Science.gov

Sample records for abstract mathematical models

  1. Abstraction in mathematics.

    PubMed Central

    Ferrari, Pier Luigi

    2003-01-01

    Some current interpretations of abstraction in mathematical settings are examined from different perspectives, including history and learning. It is argued that abstraction is a complex concept and that it cannot be reduced to generalization or decontextualization only. In particular, the links between abstraction processes and the emergence of new objects are shown. The role that representations have in abstraction is discussed, taking into account both the historical and the educational perspectives. As languages play a major role in mathematics, some ideas from functional linguistics are applied to explain to what extent mathematical notations are to be considered abstract. Finally, abstraction is examined from the perspective of mathematics education, to show that the teaching ideas resulting from one-dimensional interpretations of abstraction have proved utterly unsuccessful. PMID:12903658

  2. Designing for Mathematical Abstraction

    ERIC Educational Resources Information Center

    Pratt, Dave; Noss, Richard

    2010-01-01

    Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…

  3. Dissertation Abstracts in Mathematics Education, 1983.

    ERIC Educational Resources Information Center

    Suydam, Marilyn N., Comp.

    The dissertation abstracts in this compilation all appeared in "Dissertation Abstracts International" in 1983. The 300 dissertations cited in the annual listing of research in the July 1984 issue of the "Journal for Research in Mathematics Education" are included, as well as 55 dissertations which were located but could not be…

  4. A Dialectical Approach to the Formation of Mathematical Abstractions

    ERIC Educational Resources Information Center

    Ozmantar, Mehmet Fatih; Monaghan, John

    2007-01-01

    This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

  5. Abstraction Augmented Markov Models.

    PubMed

    Caragea, Cornelia; Silvescu, Adrian; Caragea, Doina; Honavar, Vasant

    2010-12-13

    High accuracy sequence classification often requires the use of higher order Markov models (MMs). However, the number of MM parameters increases exponentially with the range of direct dependencies between sequence elements, thereby increasing the risk of overfitting when the data set is limited in size. We present abstraction augmented Markov models (AAMMs) that effectively reduce the number of numeric parameters of k(th) order MMs by successively grouping strings of length k (i.e., k-grams) into abstraction hierarchies. We evaluate AAMMs on three protein subcellular localization prediction tasks. The results of our experiments show that abstraction makes it possible to construct predictive models that use significantly smaller number of features (by one to three orders of magnitude) as compared to MMs. AAMMs are competitive with and, in some cases, significantly outperform MMs. Moreover, the results show that AAMMs often perform significantly better than variable order Markov models, such as decomposed context tree weighting, prediction by partial match, and probabilistic suffix trees.

  6. Mathematical Modeling and Pure Mathematics

    ERIC Educational Resources Information Center

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  7. Abstraction and Concreteness in the Everyday Mathematics of Structural Engineers.

    ERIC Educational Resources Information Center

    Gainsburg, Julie

    The everyday mathematics processes of structural engineers were studied and analyzed in terms of abstraction. A main purpose of the study was to explore the degree to which the notion of a gap between school and everyday mathematics holds when the scope of practices considered "everyday" is extended. J. Lave (1988) promoted a methodology…

  8. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  9. Multimodeling and Model Abstraction

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The multiplicity of models of the same process or phenomenon is the commonplace in environmental modeling. Last 10 years brought marked interest to making use of the variety of conceptual approaches instead of attempting to find the best model or using a single preferred model. Two systematic approa...

  10. Development of abstract mathematical reasoning: the case of algebra.

    PubMed

    Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

    2014-01-01

    Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.

  11. Development of abstract mathematical reasoning: the case of algebra

    PubMed Central

    Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

    2014-01-01

    Algebra typically represents the students’ first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students’ ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16–17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15–16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students’ transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition. PMID:25228874

  12. Mathematical Modelling Approach in Mathematics Education

    ERIC Educational Resources Information Center

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  13. Teaching Mathematical Modeling in Mathematics Education

    ERIC Educational Resources Information Center

    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…

  14. Mathematical Abstraction in the Solving of Ill-Structured Problems by Elementary School Students in Korea

    ERIC Educational Resources Information Center

    Hong, Jee Yun; Kim, Min Kyeong

    2016-01-01

    Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…

  15. Abstract models of molecular walkers

    NASA Astrophysics Data System (ADS)

    Semenov, Oleg

    Recent advances in single-molecule chemistry have led to designs for artificial multi-pedal walkers that follow tracks of chemicals. The walkers, called molecular spiders, consist of a rigid chemically inert body and several flexible enzymatic legs. The legs can reversibly bind to chemical substrates on a surface, and through their enzymatic action convert them to products. We study abstract models of molecular spiders to evaluate how efficiently they can perform two tasks: molecular transport of cargo over tracks and search for targets on finite surfaces. For the single-spider model our simulations show a transient behavior wherein certain spiders move superdiffusively over significant distances and times. This gives the spiders potential as a faster-than-diffusion transport mechanism. However, analysis shows that single-spider motion eventually decays into an ordinary diffusive motion, owing to the ever increasing size of the region of products. Inspired by cooperative behavior of natural molecular walkers, we propose a symmetric exclusion process (SEP) model for multiple walkers interacting as they move over a one-dimensional lattice. We show that when walkers are sequentially released from the origin, the collective effect is to prevent the leading walkers from moving too far backwards. Hence, there is an effective outward pressure on the leading walkers that keeps them moving superdiffusively for longer times. Despite this improvement the leading spider eventually slows down and moves diffusively, similarly to a single spider. The slowdown happens because all spiders behind the leading spiders never encounter substrates, and thus they are never biased. They cannot keep up with leading spiders, and cannot put enough pressure on them. Next, we investigate search properties of a single and multiple spiders moving over one- and two-dimensional surfaces with various absorbing and reflecting boundaries. For the single-spider model we evaluate by how much the

  16. An Investigation of System Identification Techniques for Simulation Model Abstraction

    DTIC Science & Technology

    2000-02-01

    This report summarizes research into the application of system identification techniques to simulation model abstraction. System identification produces...34Mission Simulation," a simulation of a squadron of aircraft performing battlefield air interdiction. The system identification techniques were...simplified mathematical models that approximate the dynamic behaviors of the underlying stochastic simulations. Four state-space system

  17. Sound Blending of Techniques in Mathematics and Physics (abstract)

    NASA Astrophysics Data System (ADS)

    Malmini, Ranasinghe

    2009-04-01

    This paper discusses methods that can be used to inspire physics students to learn advanced differential equations. Numerous problems in physics are described by this type of equation. There has been rapid advancement in computer technology and development of computational mathematics-a branch of mathematics using computers to generate solutions to advanced differential equations. Arguably, this branch of mathematics is becoming more important to physicists than traditional analytical mathematics. Computer Algebra Software (CAS) packages have also emerged as a means to perform elaborate and complicated analytical mathematics much faster than possible by humans.

  18. Teaching Mathematical Modelling.

    ERIC Educational Resources Information Center

    Jones, Mark S.

    1997-01-01

    Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…

  19. Mathematical modeling in neuroendocrinology.

    PubMed

    Bertram, Richard

    2015-04-01

    Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.

  20. The Concrete-Representational-Abstract Sequence of Instruction in Mathematics Classrooms

    ERIC Educational Resources Information Center

    Mudaly, Vimolan; Naidoo, Jayaluxmi

    2015-01-01

    The purpose of this paper is to explore how master mathematics teachers use the concrete-representational-abstract (CRA) sequence of instruction in mathematics classrooms. Data was collected from a convenience sample of six master teachers by observations, video recordings of their teaching, and semi-structured interviews. Data collection also…

  1. Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course

    ERIC Educational Resources Information Center

    Cook, John Paul

    2015-01-01

    This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

  2. Mathematical Modeling: A Structured Process

    ERIC Educational Resources Information Center

    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…

  3. An Approach to the Design of Mathematical Task Sequences: Conceptual Learning as Abstraction

    ERIC Educational Resources Information Center

    Simon, Martin A.

    2016-01-01

    This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…

  4. [Mathematical models of hysteresis

    SciTech Connect

    Mayergoyz, I.D.

    1991-01-01

    The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our 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 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. Our 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. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.

  5. Developing mathematics understanding and abstraction: The case of equivalence in the elementary years

    NASA Astrophysics Data System (ADS)

    Warren, Elizabeth; Cooper, Tom J.

    2009-07-01

    Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data was gathered from multiple sources including interviews, videos of classroom teaching, and pre- and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

  6. Authenticity of Mathematical Modeling

    ERIC Educational Resources Information Center

    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…

  7. Richardson, mathematical modeller

    NASA Astrophysics Data System (ADS)

    Vreugdenhil, C. B.

    1994-03-01

    On the occasion of the 70th anniversary of Richardson's book Weather Prediction by Numerical Process (Cambridge University Press, Cambridge), a review is given of Richardson's scientific work. He made lasting contributions to very diverse fields of interest, such as finite-difference methods and related numerical methods, weather forecasting by computer, turbulence, international relations, and fractals. Although he was an original experimenter, the main present-day interest is in his mathematical modelling work.

  8. Abstracts

    ERIC Educational Resources Information Center

    American Biology Teacher, 1977

    1977-01-01

    Included are over 50 abstracts of papers being presented at the 1977 National Association of Biology Teachers Convention. Included in each abstract are the title, author, and summary of the paper. Topics include photographic techniques environmental studies, and biological instruction. (MA)

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

    ERIC Educational Resources Information Center

    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…

  10. Mathematical Modelling in European Education

    ERIC Educational Resources Information Center

    Ferri, Rita Borromeo

    2013-01-01

    Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…

  11. A Primer for Mathematical Modeling

    ERIC Educational Resources Information Center

    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…

  12. Mathematical Modeling: Convoying Merchant Ships

    ERIC Educational Resources Information Center

    Mathews, Susann M.

    2004-01-01

    This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

  13. Directory of Energy Information Administration Model Abstracts

    SciTech Connect

    Not Available

    1986-07-16

    This directory partially fulfills the requirements of Section 8c, of the documentation order, which states in part that: The Office of Statistical Standards will annually publish an EIA document based on the collected abstracts and the appendices. This report contains brief statements about each model's title, acronym, purpose, and status, followed by more detailed information on characteristics, uses, and requirements. Sources for additional information are identified. All models active through March 1985 are included. The main body of this directory is an alphabetical list of all active EIA models. Appendix A identifies major EIA modeling systems and the models within these systems, and Appendix B identifies active EIA models by type (basic, auxiliary, and developing). EIA also leases models developed by proprietary software vendors. Documentation for these proprietary models is the responsibility of the companies from which they are leased. EIA has recently leased models from Chase Econometrics, Inc., Data Resources, Inc. (DRI), the Oak Ridge National Laboratory (ORNL), and Wharton Econometric Forecasting Associates (WEFA). Leased models are not abstracted here. The directory is intended for the use of energy and energy-policy analysts in the public and private sectors.

  14. Mathematical models of vaccination.

    PubMed

    Scherer, Almut; McLean, Angela

    2002-01-01

    Mathematical models of epidemics have a long history of contributing to the understanding of the impact of vaccination programmes. Simple, one-line models can predict target vaccination coverage that will eradicate an infectious agent, whilst other questions require complex simulations of stochastic processes in space and time. This review introduces some simple ordinary differential equation models of mass vaccination that can be used to address important questions about the predicted impact of vaccination programmes. We show how to calculate the threshold vaccination coverage rate that will eradicate an infection, explore the impact of vaccine-induced immunity that wanes through time, and study the competitive interactions between vaccine susceptible and vaccine resistant strains of infectious agent.

  15. Model Checking Abstract PLEXIL Programs with SMART

    NASA Technical Reports Server (NTRS)

    Siminiceanu, Radu I.

    2007-01-01

    We describe a method to automatically generate discrete-state models of abstract Plan Execution Interchange Language (PLEXIL) programs that can be analyzed using model checking tools. Starting from a high-level description of a PLEXIL program or a family of programs with common characteristics, the generator lays the framework that models the principles of program execution. The concrete parts of the program are not automatically generated, but require the modeler to introduce them by hand. As a case study, we generate models to verify properties of the PLEXIL macro constructs that are introduced as shorthand notation. After an exhaustive analysis, we conclude that the macro definitions obey the intended semantics and behave as expected, but contingently on a few specific requirements on the timing semantics of micro-steps in the concrete executive implementation.

  16. Team Teaching and Cooperative Groups in Abstract Algebra: Nurturing a New Generation of Confident Mathematics Teachers

    ERIC Educational Resources Information Center

    Grassl, R.; Mingus, T. T. Y.

    2007-01-01

    Experiences in designing and teaching a reformed abstract algebra course are described. This effort was partially a result of a five year statewide National Science Foundation (NSF) grant entitled the Rocky Mountain Teacher Enhancement Collaborative. The major thrust of this grant was to implement reform in core mathematics courses that would…

  17. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    ERIC Educational Resources Information Center

    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…

  18. Teaching and Assessing Mathematical Modelling.

    ERIC Educational Resources Information Center

    Lingefjard, T.

    2002-01-01

    Reports on the observed actions of prospective Swedish secondary mathematics teachers as they were working in a modeling situation. Discusses the way the students tackled the modeling situation and their strategies and attitudes as well as the difficulties in assessing mathematical modeling performance. (KHR)

  19. Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research

    NASA Technical Reports Server (NTRS)

    Shitzer, A.

    1972-01-01

    An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.

  20. Explorations in Elementary Mathematical Modeling

    ERIC Educational Resources Information Center

    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…

  1. Visual Modeling as a Motivation for Studying Mathematics and Art

    ERIC Educational Resources Information Center

    Sendova, Evgenia; Grkovska, Slavica

    2005-01-01

    The paper deals with the possibility of enriching the curriculum in mathematics, informatics and art by means of visual modeling of abstract paintings. The authors share their belief that in building a computer model of a construct, one gains deeper insight into the construct, and is motivated to elaborate one's knowledge in mathematics and…

  2. Mathematical modelling in developmental biology.

    PubMed

    Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

    2013-06-01

    In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

  3. Abstracts

    NASA Astrophysics Data System (ADS)

    2012-09-01

    Measuring cosmological parameters with GRBs: status and perspectives New interpretation of the Amati relation The SED Machine - a dedicated transient spectrograph PTF10iue - evidence for an internal engine in a unique Type Ic SN Direct evidence for the collapsar model of long gamma-ray bursts On pair instability supernovae and gamma-ray bursts Pan-STARRS1 observations of ultraluminous SNe The influence of rotation on the critical neutrino luminosity in core-collapse supernovae General relativistic magnetospheres of slowly rotating and oscillating neutron stars Host galaxies of short GRBs GRB 100418A: a bridge between GRB-associated hypernovae and SNe Two super-luminous SNe at z ~ 1.5 from the SNLS Prospects for very-high-energy gamma-ray bursts with the Cherenkov Telescope Array The dynamics and radiation of relativistic flows from massive stars The search for light echoes from the supernova explosion of 1181 AD The proto-magnetar model for gamma-ray bursts Stellar black holes at the dawn of the universe MAXI J0158-744: the discovery of a supersoft X-ray transient Wide-band spectra of magnetar burst emission Dust formation and evolution in envelope-stripped core-collapse supernovae The host galaxies of dark gamma-ray bursts Keck observations of 150 GRB host galaxies Search for properties of GRBs at large redshift The early emission from SNe Spectral properties of SN shock breakout MAXI observation of GRBs and short X-ray transients A three-dimensional view of SN 1987A using light echo spectroscopy X-ray study of the southern extension of the SNR Puppis A All-sky survey of short X-ray transients by MAXI GSC Development of the CALET gamma-ray burst monitor (CGBM)

  4. Mathematical Modeling of Diverse Phenomena

    NASA Technical Reports Server (NTRS)

    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.

  5. Hierarchical abstract semantic model for image classification

    NASA Astrophysics Data System (ADS)

    Ye, Zhipeng; Liu, Peng; Zhao, Wei; Tang, Xianglong

    2015-09-01

    Semantic gap limits the performance of bag-of-visual-words. To deal with this problem, a hierarchical abstract semantics method that builds abstract semantic layers, generates semantic visual vocabularies, measures semantic gap, and constructs classifiers using the Adaboost strategy is proposed. First, abstract semantic layers are proposed to narrow the semantic gap between visual features and their interpretation. Then semantic visual words are extracted as features to train semantic classifiers. One popular form of measurement is used to quantify the semantic gap. The Adaboost training strategy is used to combine weak classifiers into strong ones to further improve performance. For a testing image, the category is estimated layer-by-layer. Corresponding abstract hierarchical structures for popular datasets, including Caltech-101 and MSRC, are proposed for evaluation. The experimental results show that the proposed method is capable of narrowing semantic gaps effectively and performs better than other categorization methods.

  6. Mathematical Models for Doppler Measurements

    NASA Technical Reports Server (NTRS)

    Lear, William M.

    1987-01-01

    Error analysis increases precision of navigation. Report presents improved mathematical models of analysis of Doppler measurements and measurement errors of spacecraft navigation. To take advantage of potential navigational accuracy of Doppler measurements, precise equations relate measured cycle count to position and velocity. Drifts and random variations in transmitter and receiver oscillator frequencies taken into account. Mathematical models also adapted to aircraft navigation, radar, sonar, lidar, and interferometry.

  7. Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

    ERIC Educational Resources Information Center

    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…

  8. Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

    ERIC Educational Resources Information Center

    Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

    2016-01-01

    Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

  9. Abstract Model of the SATS Concept of Operations: Initial Results and Recommendations

    NASA Technical Reports Server (NTRS)

    Dowek, Gilles; Munoz, Cesar; Carreno, Victor A.

    2004-01-01

    An abstract mathematical model of the concept of operations for the Small Aircraft Transportation System (SATS) is presented. The Concept of Operations consist of several procedures that describe nominal operations for SATS, Several safety properties of the system are proven using formal techniques. The final goal of the verification effort is to show that under nominal operations, aircraft are safely separated. The abstract model was written and formally verified in the Prototype Verification System (PVS).

  10. Computer Simulations and the Transition from Concrete Manipulation of Objects to Abstract Thinking in Elementary School Mathematics.

    ERIC Educational Resources Information Center

    Berlin, Donna; White, Arthur

    1986-01-01

    This study investigated the effects of combining interactive microcomputer simulations and concrete activities on the development of abstract thinking in elementary school mathematics. Students in grades 2-4 were assessed on tasks involving designs and patterns. (MNS)

  11. Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

    ERIC Educational Resources Information Center

    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…

  12. Mathematical Models of Gene Regulation

    NASA Astrophysics Data System (ADS)

    Mackey, Michael C.

    2004-03-01

    This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.

  13. The Mental Representation of Integers: An Abstract-to-Concrete Shift in the Understanding of Mathematical Concepts

    ERIC Educational Resources Information Center

    Varma, Sashank; Schwartz, Daniel L.

    2011-01-01

    Mathematics has a level of structure that transcends untutored intuition. What is the cognitive representation of abstract mathematical concepts that makes them meaningful? We consider this question in the context of the integers, which extend the natural numbers with zero and negative numbers. Participants made greater and lesser judgments of…

  14. A Preliminary Attempt at Teaching Abstract Mathematics to Freshmen with an A.C.T. Score of Less Than 15.

    ERIC Educational Resources Information Center

    Schremmer, A. G.

    This experiment attempted to teach abstract mathematics fo college freshmen with A.C.T. scores less than 15 in a three semester terminal course sequence. The course content included a formal mathematical language, set theory, Boolean Algebra, relations and functions, operations, cardinals and ordinals, the rational numbers, and college algebra.…

  15. Using Covariation Reasoning to Support Mathematical Modeling

    ERIC Educational Resources Information Center

    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…

  16. ASTP ranging system mathematical model

    NASA Technical Reports Server (NTRS)

    Ellis, M. R.; Robinson, L. H.

    1973-01-01

    A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.

  17. Mathematical Modeling: A Bridge to STEM Education

    ERIC Educational Resources Information Center

    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…

  18. The 24-Hour Mathematical Modeling Challenge

    ERIC Educational Resources Information Center

    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…

  19. Abstract or Concrete Examples in Learning Mathematics? A Replication and Elaboration of Kaminski, Sloutsky, and Heckler's Study

    ERIC Educational Resources Information Center

    De Bock, Dirk; Deprez, Johan; Van Dooren, Wim; Roelens, Michel; Verschaffel, Lieven

    2011-01-01

    Kaminski, Sloutsky, and Heckler (2008a) published in "Science" a study on "The advantage of abstract examples in learning math," in which they claim that students may benefit more from learning mathematics through a single abstract, symbolic representation than from multiple concrete examples. This publication elicited both enthusiastic and…

  20. Mathematical circulatory system model

    NASA Technical Reports Server (NTRS)

    Lakin, William D. (Inventor); Stevens, Scott A. (Inventor)

    2010-01-01

    A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.

  1. Abstract models for the synthesis of optimization algorithms.

    NASA Technical Reports Server (NTRS)

    Meyer, G. G. L.; Polak, E.

    1971-01-01

    Systematic approach to the problem of synthesis of optimization algorithms. Abstract models for algorithms are developed which guide the inventive process toward ?conceptual' algorithms which may consist of operations that are inadmissible in a practical method. Once the abstract models are established a set of methods for converting ?conceptual' algorithms falling into the class defined by the abstract models into ?implementable' iterative procedures is presented.

  2. Mathematical Modeling in the Undergraduate Curriculum

    ERIC Educational Resources Information Center

    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…

  3. Teachers' Conceptions of Mathematical Modeling

    ERIC Educational Resources Information Center

    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…

  4. Mathematical Modelling with Young Children

    ERIC Educational Resources Information Center

    English, Lyn D.; Watters, James J.

    2004-01-01

    This paper addresses the first year of a three-year, longitudinal study which introduces mathematical modeling to young children and provides professional development for their teachers. Four classes of third-graders (8 years of age) and their teachers participated in the first year of the program, which involved several preliminary modeling…

  5. Mathematical modeling of biological ensembles

    SciTech Connect

    Harlow, F.H.; Sandoval, D.L.; Ruppel, H.M.

    1986-07-01

    Mathematical models are proposed for three distinctly different aspects of biophysical dynamics: mental dynamics, mob dynamics, and the evolution of species. Each section is self-contained, but the approaches are unified by the employment of stochastic equations for the interactive dynamics of numerous discrete entities.

  6. Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

    ERIC Educational Resources Information Center

    Yilmaz, Suha; Tekin-Dede, Ayse

    2016-01-01

    Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

  7. Fourth SIAM conference on mathematical and computational issues in the geosciences: Final program and abstracts

    SciTech Connect

    1997-12-31

    The conference focused on computational and modeling issues in the geosciences. Of the geosciences, problems associated with phenomena occurring in the earth`s subsurface were best represented. Topics in this area included petroleum recovery, ground water contamination and remediation, seismic imaging, parameter estimation, upscaling, geostatistical heterogeneity, reservoir and aquifer characterization, optimal well placement and pumping strategies, and geochemistry. Additional sessions were devoted to the atmosphere, surface water and oceans. The central mathematical themes included computational algorithms and numerical analysis, parallel computing, mathematical analysis of partial differential equations, statistical and stochastic methods, optimization, inversion, homogenization and renormalization. The problem areas discussed at this conference are of considerable national importance, with the increasing importance of environmental issues, global change, remediation of waste sites, declining domestic energy sources and an increasing reliance on producing the most out of established oil reservoirs.

