURT, for an auxiliary locomotive that is part of a connected train; 7 when creating computer simulators for the training of locomotive drivers; 8 assessment of the vehicle dynamic indices characterizing traffic safety. Scientists around the world conduct numerical experiments related to estimation of train dynamics using mathematical models that need to be constantly improved. Originality. The authors presented the main theoretical postulates that allowed them to develop the existing mathematical models for solving problems related to the train dynamics. The analysis of scientific articles published in Ukraine, CIS countries and abroad allows us to determine the most relevant areas of application of mathematical models. Practicalvalue. The practical value of the results obtained lies in the scientific validity

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 ...

Parental modelling of mathematical affect: self-efficacy and emotional arousal

Science.gov (United States)

Bartley, Sarah R.; Ingram, Naomi

2017-12-01

This study explored the relationship between parents' mathematics self-efficacy and emotional arousal to mathematics and their 12- and 13-year-old children's mathematics self-efficacy and emotional arousal to mathematics. Parental modelling of affective relationships during homework was a focus. Eighty-four parent and child pairings from seven schools in New Zealand were examined using embedded design methodology. No significant correlations were found when the parents' mathematics self-efficacy and emotional arousal to mathematics were compared with the children's mathematics self-efficacy and emotional arousal to mathematics. However, the parents' level of emotional arousal to mathematics was found to have affected their willingness to assist with mathematics homework. For those parents who assisted, a significant positive correlation was found between their mathematics self-efficacy and their children's emotional arousal to mathematics. Parents who did assist were generally reported as being calm, and used techniques associated with positive engagement. Fathers were calmer and more likely to express readiness to assist with mathematics homework than mothers. A further significant positive correlation was found between fathers' emotional arousal to mathematics and children's mathematics self-efficacy. Implications from the study suggest directions for future research.

Dynamics of mathematical models in biology bringing mathematics to life

CERN Document Server

Zazzu, Valeria; Guarracino, Mario

2016-01-01

This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...

Mathematical Model and Stability Analysis of Inverter-Based Distributed Generator

Directory of Open Access Journals (Sweden)

Alireza Khadem Abbasi

2013-01-01

Full Text Available This paper presents a mathematical (small-signal model of an electronically interfaced distributed generator (DG by considering the effect of voltage and frequency variations of the prime source. Dynamic equations are found by linearization about an operating point. In this study, the dynamic of DC part of the interface is included in the model. The stability analysis shows with proper selection of system parameters; the system is stable during steady-state and dynamic situations, and oscillatory modes are well damped. The proposed model is useful to study stability analysis of a standalone DG or a Microgrid.

Mathematical modelling of the combustion of a single wood particle

Energy Technology Data Exchange (ETDEWEB)

Porteiro, J.; Miguez, J.L.; Granada, E.; Moran, J.C. [Departamento de Ingenieria Mecanica, Maquinas y Motores Termicos y Fluidos. Universidad de Vigo, Lagoas Marcosende 9 36200 Vigo (Spain)

2006-01-15

A mathematical model describing the thermal degradation of densified biomass particles is presented here. The model uses a novel discretisation scheme and combines intra-particle combustion processes with extra-particle transport processes, thereby including thermal and diffusional control mechanisms. The influence of structural changes on the physical-thermal properties of wood in its different stages is studied together with shrinkage of the particle during its degradation. The model is used to compare the predicted data with data on the mass loss dynamics and internal temperature of several particles from previous works and relevant literature, with good agreement. (author)

Mathematical Modeling for Scrub Typhus and Its Implications for Disease Control.

Science.gov (United States)

Min, Kyung Duk; Cho, Sung Il

2018-03-19

The incidence rate of scrub typhus has been increasing in the Republic of Korea. Previous studies have suggested that this trend may have resulted from the effects of climate change on the transmission dynamics among vectors and hosts, but a clear explanation of the process is still lacking. In this study, we applied mathematical models to explore the potential factors that influence the epidemiology of tsutsugamushi disease. We developed mathematical models of ordinary differential equations including human, rodent and mite groups. Two models, including simple and complex models, were developed, and all parameters employed in the models were adopted from previous articles that represent epidemiological situations in the Republic of Korea. The simulation results showed that the force of infection at the equilibrium state under the simple model was 0.236 (per 100,000 person-months), and that in the complex model was 26.796 (per 100,000 person-months). Sensitivity analyses indicated that the most influential parameters were rodent and mite populations and contact rate between them for the simple model, and trans-ovarian transmission for the complex model. In both models, contact rate between humans and mites is more influential than morality rate of rodent and mite group. The results indicate that the effect of controlling either rodents or mites could be limited, and reducing the contact rate between humans and mites is more practical and effective strategy. However, the current level of control would be insufficient relative to the growing mite population. © 2018 The Korean Academy of Medical Sciences.

Mathematical human body modelling for impact loading

NARCIS (Netherlands)

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

Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling

Science.gov (United States)

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…

Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

Science.gov (United States)

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

Mathematical models of viscous friction

CERN Document Server

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...

Local Stability Analysis of an Infection-Age Mathematical Model for ...

African Journals Online (AJOL)

Timothy

1Department of Mathematics/Statistics/Computer Science, Federal University of Agriculture, Makurdi, ... ABSTRACT: An infection age structured mathematical model for tuberculosis disease ...... its applications to optimal vaccination strategies.

Mathematical Modeling of Protein Misfolding Mechanisms in Neurological Diseases: A Historical Overview.

Science.gov (United States)

Carbonell, Felix; Iturria-Medina, Yasser; Evans, Alan C

2018-01-01

Protein misfolding refers to a process where proteins become structurally abnormal and lose their specific 3-dimensional spatial configuration. The histopathological presence of misfolded protein (MP) aggregates has been associated as the primary evidence of multiple neurological diseases, including Prion diseases, Alzheimer's disease, Parkinson's disease, and Creutzfeldt-Jacob disease. However, the exact mechanisms of MP aggregation and propagation, as well as their impact in the long-term patient's clinical condition are still not well understood. With this aim, a variety of mathematical models has been proposed for a better insight into the kinetic rate laws that govern the microscopic processes of protein aggregation. Complementary, another class of large-scale models rely on modern molecular imaging techniques for describing the phenomenological effects of MP propagation over the whole brain. Unfortunately, those neuroimaging-based studies do not take full advantage of the tremendous capabilities offered by the chemical kinetics modeling approach. Actually, it has been barely acknowledged that the vast majority of large-scale models have foundations on previous mathematical approaches that describe the chemical kinetics of protein replication and propagation. The purpose of the current manuscript is to present a historical review about the development of mathematical models for describing both microscopic processes that occur during the MP aggregation and large-scale events that characterize the progression of neurodegenerative MP-mediated diseases.

Cooking Potatoes: Experimentation and Mathematical Modeling.

Science.gov (United States)

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)

A Mathematical Model, Implementation and Study of a Swarm System

OpenAIRE

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...

Students’ Mathematical Problem-Solving Abilities Through The Application of Learning Models Problem Based Learning

Science.gov (United States)

Nasution, M. L.; Yerizon, Y.; Gusmiyanti, R.

2018-04-01

One of the purpose mathematic learning is to develop problem solving abilities. Problem solving is obtained through experience in questioning non-routine. Improving students’ mathematical problem-solving abilities required an appropriate strategy in learning activities one of them is models problem based learning (PBL). Thus, the purpose of this research is to determine whether the problem solving abilities of mathematical students’ who learn to use PBL better than on the ability of students’ mathematical problem solving by applying conventional learning. This research included quasi experiment with static group design and population is students class XI MIA SMAN 1 Lubuk Alung. Class experiment in the class XI MIA 5 and class control in the class XI MIA 6. The instrument of final test students’ mathematical problem solving used essay form. The result of data final test in analyzed with t-test. The result is students’ mathematical problem solving abilities with PBL better then on the ability of students’ mathematical problem solving by applying conventional learning. It’s seen from the high percentage achieved by the group of students who learn to use PBL for each indicator of students’ mathematical problem solving.

Thermoregulation in premature infants: A mathematical model.

Science.gov (United States)

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 © 2016 Elsevier Ltd. All rights reserved.

Mathematical modeling of mutant transferrin-CRM107 molecular conjugates for cancer therapy.