  8. Metagenomic Classification Using an Abstraction Augmented Markov Model

    PubMed Central

    Zhu, Xiujun (Sylvia)

    2016-01-01

    Abstract The abstraction augmented Markov model (AAMM) is an extension of a Markov model that can be used for the analysis of genetic sequences. It is developed using the frequencies of all possible consecutive words with same length (p-mers). This article will review the theory behind AAMM and apply the theory behind AAMM in metagenomic classification. PMID:26618474

  9. Strategies to Support Students' Mathematical Modeling

    ERIC Educational Resources Information Center

    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…

  10. Mathematical Modeling in the High School Curriculum

    ERIC Educational Resources Information Center

    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…

  11. Modelling abstraction licensing strategies ahead of the UK's water abstraction licensing reform

    NASA Astrophysics Data System (ADS)

    Klaar, M. J.

    2012-12-01

    Within England and Wales, river water abstractions are licensed and regulated by the Environment Agency (EA), who uses compliance with the Environmental Flow Indicator (EFI) to ascertain where abstraction may cause undesirable effects on river habitats and species. The EFI is a percentage deviation from natural flow represented using a flow duration curve. The allowable percentage deviation changes with different flows, and also changes depending on an assessment of the sensitivity of the river to changes in flow (Table 1). Within UK abstraction licensing, resource availability is expressed as a surplus or deficit of water resources in relation to the EFI, and utilises the concept of 'hands-off-flows' (HOFs) at the specified flow statistics detailed in Table 1. Use of a HOF system enables abstraction to cease at set flows, but also enables abstraction to occur at periods of time when more water is available. Compliance at low flows (Q95) is used by the EA to determine the hydrological classification and compliance with the Water Framework Directive (WFD) for identifying waterbodies where flow may be causing or contributing to a failure in good ecological status (GES; Table 2). This compliance assessment shows where the scenario flows are below the EFI and by how much, to help target measures for further investigation and assessment. Currently, the EA is reviewing the EFI methodology in order to assess whether or not it can be used within the reformed water abstraction licensing system which is being planned by the Department for Environment, Food and Rural Affairs (DEFRA) to ensure the licensing system is resilient to the challenges of climate change and population growth, while allowing abstractors to meet their water needs efficiently, and better protect the environment. In order to assess the robustness of the EFI, a simple model has been created which allows a number of abstraction, flow and licensing scenarios to be run to determine WFD compliance using the

  12. Problem Posing and Solving with Mathematical Modeling

    ERIC Educational Resources Information Center

    English, Lyn D.; Fox, Jillian L.; Watters, James J.

    2005-01-01

    Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

  13. Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

    ERIC Educational Resources Information Center

    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…

  14. Mathematical models of diabetes progression.

    PubMed

    De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels

    2008-12-01

    Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.

  15. Mathematical modeling of drug delivery.

    PubMed

    Siepmann, J; Siepmann, F

    2008-12-08

    Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design

  16. Summer Camp of Mathematical Modeling in China

    ERIC Educational Resources Information Center

    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…

  17. Mathematical Modelling of Folate Metabolism

    PubMed Central

    Panetta, John C.; Paugh, Steven W.

    2013-01-01

    Folate metabolism is a complex biological process that is influenced by many variables including transporters, co-factors and enzymes. Mathematical models provide a useful tool to evaluate this complex system and to elucidate hypotheses that would be otherwise untenable to test in vitro or in vivo. Forty years of model development and refinement along with enhancements in technology have led to systematic improvement in our biological understanding from these models. However, increased complexity does not always lead to increased understanding, and a balanced approach to modelling the system is often advantageous. This approach should address questions about sensitivity of the model to variation and incorporate genomic data. The folate model is a useful platform for investigating the effects of antifolates on the folate pathway. The utility of the model is demonstrated through interrogation of drug resistance, drug-drug interactions, drug selectivity, and drug doses and schedules. Mathematics can be used to create models with the ability to design and improve rationale therapeutic interventions. PMID:23703958

  18. ADMET: ADipocyte METabolism mathematical model.

    PubMed

    Micheloni, Alessio; Orsi, Gianni; De Maria, Carmelo; Vozzi, Giovanni

    2015-01-01

    White fat cells have an important physiological role in maintaining triglyceride and free fatty acid levels due to their fundamental storage property, as well as determining insulin resistance. ADipocyte METabolism is a mathematical model that mimics the main metabolic pathways of human white fat cell, connecting inputs (composition of culture medium) to outputs (glycerol and free fatty acid release). It is based on a set of nonlinear differential equations, implemented in Simulink® and controlled by cellular energetic state. The validation of this model is based on a comparison between the simulation results and a set of experimental data collected from the literature.

  19. Mathematical Modeling of Kidney Transport

    PubMed Central

    Layton, Anita T.

    2013-01-01

    In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease. PMID:23852667

  20. Abstraction and Consolidation

    ERIC Educational Resources Information Center

    Monaghan, John; Ozmantar, Mehmet Fatih

    2004-01-01

    What is involved in consolidating a new mathematical abstraction? This paper examines the work of one student who was working on a task designed to consolidate two recently constructed absolute function abstractions. The study adopts an activity theoretic model of abstraction in context. Selected protocol data are presented. The initial state of…

  1. Mathematical Model for Mapping Students' Cognitive Capability

    ERIC Educational Resources Information Center

    Tambunan, Hardi

    2016-01-01

    The quality mapping of educational unit program is important issue in education in Indonesia today in an effort to improve the quality of education. The objective of this study is to make a mathematical model to find out the map of students' capability in mathematics. It has been made a mathematical model to be used in the mapping of students'…

  2. Mathematical models of bipolar disorder

    NASA Astrophysics Data System (ADS)

    Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

    2009-07-01

    We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

  3. Mathematical models in medicine: Diseases and epidemics

    SciTech Connect

    Witten, M.

    1987-01-01

    This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling.

  4. Evidence-Based Practices: Applications of Concrete Representational Abstract Framework across Math Concepts for Students with Mathematics Disabilities

    ERIC Educational Resources Information Center

    Agrawal, Jugnu; Morin, Lisa L.

    2016-01-01

    Students with mathematics disabilities (MD) experience difficulties with both conceptual and procedural knowledge of different math concepts across grade levels. Research shows that concrete representational abstract framework of instruction helps to bridge this gap for students with MD. In this article, we provide an overview of this strategy…

  5. Mathematical Models Of Turbulence In Hypersonic Flow

    NASA Technical Reports Server (NTRS)

    Marvin, J. G.; Coakley, T. J.

    1991-01-01

    Report discusses mathematical models of turbulence used in numerical simulations of complicated viscous, hypersonic flows. Includes survey of essential features of models and their statuses in applications.

  6. Coupling Radar Rainfall to Hydrological Models for Water Abstraction Management

    NASA Astrophysics Data System (ADS)

    Asfaw, Alemayehu; Shucksmith, James; Smith, Andrea; MacDonald, Ken

    2015-04-01

    The impacts of climate change and growing water use are likely to put considerable pressure on water resources and the environment. In the UK, a reform to surface water abstraction policy has recently been proposed which aims to increase the efficiency of using available water resources whilst minimising impacts on the aquatic environment. Key aspects to this reform include the consideration of dynamic rather than static abstraction licensing as well as introducing water trading concepts. Dynamic licensing will permit varying levels of abstraction dependent on environmental conditions (i.e. river flow and quality). The practical implementation of an effective dynamic abstraction strategy requires suitable flow forecasting techniques to inform abstraction asset management. Potentially the predicted availability of water resources within a catchment can be coupled to predicted demand and current storage to inform a cost effective water resource management strategy which minimises environmental impacts. The aim of this work is to use a historical analysis of UK case study catchment to compare potential water resource availability using modelled dynamic abstraction scenario informed by a flow forecasting model, against observed abstraction under a conventional abstraction regime. The work also demonstrates the impacts of modelling uncertainties on the accuracy of predicted water availability over range of forecast lead times. The study utilised a conceptual rainfall-runoff model PDM - Probability-Distributed Model developed by Centre for Ecology & Hydrology - set up in the Dove River catchment (UK) using 1km2 resolution radar rainfall as inputs and 15 min resolution gauged flow data for calibration and validation. Data assimilation procedures are implemented to improve flow predictions using observed flow data. Uncertainties in the radar rainfall data used in the model are quantified using artificial statistical error model described by Gaussian distribution and

  7. Mathematical modeling of glycerol biotransformation

    NASA Astrophysics Data System (ADS)

    Popova-Krumova, Petya; Yankova, Sofia; Ilieva, Biliana

    2013-12-01

    A method for mathematical modeling of glycerol biotransformation by Klebsiella oxytoca is presented. Glycerol is a renewable resource for it is formed as a by-product during biodiesel production. Because of its large volume production, it seems to be a good idea to develop a technology that converts this waste into products of high value (1, 3-Propanediol; 2, 3-Butanediol). The kinetic model of this process consists of many equations and parameters. The minimization of the least square function will be used for model parameters identification. In cases of parameters identification in multiparameter models the minimization of the least square function is very difficult because it is multiextremal. This is the main problem in the multiextremal function minimization which will be solved on the base a hierarchical approach, using a polynomial approximation of the experimental data.

  8. Mathematical model for gyroscope effects

    NASA Astrophysics Data System (ADS)

    Usubamatov, Ryspek

    2015-05-01

    Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).

  9. Mathematical modeling of cold cap

    SciTech Connect

    Pokorny, Richard; Hrma, Pavel R.

    2012-10-13

    The ultimate goal of studies of cold cap behavior in glass melters is to increase the rate of glass processing in an energy-efficient manner. Regrettably, mathematical models, which are ideal tools for assessing the responses of melters to process parameters, have not paid adequate attention to the cold cap. In this study, we consider a cold cap resting on a pool of molten glass from which it receives a steady heat flux while temperature, velocity, and extent of conversion are functions of the position along the vertical coordinate. A one-dimensional (1D) mathematical model simulates this process by solving the differential equations for mass and energy balances with appropriate boundary conditions and constitutive relationships for material properties. The sensitivity analyses on the effects of incoming heat fluxes to the cold cap through its lower and upper boundaries show that the cold cap thickness increases as the heat flux from above increases, and decreases as the total heat flux increases. We also discuss the effects of foam, originating from batch reactions and from redox reactions in molten glass and argue that models must represent the foam layer to achieve a reliable prediction of the melting rate as a function of feed properties and melter conditions.

  10. How Pupils Use a Model for Abstract Concepts in Genetics

    ERIC Educational Resources Information Center

    Venville, Grady; Donovan, Jenny

    2008-01-01

    The purpose of this research was to explore the way pupils of different age groups use a model to understand abstract concepts in genetics. Pupils from early childhood to late adolescence were taught about genes and DNA using an analogical model (the wool model) during their regular biology classes. Changing conceptual understandings of the…

  11. A MATHEMATICAL MODEL FOR THE ANDROGENIC REGULATION OF THE PROSTATE IN INTACT AND CASTRATE ADULT MALE RATS

    EPA Science Inventory

    An abstract that provides understanding for a mathematical model by Barton and Anderson, for the dynamics of androgenic synthesis, transport, metabolism, and regulation of the rodent ventral prostate.

  12. Mathematical model for classification of EEG signals

    NASA Astrophysics Data System (ADS)

    Ortiz, Victor H.; Tapia, Juan J.

    2015-09-01

    A mathematical model to filter and classify brain signals from a brain machine interface is developed. The mathematical model classifies the signals from the different lobes of the brain to differentiate the signals: alpha, beta, gamma and theta, besides the signals from vision, speech, and orientation. The model to develop further eliminates noise signals that occur in the process of signal acquisition. This mathematical model can be used on different platforms interfaces for rehabilitation of physically handicapped persons.

  13. Concrete Model Checking with Abstract Matching and Refinement

    NASA Technical Reports Server (NTRS)

    Pasareanu Corina S.; Peianek Radek; Visser, Willem

    2005-01-01

    We propose an abstraction-based model checking method which relies on refinement of an under-approximation of the feasible behaviors of the system under analysis. The method preserves errors to safety properties, since all analyzed behaviors are feasible by definition. The method does not require an abstract transition relation to he generated, but instead executes the concrete transitions while storing abstract versions of the concrete states, as specified by a set of abstraction predicates. For each explored transition. the method checks, with the help of a theorem prover, whether there is any loss of precision introduced by abstraction. The results of these checks are used to decide termination or to refine the abstraction, by generating new abstraction predicates. If the (possibly infinite) concrete system under analysis has a finite bisimulation quotient, then the method is guaranteed to eventually explore an equivalent finite bisimilar structure. We illustrate the application of the approach for checking concurrent programs. We also show how a lightweight variant can be used for efficient software testing.

  14. The Activity System of School-Teaching Mathematics and Mathematical Modelling.

    ERIC Educational Resources Information Center

    Julie, Cyril

    2002-01-01

    Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…

  15. Mathematical modeling of the head-disk interface (abstract)

    NASA Astrophysics Data System (ADS)

    Crone, Robert M.; Jhon, Myung S.

    1993-05-01

    State-of-the-art theoretical and numerical techniques required to simulate the head-disk interface (HDI) of future magnetic storage devices is presented. The severity of operating conditions (i.e., attempts to achieve flying heights as low as 40 nm) pose several challenges. Large transient pressure gradients can be established within air bearing leading to numerical oscillations as well as to increased program execution times. Enhanced gaseous rarefaction effects must also be incorporated into the analysis. In the present study, accurate nonoscillatory air bearing pressure distributions were obtained using a high resolution finite element algorithm to solve the generalized Reynolds equation. Higher order gaseous rarefaction effects are incorporated into generalized Reynolds equations using the total mass flow rate coefficient predicted from the linearized Boltzmann equation. The form of the generalized Reynolds equation that is presented in this paper is an improved version of the continued fraction approximation previously proposed by Crone et al.1 A simple scaling analysis, which is based upon the results of the linearized Boltzmann equation, will also be presented to study the effect of slider miniaturization, as well as to obtain a novel interpretation of accelerated wear and accelerated flyability test results.

  16. An abstract specification language for Markov reliability models

    NASA Technical Reports Server (NTRS)

    Butler, R. W.

    1985-01-01

    Markov models can be used to compute the reliability of virtually any fault tolerant system. However, the process of delineating all of the states and transitions in a model of complex system can be devastatingly tedious and error-prone. An approach to this problem is presented utilizing an abstract model definition language. This high level language is described in a nonformal manner and illustrated by example.

  17. An abstract language for specifying Markov reliability models

    NASA Technical Reports Server (NTRS)

    Butler, Ricky W.

    1986-01-01

    Markov models can be used to compute the reliability of virtually any fault tolerant system. However, the process of delineating all of the states and transitions in a model of complex system can be devastatingly tedious and error-prone. An approach to this problem is presented utilizing an abstract model definition language. This high level language is described in a nonformal manner and illustrated by example.

  18. Constructing a Model of Mathematical Literacy.

    ERIC Educational Resources Information Center

    Pugalee, David K.

    1999-01-01

    Discusses briefly the call for mathematical literacy and the need for a model that articulates the fluid and dynamic nature of this form of literacy. Presents such a model which uses two concentric circles, one depicting the four processes of mathematical literacy (representing, manipulating, reasoning, and problem solving) and enablers that…

  19. Mathematical Modelling as a Professional Task

    ERIC Educational Resources Information Center

    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…

  20. Mathematical Modelling of Data: Software for Pedagogy.

    ERIC Educational Resources Information Center

    Bellomonte, L.; Sperandeo-Mineo, R. M.

    1993-01-01

    Discussion of mathematical modeling, particularly for high school physics curricula, focuses on software that is connected with laboratory work and the inference of mathematical models based on measurements of physical quantities. Fitting procedures are described, and user interface is explained. (Contains nine references.) (LRW)

  1. Modelling and Optimizing Mathematics Learning in Children

    ERIC Educational Resources Information Center

    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…

  2. Scaffolding Mathematical Modelling with a Solution Plan

    ERIC Educational Resources Information Center

    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…

  3. Mathematical Modeling of Cellular Metabolism.

    PubMed

    Berndt, Nikolaus; Holzhütter, Hermann-Georg

    Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.

  4. Rival approaches to mathematical modelling in immunology

    NASA Astrophysics Data System (ADS)

    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.

  5. Mathematical modeling in soil science

    NASA Astrophysics Data System (ADS)

    Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel

    2015-04-01

    Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.

  6. Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

    ERIC Educational Resources Information Center

    Horton, Robert M.; Leonard, William H.

    2005-01-01

    In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

  7. Particle Tracking Model and Abstraction of Transport Processes

    SciTech Connect

    B. Robinson

    2004-10-21

    The purpose of this report is to document the abstraction model being used in total system performance assessment (TSPA) model calculations for radionuclide transport in the unsaturated zone (UZ). The UZ transport abstraction model uses the particle-tracking method that is incorporated into the finite element heat and mass model (FEHM) computer code (Zyvoloski et al. 1997 [DIRS 100615]) to simulate radionuclide transport in the UZ. This report outlines the assumptions, design, and testing of a model for calculating radionuclide transport in the UZ at Yucca Mountain. In addition, methods for determining and inputting transport parameters are outlined for use in the TSPA for license application (LA) analyses. Process-level transport model calculations are documented in another report for the UZ (BSC 2004 [DIRS 164500]). Three-dimensional, dual-permeability flow fields generated to characterize UZ flow (documented by BSC 2004 [DIRS 169861]; DTN: LB03023DSSCP9I.001 [DIRS 163044]) are converted to make them compatible with the FEHM code for use in this abstraction model. This report establishes the numerical method and demonstrates the use of the model that is intended to represent UZ transport in the TSPA-LA. Capability of the UZ barrier for retarding the transport is demonstrated in this report, and by the underlying process model (BSC 2004 [DIRS 164500]). The technical scope, content, and management of this report are described in the planning document ''Technical Work Plan for: Unsaturated Zone Transport Model Report Integration'' (BSC 2004 [DIRS 171282]). Deviations from the technical work plan (TWP) are noted within the text of this report, as appropriate. The latest version of this document is being prepared principally to correct parameter values found to be in error due to transcription errors, changes in source data that were not captured in the report, calculation errors, and errors in interpretation of source data.

  8. A Seminar in Mathematical Model-Building.

    ERIC Educational Resources Information Center

    Smith, David A.

    1979-01-01

    A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)

  9. Learning with Technology: Video Modeling with Concrete-Representational-Abstract Sequencing for Students with Autism Spectrum Disorder

    ERIC Educational Resources Information Center

    Yakubova, Gulnoza; Hughes, Elizabeth M.; Shinaberry, Megan

    2016-01-01

    The purpose of this study was to determine the effectiveness of a video modeling intervention with concrete-representational-abstract instructional sequence in teaching mathematics concepts to students with autism spectrum disorder (ASD). A multiple baseline across skills design of single-case experimental methodology was used to determine the…

  10. Teaching Subtraction and Multiplication with Regrouping Using the Concrete-Representational-Abstract Sequence and Strategic Instruction Model

    ERIC Educational Resources Information Center

    Flores, Margaret M.; Hinton, Vanessa; Strozier, Shaunita D.

    2014-01-01

    Based on Common Core Standards (2010), mathematics interventions should emphasize conceptual understanding of numbers and operations as well as fluency. For students at risk for failure, the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) have been shown effective in teaching computation with an emphasis…

  11. Mathematical Modelling in the Early School Years

    ERIC Educational Resources Information Center

    English, Lyn D.; Watters, James J.

    2005-01-01

    In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

  12. Analyzing Mathematics Textbooks through a Constructive-Empirical Perspective on Abstraction: The Case of Pythagoras' Theorem

    ERIC Educational Resources Information Center

    Yang, Kai-Lin

    2016-01-01

    This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…

  13. Study of Photovoltaic Cells Engineering Mathematical Model

    NASA Astrophysics Data System (ADS)

    Zhou, Jun; Yu, Zhengping; Lu, Zhengyi; Li, Chenhui; Zhang, Ruilan

    2016-11-01

    The characteristic curve of photovoltaic cells is the theoretical basis of PV Power, which simplifies the existing mathematical model, eventually, obtains a mathematical model used in engineering. The characteristic curve of photovoltaic cells contains both exponential and logarithmic calculation. The exponential and logarithmic spread out through Taylor series, which includes only four arithmetic and use single chip microcontroller as the control center. The result shows that: the use of single chip microcontroller for calculating exponential and logarithmic functions, simplifies mathematical model of PV curve, also can meet the specific conditions’ requirement for engineering applications.

  14. Modelling the influence of irrigation abstractions on Scotland's water resources.

    PubMed

    Dunn, S M; Chalmers, N; Stalham, M; Lilly, A; Crabtree, B; Johnston, L

    2003-01-01

    Legislation to control abstraction of water in Scotland is limited and for purposes such as irrigation there are no restrictions in place over most of the country. This situation is set to change with implementation of the European Water Framework Directive. As a first step towards the development of appropriate policy for irrigation control there is a need to assess the current scale of irrigation practices in Scotland. This paper presents a modelling approach that has been used to quantify spatially the volume of water abstractions across the country for irrigation of potato crops under typical climatic conditions. A water balance model was developed to calculate soil moisture deficits and identify the potential need for irrigation. The results were then combined with spatial data on potato cropping and integrated to the sub-catchment scale to identify the river systems most at risk from over-abstraction. The results highlight that the areas that have greatest need for irrigation of potatoes are all concentrated in the central east-coast area of Scotland. The difference between irrigation demand in wet and dry years is very significant, although spatial patterns of the distribution are similar.

  15. Establishing an Explanatory Model for Mathematics Identity.

    PubMed

    Cribbs, Jennifer D; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M

    2015-04-01

    This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence in mathematics directly impact their identity as a "math person," findings indicate that students' self-perceptions related to competence and performance have an indirect effect on their mathematics identity, primarily by association with students' interest and external recognition in mathematics. Thus, the model indicates that students' competence and performance beliefs are not sufficient for their mathematics identity development, and it highlights the roles of interest and recognition.

  16. Symbolic LTL Compilation for Model Checking: Extended Abstract

    NASA Technical Reports Server (NTRS)

    Rozier, Kristin Y.; Vardi, Moshe Y.

    2007-01-01

    In Linear Temporal Logic (LTL) model checking, we check LTL formulas representing desired behaviors against a formal model of the system designed to exhibit these behaviors. To accomplish this task, the LTL formulas must be translated into automata [21]. We focus on LTL compilation by investigating LTL satisfiability checking via a reduction to model checking. Having shown that symbolic LTL compilation algorithms are superior to explicit automata construction algorithms for this task [16], we concentrate here on seeking a better symbolic algorithm.We present experimental data comparing algorithmic variations such as normal forms, encoding methods, and variable ordering and examine their effects on performance metrics including processing time and scalability. Safety critical systems, such as air traffic control, life support systems, hazardous environment controls, and automotive control systems, pervade our daily lives, yet testing and simulation alone cannot adequately verify their reliability [3]. Model checking is a promising approach to formal verification for safety critical systems which involves creating a formal mathematical model of the system and translating desired safety properties into a formal specification for this model. The complement of the specification is then checked against the system model. When the model does not satisfy the specification, model-checking tools accompany this negative answer with a counterexample, which points to an inconsistency between the system and the desired behaviors and aids debugging efforts.

  17. Mathematical Modeling of Chemical Stoichiometry

    ERIC Educational Resources Information Center

    Croteau, Joshua; Fox, William P.; Varazo, Kristofoland

    2007-01-01

    In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…

  18. Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms

    ERIC Educational Resources Information Center

    Eric, Chan Chun Ming

    2009-01-01

    The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…

  19. Mathematical Model Development and Simulation Support

    NASA Technical Reports Server (NTRS)

    Francis, Ronald C.; Tobbe, Patrick A.

    2000-01-01

    This report summarizes the work performed in support of the Contact Dynamics 6DOF Facility and the Flight Robotics Lab at NASA/ MSFC in the areas of Mathematical Model Development and Simulation Support.

  20. Cooking Potatoes: Experimentation and Mathematical Modeling.

    ERIC Educational Resources Information Center

    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)

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

    ERIC Educational Resources Information Center

    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…

  2. Automatic mathematical modeling for space application

    NASA Technical Reports Server (NTRS)

    Wang, Caroline K.

    1987-01-01

    A methodology for automatic mathematical modeling is described. The major objective is to create a very friendly environment for engineers to design, maintain and verify their model and also automatically convert the mathematical model into FORTRAN code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine simulation mathematical model called Propulsion System Automatic Modeling (PSAM). PSAM provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. PSAM contains an initial set of component process elements for the Space Shuttle Main Engine simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. PSAM is then able to automatically generate the model and the FORTRAN code. A future goal is to download the FORTRAN code to the VAX/VMS system for conventional computation.

  3. Modelling Mathematical Reasoning in Physics Education

    NASA Astrophysics Data System (ADS)

    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.

  4. Mathematical Modeling of Circadian and Homeostatic Interaction

    DTIC Science & Technology

    2011-11-16

    REM ) sleep , and non- REM ( NREM ) sleep states. Using this mathematical modeling framework, the Pis conducted modeling studies on several...The model network exhibits realistic polyphasic sleep -wake behavior consisting of wake, rapid eye movement ( REM ) sleep , and non- REM ( NREM ) sleep ...states. In addition, the model captures stereotypical sleep patterning including cycling between NREM and REM sleep . Using this

  5. Mathematics Test, Numerical, and Abstraction Anxieties and Their Relation to Elementary Teachers' Views on Preparing Students for the Study of Algebra.

    ERIC Educational Resources Information Center

    Brown, Martha A.; Gray, Mary W.

    1992-01-01

    Reports a correlational study to determine whether teacher's mathematics anxiety might inhibit the introduction of more problem solving and abstraction in elementary schools to enable more ninth graders to enroll in algebra. Correlations on 19 variables for 116 teachers indicated that anxiety decreased with increased mathematics content studied…

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

    ERIC Educational Resources Information Center

    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…

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

    ERIC Educational Resources Information Center

    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…

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

    ERIC Educational Resources Information Center

    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…

  9. Mathematical biodynamic feedthrough model applied to rotorcraft.

    PubMed

    Venrooij, Joost; Mulder, Mark; Abbink, David A; van Paassen, Marinus M; Mulder, Max; van der Helm, Frans C T; Bulthoff, Heinrich H

    2014-07-01

    Biodynamic feedthrough (BDFT) occurs when vehicle accelerations feed through the human body and cause involuntary control inputs. This paper proposes a model to quantitatively predict this effect in rotorcraft. This mathematical BDFT model aims to fill the gap between the currently existing black box BDFT models and physical BDFT models. The model structure was systematically constructed using asymptote modeling, a procedure described in detail in this paper. The resulting model can easily be implemented in many typical rotorcraft BDFT studies, using the provided model parameters. The model's performance was validated in both the frequency and time domain. Furthermore, it was compared with several recent BDFT models. The results show that the proposed mathematical model performs better than typical black box models and is easier to parameterize and implement than a recent physical model.

  10. Molecular modeling: An open invitation for applied mathematics

    NASA Astrophysics Data System (ADS)

    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.

  11. Entity-Centric Abstraction and Modeling Framework for Transportation Architectures

    NASA Technical Reports Server (NTRS)

    Lewe, Jung-Ho; DeLaurentis, Daniel A.; Mavris, Dimitri N.; Schrage, Daniel P.

    2007-01-01

    A comprehensive framework for representing transpportation architectures is presented. After discussing a series of preceding perspectives and formulations, the intellectual underpinning of the novel framework using an entity-centric abstraction of transportation is described. The entities include endogenous and exogenous factors and functional expressions are offered that relate these and their evolution. The end result is a Transportation Architecture Field which permits analysis of future concepts under the holistic perspective. A simulation model which stems from the framework is presented and exercised producing results which quantify improvements in air transportation due to advanced aircraft technologies. Finally, a modeling hypothesis and its accompanying criteria are proposed to test further use of the framework for evaluating new transportation solutions.

  12. Mathematical Modelling with 9-Year-Olds

    ERIC Educational Resources Information Center

    English, Lyn D.; Watters, James J.

    2005-01-01

    This paper reports on the mathematical modelling of four classes of 4th-grade children as they worked on a modelling problem involving the selection of an Australian swimming team for the 2004 Olympics. The problem was implemented during the second year of the children's participation in a 3-year longitudinal program of modelling experiences…

  13. Mathematical Models of Tuberculosis Reactivation and Relapse

    PubMed Central

    Wallis, Robert S.

    2016-01-01

    The natural history of human infection with Mycobacterium tuberculosis (Mtb) is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiologic mechanism of tuberculosis in patients treated with tumor necrosis factor blockers, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic. PMID:27242697

  14. The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

    ERIC Educational Resources Information Center

    Ciltas, Alper; Isik, Ahmet

    2013-01-01

    The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

  15. A mathematical model of a cloud

    NASA Astrophysics Data System (ADS)

    Wang, A. P.

    1980-07-01

    The model under consideration is a pencil of radiation incident on a cloud, and the problem is to determine the reflection and transmitted radiation. Based on the method of 'principle of invariance', three mathematical models are constructed. The first is the basic model, which describes the radiation system completely. The second is the flux integral model, in which the integral average intensity is considered. The third is the diffusion model, which gives the most important information about the diffused radiation field.

  16. Mathematical Modeling in Continuum Mechanics

    NASA Astrophysics Data System (ADS)

    Temam, Roger; Miranville, Alain

    2005-06-01

    Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

  17. About a mathematical model of market

    NASA Astrophysics Data System (ADS)

    Kulikov, D. A.

    2017-01-01

    In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.

  18. Comprehensive Mathematical Model Of Real Fluids

    NASA Technical Reports Server (NTRS)

    Anderson, Peter G.

    1996-01-01

    Mathematical model of thermodynamic properties of water, steam, and liquid and gaseous hydrogen and oxygen developed for use in computational simulations of flows of mass and heat in main engine of space shuttle. Similar models developed for other fluids and applications. Based on HBMS equation of state.

  19. Mathematical model for predicting human vertebral fracture

    NASA Technical Reports Server (NTRS)

    Benedict, J. V.

    1973-01-01

    Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.

  20. Mathematical Model For Scattering From Mirrors

    NASA Technical Reports Server (NTRS)

    Wang, Yaujen

    1988-01-01

    Additional terms account for effects of particulate contamination. Semiempirical mathematical model of scattering of light from surface of mirror gives improved account of effects of particulate contamination. Models that treated only scattering by microscopic irregularities in surface gave bidirectional reflectance distribution functions differing from measured scattering intensities over some ranges of angles.

  1. Mathematical modeling relevant to closed artificial ecosystems

    USGS Publications Warehouse

    DeAngelis, D.L.

    2003-01-01

    The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.

  2. Mathematical modeling relevant to closed artificial ecosystems.

    PubMed

    DeAngelis, Donald L

    2003-01-01

    The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space.

  3. Mathematical modeling of molecular diffusion through mucus

    PubMed Central

    Cu, Yen; Saltzman, W. Mark

    2008-01-01

    The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488

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

    ERIC Educational Resources Information Center

    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…

  5. The (Mathematical) Modeling Process in Biosciences.

    PubMed

    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.

  6. The (Mathematical) Modeling Process in Biosciences

    PubMed Central

    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. PMID:26734063

  7. Two Mathematical Models of Nonlinear Vibrations

    NASA Technical Reports Server (NTRS)

    Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William

    2007-01-01

    Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.

  8. To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling

    ERIC Educational Resources Information Center

    Lingefjard, Thomas; Holmquist, Mikael

    2005-01-01

    Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…

  9. Mathematical Modeling of Wildfire Dynamics

    NASA Astrophysics Data System (ADS)

    Del Bene, Kevin; Drew, Donald

    2012-11-01

    Wildfires have been a long-standing problem in today's society. In this paper, we derive and solve a fluid dynamics model to study a specific type of wildfire, namely, a two dimensional flow around a rising plume above a concentrated heat source, modeling a fire line. This flow assumes a narrow plume of hot gas rising and entraining the surrounding air. The surrounding air is assumed to have constant density and is irrotational far from the fire line. The flow outside the plume is described by a Biot-Savart integral with jump conditions across the position of the plume. The plume model describes the unsteady evolution of the mass, momentum, energy, and vorticity inside the plume, with sources derived to model mixing in the style of Morton, et al. 1956]. The fire is then modeled using a conservation derivation, allowing the fire to propagate, coupling back to the plume model. The results show that this model is capable of capturing the complex interaction of the plume with the surrounding air and fuel layer. Funded by NSF GRFP.

  10. Establishing an Explanatory Model for Mathematics Identity

    ERIC Educational Resources Information Center

    Cribbs, Jennifer D.; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M.

    2015-01-01

    This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…

  11. Introduction to mathematical models and methods

    SciTech Connect

    Siddiqi, A. H.; Manchanda, P.

    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.

  12. Identification of the noise using mathematical modelling

    NASA Astrophysics Data System (ADS)

    Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav

    2016-03-01

    In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today's computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.

  13. Mathematical Modeling of Loop Heat Pipes

    NASA Technical Reports Server (NTRS)

    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.

  14. Mathematical models for principles of gyroscope theory

    NASA Astrophysics Data System (ADS)

    Usubamatov, Ryspek

    2017-01-01

    Gyroscope devices are primary units for navigation and control systems that have wide application in engineering. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which known mathematical models have been formulated on the law of kinetic energy conservation and the change in the angular momentum. The gyroscope theory is represented by numerous publications, which mathematical models do not match the actual torques and motions in these devices.. The nature of gyroscope effects is more complex than represented in known publications. Recent investigations in this area have demonstrated that on a gyroscope can act until eleven internal torques simultaneously and interdependently around two axes. These gyroscope torques are generated by spinning rotor's mass-elements and by the gyroscope center-mass based on action of several inertial forces. The change in the angular momentum does not play first role for gyroscope motions. The external load generates several internal torques which directions may be distinguished. This situation leads changing of the angular velocities of gyroscope motions around two axes. Formulated mathematical models of gyroscope internal torques are representing the fundamental principle of gyroscope theory. In detail, the gyroscope is experienced the resistance torque generated by the centrifugal and Coriolis forces of the spinning rotor and the precession torque generated by the common inertial forces and the change in the angular momentum. The new mathematical models for the torques and motions of the gyroscope confirmed for most unsolvable problems. The mathematical models practically tested and the results are validated the theoretical approach.

  15. A Mathematical Model for Railway Control Systems

    NASA Technical Reports Server (NTRS)

    Hoover, D. N.

    1996-01-01

    We present a general method for modeling safety aspects of railway control systems. Using our modeling method, one can progressively refine an abstract railway safety model, sucessively adding layers of detail about how a real system actually operates, while maintaining a safety property that refines the original abstract safety property. This method supports a top-down approach to specification of railway control systems and to proof of a variety of safety-related properties. We demonstrate our method by proving safety of the classical block control system.

  16. Determining the Views of Mathematics Student Teachers Related to Mathematical Modelling

    ERIC Educational Resources Information Center

    Tekin, Ayse; Kula, Semiha; Hidiroglu, Caglar Naci; Bukova-Guzel, Esra; Ugurel, Isikhan

    2012-01-01

    The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions…

  17. An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

    ERIC Educational Resources Information Center

    Bukova-Guzel, Esra

    2011-01-01

    This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

  18. Selected translated abstracts of Russian-language climate-change publications. 4: General circulation models

    SciTech Connect

    Burtis, M.D.; Razuvaev, V.N.; Sivachok, S.G.

    1996-10-01

    This report presents English-translated abstracts of important Russian-language literature concerning general circulation models as they relate to climate change. Into addition to the bibliographic citations and abstracts translated into English, this report presents the original citations and abstracts in Russian. Author and title indexes are included to assist the reader in locating abstracts of particular interest.

  19. Mathematical models of malaria - a review

    PubMed Central

    2011-01-01

    Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease PMID:21777413

  20. An Experimental Approach to Mathematical Modeling in Biology

    ERIC Educational Resources Information Center

    Ledder, Glenn

    2008-01-01

    The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

  1. Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology.

    ERIC Educational Resources Information Center

    Lingefjard, Thomas

    2002-01-01

    Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…

  2. Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum.

    ERIC Educational Resources Information Center

    Swetz, Frank

    1991-01-01

    Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)

  3. Voters' Fickleness:. a Mathematical Model

    NASA Astrophysics Data System (ADS)

    Boccara, Nino

    This paper presents a spatial agent-based model in order to study the evolution of voters' choice during the campaign of a two-candidate election. Each agent, represented by a point inside a two-dimensional square, is under the influence of its neighboring agents, located at a Euclidean distance less than or equal to d, and under the equal influence of both candidates seeking to win its support. Moreover, each agent located at time t at a given point moves at the next timestep to a randomly selected neighboring location distributed normally around its position at time t. Besides their location in space, agents are characterized by their level of awareness, a real a ∈ [0, 1], and their opinion ω ∈ {-1, 0, +1}, where -1 and +1 represent the respective intentions to cast a ballot in favor of one of the two candidates while 0 indicates either disinterest or refusal to vote. The essential purpose of the paper is qualitative; its aim is to show that voters' fickleness is strongly correlated to the level of voters' awareness and the efficiency of candidates' propaganda.

  4. Mathematical Modelling of Turbidity Currents

    NASA Astrophysics Data System (ADS)

    Fay, G. L.; Fowler, A.; Howell, P.

    2011-12-01

    A turbidity current is a submarine sediment flow which propagates downslope through the ocean into the deep sea. Turbidity currents can occur randomly and without much warning and consequently are hard to observe and measure. The driving force in a turbidity current is the presence of sediment in the current - gravity acts on the sediment in suspension, causing it to move downstream through the ocean water. A phenomenon known as ignition or autosuspension has been observed in turbidity currents in submarine canyons, and it occurs when a current travelling downslope gathers speed as it erodes sediment from the sea floor in a self-reinforcing cycle. Using the turbidity current model of Parker et al. (Journal of Fluid Mechanics, 1986) we investigate the evolution of a 1-D turbidity current as it moves downstream. To seek a better understanding of the dynamics of flow as the current evolves in space and time, we present analytical results alongside computed numerical solutions, incorporating entrainment of water and erosion and deposition of sediment. We consider varying slope functions and inlet conditions and attempt to predict when the current will become extinct. We examine currents which are in both supercritical and subcritical flow regimes and consider the dynamics of the flow as the current switches regime.

  5. Mathematical Models of College Myopia

    PubMed Central

    Greene, Peter R.; Grill, Zachary W.; Medina, Antonio

    2015-01-01

    Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/−0.31 D. over a 14 year interval. Typical college myopia rate is −0.3 to −0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia. PMID:26709316

  6. Mathematical Models Of Turbulence In Transonic Flow

    NASA Technical Reports Server (NTRS)

    Rubesin, Morris W.; Viegas, John R.

    1989-01-01

    Predictions of several models compared with measurements of well-documented flow. Report reviews performances of variety of mathematical models of turbulence in transonic flow. Predictions of models compared with measurements of flow in wind tunnel along outside of cylinder having axisymmetric bump of circular-arc cross section in meridional plane. Review part of continuing effort to calibrate and verify computer codes for prediction of transonic flows about airfoils. Johnson-and-King model proved superior in predicting transonic flow over bumpy cylinder.

  7. Building Mathematical Models of Simple Harmonic and Damped Motion.

    ERIC Educational Resources Information Center

    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)

  8. Mathematical modeling of vertebrate limb development.

    PubMed

    Zhang, Yong-Tao; Alber, Mark S; Newman, Stuart A

    2013-05-01

    In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton.

  9. Generalizing in Interaction: Middle School Mathematics Students Making Mathematical Generalizations in a Population-Modeling Project

    ERIC Educational Resources Information Center

    Jurow, A. Susan

    2004-01-01

    Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The…

  10. Assessing Science Students' Attitudes to Mathematics: A Case Study on a Modelling Project with Mathematical Software

    ERIC Educational Resources Information Center

    Lim, L. L.; Tso, T. -Y.; Lin, F. L.

    2009-01-01

    This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a…

  11. "Model Your Genes the Mathematical Way"--A Mathematical Biology Workshop for Secondary School Teachers

    ERIC Educational Resources Information Center

    Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard

    2008-01-01

    This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…

  12. Mathematical modelling of the lower urinary tract.

    PubMed

    Paya, Antonio Soriano; Fernandez, Daniel Ruiz; Gil, David; Garcia Chamizo, Juan Manuel; Perez, Francisco Macia

    2013-03-01

    The lower urinary tract is one of the most complex biological systems of the human body as it involved hydrodynamic properties of urine and muscle. Moreover, its complexity is increased to be managed by voluntary and involuntary neural systems. In this paper, a mathematical model of the lower urinary tract it is proposed as a preliminary study to better understand its functioning. Furthermore, another goal of that mathematical model proposal is to provide a basis for developing artificial control systems. Lower urinary tract is comprised of two interacting systems: the mechanical system and the neural regulator. The latter has the function of controlling the mechanical system to perform the voiding process. The results of the tests reproduce experimental data with high degree of accuracy. Also, these results indicate that simulations not only with healthy patients but also of patients with dysfunctions with neurological etiology present urodynamic curves very similar to those obtained in clinical studies.

  13. Mathematical modelling of leprosy and its control.

    PubMed

    Blok, David J; de Vlas, Sake J; Fischer, Egil A J; Richardus, Jan Hendrik

    2015-03-01

    Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital.

  14. Mathematical Model For Deposition Of Soot

    NASA Technical Reports Server (NTRS)

    Makel, Darby B.

    1991-01-01

    Semiempirical mathematical model predicts deposition of soot in tubular gas generator in which hydrocarbon fuel burned in very-fuel-rich mixture with pure oxygen. Developed in response to concern over deposition of soot in gas generators and turbomachinery of rocket engines. Also of interest in terrestrial applications involving fuel-rich combustion or analogous process; e.g., purposeful deposition of soot to manufacture carbon black pigments.

  15. On mathematical modelling of flameless combustion

    SciTech Connect

    Mancini, Marco; Schwoeppe, Patrick; Weber, Roman; Orsino, Stefano

    2007-07-15

    A further analysis of the IFRF semi-industrial-scale experiments on flameless (mild) combustion of natural gas is carried out. The experimental burner features a strong oxidizer jet and two weak natural gas jets. Numerous publications have shown the inability of various RANS-based mathematical models to predict the structure of the weak jet. We have proven that the failure is in error predictions of the entrainment and therefore is not related to any chemistry submodels, as has been postulated. (author)

  16. Mathematical Models and the Experimental Analysis of Behavior

    ERIC Educational Resources Information Center

    Mazur, James E.

    2006-01-01

    The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make…

  17. Mathematical Programming Model for Fighter Training Squadron Pilot Scheduling

    DTIC Science & Technology

    2007-03-01

    of Defense, or the United States Government. AFIT/GOR/ENS/07-17 MATHEMATICAL PROGAMMING MODEL FOR...March 2007 APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. AFIT/GOR/ENS/07-17 MATHEMATICAL PROGAMMING MODEL FOR FIGHTER...80 x MATHEMATICAL PROGAMMING MODEL FOR FIGHTER TRAINING SQUADRON PILOT

  18. Biology by numbers: mathematical modelling in developmental biology.

    PubMed

    Tomlin, Claire J; Axelrod, Jeffrey D

    2007-05-01

    In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.

  19. Mathematics.

    ERIC Educational Resources Information Center

    Costellano, Janet; Scaffa, Matthew

    The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…

  20. Mathematical modeling of deformation during hot rolling

    SciTech Connect

    Jin, D.; Stachowiak, R.G.; Samarasekera, I.V.; Brimacombe, J.K.

    1994-12-31

    The deformation that occurs in the roll bite during the hot rolling of steel, particularly the strain-rate and strain distribution, has been mathematically modeled using finite-element analysis. In this paper three different finite-element models are compared with one another and with industrial measurements. The first model is an Eulerian analysis based on the flow formulation method, while the second utilizes an Updated Lagrangian approach. The third model is based on a commercially available program DEFORM which also utilizes a Lagrangian reference frame. Model predictions of strain and strain-rate distribution, particularly near the surface of the slab, are strongly influenced by the treatment of friction at the boundary and the magnitude of the friction coefficient or shear factor. Roll forces predicted by the model have been compared with industrial rolling loads from a seven-stand hot-strip mill.

  1. Mathematical models of human african trypanosomiasis epidemiology.

    PubMed

    Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul

    2015-03-01

    Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.

  2. A mathematical model of 'Pride and Prejudice'.

    PubMed

    Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro

    2014-04-01

    A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.

  3. Aircraft engine mathematical model - linear system approach

    NASA Astrophysics Data System (ADS)

    Rotaru, Constantin; Roateşi, Simona; Cîrciu, Ionicǎ

    2016-06-01

    This paper examines a simplified mathematical model of the aircraft engine, based on the theory of linear and nonlinear systems. The dynamics of the engine was represented by a linear, time variant model, near a nominal operating point within a finite time interval. The linearized equations were expressed in a matrix form, suitable for the incorporation in the MAPLE program solver. The behavior of the engine was included in terms of variation of the rotational speed following a deflection of the throttle. The engine inlet parameters can cover a wide range of altitude and Mach numbers.

  4. Exploring the Relationship between Mathematical Modelling and Classroom Discourse

    ERIC Educational Resources Information Center

    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…

  5. Assessment of Primary 5 Students' Mathematical Modelling Competencies

    ERIC Educational Resources Information Center

    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…

  6. Lateral-Directional Parameter Estimation on the X-48B Aircraft Using an Abstracted, Multi-Objective Effector Model

    NASA Technical Reports Server (NTRS)

    Ratnayake, Nalin A.; Waggoner, Erin R.; Taylor, Brian R.