Science.gov (United States)

Yoon, Dennis J; Chen, Kevin Y; Lopes, André M; Pan, April A; Shiloach, Joseph; Mason, Anne B; Kamei, Daniel T

2017-03-07

The transferrin (Tf) trafficking pathway is a promising mechanism for use in targeted cancer therapy due to the overexpression of transferrin receptors (TfRs) on cancerous cells. We have previously developed a mathematical model of the Tf/TfR trafficking pathway to improve the efficiency of Tf as a drug carrier. By using diphtheria toxin (DT) as a model toxin, we found that mutating the Tf protein to change its iron release rate improves cellular association and efficacy of the drug. Though this is an improvement upon using wild-type Tf as the targeting ligand, conjugated toxins like DT are unfortunately still highly cytotoxic at off-target sites. In this work, we address this hurdle in cancer research by developing a mathematical model to predict the efficacy and selectivity of Tf conjugates that use an alternative toxin. For this purpose, we have chosen to study a mutant of DT, cross-reacting material 107 (CRM107). First, we developed a mathematical model of the Tf-DT trafficking pathway by extending our Tf/TfR model to include intracellular trafficking via DT and DT receptors. Using this mathematical model, we subsequently investigated the efficacy of several conjugates in cancer cells: DT and CRM107 conjugated to wild-type Tf, as well as to our engineered mutant Tf proteins (K206E/R632A Tf and K206E/R534A Tf). We also investigated the selectivity of mutant Tf-CRM107 against non-neoplastic cells. Through the use of our mathematical model, we predicted that (i) mutant Tf-CRM107 exhibits a greater cytotoxicity than wild-type Tf-CRM107 against cancerous cells, (ii) this improvement was more drastic with CRM107 conjugates than with DT conjugates, and (iii) mutant Tf-CRM107 conjugates were selective against non-neoplastic cells. These predictions were validated with in vitro cytotoxicity experiments, demonstrating that mutant Tf-CRM107 conjugates is indeed a more suitable therapeutic agent. Validation from in vitro experiments also confirmed that such whole

Mathematics Instructional Model Based on Realistic Mathematics Education to Promote Problem Solving Ability at Junior High School Padang

OpenAIRE

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...

Uncertainty and Complexity in Mathematical Modeling

Science.gov (United States)

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…

Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

Science.gov (United States)

Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

2011-01-01

This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

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.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

Science.gov (United States)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization

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 modelling of simultaneous solvent evaporation and chemical curing in thermoset coatings: A parameter study

DEFF Research Database (Denmark)

Kiil, Søren

2011-01-01

A mathematical model, describing the curing behaviour of a two-component, solvent-based, thermoset coating, is used to conduct a parameter study. The model includes curing reactions, solvent intra-film diffusion and evaporation, film gelation, vitrification, and crosslinking. A case study with a ...

Mathematical model for cross-flow-induced vibrations of tube rows

International Nuclear Information System (INIS)

Chen, S.S.

1976-09-01

A mathematical model for flow-induced vibrations in heat exchanger tube banks is presented which includes the effects of vortex shedding, fluidelastic coupling, drag force, and fluid inertia coupling. Once the fluid forces are known, the model can predict the details of complex tube-fluid interactions: (1) natural frequencies and mode shapes of coupled vibrations; (2) critical flow velocities; (3) responses to vortex shedding, drag force, and other types of excitations; and (4) the dominant excitation mechanism at a given flow velocity. The analytical results are in good agreement with the published experimental results

Mathematical models of human paralyzed muscle after long-term training

OpenAIRE

Frey Law, L.A.; Shields, R.K.

2007-01-01

Spinal cord injury (SCI) results in major musculoskeletal adaptations, including muscle atrophy, faster contractile properties, increased fatigability, and bone loss. The use of functional electrical stimulation (FES) provides a method to prevent paralyzed muscle adaptations in order to sustain force-generating capacity. Mathematical muscle models may be able to predict optimal activation strategies during FES, however muscle properties further adapt with long-term training. The purpose of th...

Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification

Directory of Open Access Journals (Sweden)

Grzegorz Mikułowski

2016-01-01

Full Text Available Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA, which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.

Mathematical modelling for magnetite (crude removal from primary heat transfer loop by ion-exchange resins

Directory of Open Access Journals (Sweden)

Zeeshan Nawaz

2009-04-01

Full Text Available The present research focuses to develop mathematical model for the removal of iron (magnetite by ion-exchange resin from primary heat transfer loop of process industries. This mathematical model is based on operating capacities (that’s provide more effective design as compared to loading capacity from static laboratory tests. Results showed non-steady state distribution of external Fe2+ and limitations imposed on operating conditions, these conditions includes; loading and elution cycle time, flow rate, concentration of both loading and removal, volume of resin required. Number of generalized assumptions was made under shortcut modeling techniques to overcome the gap of theoretical and actual process design.