    2011-01-01

    The problem of parameter estimation on hybrid-wing-body aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aerodynamic control effectors that act in coplanar motion. This adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of flight and simulation data must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, time-decorrelation techniques are applied to a model structure selected through stepwise regression for simulated and flight-generated lateral-directional parameter estimation data. A virtual effector model that uses mathematical abstractions to describe the multi-axis effects of clamshell surfaces is developed and applied. Comparisons are made between time history reconstructions and observed data in order to assess the accuracy of the regression model. The Cram r-Rao lower bounds of the estimated parameters are used to assess the uncertainty of the regression model relative to alternative models. Stepwise regression was found to be a useful technique for lateral-directional model design for hybrid-wing-body aircraft, as suggested by available flight data. Based on the results of this study, linear regression parameter estimation methods using abstracted effectors are expected to perform well for hybrid-wing-body aircraft properly equipped for the task.

  7. Declarative representation of uncertainty in mathematical models.

    PubMed

    Miller, Andrew K; Britten, Randall D; Nielsen, Poul M F

    2012-01-01

    An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.

  8. Mathematical Modeling of an Oscillating Droplet

    NASA Technical Reports Server (NTRS)

    Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)

    2000-01-01

    Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.

  9. Mathematical modelling of submarine landslide motion

    NASA Astrophysics Data System (ADS)

    Burminskij, A.

    2012-04-01

    Mathematical modelling of submarine landslide motion The paper presents a mathematical model to calculate dynamic parameters of a submarine landslide. The problem of estimation possible submarine landslides dynamic parameters and run-out distances as well as their effect on submarine structures becomes more and more actual because they can have significant impacts on infrastructure such as the rupture of submarine cables and pipelines, damage to offshore drilling platforms, cause a tsunami. In this paper a landslide is considered as a viscoplastic flow and is described by continuum mechanics equations, averaged over the flow depth. The model takes into account friction at the bottom and at the landslide-water boundary, as well as the involvement of bottom material in motion. A software was created and series of test calculations were performed. Calculations permitted to estimate the contribution of various model coefficients and initial conditions. Motion down inclined bottom was studied both for constant and variable slope angle. Examples of typical distributions of the flow velocity, thickness and density along the landslide body at different stages of motion are given.

  10. Mathematical Modeling of Extinction of Inhomogeneous Populations

    PubMed Central

    Karev, G.P.; Kareva, I.

    2016-01-01

    Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117

  11. Mathematical modeling of the coating process.

    PubMed

    Toschkoff, Gregor; Khinast, Johannes G

    2013-12-05

    Coating of tablets is a common unit operation in the pharmaceutical industry. In most cases, the final product must meet strict quality requirements; to meet them, a detailed understanding of the coating process is required. To this end, numerous experiment studies have been performed. However, to acquire a mechanistic understanding, experimental data must be interpreted in the light of mathematical models. In recent years, a combination of analytical modeling and computational simulations enabled deeper insights into the nature of the coating process. This paper presents an overview of modeling and simulation approaches of the coating process, covering various relevant aspects from scale-up considerations to coating mass uniformity investigations and models for drop atomization. The most important analytical and computational concepts are presented and the findings are compared.

  12. Mathematical modelling of hepatic lipid metabolism.

    PubMed

    Pratt, Adrian C; Wattis, Jonathan A D; Salter, Andrew M

    2015-04-01

    The aim of this paper is to develop a mathematical model capable of simulating the metabolic response to a variety of mixed meals in fed and fasted conditions with particular emphasis placed on the hepatic triglyceride element of the model. Model validation is carried out using experimental data for the ingestion of three mixed composition meals over a 24-h period. Comparison with experimental data suggests the model predicts key plasma lipids accurately given a prescribed insulin profile. One counter-intuitive observation to arise from simulations is that liver triglyceride initially decreases when a high fat meal is ingested, a phenomenon potentially explained by the carbohydrate portion of the meal raising plasma insulin.

  13. Predictive mathematical models of cancer signalling pathways.

    PubMed

    Bachmann, J; Raue, A; Schilling, M; Becker, V; Timmer, J; Klingmüller, U

    2012-02-01

    Complex intracellular signalling networks integrate extracellular signals and convert them into cellular responses. In cancer cells, the tightly regulated and fine-tuned dynamics of information processing in signalling networks is altered, leading to uncontrolled cell proliferation, survival and migration. Systems biology combines mathematical modelling with comprehensive, quantitative, time-resolved data and is most advanced in addressing dynamic properties of intracellular signalling networks. Here, we introduce different modelling approaches and their application to medical systems biology, focusing on the identifiability of parameters in ordinary differential equation models and their importance in network modelling to predict cellular decisions. Two related examples are given, which include processing of ligand-encoded information and dual feedback regulation in erythropoietin (Epo) receptor signalling. Finally, we review the current understanding of how systems biology could foster the development of new treatment strategies in the context of lung cancer and anaemia.

  14. Mathematical Models of Continuous Flow Electrophoresis

    NASA Technical Reports Server (NTRS)

    Saville, D. A.; Snyder, R. S.

    1985-01-01

    Development of high resolution continuous flow electrophoresis devices ultimately requires comprehensive understanding of the ways various phenomena and processes facilitate or hinder separation. A comprehensive model of the actual three dimensional flow, temperature and electric fields was developed to provide guidance in the design of electrophoresis chambers for specific tasks and means of interpreting test data on a given chamber. Part of the process of model development includes experimental and theoretical studies of hydrodynamic stability. This is necessary to understand the origin of mixing flows observed with wide gap gravitational effects. To insure that the model accurately reflects the flow field and particle motion requires extensive experimental work. Another part of the investigation is concerned with the behavior of concentrated sample suspensions with regard to sample stream stability particle-particle interactions which might affect separation in an electric field, especially at high field strengths. Mathematical models will be developed and tested to establish the roles of the various interactions.

  15. Mathematical model of laser PUVA psoriasis treatment

    NASA Astrophysics Data System (ADS)

    Medvedev, Boris A.; Tuchin, Valery V.; Yaroslavsky, Ilya V.

    1991-05-01

    In order to optimize laser PUVA psoriasis treatment we develop the mathematical model of the dynamics of cell processes within epidermis. We consider epidermis as a structure consisting of N cell monolayers. There are four kinds of cells that correspond to four epidermal strata. The different kinds of cells can exist within a given monolayer. We assume that the following cell processes take place: division, death and transition from one stratum to the following. Discrete transition of cells from stratum j to j + 1 approximates to real differentiation.

  16. Mathematical modelling of risk reduction in reinsurance

    NASA Astrophysics Data System (ADS)

    Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

    2017-01-01

    The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

  17. A mathematical model of aortic aneurysm formation

    PubMed Central

    Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai

    2017-01-01

    Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412

  18. Mathematical modeling of human brain physiological data

    NASA Astrophysics Data System (ADS)

    Böhm, Matthias; Faltermeier, Rupert; Brawanski, Alexander; Lang, Elmar W.

    2013-12-01

    Recently, a mathematical model of the basic physiological processes regulating the cerebral perfusion and oxygen supply was introduced [Jung , J. Math. Biol.JMBLAJ0303-681210.1007/s00285-005-0343-5 51, 491 (2005)]. Although this model correctly describes the interdependence of arterial blood pressure (ABP) and intracranial pressure (ICP), it fails badly when it comes to explaining certain abnormal correlations seen in about 80% of the recordings of ABP together with ICP and the partial oxygen pressure (TiPO2) of the neuronal tissue, taken at an intensive care unit during neuromonitoring of patients with a severe brain trauma. Such recordings occasionally show segments, where the mean arterial blood pressure is correlated with the partial oxygen pressure in tissue but anticorrelated with the intracranial pressure. The origin of such abnormal correlations has not been fully understood yet. Here, two extensions to the previous approach are proposed which can reproduce such abnormal correlations in simulations quantitatively. Furthermore, as the simulations are based on a mathematical model, additional insight into the physiological mechanisms from which such abnormal correlations originate can be gained.

  19. Mathematical modeling of infectious disease dynamics

    PubMed Central

    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

  20. A mathematical model of aortic aneurysm formation.

    PubMed

    Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R; Friedman, Avner; Zhu, Dai

    2017-01-01

    Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient's aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient's abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material.

  1. Modeling situated abstraction : action coalescence via multidimensional coherence.

    SciTech Connect

    Sallach, D. L.; Decision and Information Sciences; Univ. of Chicago

    2007-01-01

    Situated social agents weigh dozens of priorities, each with its own complexities. Domains of interest are intertwined, and progress in one area either complements or conflicts with other priorities. Interpretive agents address these complexities through: (1) integrating cognitive complexities through the use of radial concepts, (2) recognizing the role of emotion in prioritizing alternatives and urgencies, (3) using Miller-range constraints to avoid oversimplified notions omniscience, and (4) constraining actions to 'moves' in multiple prototype games. Situated agent orientations are dynamically grounded in pragmatic considerations as well as intertwined with internal and external priorities. HokiPoki is a situated abstraction designed to shape and focus strategic agent orientations. The design integrates four pragmatic pairs: (1) problem and solution, (2) dependence and power, (3) constraint and affordance, and (4) (agent) intent and effect. In this way, agents are empowered to address multiple facets of a situation in an exploratory, or even arbitrary, order. HokiPoki is open to the internal orientation of the agent as it evolves, but also to the communications and actions of other agents.

  2. Automatic mathematical modeling for real time simulation program (AI application)

    NASA Technical Reports Server (NTRS)

    Wang, Caroline; Purinton, Steve

    1989-01-01

    A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.

  3. A mathematical model of elastic fin micromotors

    NASA Astrophysics Data System (ADS)

    Lu, Pin; Lee, Kwok Hong; Piang Lim, Siak; Dong, Shuxiang; Zhong Lin, Wu

    2000-08-01

    In the present work, a simplified mathematical model of ultrasonic elastic fin micromotors has been developed. According to the operating principle of this type of motor, the motions of a rotor in each cycle of the stator vibration are divided into several stages based on whether the fin tip and the stator are in contact with slip, contact without slip or separation. The equations of motion of the rotor in each stage are derived. The valid range of the model has been discussed through numerical examples. This work provides an initial effort to construct a model for the elastic fin motor by considering the dynamical deformation of the rotor as well as the intermittent contacts.

  4. A mathematical model of leptin resistance.

    PubMed

    Jacquier, Marine; Soula, Hédi A; Crauste, Fabien

    2015-09-01

    Obesity is often associated with leptin resistance, which leads to a physiological system with high leptin concentration but unable to respond to leptin signals and to regulate food intake. We propose a mathematical model of the leptin-leptin receptors system, based on the assumption that leptin is a regulator of its own receptor activity, and investigate its qualitative behavior. Based on current knowledge and previous models developed for body weight dynamics in rodents, the model includes the dynamics of leptin, leptin receptors and the regulation of food intake and body weight. It displays two stable equilibria, one representing a healthy state and the other one an obese and leptin resistant state. We show that a constant leptin injection can lead to leptin resistance and that a temporal variation in some parameter values influencing food intake can induce a change of equilibrium and a pathway to leptin resistance and obesity.

  5. Towards an Abstraction-Friendly Programming Model for High Productivity and High Performance Computing

    SciTech Connect

    Liao, C; Quinlan, D; Panas, T

    2009-10-06

    General purpose languages, such as C++, permit the construction of various high level abstractions to hide redundant, low level details and accelerate programming productivity. Example abstractions include functions, data structures, classes, templates and so on. However, the use of abstractions significantly impedes static code analyses and optimizations, including parallelization, applied to the abstractions complex implementations. As a result, there is a common perception that performance is inversely proportional to the level of abstraction. On the other hand, programming large scale, possibly heterogeneous high-performance computing systems is notoriously difficult and programmers are less likely to abandon the help from high level abstractions when solving real-world, complex problems. Therefore, the need for programming models balancing both programming productivity and execution performance has reached a new level of criticality. We are exploring a novel abstraction-friendly programming model in order to support high productivity and high performance computing. We believe that standard or domain-specific semantics associated with high level abstractions can be exploited to aid compiler analyses and optimizations, thus helping achieving high performance without losing high productivity. We encode representative abstractions and their useful semantics into an abstraction specification file. In the meantime, an accessible, source-to-source compiler infrastructure (the ROSE compiler) is used to facilitate recognizing high level abstractions and utilizing their semantics for more optimization opportunities. Our initial work has shown that recognizing abstractions and knowing their semantics within a compiler can dramatically extend the applicability of existing optimizations, including automatic parallelization. Moreover, a new set of optimizations have become possible within an abstraction-friendly and semantics-aware programming model. In the future, we will

  6. Developing mathematical models of neurobehavioral performance for the "real world".

    PubMed

    Dean, Dennis A; Fletcher, Adam; Hursh, Steven R; Klerman, Elizabeth B

    2007-06-01

    Work-related operations requiring extended wake durations, night, or rotating shifts negatively affect worker neurobehavioral performance and health. These types of work schedules are required in many industries, including the military, transportation, and health care. These industries are increasingly using or considering the use of mathematical models of neurobehavioral performance as a means to predict the neurobehavioral deficits due to these operational demands, to develop interventions that decrease these deficits, and to provide additional information to augment existing decision-making processes. Recent advances in mathematical modeling have allowed its application to real-world problems. Developing application-specific expertise is necessary to successfully apply mathematical models, in part because development of new algorithms and methods linking the models to the applications may be required. During a symposium, "Modeling Human Neurobehavioral Performance II: Towards Operational Readiness," at the 2006 SIAM-SMB Conference on the Life Sciences, examples of the process of applying mathematical models, including model construction, model validation, or developing model-based interventions, were presented. The specific applications considered included refining a mathematical model of sleep/wake patterns of airline flight crew, validating a mathematical model using railroad operations data, and adapting a mathematical model to develop appropriate countermeasure recommendations based on known constraints. As mathematical models and their associated analytical methods continue to transition into operational settings, such additional development will be required. However, major progress has been made in using mathematical model outputs to inform those individuals making schedule decisions for their workers.

  7. Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra

    ERIC Educational Resources Information Center

    Jung, Hyunyi; Mintos, Alexia; Newton, Jill

    2015-01-01

    This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…

  8. Learning with Technology: Video Modeling with Concrete-Representational-Abstract Sequencing for Students with Autism Spectrum Disorder.

    PubMed

    Yakubova, Gulnoza; Hughes, Elizabeth M; Shinaberry, Megan

    2016-07-01

    The purpose of this study was to determine the effectiveness of a video modeling intervention with concrete-representational-abstract instructional sequence in teaching mathematics concepts to students with autism spectrum disorder (ASD). A multiple baseline across skills design of single-case experimental methodology was used to determine the effectiveness of the intervention on the acquisition and maintenance of addition, subtraction, and number comparison skills for four elementary school students with ASD. Findings supported the effectiveness of the intervention in improving skill acquisition and maintenance at a 3-week follow-up. Implications for practice and future research are discussed.

  9. Applying model abstraction techniques to optimize monitoring networks for detecting subsurface contaminant transport

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Improving strategies for monitoring subsurface contaminant transport includes performance comparison of competing models, developed independently or obtained via model abstraction. Model comparison and parameter discrimination involve specific performance indicators selected to better understand s...

  10. Derivation of Rigid Body Analysis Models from Vehicle Architecture Abstractions

    DTIC Science & Technology

    2011-06-17

    simultaneously with the model creation. The author has described the evolution of the car design process from the conventional approach to the new development...models of every type have their basis in some type of physical representation of the design domain. Rather than describing three-dimensional continua of...arrangement, while capturing just enough physical detail to be used as the basis for a meaningful representation of the design , and eventually, analyses that

  11. Mathematical modeling of a thermovoltaic cell

    NASA Technical Reports Server (NTRS)

    White, Ralph E.; Kawanami, Makoto

    1992-01-01

    A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.

  12. Missing the Promise of Mathematical Modeling

    ERIC Educational Resources Information Center

    Meyer, Dan

    2015-01-01

    The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…

  13. Teaching Mathematical Modelling for Earth Sciences via Case Studies

    NASA Astrophysics Data System (ADS)

    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).

  14. Using a Functional Model to Develop a Mathematical Formula

    ERIC Educational Resources Information Center

    Otto, Charlotte A.; Everett, Susan A.; Luera, Gail R.

    2008-01-01

    The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

  15. Mathematical modeling of acid-base physiology

    PubMed Central

    Occhipinti, Rossana; Boron, Walter F.

    2015-01-01

    pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3− , NH4+) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cell–which to our knowledge is the first one capable of handling a multitude of buffer reaction–that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3− influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. PMID:25617697

  16. Incorporating neurophysiological concepts in mathematical thermoregulation models

    NASA Astrophysics Data System (ADS)

    Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.

    2014-01-01

    Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR < 0.27. Tskin simulation results were within 0.37 °C of the measured mean skin temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.

  17. Efficient Plasma Ion Source Modeling With Adaptive Mesh Refinement (Abstract)

    SciTech Connect

    Kim, J.S.; Vay, J.L.; Friedman, A.; Grote, D.P.

    2005-03-15

    Ion beam drivers for high energy density physics and inertial fusion energy research require high brightness beams, so there is little margin of error allowed for aberration at the emitter. Thus, accurate plasma ion source computer modeling is required to model the plasma sheath region and time-dependent effects correctly.A computer plasma source simulation module that can be used with a powerful heavy ion fusion code, WARP, or as a standalone code, is being developed. In order to treat the plasma sheath region accurately and efficiently, the module will have the capability of handling multiple spatial scale problems by using Adaptive Mesh Refinement (AMR). We will report on our progress on the project.

  18. Mathematical model of tumor-immune surveillance.

    PubMed

    Mahasa, Khaphetsi Joseph; Ouifki, Rachid; Eladdadi, Amina; Pillis, Lisette de

    2016-09-07

    We present a novel mathematical model involving various immune cell populations and tumor cell populations. The model describes how tumor cells evolve and survive the brief encounter with the immune system mediated by natural killer (NK) cells and the activated CD8(+) cytotoxic T lymphocytes (CTLs). The model is composed of ordinary differential equations describing the interactions between these important immune lymphocytes and various tumor cell populations. Based on up-to-date knowledge of immune evasion and rational considerations, the model is designed to illustrate how tumors evade both arms of host immunity (i.e. innate and adaptive immunity). The model predicts that (a) an influx of an external source of NK cells might play a crucial role in enhancing NK-cell immune surveillance; (b) the host immune system alone is not fully effective against progression of tumor cells; (c) the development of immunoresistance by tumor cells is inevitable in tumor immune surveillance. Our model also supports the importance of infiltrating NK cells in tumor immune surveillance, which can be enhanced by NK cell-based immunotherapeutic approaches.

  19. The use of mathematical models in teaching wastewater treatment engineering.

    PubMed

    Morgenroth, E; Arvin, E; 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.

  20. Phase Transitions in a Model of Y-Molecules Abstract

    NASA Astrophysics Data System (ADS)

    Holz, Danielle; Ruth, Donovan; Toral, Raul; Gunton, James

    Immunoglobulin is a Y-shaped molecule that functions as an antibody to neutralize pathogens. In special cases where there is a high concentration of immunoglobulin molecules, self-aggregation can occur and the molecules undergo phase transitions. This prevents the molecules from completing their function. We used a simplified model of 2-Dimensional Y-molecules with three identical arms on a triangular lattice with 2-dimensional Grand Canonical Ensemble. The molecules were permitted to be placed, removed, rotated or moved on the lattice. Once phase coexistence was found, we used histogram reweighting and multicanonical sampling to calculate our phase diagram.

  1. Abstract: Sample Size Planning for Latent Curve Models.

    PubMed

    Lai, Keke

    2011-11-30

    When designing a study that uses structural equation modeling (SEM), an important task is to decide an appropriate sample size. Historically, this task is approached from the power analytic perspective, where the goal is to obtain sufficient power to reject a false null hypothesis. However, hypothesis testing only tells if a population effect is zero and fails to address the question about the population effect size. Moreover, significance tests in the SEM context often reject the null hypothesis too easily, and therefore the problem in practice is having too much power instead of not enough power. An alternative means to infer the population effect is forming confidence intervals (CIs). A CI is more informative than hypothesis testing because a CI provides a range of plausible values for the population effect size of interest. Given the close relationship between CI and sample size, the sample size for an SEM study can be planned with the goal to obtain sufficiently narrow CIs for the population model parameters of interest. Latent curve models (LCMs) is an application of SEM with mean structure to studying change over time. The sample size planning method for LCM from the CI perspective is based on maximum likelihood and expected information matrix. Given a sample, to form a CI for the model parameter of interest in LCM, it requires the sample covariance matrix S, sample mean vector [Formula: see text], and sample size N. Therefore, the width (w) of the resulting CI can be considered a function of S, [Formula: see text], and N. Inverting the CI formation process gives the sample size planning process. The inverted process requires a proxy for the population covariance matrix Σ, population mean vector μ, and the desired width ω as input, and it returns N as output. The specification of the input information for sample size planning needs to be performed based on a systematic literature review. In the context of covariance structure analysis, Lai and Kelley

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

    ERIC Educational Resources Information Center

    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…

  3. Mathematical Modelling: A Path to Political Reflection in the Mathematics Class

    ERIC Educational Resources Information Center

    Jacobini, Otavio Roberto; Wodewotzki, Maria Lucia L.

    2006-01-01

    This paper describes the construction of pedagogical environments in mathematics classes, centred on mathematical modelling and denominated "investigative scenarios", which stimulate students to investigation, to formulation of problems and to political reflection, as well as the sharing of acquired knowledge with other persons in the community.…

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

    ERIC Educational Resources Information Center

    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…

  5. Leading a New Pedagogical Approach to Australian Curriculum Mathematics: Using the Dual Mathematical Modelling Cycle Framework

    ERIC Educational Resources Information Center

    Lamb, Janeen; Kawakami, Takashi; Saeki, Akihiko; Matsuzaki, Akio

    2014-01-01

    The aim of this study was to investigate the use of the "dual mathematical modelling cycle framework" as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an "Oil Tank Task" that required them to develop two…

  6. Mathematical model for contemplative amoeboid locomotion

    NASA Astrophysics Data System (ADS)

    Ueda, Kei-Ichi; Takagi, Seiji; Nishiura, Yasumasa; Nakagaki, Toshiyuki

    2011-02-01

    It has recently been reported that even single-celled organisms appear to be “indecisive” or “contemplative” when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously. Here, we develop a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). The biological justification of the model is tested by comparing with experimentally measured spatiotemporal profiles of the cell thickness. The experimentally observed types of behavior are reproduced in simulations based on our model, and the core logic of the modeled behavior is clarified by means of nonlinear dynamics. An on-off transition between the refractory and activated states of the chemical reactivity that takes place at the leading edge of the plasmodium plays a key role in the emergence of contemplative behavior.

  7. Mathematical foundations of the dendritic growth models.

    PubMed

    Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos

    2007-11-01

    At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.

  8. Genetic demographic networks: Mathematical model and applications.

    PubMed

    Kimmel, Marek; Wojdyła, Tomasz

    2016-10-01

    Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise

  9. Mathematical analysis of epidemiological models with heterogeneity

    SciTech Connect

    Van Ark, J.W.

    1992-01-01

    For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.

  10. Mathematical Modeling of the Origins of Life

    NASA Technical Reports Server (NTRS)

    Pohorille, Andrew

    2006-01-01

    The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.

  11. Metaphorical motion in mathematical reasoning: further evidence for pre-motor implementation of structure mapping in abstract domains.

    PubMed

    Fields, Chris

    2013-08-01

    The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation.

  12. Some Reflections on the Teaching of Mathematical Modeling

    ERIC Educational Resources Information Center

    Warwick, Jon

    2007-01-01

    This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve…

  13. Review and verification of CARE 3 mathematical model and code

    NASA Technical Reports Server (NTRS)

    Rose, D. M.; Altschul, R. E.; Manke, J. W.; Nelson, D. L.

    1983-01-01

    The CARE-III mathematical model and code verification performed by Boeing Computer Services were documented. The mathematical model was verified for permanent and intermittent faults. The transient fault model was not addressed. The code verification was performed on CARE-III, Version 3. A CARE III Version 4, which corrects deficiencies identified in Version 3, is being developed.

  14. The Aircraft Availability Model: Conceptual Framework and Mathematics

    DTIC Science & Technology

    1983-06-01

    THE AIRCRAFT AVAILABILITY MODEL: CONCEPTUAL FRAMEWORK AND MATHEMATICS June 1983 T. J. O’Malley Prepared pursuant to Department of Defense Contract No...OF REPORT & PERIOD COVERED The Aircraft Availability Model: Model Documentation Conceptual Framework and Mathematics 6. PERFORMING ORG. REPORT NUMBER

  15. Noise in restaurants: levels and mathematical model.

    PubMed

    To, Wai Ming; Chung, Andy

    2014-01-01

    Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.

  16. Mathematical modeling plasma transport in tokamaks

    SciTech Connect

    Quiang, Ji

    1997-01-01

    In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 1020/m3 with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%.

  17. Mathematical Model for the Mineralization of Bone

    NASA Technical Reports Server (NTRS)

    Martin, Bruce

    1994-01-01

    A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

  18. Mathematical Model for the Mineralization of Bone

    NASA Technical Reports Server (NTRS)

    Martin, Bruce

    1994-01-01

    A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. The model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.

  19. Cocaine addiction and personality: a mathematical model.

    PubMed

    Caselles, Antonio; Micó, Joan C; Amigó, Salvador

    2010-05-01

    The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.

  20. Mathematical modelling of animate and intentional motion.

    PubMed Central

    Rittscher, Jens; Blake, Andrew; Hoogs, Anthony; Stein, Gees

    2003-01-01

    Our aim is to enable a machine to observe and interpret the behaviour of others. Mathematical models are employed to describe certain biological motions. The main challenge is to design models that are both tractable and meaningful. In the first part we will describe how computer vision techniques, in particular visual tracking, can be applied to recognize a small vocabulary of human actions in a constrained scenario. Mainly the problems of viewpoint and scale invariance need to be overcome to formalize a general framework. Hence the second part of the article is devoted to the question whether a particular human action should be captured in a single complex model or whether it is more promising to make extensive use of semantic knowledge and a collection of low-level models that encode certain motion primitives. Scene context plays a crucial role if we intend to give a higher-level interpretation rather than a low-level physical description of the observed motion. A semantic knowledge base is used to establish the scene context. This approach consists of three main components: visual analysis, the mapping from vision to language and the search of the semantic database. A small number of robust visual detectors is used to generate a higher-level description of the scene. The approach together with a number of results is presented in the third part of this article. PMID:12689374

  1. Problems of Abstraction: Defining an American Standard for Mathematics Education at the Turn of the Twentieth Century

    ERIC Educational Resources Information Center

    Fiss, Andrew

    2012-01-01

    Throughout the nineteenth century, the sciences in the United States went through many professional and disciplinary shifts. While the impact of these changes on university education has been well established, their consequences at the level of high school education have been often overlooked. In mathematics, debates at the level of university…

  2. Turbulent motion of mass flows. Mathematical modeling

    NASA Astrophysics Data System (ADS)

    Eglit, Margarita; Yakubenko, Alexander; Yakubenko, Tatiana

    2016-04-01

    New mathematical models for unsteady turbulent mass flows, e.g., dense snow avalanches and landslides, are presented. Such models are important since most of large scale flows are turbulent. In addition to turbulence, the two other important points are taken into account: the entrainment of the underlying material by the flow and the nonlinear rheology of moving material. The majority of existing models are based on the depth-averaged equations and the turbulent character of the flow is accounted by inclusion of drag proportional to the velocity squared. In this paper full (not depth-averaged) equations are used. It is assumed that basal entrainment takes place if the bed friction equals the shear strength of the underlying layer (Issler D, M. Pastor Peréz. 2011). The turbulent characteristics of the flow are calculated using a three-parameter differential model (Lushchik et al., 1978). The rheological properties of moving material are modeled by one of the three types of equations: 1) Newtonian fluid with high viscosity, 2) power-law fluid and 3) Bingham fluid. Unsteady turbulent flows down long homogeneous slope are considered. The flow dynamical parameters and entrainment rate behavior in time as well as their dependence on properties of moving and underlying materials are studied numerically. REFERENCES M.E. Eglit and A.E. Yakubenko, 2014. Numerical modeling of slope flows entraining bottom material. Cold Reg. Sci. Technol., 108, 139-148 Margarita E. Eglit and Alexander E. Yakubenko, 2016. The effect of bed material entrainment and non-Newtonian rheology on dynamics of turbulent slope flows. Fluid Dynamics, 51(3) Issler D, M. Pastor Peréz. 2011. Interplay of entrainment and rheology in snow avalanches; a numerical study. Annals of Glaciology, 52(58), 143-147 Lushchik, V.G., Paveliev, A.A. , and Yakubenko, A.E., 1978. Three-parameter model of shear turbulence. Fluid Dynamics, 13, (3), 350-362

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

    ERIC Educational Resources Information Center

    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…

  4. Mathematical model insights into arsenic detoxification

    PubMed Central

    2011-01-01

    Background Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs), which then undergoes hepatic methylation to methylarsonic acid (MMAs) and a second methylation to dimethylarsinic acid (DMAs). Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation. Methods We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects. Results We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic methyltransferase has been

  5. On Mathematical Modeling Of Quantum Systems

    SciTech Connect

    Achuthan, P.; Narayanankutty, Karuppath

    2009-07-02

    The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.

  6. On Mathematical Modeling Of Quantum Systems

    NASA Astrophysics Data System (ADS)

    Achuthan, P.; Narayanankutty, Karuppath

    2009-07-01

    The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.

  7. Mathematical Models of Cardiac Pacemaking Function

    NASA Astrophysics Data System (ADS)

    Li, Pan; Lines, Glenn T.; Maleckar, Mary M.; Tveito, Aslak

    2013-10-01

    Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.

  8. Mathematical Modeling of Electrochemical Flow Capacitors

    SciTech Connect

    Hoyt, NC; Wainright, JS; Savinell, RF

    2015-01-13

    Electrochemical flow capacitors (EFCs) for grid-scale energy storage are a new technology that is beginning to receive interest. Prediction of the expected performance of such systems is important as modeling can be a useful avenue in the search for design improvements. Models based off of circuit analogues exist to predict EFC performance, but these suffer from deficiencies (e.g. a multitude of fitting constants that are required and the ability to analyze only one spatial direction at a time). In this paper mathematical models based off of three-dimensional macroscopic balances (similar to models for porous electrodes) are reported. Unlike existing three-dimensional porous electrode-based approaches for modeling slurry electrodes, advection (i.e., transport associated with bulk fluid motion) of the overpotential is included in order to account for the surface charge at the interface between flowing particles and the electrolyte. Doing so leads to the presence of overpotential boundary layers that control the performance of EFCs. These models were used to predict the charging behavior of an EFC under both flowing and non-flowing conditions. Agreement with experimental data was good, including proper prediction of the steady-state current that is achieved during charging of a flowing EFC. (C) The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives 4.0 License (CC BY-NC-ND, http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is not changed in any way and is properly cited. For permission for commercial reuse, please email: oa@electrochem.org. All rights reserved.

  9. Modelling Mathematical Reasoning in Physics Education

    ERIC Educational Resources Information Center

    Uhden, Olaf; Karam, Ricardo; Pietrocola, Mauricio; Pospiech, Gesche

    2012-01-01

    Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…

  10. Model Learner Outcomes for Mathematics Education.

    ERIC Educational Resources Information Center

    Halvorson, Judith K.; Stenglein, Sharon M.

    Awareness of the need for essential reforms within mathematics education evolved fundamentally as the consequence of several national reports, culminating in the documentation of this need with "Everybody Counts" in January 1989. The publication of "Curriculum and Evaluation Standards for School Mathematics" by the National…

  11. Mathematical Manipulative Models: In Defense of "Beanbag Biology"

    ERIC Educational Resources Information Center

    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…

  12. Mathematical modeling of moving boundary problems in thermal energy storage

    NASA Technical Reports Server (NTRS)

    Solomon, A. D.

    1980-01-01

    The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.

  13. iSTEM: Promoting Fifth Graders' Mathematical Modeling

    ERIC Educational Resources Information Center

    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…

  14. Mathematical Models of the Value of Achievement Testing.

    ERIC Educational Resources Information Center

    Pinsky, Paul D.

    The mathematical models of this paper were developed as an outgrowth of working with the Comprehensive Achievement Monitoring project (Project CAM) which was conceived as a model and application of sampling procedures such as those used in industrial quality control techniques to educational measurement. This paper explores mathematical modeling…

  15. Students' Approaches to Learning a New Mathematical Model

    ERIC Educational Resources Information Center

    Flegg, Jennifer A.; Mallet, Daniel G.; Lupton, Mandy

    2013-01-01

    In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quantitative data based around the students' approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to…

  16. Mathematical Modelling Research in Turkey: A Content Analysis Study

    ERIC Educational Resources Information Center

    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.…

  17. Mathematical modeling of Chikungunya fever control

    NASA Astrophysics Data System (ADS)

    Hincapié-Palacio, Doracelly; Ospina, Juan

    2015-05-01

    Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.

  18. Mathematical model I. Electron and quantum mechanics

    NASA Astrophysics Data System (ADS)

    Gadre, Nitin Ramchandra

    2011-03-01

    The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.

  19. A Mathematical Model of Forgetting and Amnesia

    PubMed Central

    Murre, Jaap M. J.; Chessa, Antonio G.; Meeter, Martijn

    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 strength (2) while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i) the temporal gradient of retrograde amnesia (Ribot’s Law), (ii) forgetting curves with and without anterograde amnesia, and (iii) learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff’s Disease, Alzheimer’s Dementia, Huntington’s Disease, and other disorders. PMID:23450438

  20. The academic merits of modelling in higher mathematics education: A case study

    NASA Astrophysics Data System (ADS)

    Perrenet, Jacob; Adan, Ivo

    2010-09-01

    Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge useful for the problem at hand. A detailed analysis of the academic profile of the curriculum is presented, using a framework of competencies and dimensions, developed at this university by the project, Academic Competencies and Quality Assurance (ACQA). The profile is constructed from the perspective of teachers' ambitions. The research question for the present study is: Are there certain academic characteristics typical for the Modelling Track compared to the characteristics of the other courses in the Eindhoven Bachelor curriculum of Applied Mathematics? The analysis shows that the modelling projects are essential for the development of the designing competencies in the curriculum. Other courses in the curriculum are more intended to develop abstraction capabilities. These results provide supporting arguments for the realistic approach chosen for mathematical modelling education.

  1. Mathematical Modeling Tools to Study Preharvest Food Safety.

    PubMed

    Lanzas, Cristina; Chen, Shi

    2016-08-01

    This article provides an overview of the emerging field of mathematical modeling in preharvest food safety. We describe the steps involved in developing mathematical models, different types of models, and their multiple applications. The introduction to modeling is followed by several sections that introduce the most common modeling approaches used in preharvest systems. We finish the chapter by outlining potential future directions for the field.

  2. Mathematical models in biology: from molecules to life.

    PubMed

    Kaznessis, Yiannis N

    2011-01-01

    A vexing question in the biological sciences is the following: can biological phenotypes be explained with mathematical models of molecules that interact according to physical laws? At the crux of the matter lies the doubt that humans can develop physically faithful mathematical representations of living organisms. We discuss advantages that synthetic biological systems confer that may help us describe life's distinctiveness with tractable mathematics that are grounded on universal laws of thermodynamics and molecular biology.

  3. Mathematical models in biology: from molecules to life

    PubMed Central

    Kaznessis, Yiannis N.

    2011-01-01

    A vexing question in the biological sciences is the following: can biological phenotypes be explained with mathematical models of molecules that interact according to physical laws? At the crux of the matter lies the doubt that humans can develop physically faithful mathematical representations of living organisms. We discuss advantages that synthetic biological systems confer that may help us describe life’s distinctiveness with tractable mathematics that are grounded on universal laws of thermodynamics and molecular biology. PMID:21472998

  4. Modeling aspects of estuarine eutrophication. (Latest citations from the Selected Water Resources Abstracts database). Published Search

    SciTech Connect

    Not Available

    1993-05-01

    The bibliography contains citations concerning mathematical modeling of existing water quality stresses in estuaries, harbors, bays, and coves. Both physical hydraulic and numerical models for estuarine circulation are discussed. (Contains a minimum of 96 citations and includes a subject term index and title list.)

  5. Fractured rock hydrogeology: Modeling studies. (Latest citations from the Selected Water Resources Abstracts database). Published Search

    SciTech Connect

    Not Available

    1993-07-01

    The bibliography contains citations concerning the use of mathematical and conceptual models in describing the hydraulic parameters of fluid flow in fractured rock. Topics include the use of tracers, solute and mass transport studies, and slug test analyses. The use of modeling techniques in injection well performance prediction is also discussed. (Contains 250 citations and includes a subject term index and title list.)

  6. The roughness surface expressed by the mathematical model

    NASA Astrophysics Data System (ADS)

    Macurova, Anna

    2010-07-01

    The work investigates the effect of some characteristics of a cut surface and studies roughness of the cutting process. There is elaborated theoretical information and new aspects on calculation of the theoretical values of the roughness of the cut surface for the chosen materials are formulated. In the area of the experimental investigation, results on characteristics of the chosen materials are formulated in this work. Obtained results are fundamental for the mathematical modulation and mathematical analysis for the investigated dependencies for the cut surfaces. The mathematical model also represents the specific dependencies of the technological process. The characteristics of the observed parameters are approximated by characteristics of the quasi-linear models. The solution of this model offers acceptable results. The mathematical models of the roughness of the cut surface are a mathematical description of the dependency of the maximum roughness of the cut surface of the feed represented by the differential equation and by the integral curves.

  7. A Mathematical Model for Suppression Subtractive Hybridization

    PubMed Central

    Gadgil, Chetan; Rink, Anette; Beattie, Craig

    2002-01-01

    Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assessing the effect of various parameters to facilitate its optimization. We derive an equation for the probability that a particular differentially expressed species is successfully isolated and use this to quantify the effect of the following parameters related to the cDNA sample: (a) mRNA abundance; (b) partial sequence complementarity to other species; and (3) degree of differential expression. We also evaluate the effect of parameters related to the process, including: (a) reaction times; and (b) extent of driver excess used in the two hybridization reactions. The optimum set of process parameters for successful isolation of differentially expressed species depends on transcript abundance. We show that the reaction conditions have a significant effect on the occurrence of false-positives and formulate strategies to isolate specific subsets of differentially expressed genes. We also quantify the effect of non-specific hybridization on the false-positive results and present strategies for spiking cDNA sequences to address this problem. PMID:18629052

  8. Mathematical modelling for nanotube bundle oscillators

    NASA Astrophysics Data System (ADS)

    Thamwattana, Ngamta; Cox, Barry J.; Hill, James M.

    2009-07-01

    This paper investigates the mechanics of a gigahertz oscillator comprising a nanotube oscillating within the centre of a uniform concentric ring or bundle of nanotubes. The study is also extended to the oscillation of a fullerene inside a nanotube bundle. In particular, certain fullerene-nanotube bundle oscillators are studied, namely C60-carbon nanotube bundle, C60-boron nitride nanotube bundle, B36N36-carbon nanotube bundle and B36N36-boron nitride nanotube bundle. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the fullerene and the nanotube bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques which provides considerable insight into the underlying mechanisms. The paper presents a synopsis of the major results derived in detail by the present authors in [1, 2].

  9. Language and modeling word problems in mathematics among bilinguals.

    PubMed

    Bernardo, Allan B I

    2005-09-01

    The study was conducted to determine whether the language of math word problems would affect how Filipino-English bilingual problem solvers would model the structure of these word problems. Modeling the problem structure was studied using the problem-completion paradigm, which involves presenting problems without the question. The paradigm assumes that problem solvers can infer the appropriate question of a word problem if they correctly grasp its problem structure. Arithmetic word problems in Filipino and English were given to bilingual students, some of whom had Filipino as a first language and others who had English as a first language. The problem-completion data and solution data showed similar results. The language of the problem had no effect on problem-structure modeling. The results were discussed in relation to a more circumscribed view about the role of language in word problem solving among bilinguals. In particular, the results of the present study showed that linguistic factors do not affect the more mathematically abstract components of word problem solving, although they may affect the other components such as those related to reading comprehension and understanding.

  10. Helping Students Become Better Mathematical Modelers: Pseudosteady-State Approximations.

    ERIC Educational Resources Information Center

    Bunge, Annette L.; Miller, Ronald L.

    1997-01-01

    Undergraduate and graduate students are often confused about several aspects of modeling physical systems. Describes an approach to address these issues using a single physical transport problem that can be analyzed with multiple mathematical models. (DKM)

  11. A Cognitive Model of College Mathematics Placement

    DTIC Science & Technology

    1989-08-01

    Programs 17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number) FIELD GROUP SUB-GROUP 19. ABSTRACT (Continue on...reverse if necessary and identify by block number) 20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION r[UNCLASSIFIED...represent It Internally, (b) an internal representation of the goal state, (c) a comparator to compare the present state to the goal state, and (d) a plan of

  12. Typhoid transmission: a historical perspective on mathematical model development.

    PubMed

    Bakach, Iurii; Just, Matthew R; Gambhir, Manoj; Fung, Isaac Chun-Hai

    2015-11-01

    Mathematical models of typhoid transmission were first developed nearly half a century ago. To facilitate a better understanding of the historical development of this field, we reviewed mathematical models of typhoid and summarized their structures and limitations. Eleven models, published in 1971 to 2014, were reviewed. While models of typhoid vaccination are well developed, we highlight the need to better incorporate water, sanitation and hygiene interventions into models of typhoid and other foodborne and waterborne diseases. Mathematical modeling is a powerful tool to test and compare different intervention strategies which is important in the world of limited resources. By working collaboratively, epidemiologists and mathematicians should build better mathematical models of typhoid transmission, including pharmaceutical and non-pharmaceutical interventions, which will be useful in epidemiological and public health practice.

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

    PubMed

    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.

  14. Mathematical Modeling, Sense Making, and the Common Core State Standards

    ERIC Educational Resources Information Center

    Schoenfeld, Alan H.

    2013-01-01

    On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…

  15. Teaching Writing and Communication in a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Linhart, Jean Marie

    2014-01-01

    Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

  16. The Berlin-White Integrated Science and Mathematics Model.

    ERIC Educational Resources Information Center

    Berlin, Donna F.; White, Arthur L.

    1994-01-01

    Discusses six aspects of the Berlin-White Integrated Science and Mathematics Model developed to address the need for a definition of the integration of science and mathematics education. These aspects are ways of learning; ways of knowing; process and thinking skills; content knowledge; attitudes and perceptions; and teaching strategies. (MKR)

  17. Mathematics in the Biology Classroom: A Model of Interdisciplinary Education

    ERIC Educational Resources Information Center

    Hodgson, Ted; Keck, Robert; Patterson, Richard; Maki, Dan

    2005-01-01

    This article describes an interdisciplinary course that develops essential mathematical modeling skills within an introductory biology setting. The course embodies recent recommendations regarding the need for interdisciplinary, inquiry-based mathematical preparation of undergraduates in the biological sciences. Evaluation indicates that the…

  18. Mathematical Manipulative Models: In Defense of “Beanbag Biology”

    PubMed Central

    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. PMID:20810952

  19. Using Spreadsheets to Teach Aspects of Biology Involving Mathematical Models

    ERIC Educational Resources Information Center

    Carlton, Kevin; Nicholls, Mike; Ponsonby, David

    2004-01-01

    Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…

  20. Modelling Reality in Mathematics Classrooms: The Case of Word Problems.

    ERIC Educational Resources Information Center

    Greer, Brian

    1997-01-01

    Word problems as used within the culture of mathematics education often promote a suspension of sense making by the students. In the papers in this issue, an alternative conceptualization of word problems is proposed that calls for mathematical modelling that takes real world knowledge into account. (SLD)

  1. An Assessment Model for Proof Comprehension in Undergraduate Mathematics

    ERIC Educational Resources Information Center

    Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron

    2012-01-01

    Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

  2. Problems of Abstraction: Defining an American Standard for Mathematics Education at the Turn of the Twentieth Century

    NASA Astrophysics Data System (ADS)

    Fiss, Andrew

    2012-08-01

    Throughout the nineteenth century, the sciences in the United States went through many professional and disciplinary shifts. While the impact of these changes on university education has been well established, their consequences at the level of high school education have been often overlooked. In mathematics, debates at the level of university officials found clear outlets in the reform movement concerning secondary school offerings and college entrance requirements. This article therefore focuses on these debates and also the attempts to achieve compromises through standardized curricula in the recommendations of the Committee of Ten. In discussing the interplay between university and secondary education, it exposes a feature of the history of science education that has been neglected.

  3. Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

    ERIC Educational Resources Information Center

    Wright, Vince

    2014-01-01

    Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

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

    PubMed

    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.

  5. Mathematical Modeling and Simulation of Seated Stability

    PubMed Central

    Tanaka, Martin L.; Ross, Shane D.; Nussbaum, Maury A.

    2009-01-01

    Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications. PMID:20018288

  6. Mathematical models and their applications in medicine and health.

    PubMed

    Verma, B l; Ray, S K; Srivastava, R N

    1981-01-01

    Mathematical models have great potentialities as regards their utility in different disciplines of medicine and health. This paper attempts to elucidate their uses in the field. A brief mention of some models has also been made. Mathematical models are useful in epidemiologic research, planning and evaluation of preventive and control programmes, clinical trials, measurement of health, cost-benefit analysis, diagnosis of patients and in maximizing effectiveness of operations aimed at attaining specified goals within existing resources.

  7. Adding Abstraction and Reuse to a Network Modelling Tool Using the Reuseware Composition Framework

    NASA Astrophysics Data System (ADS)

    Johannes, Jendrik; Fernández, Miguel A.