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,.

Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program

DEFF Research Database (Denmark)

Jurlewicz, Agnieszka; Nunes, Claudia; Russo, Giovanni

2018-01-01

Modeling Clinic for Industrial Mathematics (MODCLIM) is a Strategic Partnership for the Development of Training Workshops and Modeling Clinic for Industrial Mathematics, funded through the European Commission under the Erasmus Plus Program, Key Action 2: Cooperation for innovation and the exchang...

Solutions manual to accompany finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

Mathematical modeling of optical glazing performance

NARCIS (Netherlands)

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

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.

A mathematical model for supplying air-cooling for a building using a packed bed

Energy Technology Data Exchange (ETDEWEB)

Marewo, G.T. [Zimbabwe Univ., Mathematics Dept., Harare (Zimbabwe); Henwood, D.J. [School of Computing and Mathematical Sciences, Brighton (United Kingdom)

2006-01-15

The cooling system at the Harare International School uses a packed bed system for storing the coldness of the night-time to be used later for day-time air-conditioning. A two-phase mathematical model is described for the packed bed which includes heat dispersion in the fluid, and heat loss to the environment. This is in contrast to other studies, where at least one of these terms is neglected to simplify the mathematical model. A numerical method for obtaining a solution is proposed and implemented. Using measured inlet temperatures, the measured and predicted outlet temperatures of the bed show good trend agreement. The differences in detail are examined through sensitivity analyses for both the heat convection transfer and air velocity. It is apparent that adjusting these parameters can increase the agreement between the predicted and measured data. A parametric study for heat storage with various materials and bed sizes is given, which indicates how the code may be used as a tool for improving design and operational parameters. Practical application: A mathematical model of a packed bed is described; the bed is made up of fluid flowing over solid material with heat interchange between the two. The solid material is idealized as spheres and the fluid temperature is assumed uniform in a cross-section of the bed. The model includes heat interchange between the bed and its surrounding environment and allows for time varying fluid velocity. The input data is the inlet temperature to the bed, which may be measured. The comparison with measured data may be helpful to anyone attempting to develop and test a similar model. The sensitivity tests give an understanding of the significance of some of the parameters involved. The Appendix gives a mathematical statement of the problem and an outline of an approach to developing computer code for a numerical solution. (Author)

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 modelling and numerical simulation of forces in milling process

Science.gov (United States)

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.

Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.

Science.gov (United States)

Yates, James W T

2008-07-03

One feature of recent research in pharmacodynamic modelling has been the move towards more mechanistically based model structures. However, in all of these models there are common sub-systems, such as feedback loops and time-delays, whose properties and contribution to the model behaviour merit some mathematical analysis. In this paper a common pharmacodynamic model sub-structure is considered: the linear transit compartment. These models have a number of interesting properties as the length of the cascade chain is increased. In the limiting case a pure time-delay is achieved [Milsum, J.H., 1966. Biological Control Systems Analysis. McGraw-Hill Book Company, New York] and the initial behaviour becoming increasingly sensitive to parameter value perturbation. It is also shown that the modelled drug effect is attenuated, though the duration of action is longer. Through this analysis the range of behaviours that such models are capable of reproducing are characterised. The properties of these models and the experimental requirements are discussed in order to highlight how mathematical analysis prior to experimentation can enhance the utility of mathematical modelling.

Mathematical-statistical models and qualitative theories for economic and social sciences

CERN Document Server

Maturo, Fabrizio; Kacprzyk, Janusz

2017-01-01

This book presents a broad spectrum of problems related to statistics, mathematics, teaching, social science, and economics as well as a range of tools and techniques that can be used to solve these problems. It is the result of a scientific collaboration between experts in the field of economic and social systems from the University of Defence in Brno (Czech Republic), G. d’Annunzio University of Chieti-Pescara (Italy), Pablo de Olavid eUniversity of Sevilla (Spain), and Ovidius University in Constanţa, (Romania). The studies included were selected using a peer-review process and reflect heterogeneity and complexity of economic and social phenomena. They and present interesting empirical research from around the globe and from several research fields, such as statistics, decision making, mathematics, complexity, psychology, sociology and economics. The volume is divided into two parts. The first part, “Recent trends in mathematical and statistical models for economic and social sciences”, collects pap...