    Domain-specific modelling (DSM) environments enable experts in a certain domain to actively participate in model-driven development. Developing DSM environments need to be cost-efficient, since they are only used by a limited group of domain experts. Different model-driven technologies promise to allow this cost-efficient development. [1] presented experiences in developing a DSM environment for telecommunication network modelling. There, challenges were identified that need to be addressed by other new modelling technologies. In this paper, we now present the results of addressing one of theses challenges - abstraction and reuse support - with the Reuseware Composition Framework. We show how we identified the abstraction and reuse features required in the telecommunication DSM environment in a case study and extended the existing environment with these features using Reuseware. We discuss the advantages of using this technology and propose a process for further improving the abstraction and reuse capabilities of the DSM environment in the future.

  8. PREFACE: Physics-Based Mathematical Models for Nanotechnology

    NASA Astrophysics Data System (ADS)

    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

  9. Mathematical modelling of the MAP kinase pathway using proteomic datasets.

    PubMed

    Tian, Tianhai; Song, Jiangning

    2012-01-01

    The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.

  10. a Discrete Mathematical Model to Simulate Malware Spreading

    NASA Astrophysics Data System (ADS)

    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.

  11. Mathematics of tsunami: modelling and identification

    NASA Astrophysics Data System (ADS)

    Krivorotko, Olga; Kabanikhin, Sergey

    2015-04-01

    Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of

  12. Adequate mathematical modelling of environmental processes

    NASA Astrophysics Data System (ADS)

    Chashechkin, Yu. D.

    2012-04-01

    In environmental observations and laboratory visualization both large scale flow components like currents, jets, vortices, waves and a fine structure are registered (different examples are given). The conventional mathematical modeling both analytical and numerical is directed mostly on description of energetically important flow components. The role of a fine structures is still remains obscured. A variety of existing models makes it difficult to choose the most adequate and to estimate mutual assessment of their degree of correspondence. The goal of the talk is to give scrutiny analysis of kinematics and dynamics of flows. A difference between the concept of "motion" as transformation of vector space into itself with a distance conservation and the concept of "flow" as displacement and rotation of deformable "fluid particles" is underlined. Basic physical quantities of the flow that are density, momentum, energy (entropy) and admixture concentration are selected as physical parameters defined by the fundamental set which includes differential D'Alembert, Navier-Stokes, Fourier's and/or Fick's equations and closing equation of state. All of them are observable and independent. Calculations of continuous Lie groups shown that only the fundamental set is characterized by the ten-parametric Galilelian groups reflecting based principles of mechanics. Presented analysis demonstrates that conventionally used approximations dramatically change the symmetries of the governing equations sets which leads to their incompatibility or even degeneration. The fundamental set is analyzed taking into account condition of compatibility. A high order of the set indicated on complex structure of complete solutions corresponding to physical structure of real flows. Analytical solutions of a number problems including flows induced by diffusion on topography, generation of the periodic internal waves a compact sources in week-dissipative media as well as numerical solutions of the same

  13. Abstraction and Consolidation

    ERIC Educational Resources Information Center

    Monaghan, John; Ozmantar, Mehmet Fatih

    2006-01-01

    The framework for this paper is a recently developed theory of abstraction in context. The paper reports on data collected from one student working on tasks concerned with absolute value functions. It examines the relationship between mathematical constructions and abstractions. It argues that an abstraction is a consolidated construction that can…

  14. Modeling Students' Interest in Mathematics Homework

    ERIC Educational Resources Information Center

    Xu, Jianzhong; Yuan, Ruiping; Xu, Brian; Xu, Melinda

    2016-01-01

    The authors examine the factors influencing mathematics homework interest for Chinese students and compare the findings with a recent study involving U.S. students. The findings from multilevel analyses revealed that some predictors for homework interest functioned similarly (e.g., affective attitude toward homework, learning-oriented reasons,…

  15. Key Concept Mathematics and Management Science Models

    ERIC Educational Resources Information Center

    Macbeth, Thomas G.; Dery, George C.

    1973-01-01

    The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)

  16. Making Insulation Decisions through Mathematical Modeling

    ERIC Educational Resources Information Center

    Yanik, H. Bahadir; Memis, Yasin

    2014-01-01

    Engaging students in studies about conservation and sustainability can support their understanding of making environmental conscious decisions to conserve Earth. This article aims to contribute these efforts and direct students' attention to how they can use mathematics to make environmental decisions. Contributors to iSTEM: Integrating…

  17. MAPCLUS: A Mathematical Programming Approach to Fitting the ADCLUS Model.

    ERIC Educational Resources Information Center

    Arabie, Phipps

    1980-01-01

    A new computing algorithm, MAPCLUS (Mathematical Programming Clustering), for fitting the Shephard-Arabie ADCLUS (Additive Clustering) model is presented. Details and benefits of the algorithm are discussed. (Author/JKS)

  18. The Mathematical Concept of Set and the 'Collection' Model.

    ERIC Educational Resources Information Center

    Fischbein, Efraim; Baltsan, Madlen

    1999-01-01

    Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)

  19. Mechanical-mathematical modeling for landslide process

    NASA Astrophysics Data System (ADS)

    Svalova, V.

    2009-04-01

    500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.

  20. Some Aspects of Mathematical Model of Collaborative Learning

    ERIC Educational Resources Information Center

    Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu

    2012-01-01

    There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…

  1. Academic Libraries as a Context for Teaching Mathematical Modeling

    ERIC Educational Resources Information Center

    Warwick, Jon

    2008-01-01

    The teaching of mathematical modeling to undergraduate students requires that students are given ample opportunity to develop their own models and experience first-hand the process of model building. Finding an appropriate context within which modeling can be undertaken is not a simple task as it needs to be readily understandable and seen as…

  2. Modelling, abstraction, and computation in systems biology: A view from computer science.

    PubMed

    Melham, Tom

    2013-04-01

    Systems biology is centrally engaged with computational modelling across multiple scales and at many levels of abstraction. Formal modelling, precise and formalised abstraction relationships, and computation also lie at the heart of computer science--and over the past decade a growing number of computer scientists have been bringing their discipline's core intellectual and computational tools to bear on biology in fascinating new ways. This paper explores some of the apparent points of contact between the two fields, in the context of a multi-disciplinary discussion on conceptual foundations of systems biology.

  3. Mathematical modelling for the new millenium: medicine by numbers.

    PubMed

    Smye, Stephen W; Clayton, Richard H

    2002-11-01

    Physicists, engineers and mathematicians are accustomed to the combination of elegance, rigour and utility that characterise mathematical models. They are familiar with the need to dip into their mathematical toolbox to select the technique of choice. However, medicine and biology have not been characterised, in general, by a mathematical formalism. The relative paucity of mathematical models in biology and medicine reflects in part the difficulty in making accurate and appropriate experimental measurements in the field. Signal noise, the lack of appropriate sensors, and uncertainty as to what constitutes the significant measurements are largely to blame for this. The purpose of this paper is to characterise a 'good' model, encourage the development and application of such models to new areas, and outline future developments in the field. It is proposed that a good model will be accurate, predictive, economical, unique and elegant. These principles will be illustrated with reference to four models: radiosensitisation of tumours, modelling solute clearance in haemodialysis, the myogenic response in reactive hyperaemia and cardiac electrical activity. It is suggested that, in the immediate future, the mathematical model will become a useful adjunct to laboratory experiment (and possibly clinical trial), and the provision of 'in silico' models will become routine.

  4. Hydrogen-atom abstraction from a model amino acid: dependence on the attacking radical.

    PubMed

    Amos, Ruth I J; Chan, Bun; Easton, Christopher J; Radom, Leo

    2015-01-22

    We have used computational chemistry to examine the reactivity of a model amino acid toward hydrogen abstraction by HO•, HOO•, and Br•. The trends in the calculated condensed-phase (acetic acid) free energy barriers are in accord with experimental relative reactivities. Our calculations suggest that HO• is likely to be the abstracting species for reactions with hydrogen peroxide. For HO• abstractions, the barriers decrease as the site of reaction becomes more remote from the electron-withdrawing α-substituents, in accord with a diminishing polar deactivating effect. We find that the transition structures for α- and β-abstractions have additional hydrogen-bonding interactions, which lead to lower gas-phase vibrationless electronic barriers at these positions. Such favorable interactions become less important in a polar solvent such as acetic acid, and this leads to larger calculated barriers when the effect of solvation is taken into account. For Br• abstractions, the α-barrier is the smallest while the β-barrier is the largest, with the barrier gradually becoming smaller further along the side chain. We attribute the low barrier for the α-abstraction in this case to the partial reflection of the thermodynamic effect of the captodatively stabilized α-radical product in the more product-like transition structure, while the trend of decreasing barriers in the order β > γ > δ ∼ ε is explained by the diminishing polar deactivating effect. More generally, the favorable influence of thermodynamic effects on the α-abstraction barrier is found to be smaller when the transition structure for hydrogen abstraction is earlier.

  5. Mathematical Modeling Is Also Physics--Interdisciplinary Teaching between Mathematics and Physics in Danish Upper Secondary Education

    ERIC Educational Resources Information Center

    Michelsen, Claus

    2015-01-01

    Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

  6. Evaluation of limb load asymmetry using two new mathematical models.

    PubMed

    Kumar, Senthil N S; Omar, Baharudin; Joseph, Leonard H; Htwe, Ohnmar; Jagannathan, K; Hamdan, Nor M Y; Rajalakshmi, D

    2014-09-25

    Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns.

  7. [Mathematical approach to modeling of the treatment of suppurative processes].

    PubMed

    Men'shikov, D D; Enileev, R Kh

    1989-03-01

    Consideration of an inflammation focus as an "open system" provided analogy between microbiological processes in inflamed wounds and in systems of continuous cultivation of microorganisms. Mathematical modeling of such systems is widely used. Some of the methods for the mathematical modeling were applied to chemoprophylaxis and chemotherapy of postoperative wounds. In modeling continuous cultivation of microorganisms it is usually necessary to determine optimal conditions for the maximum yield of their biomass. In modeling of wound treatment the aim was to determine the process parameters providing the minimum biomass. The described simple models showed that there could be certain optimal flow rate of the washing fluid in the aspiration-washing procedure for wound treatment at which the drug was not completely washed out while the growth rate of the microbial population was minimal. Such mathematical models were shown valuable in optimizing the use of bactericidal and bacteriostatic antibiotics.

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

    NASA Astrophysics Data System (ADS)

    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.

  9. Geochemistry Model Abstraction and Sensitivity Studies for the 21 PWR CSNF Waste Package

    SciTech Connect

    P. Bernot; S. LeStrange; E. Thomas; K. Zarrabi; S. Arthur

    2002-10-29

    The CSNF geochemistry model abstraction, as directed by the TWP (BSC 2002b), was developed to provide regression analysis of EQ6 cases to obtain abstracted values of pH (and in some cases HCO{sub 3}{sup -} concentration) for use in the Configuration Generator Model. The pH of the system is the controlling factor over U mineralization, CSNF degradation rate, and HCO{sub 3}{sup -} concentration in solution. The abstraction encompasses a large variety of combinations for the degradation rates of materials. The ''base case'' used EQ6 simulations looking at differing steel/alloy corrosion rates, drip rates, and percent fuel exposure. Other values such as the pH/HCO{sub 3}{sup -} dependent fuel corrosion rate and the corrosion rate of A516 were kept constant. Relationships were developed for pH as a function of these differing rates to be used in the calculation of total C and subsequently, the fuel rate. An additional refinement to the abstraction was the addition of abstracted pH values for cases where there was limited O{sub 2} for waste package corrosion and a flushing fluid other than J-13, which has been used in all EQ6 calculation up to this point. These abstractions also used EQ6 simulations with varying combinations of corrosion rates of materials to abstract the pH (and HCO{sub 3}{sup -} in the case of the limiting O{sub 2} cases) as a function of WP materials corrosion rates. The goodness of fit for most of the abstracted values was above an R{sup 2} of 0.9. Those below this value occurred during the time at the very beginning of WP corrosion when large variations in the system pH are observed. However, the significance of F-statistic for all the abstractions showed that the variable relationships are significant. For the abstraction, an analysis of the minerals that may form the ''sludge'' in the waste package was also presented. This analysis indicates that a number a different iron and aluminum minerals may form in the waste package other than those

  10. Technical Work Plan for: Near Field Environment: Engineered System: Radionuclide Transport Abstraction Model Report

    SciTech Connect

    J.D. Schreiber

    2006-12-08

    This technical work plan (TWP) describes work activities to be performed by the Near-Field Environment Team. The objective of the work scope covered by this TWP is to generate Revision 03 of EBS Radionuclide Transport Abstraction, referred to herein as the radionuclide transport abstraction (RTA) report. The RTA report is being revised primarily to address condition reports (CRs), to address issues identified by the Independent Validation Review Team (IVRT), to address the potential impact of transport, aging, and disposal (TAD) canister design on transport models, and to ensure integration with other models that are closely associated with the RTA report and being developed or revised in other analysis/model reports in response to IVRT comments. The RTA report will be developed in accordance with the most current version of LP-SIII.10Q-BSC and will reflect current administrative procedures (LP-3.15Q-BSC, ''Managing Technical Product Inputs''; LP-SIII.2Q-BSC, ''Qualification of Unqualified Data''; etc.), and will develop related Document Input Reference System (DIRS) reports and data qualifications as applicable in accordance with prevailing procedures. The RTA report consists of three models: the engineered barrier system (EBS) flow model, the EBS transport model, and the EBS-unsaturated zone (UZ) interface model. The flux-splitting submodel in the EBS flow model will change, so the EBS flow model will be validated again. The EBS transport model and validation of the model will be substantially revised in Revision 03 of the RTA report, which is the main subject of this TWP. The EBS-UZ interface model may be changed in Revision 03 of the RTA report due to changes in the conceptualization of the UZ transport abstraction model (a particle tracker transport model based on the discrete fracture transfer function will be used instead of the dual-continuum transport model previously used). Validation of the EBS-UZ interface model will be revised to be consistent with

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

    PubMed

    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?"

  12. Mathematical modeling of physiological systems: An essential tool for discovery

    PubMed Central

    Glynn, Patric; Unudurthi, Sathya D.; Hund, Thomas J.

    2014-01-01

    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?” PMID:25064823

  13. Mathematical Models for Manpower and Personnel Planning, Research Report.

    ERIC Educational Resources Information Center

    Charnes, A.; And Others

    Current work in mathematical modeling for manpower planning and personnel administration is reviewed with special reference to selected cases in the U.S. Navy. This included: (1) assignment models and their dynamic extensions, (2) Stochastic models with special reference to Markoff Processes, including the Office of Civilian Manpower and…

  14. A Mathematical Model for the Middle Ear Ventilation

    NASA Astrophysics Data System (ADS)

    Molnárka, G.; Miletics, E. M.; Fücsek, M.

    2008-09-01

    The otitis media is one of the mostly existing illness for the children, therefore investigation of the human middle ear ventilation is an actual problem. In earlier investigations both experimental and theoretical approach one can find in ([l]-[3]). Here we give a new mathematical and computer model to simulate this ventilation process. This model able to describe the diffusion and flow processes simultaneously, therefore it gives more precise results than earlier models did. The article contains the mathematical model and some results of the simulation.

  15. Validation and upgrading of physically based mathematical models

    NASA Technical Reports Server (NTRS)

    Duval, Ronald

    1992-01-01

    The validation of the results of physically-based mathematical models against experimental results was discussed. Systematic techniques are used for: (1) isolating subsets of the simulator mathematical model and comparing the response of each subset to its experimental response for the same input conditions; (2) evaluating the response error to determine whether it is the result of incorrect parameter values, incorrect structure of the model subset, or unmodeled external effects of cross coupling; and (3) modifying and upgrading the model and its parameter values to determine the most physically appropriate combination of changes.

  16. Modelling fate and transport of pesticides in river catchments with drinking water abstractions

    NASA Astrophysics Data System (ADS)

    Desmet, Nele; Seuntjens, Piet; Touchant, Kaatje

    2010-05-01

    When drinking water is abstracted from surface water, the presence of pesticides may have a large impact on the purification costs. In order to respect imposed thresholds at points of drinking water abstraction in a river catchment, sustainable pesticide management strategies might be required in certain areas. To improve management strategies, a sound understanding of the emission routes, the transport, the environmental fate and the sources of pesticides is needed. However, pesticide monitoring data on which measures are founded, are generally scarce. Data scarcity hampers the interpretation and the decision making. In such a case, a modelling approach can be very useful as a tool to obtain complementary information. Modelling allows to take into account temporal and spatial variability in both discharges and concentrations. In the Netherlands, the Meuse river is used for drinking water abstraction and the government imposes the European drinking water standard for individual pesticides (0.1 ?g.L-1) for surface waters at points of drinking water abstraction. The reported glyphosate concentrations in the Meuse river frequently exceed the standard and this enhances the request for targeted measures. In this study, a model for the Meuse river was developed to estimate the contribution of influxes at the Dutch-Belgian border on the concentration levels detected at the drinking water intake 250 km downstream and to assess the contribution of the tributaries to the glyphosate loads. The effects of glyphosate decay on environmental fate were considered as well. Our results show that the application of a river model allows to asses fate and transport of pesticides in a catchment in spite of monitoring data scarcity. Furthermore, the model provides insight in the contribution of different sub basins to the pollution level. The modelling results indicate that the effect of local measures to reduce pesticides concentrations in the river at points of drinking water

  17. Mathematical modeling in metal metabolism: overview and perspectives.

    PubMed

    Curis, Emmanuel; Nicolis, Ioannis; Bensaci, Jalil; Deschamps, Patrick; Bénazeth, Simone

    2009-10-01

    A review of mathematical modeling in metal metabolism is presented. Both endogenous and exogenous metals are considered. Four classes of methods are considered: Petri nets, multi-agent systems, determinist models based on differential equations and stochastic models. For each, a basic theoretical background is given, then examples of applications are given, detailed and commented. Advantages and disadvantages of each class of model are presented. A special attention is given to determinist differential equation models, since almost all models belong to this class.

  18. A mathematical model for evolution and SETI.

    PubMed

    Maccone, Claudio

    2011-12-01

    Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.

  19. Model-based object classification using unification grammars and abstract representations

    NASA Astrophysics Data System (ADS)

    Liburdy, Kathleen A.; Schalkoff, Robert J.

    1993-04-01

    The design and implementation of a high level computer vision system which performs object classification is described. General object labelling and functional analysis require models of classes which display a wide range of geometric variations. A large representational gap exists between abstract criteria such as `graspable' and current geometric image descriptions. The vision system developed and described in this work addresses this problem and implements solutions based on a fusion of semantics, unification, and formal language theory. Object models are represented using unification grammars, which provide a framework for the integration of structure and semantics. A methodology for the derivation of symbolic image descriptions capable of interacting with the grammar-based models is described and implemented. A unification-based parser developed for this system achieves object classification by determining if the symbolic image description can be unified with the abstract criteria of an object model. Future research directions are indicated.

  20. Mathematical models to characterize early epidemic growth: A review

    NASA Astrophysics Data System (ADS)

    Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

    2016-09-01

    There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

  1. The Concept of Model. What is Remarkable in Mathematical Models

    NASA Astrophysics Data System (ADS)

    Bezruchko, Boris P.; Smirnov, Dmitry A.

    Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.

  2. Vehicle Concept Model Abstractions for Integrated Geometric, Inertial, Rigid Body, Powertrain, and FE Analysis

    DTIC Science & Technology

    2011-01-01

    including abstractions specific to 2 The nomenclature “simplified model” has also been...applied to attribute- based FEMs. We avoid this terminology because these models, while small in terms of element count, involve modeling decisions...TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) U.S. Army Research, Development and Engineering Command (RDECOM

  3. Mathematical model of layered metallurgical furnaces and units

    NASA Astrophysics Data System (ADS)

    Shvydkiy, V. S.; Spirin, N. A.; Lavrov, V. V.

    2016-09-01

    The basic approaches to mathematical modeling of the layered steel furnaces and units are considered. It is noted that the particular importance have the knowledge about the mechanisms and physical nature of processes of the charge column movement and the gas flow in the moving layer, as well as regularities of development of heat- and mass-transfer in them. The statement and mathematical description of the problem solution targeting the potential gas flow in the layered unit of an arbitrary profile are presented. On the basis of the proposed mathematical model the software implementation of information-modeling system of BF gas dynamics is carried out. The results of the computer modeling of BF non-isothermal gas dynamics with regard to the cohesion zone, gas dynamics of the combustion zone and calculation of hot-blast stoves are provided

  4. Nonlinear mathematical model for a biaxial MOEMS scanning mirror

    NASA Astrophysics Data System (ADS)

    Ma, Yunfei; Davis, Wyatt O.; Ellis, Matt; Brown, Dean

    2010-02-01

    In this paper, a nonlinear mathematic model for Microvision's MOEMS scanning mirror is presented. The pixel placement accuracy requirement for scanned laser spot displays translates into a roughly 80dB signal to noise ratio, noise being a departure from the ideal trajectory. To provide a tool for understanding subtle nonidealities, a detailed nonlinear mathematical model is derived, using coefficients derived from physics, finite element analysis, and experiments. Twelve degrees of freedom parameterize the motion of a gimbal plate and a suspended micromirror; a thirteenth is the device temperature. Illustrations of the application of the model to capture subtleties about the device dynamics and transfer functions are presented.

  5. Mathematical modeling of renal hemodynamics in physiology and pathophysiology.

    PubMed

    Sgouralis, Ioannis; Layton, Anita T

    2015-06-01

    In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease.

  6. Mathematical Modeling of Primary Wood Processing

    NASA Astrophysics Data System (ADS)

    Szyszka, Barbara; Rozmiarek, Klaudyna

    2008-09-01

    This work presents a way of optimizing wood logs' conversion into semi-products. Calculating algorithms have been used in order to choose the cutting patterns and the number of logs needed to realize an order, including task specification. What makes it possible for the author's computer program TARPAK1 to be written is the visualization of the results, the generation pattern of wood logs' conversion for given entry parameters and prediction of sawn timber manufacture. This program has been created with the intention of being introduced to small and medium sawmills in Poland. The Project has been financed from government resources and written by workers of the Institute of Mathematics (Poznan University of Technology) and the Department of Mechanical Wood Technology (Poznan University of Life Sciences).

  7. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  8. A mathematical model of population dynamics for Batesian mimicry system.

    PubMed

    Seno, Hiromi; Kohno, Takahiro

    2012-01-01

    We analyse a mathematical model of the population dynamics among a mimic, a corresponding model, and their common predator populations. Predator changes its search-and-attack probability by forming and losing its search image. It cannot distinguish the mimic from the model. Once a predator eats a model individual, it comes to omit both the model and the mimic species from its diet menu. If a predator eats a mimic individual, it comes to increase the search-and-attack probability for both model and mimic. The predator may lose the repulsive/attractive search image with a probability per day. By analysing our model, we can derive the mathematical condition for the persistence of model and mimic populations, and then get the result that the condition for the persistence of model population does not depend on the mimic population size, while the condition for the persistence of mimic population does depend the predator's memory of search image.

  9. Identifying crop vulnerability to groundwater abstraction: modelling and expert knowledge in a GIS.

    PubMed

    Procter, Chris; Comber, Lex; Betson, Mark; Buckley, Dennis; Frost, Andy; Lyons, Hester; Riding, Alison; Voyce, Kevin

    2006-11-01

    Water use is expected to increase and climate change scenarios indicate the need for more frequent water abstraction. Abstracting groundwater may have a detrimental effect on soil moisture availability for crop growth and yields. This work presents an elegant and robust method for identifying zones of crop vulnerability to abstraction. Archive groundwater level datasets were used to generate a composite groundwater surface that was subtracted from a digital terrain model. The result was the depth from surface to groundwater and identified areas underlain by shallow groundwater. Knowledge from an expert agronomist was used to define classes of risk in terms of their depth below ground level. Combining information on the permeability of geological drift types further refined the assessment of the risk of crop growth vulnerability. The nature of the mapped output is one that is easy to communicate to the intended farming audience because of the general familiarity of mapped information. Such Geographic Information System (GIS)-based products can play a significant role in the characterisation of catchments under the EU Water Framework Directive especially in the process of public liaison that is fundamental to the setting of priorities for management change. The creation of a baseline allows the impact of future increased water abstraction rates to be modelled and the vulnerability maps are in a format that can be readily understood by the various stakeholders. This methodology can readily be extended to encompass additional data layers and for a range of groundwater vulnerability issues including water resources, ecological impacts, nitrate and phosphorus.

  10. The Mathematics Workshop Model: An Interview with Uri Treisman.

    ERIC Educational Resources Information Center

    Garland, May; Treisman, Uri

    1993-01-01

    Uri Treisman describes the development of his model to help minority students succeed and progress in mathematics, emphasizing group work and integrated instruction and student services. Explains his influences, core ideas informing the workshop model, structural impediments to success in the curriculum, existing programs, and other related…

  11. Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.

    PubMed

    Millat, Thomas; Winzer, Klaus

    2017-03-01

    Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the 'evolution' of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.

  12. Mathematical and computational modeling simulation of solar drying Systems

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Mathematical modeling of solar drying systems has the primary aim of predicting the required drying time for a given commodity, dryer type, and environment. Both fundamental (Fickian diffusion) and semi-empirical drying models have been applied to the solar drying of a variety of agricultural commo...

  13. The Singing Wineglass: An Exercise in Mathematical Modelling

    ERIC Educational Resources Information Center

    Voges, E. L.; Joubert, S. V.

    2008-01-01

    Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

  14. Applicability of mathematical modeling to problems of environmental physiology

    NASA Technical Reports Server (NTRS)

    White, Ronald J.; Lujan, Barbara F.; Leonard, Joel I.; Srinivasan, R. Srini

    1988-01-01

    The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.

  15. Diagnostic Models for Procedural Bugs in Basic Mathematics Skills.

    ERIC Educational Resources Information Center

    Brown, John Seely; Burton, Richard R.

    A new diagnostic modeling system for automatically synthesizing a deep structure model of a student's misconceptions or bugs in his/her basic mathematics skills provides a mechanism for explaining why a student is making a mistake as opposed to simply identifying the mistake. This report consists of four sections. The first provides examples of…

  16. Mathematical model of glucose-insulin homeostasis in healthy rats.

    PubMed

    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.

  17. Mathematical modeling of steel fiber concrete under dynamic impact

    NASA Astrophysics Data System (ADS)

    Belov, N. N.; Yugov, N. T.; Kopanitsa, D. G.; Kopanitsa, G. D.; Yugov, A. A.; Shashkov, V. V.

    2015-01-01

    This paper introduces a continuum mechanics mathematical model that describes the processes of deformation and destruction of steel-fiber-concrete under a shock wave impact. A computer modeling method was applied to study the processes of shock wave impact of a steel cylindrical rod and concrete and steel fiber concrete plates. The impact speeds were within 100-500 m/s.

  18. Mathematical model of an air-filled alpha stirling refrigerator

    NASA Astrophysics Data System (ADS)

    McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

    2013-10-01

    This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

  19. Mathematical modeling of moving contact lines in heat transfer applications

    NASA Astrophysics Data System (ADS)

    Ajaev, Vladimir S.; Klentzman, J.; Sodtke, C.; Stephan, P.

    2007-10-01

    We provide an overview of research on the mathematical modeling of apparent contact lines in non-isothermal systems conducted over the past several decades and report a number of recent developments in the field. The latter involve developing mathematical models of evaporating liquid droplets that account not only for liquid flow and evaporation, but also for unsteady heat conduction in the substrate. The droplet is placed on a flat heated solid substrate and is assumed to be in contact with a saturated vapor. Furthermore, we discuss a careful comparison between mathematical models and experimental work that involves simultaneous measurement of shapes of evaporating droplets and temperature profiles in the solid substrate. The latter is accomplished using thermochromic liquid crystals. Applications to new research areas, such as studies of the effect of evaporation on fingering instabilities in gravity-driven liquid films, are also discussed.

  20. Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration

    ERIC Educational Resources Information Center

    Warwick, Jon

    2015-01-01

    This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…

  1. Mathematical Modelling in the International Baccalaureate, Teacher Beliefs and Technology Usage.

    ERIC Educational Resources Information Center

    Brown, R.

    2002-01-01

    Investigates the introduction of mathematical modeling into the mathematics assessment program of the International Baccalaureate Diploma. Considers structured and open modeling in the pre-university mathematics program. Discusses influences of the use of hand-held technology on mathematical modeling and teacher and assessor beliefs about modeling…

  2. Environmental factors in breast cancer invasion: a mathematical modelling review.

    PubMed

    Simmons, Alex; Burrage, Pamela M; Nicolau, Dan V; Lakhani, Sunil R; Burrage, Kevin

    2017-02-01

    This review presents a brief overview of breast cancer, focussing on its heterogeneity and the role of mathematical modelling and simulation in teasing apart the underlying biophysical processes. Following a brief overview of the main known pathophysiological features of ductal carcinoma, attention is paid to differential equation-based models (both deterministic and stochastic), agent-based modelling, multi-scale modelling, lattice-based models and image-driven modelling. A number of vignettes are presented where these modelling approaches have elucidated novel aspects of breast cancer dynamics, and we conclude by offering some perspectives on the role mathematical modelling can play in understanding breast cancer development, invasion and treatment therapies.

  3. The Mathematical Structure of Error Correction Models.

    DTIC Science & Technology

    1985-05-01

    The error correction model for a vector valued time series has been proposed and applied in the economic literature with the papers by Sargan (1964...the notion of cointegratedness of a vector process and showed the relation between cointegration and error correction models. This paper defines a...general error correction model, that encompasses the usual error correction model as well as the integral correction model by allowing a finite number of

  4. EBS Radionuclide Transport Abstraction

    SciTech Connect

    J. Prouty

    2006-07-14

    The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment (TSPA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers advective transport and diffusive transport

  5. Exploiting mid-range DNA patterns for sequence classification: binary abstraction Markov models

    PubMed Central

    Shepard, Samuel S.; McSweeny, Andrew; Serpen, Gursel; Fedorov, Alexei

    2012-01-01

    Messenger RNA sequences possess specific nucleotide patterns distinguishing them from non-coding genomic sequences. In this study, we explore the utilization of modified Markov models to analyze sequences up to 44 bp, far beyond the 8-bp limit of conventional Markov models, for exon/intron discrimination. In order to analyze nucleotide sequences of this length, their information content is first reduced by conversion into shorter binary patterns via the application of numerous abstraction schemes. After the conversion of genomic sequences to binary strings, homogenous Markov models trained on the binary sequences are used to discriminate between exons and introns. We term this approach the Binary Abstraction Markov Model (BAMM). High-quality abstraction schemes for exon/intron discrimination are selected using optimization algorithms on supercomputers. The best MM classifiers are then combined using support vector machines into a single classifier. With this approach, over 95% classification accuracy is achieved without taking reading frame into account. With further development, the BAMM approach can be applied to sequences lacking the genetic code such as ncRNAs and 5′-untranslated regions. PMID:22344692

  6. A full body mathematical model of an oil palm harvester

    NASA Astrophysics Data System (ADS)

    Tumit, NP; Rambely, A. S.; BMT, Shamsul; Shahriman A., B.; Ng Y., G.; Deros, B. M.; Zailina, H.; Goh Y., M.; Arumugam, Manohar; Ismail I., A.; Abdul Hafiz A., R.

    2015-09-01

    The main purpose of this article is to develop a mathematical model of human body during harvesting via Kane's method. This paper is an extension model of previous biomechanical model representing a harvester movement during harvesting a Fresh Fruit Bunch (FFB) from a palm oil tree. The ten segment model consists of foot, leg, trunk, the head and the arms segment. Finally, the inverse dynamic equations are represented in a matrix form.

  7. Mathematically modelling proportions of Japanese populations by industry

    NASA Astrophysics Data System (ADS)

    Hirata, Yoshito

    2016-10-01

    I propose a mathematical model for temporal changes of proportions for industrial sectors. I prove that the model keeps the proportions for the primary, the secondary, and the tertiary sectors between 0 and 100% and preserves their total as 100%. The model fits the Japanese historical data between 1950 and 2005 for the population proportions by industry very well. The model also predicts that the proportion for the secondary industry becomes negligible and becomes less than 1% at least around 2080.

  8. Modeling eBook acceptance: A study on mathematics teachers

    NASA Astrophysics Data System (ADS)

    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.

  9. Mathematical model in controlling dengue transmission with sterile mosquito strategies

    NASA Astrophysics Data System (ADS)

    Aldila, D.; Nuraini, N.; Soewono, E.

    2015-09-01

    In this article, we propose a mathematical model for controlling dengue disease transmission with sterile mosquito techniques (SIT). Sterile male introduced from lab in to habitat to compete with wild male mosquito for mating with female mosquito. Our aim is to displace gradually the natural mosquito from the habitat. Mathematical model analysis for steady states and the basic reproductive ratio are performed analytically. Numerical simulation are shown in some different scenarios. We find that SIT intervention is potential to controlling dengue spread among humans population

  10. A mathematical look at a physical power prediction model

    SciTech Connect

    Landberg, L.

    1997-12-31

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

  11. Mathematical modelling in the computer-aided process planning

    NASA Astrophysics Data System (ADS)

    Mitin, S.; Bochkarev, P.

    2016-04-01

    This paper presents new approaches to organization of manufacturing preparation and mathematical models related to development of the computer-aided multi product process planning (CAMPP) system. CAMPP system has some peculiarities compared to the existing computer-aided process planning (CAPP) systems: fully formalized developing of the machining operations; a capacity to create and to formalize the interrelationships among design, process planning and process implementation; procedures for consideration of the real manufacturing conditions. The paper describes the structure of the CAMPP system and shows the mathematical models and methods to formalize the design procedures.

  12. Medical record review conduction model for improving interrater reliability of abstracting medical-related information.

    PubMed

    Engel, Lisa; Henderson, Courtney; Fergenbaum, Jennifer; Colantonio, Angela

    2009-09-01

    Medical record review (MRR) is often used in clinical research and evaluation, yet there is limited literature regarding best practices in conducting a MRR, and there are few studies reporting interrater reliability (IRR) from MRR data. The aim of this research was twofold: (a) to develop a MRR abstraction tool and standardize the MRR process and (b) to examine the IRR from MRR data. This study introduces the MRR-Conduction Model, which was used to implement a MRR, and examines the IRR between two abstractors who collected preinjury medical and psychiatric, incident-related medical and postinjury head symptom information from the medical records of 47 neurologically injured workers. Results showed that the percentage agreement was > or =85% and the unweighted kappa statistic was > or =.60 for most variables, indicating substantial IRR. An effective and reliable MRR to abstract medical-related information requires planning and time. The MRR-Conduction Model is proposed to guide the process of creating a MRR.

  13. A salamander's flexible spinal network for locomotion, modeled at two levels of abstraction.

    PubMed

    Knüsel, Jeremie; Bicanski, Andrej; Ryczko, Dimitri; Cabelguen, Jean-Marie; Ijspeert, Auke Jan

    2013-08-01

    Animals have to coordinate a large number of muscles in different ways to efficiently move at various speeds and in different and complex environments. This coordination is in large part based on central pattern generators (CPGs). These neural networks are capable of producing complex rhythmic patterns when activated and modulated by relatively simple control signals. Although the generation of particular gaits by CPGs has been successfully modeled at many levels of abstraction, the principles underlying the generation and selection of a diversity of patterns of coordination in a single neural network are still not well understood. The present work specifically addresses the flexibility of the spinal locomotor networks in salamanders. We compare an abstract oscillator model and a CPG network composed of integrate-and-fire neurons, according to their ability to account for different axial patterns of coordination, and in particular the transition in gait between swimming and stepping modes. The topology of the network is inspired by models of the lamprey CPG, complemented by additions based on experimental data from isolated spinal cords of salamanders. Oscillatory centers of the limbs are included in a way that preserves the flexibility of the axial network. Similarly to the selection of forward and backward swimming in lamprey models via different excitation to the first axial segment, we can account for the modification of the axial coordination pattern between swimming and forward stepping on land in the salamander model, via different uncoupled frequencies in limb versus axial oscillators (for the same level of excitation). These results transfer partially to a more realistic model based on formal spiking neurons, and we discuss the difference between the abstract oscillator model and the model built with formal spiking neurons.

  14. Mathematical modeling and the neuroscience of metaphor

    NASA Astrophysics Data System (ADS)

    Rising, Hawley K., III

    2008-02-01

    We look at a characterization of metaphor from cognitive linguistics, extracting the salient features of metaphorical processing. We examine the neurobiology of dendrites, specifically spike timing-dependent plasticity (STDP), and the modulation of backpropagating action potentials (bAPs), to generate a neuropil-centric model of cortical processing based on signal timing and reverberation between regions. We show how this model supports the basic features of metaphorical processing previously extracted. Finally, we model this system using a combination of euclidean, projective, and hyperbolic geometries, and show how the resulting model accounts for this processing, and relates to other neural network models

  15. A hot-atom reaction kinetic model for H abstraction from solid surfaces

    NASA Astrophysics Data System (ADS)

    Kammler, Th.; Kolovos-Vellianitis, D.; Küppers, J.

    2000-07-01

    Measurements of the abstraction reaction kinetics in the interaction of gaseous H atoms with D adsorbed on metal and semiconductor surfaces, H(g)+D(ad)/S→ products, have shown that the kinetics of the HD products are at variance with the expectations drawn from the operation of Eley-Rideal mechanisms. Furthermore, in addition to HD product molecules, D 2 products were observed which are not expected in an Eley-Rideal scenario. Products and kinetics of abstraction reactions on Ni(100), Pt(111), and Cu(111) surfaces were recently explained by a random-walk model based solely on the operation of hot-atom mechanistic steps. Based on the same reaction scenario, the present work provides numerical solutions of the appropriate kinetic equations in the limit of the steady-state approximation for hot-atom species. It is shown that the HD and D 2 product kinetics derived from global kinetic rate constants are the same as those obtained from local probabilities in the random walk model. The rate constants of the hot-atom kinetics provide a background for the interpretation of measured data, which was missing up to now. Assuming that reconstruction affects the competition between hot-atom sticking and hot-atom reaction, the application of the present model at D abstraction from Cu(100) surfaces reproduces the essential characteristics of the experimentally determined kinetics.

  16. An initial-abstraction, constant-loss model for unit hydrograph modeling for applicable watersheds in Texas

    USGS Publications Warehouse

    Asquith, William H.; Roussel, Meghan C.

    2007-01-01

    Estimation of representative hydrographs from design storms, which are known as design hydrographs, provides for cost-effective, riskmitigated design of drainage structures such as bridges, culverts, roadways, and other infrastructure. During 2001?07, the U.S. Geological Survey (USGS), in cooperation with the Texas Department of Transportation, investigated runoff hydrographs, design storms, unit hydrographs,and watershed-loss models to enhance design hydrograph estimation in Texas. Design hydrographs ideally should mimic the general volume, peak, and shape of observed runoff hydrographs. Design hydrographs commonly are estimated in part by unit hydrographs. A unit hydrograph is defined as the runoff hydrograph that results from a unit pulse of excess rainfall uniformly distributed over the watershed at a constant rate for a specific duration. A time-distributed, watershed-loss model is required for modeling by unit hydrographs. This report develops a specific time-distributed, watershed-loss model known as an initial-abstraction, constant-loss model. For this watershed-loss model, a watershed is conceptualized to have the capacity to store or abstract an absolute depth of rainfall at and near the beginning of a storm. Depths of total rainfall less than this initial abstraction do not produce runoff. The watershed also is conceptualized to have the capacity to remove rainfall at a constant rate (loss) after the initial abstraction is satisfied. Additional rainfall inputs after the initial abstraction is satisfied contribute to runoff if the rainfall rate (intensity) is larger than the constant loss. The initial abstraction, constant-loss model thus is a two-parameter model. The initial-abstraction, constant-loss model is investigated through detailed computational and statistical analysis of observed rainfall and runoff data for 92 USGS streamflow-gaging stations (watersheds) in Texas with contributing drainage areas from 0.26 to 166 square miles. The analysis is

  17. Mathematical modeling of the human knee joint

    SciTech Connect

    Ricafort, Juliet

    1996-05-01

    A model was developed to determine the forces exerted by several flexor and extensor muscles of the human knee under static conditions. The following muscles were studied: the gastrocnemius, biceps femoris, semitendinosus, semimembranosus, and the set of quadricep muscles. The tibia and fibula were each modeled as rigid bodies; muscles were modeled by their functional lines of action in space. Assumptions based on previous data were used to resolve the indeterminacy.

  18. Mathematical modeling of damage in unidirectional composites

    NASA Technical Reports Server (NTRS)

    Goree, J. G.; Dharani, L. R.; Jones, W. F.

    1981-01-01

    A review of some approximate analytical models for damaged, fiber reinforced composite materials is presented. Using the classical shear lag stress displacement assumption, solutions are presented for a unidirectional laminate containing a notch, a rectangular cut-out, and a circular hole. The models account for longitudinal matrix yielding and splitting as well as transverse matrix yielding and fiber breakage. The constraining influence of a cover sheet on the unidirectional laminate is also modeled.

  19. Mathematical modeling of lithium iodine discharge data

    SciTech Connect

    Kim, J.S.; Brennen, K.R.

    1980-01-01

    An improved numerical model has been developed to project the capacities of Li/I/sub 2/ cardiac pacemaker batteries. The model uses accelerated rate discharge data, collected over a two year period, to project the capacities of batteries that will not be depleted in the field for approximately 8 years. Inclusion of new terms to account for self-discharge results in increased accuracy in this new model. Self-discharge is shown to be a small loss in the batteries modeled. 3 refs.

  20. Unlocking the black box: teaching mathematical modeling with popular culture.

    PubMed

    Lofgren, Eric T

    2016-10-01

    Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding.

  1. Mathematical analysis and numerical simulation of a model of morphogenesis.

    PubMed

    Muñoz, Ana I; Tello, José Ignacio

    2011-10-01

    We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters.

  2. A Computational and Mathematical Model for Device Induced Thrombosis

    NASA Astrophysics Data System (ADS)

    Wu, Wei-Tao; Aubry, Nadine; Massoudi, Mehrdad; Antaki, James

    2015-11-01

    Based on the Sorenson's model of thrombus formation, a new mathematical model describing the process of thrombus growth is developed. In this model the blood is treated as a Newtonian fluid, and the transport and reactions of the chemical and biological species are modeled using CRD (convection-reaction-diffusion) equations. A computational fluid dynamic (CFD) solver for the mathematical model is developed using the libraries of OpenFOAM. Applying the CFD solver, several representative benchmark problems are studied: rapid thrombus growth in vivo by injecting Adenosine diphosphate (ADP) using iontophoretic method and thrombus growth in rectangular microchannel with a crevice which usually appears as a joint between components of devices and often becomes nidus of thrombosis. Very good agreements between the numerical and the experimental results validate the model and indicate its potential to study a host of complex and practical problems in the future, such as thrombosis in blood pumps and artificial lungs.

  3. A mathematical prognosis model for pancreatic cancer patients receiving immunotherapy.

    PubMed

    Li, Xuefang; Xu, Jian-Xin

    2016-10-07

    Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon-γ (IFN-γ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013). The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model.

  4. Mathematical Model of Estuarial Sediment Transport.

    DTIC Science & Technology

    1977-10-01

    NUMBERS» Contract No. ^Ar DACW39-75-C-0080 ^^ 9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of Civil Engineering...The original model, SEDIMENT I, was verified by comparison with measurements in a recirculating flume. The modified model, SEDIMENT II, developed for... organic matter from contiguous drainage areas, and waste materials. Clay minerals are hydrated aluminum silicates in a layer lattice crystal

  5. Mathematical Modelling of Laser/Material Interactions.

    DTIC Science & Technology

    1983-11-25

    translated to the model input. Even an experimental mode print can also be digitalised for the model. In trying to describe high order modes matliematically...4. Mazumder J. Steen W.M. "Welding of Ti 6al - 4V by continuous wave CO2 laser". Metal construction Sept. 1980 pp423 - 427. 5. Kogelnik H, Li.T Proc

  6. A mathematical model of intestinal oedema formation.

    PubMed

    Young, Jennifer; Rivière, Béatrice; Cox, Charles S; Uray, Karen

    2014-03-01

    Intestinal oedema is a medical condition referring to the build-up of excess fluid in the interstitial spaces of the intestinal wall tissue. Intestinal oedema is known to produce a decrease in intestinal transit caused by a decrease in smooth muscle contractility, which can lead to numerous medical problems for the patient. Interstitial volume regulation has thus far been modelled with ordinary differential equations, or with a partial differential equation system where volume changes depend only on the current pressure and not on updated tissue stress. In this work, we present a computational, partial differential equation model of intestinal oedema formation that overcomes the limitations of past work to present a comprehensive model of the phenomenon. This model includes mass and momentum balance equations which give a time evolution of the interstitial pressure, intestinal volume changes and stress. The model also accounts for the spatially varying mechanical properties of the intestinal tissue and the inhomogeneous distribution of fluid-leaking capillaries that create oedema. The intestinal wall is modelled as a multi-layered, deforming, poroelastic medium, and the system of equations is solved using a discontinuous Galerkin method. To validate the model, simulation results are compared with results from four experimental scenarios. A sensitivity analysis is also provided. The model is able to capture the final submucosal interstitial pressure and total fluid volume change for all four experimental cases, and provide further insight into the distribution of these quantities across the intestinal wall.

  7. A mathematical model of intestinal oedema formation

    PubMed Central

    Young, Jennifer; Rivière, Béatrice; Cox, Charles S.; Uray, Karen

    2014-01-01

    Intestinal oedema is a medical condition referring to the build-up of excess fluid in the interstitial spaces of the intestinal wall tissue. Intestinal oedema is known to produce a decrease in intestinal transit caused by a decrease in smooth muscle contractility, which can lead to numerous medical problems for the patient. Interstitial volume regulation has thus far been modelled with ordinary differential equations, or with a partial differential equation system where volume changes depend only on the current pressure and not on updated tissue stress. In this work, we present a computational, partial differential equation model of intestinal oedema formation that overcomes the limitations of past work to present a comprehensive model of the phenomenon. This model includes mass and momentum balance equations which give a time evolution of the interstitial pressure, intestinal volume changes and stress. The model also accounts for the spatially varying mechanical properties of the intestinal tissue and the inhomogeneous distribution of fluid-leaking capillaries that create oedema. The intestinal wall is modelled as a multi-layered, deforming, poroelastic medium, and the system of equations is solved using a discontinuous Galerkin method. To validate the model, simulation results are compared with results from four experimental scenarios. A sensitivity analysis is also provided. The model is able to capture the final submucosal interstitial pressure and total fluid volume change for all four experimental cases, and provide further insight into the distribution of these quantities across the intestinal wall. PMID:23036806

  8. Undergraduate Research: Mathematical Modeling of Mortgages

    ERIC Educational Resources Information Center

    Choi, Youngna; Spero, Steven

    2010-01-01

    In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current…

  9. Rotor systems research aircraft simulation mathematical model

    NASA Technical Reports Server (NTRS)

    Houck, J. A.; Moore, F. L.; Howlett, J. J.; Pollock, K. S.; Browne, M. M.