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.

An integrated mathematical model for chemical oxygen demand (COD) removal in moving bed biofilm reactors (MBBR) including predation and hydrolysis.

Science.gov (United States)

Revilla, Marta; Galán, Berta; Viguri, Javier R

2016-07-01

An integrated mathematical model is proposed for modelling a moving bed biofilm reactor (MBBR) for removal of chemical oxygen demand (COD) under aerobic conditions. The composite model combines the following: (i) a one-dimensional biofilm model, (ii) a bulk liquid model, and (iii) biological processes in the bulk liquid and biofilm considering the interactions among autotrophic, heterotrophic and predator microorganisms. Depending on the values for the soluble biodegradable COD loading rate (SCLR), the model takes into account a) the hydrolysis of slowly biodegradable compounds in the bulk liquid, and b) the growth of predator microorganisms in the bulk liquid and in the biofilm. The integration of the model and the SCLR allows a general description of the behaviour of COD removal by the MBBR under various conditions. The model is applied for two in-series MBBR wastewater plant from an integrated cellulose and viscose production and accurately describes the experimental concentrations of COD, total suspended solids (TSS), nitrogen and phosphorous obtained during 14 months working at different SCLRs and nutrient dosages. The representation of the microorganism group distribution in the biofilm and in the bulk liquid allow for verification of the presence of predator microorganisms in the second reactor under some operational conditions. Copyright © 2016 Elsevier Ltd. All rights reserved.

Identification of Chemical Reactor Plant’s Mathematical Model

OpenAIRE

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.

Rationale and Resources for Teaching the Mathematical Modeling of Athletic Training and Performance

Science.gov (United States)

Clarke, David C.; Skiba, Philip F.

2013-01-01

A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of…

Mathematical Sciences Institute Workshop

CERN Document Server

Scott, Philip

1990-01-01

A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions ...

A mathematical model of forgetting and amnesia

NARCIS (Netherlands)

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

Optimization and mathematical modeling in computer architecture

CERN Document Server

Sankaralingam, Karu; Nowatzki, Tony

2013-01-01

In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t

Mathematical models of soft tissue injury repair : towards understanding musculoskeletal disorders

OpenAIRE

Dunster, Joanne L.

2012-01-01

The process of soft tissue injury repair at the cellular lew I can be decomposed into three phases: acute inflammation including coagulation, proliferation and remodelling. While the later phases are well understood the early phase is less so. We produce a series of new mathematical models for the early phases coagulation and inflammation. The models produced are relevant not only to soft tissue injury repair but also to the many disease states in which coagulation and inflammation play a rol...

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.

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...

Well test mathematical model for fractures network in tight oil reservoirs

Science.gov (United States)

Diwu, Pengxiang; Liu, Tongjing; Jiang, Baoyi; Wang, Rui; Yang, Peidie; Yang, Jiping; Wang, Zhaoming

2018-02-01

Well test, especially build-up test, has been applied widely in the development of tight oil reservoirs, since it is the only available low cost way to directly quantify flow ability and formation heterogeneity parameters. However, because of the fractures network near wellbore, generated from artificial fracturing linking up natural factures, traditional infinite and finite conductivity fracture models usually result in significantly deviation in field application. In this work, considering the random distribution of natural fractures, physical model of fractures network is proposed, and it shows a composite model feature in the large scale. Consequently, a nonhomogeneous composite mathematical model is established with threshold pressure gradient. To solve this model semi-analytically, we proposed a solution approach including Laplace transform and virtual argument Bessel function, and this method is verified by comparing with existing analytical solution. The matching data of typical type curves generated from semi-analytical solution indicates that the proposed physical and mathematical model can describe the type curves characteristic in typical tight oil reservoirs, which have up warping in late-term rather than parallel lines with slope 1/2 or 1/4. It means the composite model could be used into pressure interpretation of artificial fracturing wells in tight oil reservoir.

Mathematical epidemiology

CERN Document Server

Driessche, Pauline; Wu, Jianhong

2008-01-01

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downlo...

A novel mathematical model for controllable near-field electrospinning

Science.gov (United States)

Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun

2014-01-01

Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.

A novel mathematical model for controllable near-field electrospinning

International Nuclear Information System (INIS)

Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun

2014-01-01

Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers

A novel mathematical model for controllable near-field electrospinning