    1977-01-01

    An analytical model developed for evaluating and verifying advanced rotor concepts is discussed. The model was used during in both open loop and real time man-in-the-loop simulation during the rotor systems research aircraft design. Future applications include: pilot training, preflight of test programs, and the evaluation of promising concepts before their implementation on the flight vehicle.

  10. Cancer evolution: mathematical models and computational inference.

    PubMed

    Beerenwinkel, Niko; Schwarz, Roland F; Gerstung, Moritz; Markowetz, Florian

    2015-01-01

    Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy.

  11. Cancer Evolution: Mathematical Models and Computational Inference

    PubMed Central

    Beerenwinkel, Niko; Schwarz, Roland F.; Gerstung, Moritz; Markowetz, Florian

    2015-01-01

    Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy. PMID:25293804

  12. Mathematical Modeling Of Life-Support Systems

    NASA Technical Reports Server (NTRS)

    Seshan, Panchalam K.; Ganapathi, Balasubramanian; Jan, Darrell L.; Ferrall, Joseph F.; Rohatgi, Naresh K.

    1994-01-01

    Generic hierarchical model of life-support system developed to facilitate comparisons of options in design of system. Model represents combinations of interdependent subsystems supporting microbes, plants, fish, and land animals (including humans). Generic model enables rapid configuration of variety of specific life support component models for tradeoff studies culminating in single system design. Enables rapid evaluation of effects of substituting alternate technologies and even entire groups of technologies and subsystems. Used to synthesize and analyze life-support systems ranging from relatively simple, nonregenerative units like aquariums to complex closed-loop systems aboard submarines or spacecraft. Model, called Generic Modular Flow Schematic (GMFS), coded in such chemical-process-simulation languages as Aspen Plus and expressed as three-dimensional spreadsheet.

  13. Program Helps Generate Boundary-Element Mathematical Models

    NASA Technical Reports Server (NTRS)

    Goldberg, R. K.

    1995-01-01

    Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).

  14. A mathematical model of the CH-53 helicopter

    NASA Technical Reports Server (NTRS)

    Sturgeon, W. R.; Phillips, J. D.

    1980-01-01

    A mathematical model suitable for real time simulation of the CH-53 helicopter is presented. This model, which is based on modified nonlinear classical rotor theory and nonlinear fuselage aerodynamics, will be used to support terminal-area guidance and navigation studies on a fixed-base simulator. Validation is achieved by comparing the model response with that of a similar aircraft and by a qualitative comparison of the handling characteristics made by experienced pilots.

  15. A Mathematical Model of the Thermo-Anemometric Flowmeter.

    PubMed

    Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

    2015-09-11

    A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.

  16. The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

    ERIC Educational Resources Information Center

    Mischo, Christoph; Maaß, Katja

    2013-01-01

    This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

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

    ERIC Educational Resources Information Center

    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…

  18. Mathematical model of cancer with competition

    NASA Astrophysics Data System (ADS)

    Chrobak, Joanna M.; Herrero, Henar

    2009-05-01

    In this paper we present a model of tumor based on the use of an autonomous system of ordinary differential equations (ODE). The model assumes that normal cells and cancer cells coexist in an environment as two different species which compete for nutrients and space. The immune system and the tumor cells fight against each other. The analysis of the linear stability of the fixed points of the model yields to two groups of solutions. In the first one, the immune system wins against the tumor cells, so the cancer disappears. In the second one, the cancer grows until some fixed level and then stabilizes.

  19. Models of Intervention in Mathematics: Reweaving the Tapestry

    ERIC Educational Resources Information Center

    Fosnot, Catherine

    2010-01-01

    Explore successful models of intervention. No Child Left Behind has set the high expectation that every child meet grade level expectations. This publication synthesizes the research on intervention programs and best practices related to mathematical instructional pedagogy and differentiation to assist teachers, schools, and school districts in…

  20. A Mathematical Model for HIV Drug-Resistance

    NASA Astrophysics Data System (ADS)

    Faedo, Ivan; Raimundo, Silvia Martorano; Venturino, Ezio

    2010-09-01

    In this paper we present a mathematical model of the transmission of HIV infection here the individuals receive antiretroviral drugs but may not respond to treatment. In such case the latter can be changed to a different therapy, and individuals may or may not respond also to this second set of drugs.

  1. A mathematical model of a large open fire

    NASA Technical Reports Server (NTRS)

    Harsha, P. T.; Bragg, W. N.; Edelman, R. B.

    1981-01-01

    A mathematical model capable of predicting the detailed characteristics of large, liquid fuel, axisymmetric, pool fires is described. The predicted characteristics include spatial distributions of flame gas velocity, soot concentration and chemical specie concentrations including carbon monoxide, carbon dioxide, water, unreacted oxygen, unreacted fuel and nitrogen. Comparisons of the predictions with experimental values are also given.

  2. Engaging Students in Mathematical Modeling through Service-Learning

    ERIC Educational Resources Information Center

    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…

  3. Mathematical modeling of the instability of viscous fluid films

    NASA Astrophysics Data System (ADS)

    Prokudina, L. A.

    2016-08-01

    Nonlinear mathematical model of free surface fluid film is presents. Increment, frequency, phase velocity for thin layers of viscous liquids at low Reynolds numbers are calculated. The instability region is found. Optimal flow regimes of films of water and alcohol, corresponding to the maximum values of increment, are calculated.

  4. Science and Mathematics Together: Implementing a Theoretical Model.

    ERIC Educational Resources Information Center

    Berlin, Donna F.; White, Arthur L.

    2001-01-01

    Describes the Berlin-White Integrated Science and Mathematics Model, which includes six aspects: (1) ways of learning; (2) ways of knowing; (3) content knowledge; (4) process and thinking skills; (5) attitudes and perceptions; and (6) teaching strategies. Presents a classroom example on the topic of natural selection. (Contains 20 references.)…

  5. Mathematical Modelling of Bacterial Quorum Sensing: A Review.

    PubMed

    Pérez-Velázquez, Judith; Gölgeli, Meltem; García-Contreras, Rodolfo

    2016-08-01

    Bacterial quorum sensing (QS) refers to the process of cell-to-cell bacterial communication enabled through the production and sensing of the local concentration of small molecules called autoinducers to regulate the production of gene products (e.g. enzymes or virulence factors). Through autoinducers, bacteria interact with individuals of the same species, other bacterial species, and with their host. Among QS-regulated processes mediated through autoinducers are aggregation, biofilm formation, bioluminescence, and sporulation. Autoinducers are therefore "master" regulators of bacterial lifestyles. For over 10 years, mathematical modelling of QS has sought, in parallel to experimental discoveries, to elucidate the mechanisms regulating this process. In this review, we present the progress in mathematical modelling of QS, highlighting the various theoretical approaches that have been used and discussing some of the insights that have emerged. Modelling of QS has benefited almost from the onset of the involvement of experimentalists, with many of the papers which we review, published in non-mathematical journals. This review therefore attempts to give a broad overview of the topic to the mathematical biology community, as well as the current modelling efforts and future challenges.

  6. Mathematical Model Of Variable-Polarity Plasma Arc Welding

    NASA Technical Reports Server (NTRS)

    Hung, R. J.

    1996-01-01

    Mathematical model of variable-polarity plasma arc (VPPA) welding process developed for use in predicting characteristics of welds and thus serves as guide for selection of process parameters. Parameters include welding electric currents in, and durations of, straight and reverse polarities; rates of flow of plasma and shielding gases; and sizes and relative positions of welding electrode, welding orifice, and workpiece.

  7. Schoolwide Mathematics Achievement within the Gifted Cluster Grouping Model

    ERIC Educational Resources Information Center

    Brulles, Dina; Peters, Scott J.; Saunders, Rachel

    2012-01-01

    An increasing number of schools are implementing gifted cluster grouping models as a cost-effective way to provide gifted services. This study is an example of comparative action research in the form of a quantitative case study that focused on mathematic achievement for nongifted students in a district that incorporated a schoolwide cluster…

  8. Mathematical modeling of the aerodynamic characteristics in flight dynamics

    NASA Technical Reports Server (NTRS)

    Tobak, M.; Chapman, G. T.; Schiff, L. B.

    1984-01-01

    Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.

  9. Some mathematical models of intermolecular autophosphorylation.

    PubMed

    Doherty, Kevin; Meere, Martin; Piiroinen, Petri T

    2015-04-07

    Intermolecular autophosphorylation refers to the process whereby a molecule of an enzyme phosphorylates another molecule of the same enzyme. The enzyme thereby catalyses its own phosphorylation. In the present paper, we develop two generic models of intermolecular autophosphorylation that also include dephosphorylation by a phosphatase of constant concentration. The first of these, a solely time-dependent model, is written as one ordinary differential equation that relies upon mass-action and Michaelis-Menten kinetics. Beginning with the enzyme in its dephosphorylated state, it predicts a lag before the enzyme becomes significantly phosphorylated, for suitable parameter values. It also predicts that there exists a threshold concentration for the phosphorylation of enzyme and that for suitable parameter values, a continuous or discontinuous switch in the phosphorylation of enzyme are possible. The model developed here has the advantage that it is relatively easy to analyse compared with most existing models for autophosphorylation and can qualitatively describe many different systems. We also extend our time-dependent model of autophosphorylation to include a spatial dependence, as well as localised binding reactions. This spatio-temporal model consists of a system of partial differential equations that describe a soluble autophosphorylating enzyme in a spherical geometry. We use the spatio-temporal model to describe the phosphorylation of an enzyme throughout the cell due to an increase in local concentration by binding. Using physically realistic values for model parameters, our results provide a proof-of-concept of the process of activation by local concentration and suggest that, in the presence of a phosphatase, this activation can be irreversible.

  10. Mathematical Modeling of Flow Through Vegetated Regions

    DTIC Science & Technology

    2013-08-01

    including stem population density and flow Reynolds number. These results are compared to well-respected experimental results. We model real- life beds of...We model real- life beds of Spartina alterniflora grass with represen- tative beds of flexible beams and perform similar comparisons. x 13 Table of...and pressure contours ( right ) for instanta- neous snapshots of flows of various Reynolds numbers in 2D porous media domain with circle diameter 0.25 m

  11. Asymptotic properties of mathematical models of excitability.

    PubMed

    Biktasheva, I V; Simitev, R D; Suckley, R; Biktashev, V N

    2006-05-15

    We analyse small parameters in selected models of biological excitability, including Hodgkin-Huxley (Hodgkin & Huxley 1952 J. Physiol.117, 500-544) model of nerve axon, Noble (Noble 1962 J. Physiol.160, 317-352) model of heart Purkinje fibres and Courtemanche et al. (Courtemanche et al. 1998 Am. J. Physiol.275, H301-H321) model of human atrial cells. Some of the small parameters are responsible for differences in the characteristic time-scales of dynamic variables, as in the traditional singular perturbation approaches. Others appear in a way which makes the standard approaches inapplicable. We apply this analysis to study the behaviour of fronts of excitation waves in spatially extended cardiac models. Suppressing the excitability of the tissue leads to a decrease in the propagation speed, but only to a certain limit; further suppression blocks active propagation and leads to a passive diffusive spread of voltage. Such a dissipation may happen if a front propagates into a tissue recovering after a previous wave, e.g. re-entry. A dissipated front does not recover even when the excitability restores. This has no analogy in FitzHugh-Nagumo model and its variants, where fronts can stop and then start again. In two spatial dimensions, dissipation accounts for breakups and self-termination of re-entrant waves in excitable media with Courtemanche et al. kinetics.

  12. Mathematical modeling of polymer electrolyte fuel cells

    NASA Astrophysics Data System (ADS)

    Sousa, Ruy; Gonzalez, Ernesto R.

    Fuel cells with a polymer electrolyte membrane have been receiving more and more attention. Modeling plays an important role in the development of fuel cells. In this paper, the state-of-the-art regarding modeling of fuel cells with a polymer electrolyte membrane is reviewed. Modeling has allowed detailed studies concerning the development of these cells, e.g. in discussing the electrocatalysis of the reactions and the design of water-management schemes to cope with membrane dehydration. Two-dimensional models have been used to represent reality, but three-dimensional models can cope with some important additional aspects. Consideration of two-phase transport in the air cathode of a proton exchange membrane fuel cell seems to be very appropriate. Most fuel cells use hydrogen as a fuel. Besides safety concerns, there are problems associated with production, storage and distribution of this fuel. Methanol, as a liquid fuel, can be the solution to these problems and direct methanol fuel cells (DMFCs) are attractive for several applications. Mass transport is a factor that may limit the performance of the cell. Adsorption steps may be coupled to Tafel kinetics to describe methanol oxidation and methanol crossover must also be taken into account. Extending the two-phase approach to the DMFC modeling is a recent, important point.

  13. Mathematical Model for the Behavior of Wildfires

    NASA Astrophysics Data System (ADS)

    Delbene, Kevin; Drew, Donald

    2009-11-01

    Wildfires have been a long-standing problem in today's society. In this paper, we derive and solve a fluid dynamics model to study a specific type of wildfire, namely, a two dimensional flow around a concentrated line of fire, resulting in a narrow plume of hot gas rising and entraining the surrounding air. The model assumes that the surrounding air is constant density and irrotational, and uses an unsteady plume model to describe the evolution of the mass, momentum and energy inside the plume, with sources derived to model mixing in the style of Morton, Taylor, and Turner (Proc. Roy. Soc. London, A 234, 1-23, 1956). The sources to the dynamical processes in the plume couple to the motion through the surrounding air through a Biot-Savart integral formulation to solve the equations of motion with a line of singularities along the plume. The singularities model a vortex sheet in the same manner as Alben and Shelley (Phys. Rev. Letters, 100, 074301, 2008), except that we include a sink term in the Biot-Savart integral to couple the entrainment. The results show that this model is capable of capturing a complicated interaction of the plume with the surrounding air.

  14. [The discussion of the infiltrative model of mathematical knowledge to genetics teaching].

    PubMed

    Liu, Jun; Luo, Pei-Gao

    2011-11-01

    Genetics, the core course of biological field, is an importance major-basic course in curriculum of many majors related with biology. Due to strong theoretical and practical as well as abstract of genetics, it is too difficult to study on genetics for many students. At the same time, mathematics is one of the basic courses in curriculum of the major related natural science, which has close relationship with the establishment, development and modification of genetics. In this paper, to establish the intrinsic logistic relationship and construct the integral knowledge network and to help students improving the analytic, comprehensive and logistic abilities, we applied some mathematical infiltrative model genetic knowledge in genetics teaching, which could help students more deeply learn and understand genetic knowledge.

  15. Mathematical Existence Results for the Doi-Edwards Polymer Model

    NASA Astrophysics Data System (ADS)

    Chupin, Laurent

    2017-01-01

    In this paper, we present some mathematical results on the Doi-Edwards model describing the dynamics of flexible polymers in melts and concentrated solutions. This model, developed in the late 1970s, has been used and extensively tested in modeling and simulation of polymer flows. From a mathematical point of view, the Doi-Edwards model consists in a strong coupling between the Navier-Stokes equations and a highly nonlinear constitutive law. The aim of this article is to provide a rigorous proof of the well-posedness of the Doi-Edwards model, namely that it has a unique regular solution. We also prove, which is generally much more difficult for flows of viscoelastic type, that the solution is global in time in the two dimensional case, without any restriction on the smallness of the data.

  16. A mathematical model of the dynamics of antitumor laser immunotherapy

    NASA Astrophysics Data System (ADS)

    Dawkins, Bryan A.; Laverty, Sean M.

    2014-02-01

    We use a mathematical model to describe and predict the population dynamics of tumor cells, immune cells, and other immune components in a host undergoing laser immunotherapy treatment against metastatic cancer. We incorporate key elements of the treatment into the model: a function describing the laser-induced primary tumor cell death and parameters capturing the role and strength of the primary immunoadjuvant, glycated chitosan. We focus on identifying conditions that ensure a successful treatment. In particular, we study the patient response (i.e., anti-tumor immune dynamics and treatment outcome) in two different but related mathematical models as we vary quantitative features of the immune system (supply, proliferation, death, and interaction rates). We compare immune dynamics of a `baseline' immune model against an `augmented' model (with additional cell types and antibodies) and in both, we find that using strong immunoadjuvants, like glycated chitosan, that enhance dendritic cell activity yields more promising patient outcomes.

  17. Mathematical model for corundum single crystal growth by Verneuil method

    NASA Astrophysics Data System (ADS)

    Grzymkowski, Radosław; Mochnacki, Bohdan; Suchy, Józef

    1983-05-01

    A mathematical model which is an attempt to describe the complex process of monocrystallization by the Verneuil method is presented. The problem has been solved through the method of finite differences and at the same time making use of a certain modification of the mathematical description of Stefan's problem called the the alternating phase truncation method [9]. The elaborated algorithm and the examples of solutions given at the end of the present study point at the usefulness of the presented method of numerical simulation for modern designing and controlling the processes of crystal production.

  18. Innovative mathematical modeling in environmental remediation.

    PubMed

    Yeh, Gour-Tsyh; Gwo, Jin-Ping; Siegel, Malcolm D; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steve B

    2013-05-01

    There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g., Ni, Cr, Co). The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport

  19. Mathematical modeling to predict residential solid waste generation

    SciTech Connect

    Ojeda Benitez, Sara; Vega, Carolina Armijo de

    2008-07-01

    One of the challenges faced by waste management authorities is determining the amount of waste generated by households in order to establish waste management systems, as well as trying to charge rates compatible with the principle applied worldwide, and design a fair payment system for households according to the amount of residential solid waste (RSW) they generate. The goal of this research work was to establish mathematical models that correlate the generation of RSW per capita to the following variables: education, income per household, and number of residents. This work was based on data from a study on generation, quantification and composition of residential waste in a Mexican city in three stages. In order to define prediction models, five variables were identified and included in the model. For each waste sampling stage a different mathematical model was developed, in order to find the model that showed the best linear relation to predict residential solid waste generation. Later on, models to explore the combination of included variables and select those which showed a higher R{sup 2} were established. The tests applied were normality, multicolinearity and heteroskedasticity. Another model, formulated with four variables, was generated and the Durban-Watson test was applied to it. Finally, a general mathematical model is proposed to predict residential waste generation, which accounts for 51% of the total.

  20. Comprehensive Mathematical Model for Simulating Electroslag Remelting

    NASA Astrophysics Data System (ADS)

    Dong, Yan-Wu; Jiang, Zhou-Hua; Fan, Jin-Xi; Cao, Yu-Long; Hou, Dong; Cao, Hai-Bo

    2016-04-01

    Droplet formation and departure from an electrode tip affect the temperature distribution in liquid slag and a molten steel pool, as well as the removal of nonmetallic inclusions in the electroslag remelting process. In this article, magneto-hydrodynamics modules coupled with a volume of fluid (VOF) model (as described in VOF model theory) for tracking phase distribution have been employed to develop the electrode fusion model and to investigate formation and departure of a droplet from the electrode tip. Subsequently, the remelting rate and molten steel pool have been achieved based on the electrode fusion model. Results indicate that a droplet can increase the flow rate of liquid slag, especially the region of droplet fall through the slag pool; yet it has little impact on the flow distribution. Asymmetric flow can take place in a slag pool due to the action of the droplet. The depth of the molten steel pool increases in the presence of droplets, but the width of the mushy zone decreases. In addition, the shape of the electrode tip is not constant but changes with its fusion. The remelting rate is calculated instead of being imposed in this work. The development of the model supports further understanding of the process and the ability to set the appropriate operating parameters, especially for expensive and easy segregation materials.

  1. [Mathematical models of decision making and learning].

    PubMed

    Ito, Makoto; Doya, Kenji

    2008-07-01

    Computational models of reinforcement learning have recently been applied to analysis of brain imaging and neural recording data to identity neural correlates of specific processes of decision making, such as valuation of action candidates and parameters of value learning. However, for such model-based analysis paradigms, selecting an appropriate model is crucial. In this study we analyze the process of choice learning in rats using stochastic rewards. We show that "Q-learning," which is a standard reinforcement learning algorithm, does not adequately reflect the features of choice behaviors. Thus, we propose a generalized reinforcement learning (GRL) algorithm that incorporates the negative reward effect of reward loss and forgetting of values of actions not chosen. Using the Bayesian estimation method for time-varying parameters, we demonstrated that the GRL algorithm can predict an animal's choice behaviors as efficiently as the best Markov model. The results suggest the usefulness of the GRL for the model-based analysis of neural processes involved in decision making.

  2. Mathematical Model of Porous Medium Dynamics

    NASA Astrophysics Data System (ADS)

    Gerschuk, Peotr; Sapozhnikov, Anatoly

    1999-06-01

    Semiempirical model describing porous material strains under pulse mechanical and thermal loadings is proposed. Porous medium is considered as continuous one but with special form of pressure dependence upon strain. This model takes into account principal features of porous materials behavior which can be observed when the material is strained in dynamic and static experiments ( non-reversibility of large strains, nonconvexity of loading curve). Elastoplastic properties of porous medium, its damages when it is strained and dynamic fracture are also taken into account. Dispersion of unidirectional motion caused by medium heterogeneity (porousness) is taken into acount by introducing the physical viscosity depending upon pores size. It is supposed that at every moment of time pores are in equilibrium with pressure i.e. kinetic of pores collapse is not taken into account. The model is presented by the system of differential equations connecting pressure and energy of porous medium with its strain. These equations close system of equations of motion and continuity which then is integrated numerically. The proposed model has been tested on carbon materials and porous copper . Results of calculation of these materials shock compressing are in satisfactory agreement with experimental data. Results of calculation of thin plate with porous copper layer collision are given as an illustration.

  3. Mathematical models for space shuttle ground systems

    NASA Technical Reports Server (NTRS)

    Tory, E. G.

    1985-01-01

    Math models are a series of algorithms, comprised of algebraic equations and Boolean Logic. At Kennedy Space Center, math models for the Space Shuttle Systems are performed utilizing the Honeywell 66/80 digital computers, Modcomp II/45 Minicomputers and special purpose hardware simulators (MicroComputers). The Shuttle Ground Operations Simulator operating system provides the language formats, subroutines, queueing schemes, execution modes and support software to write, maintain and execute the models. The ground systems presented consist primarily of the Liquid Oxygen and Liquid Hydrogen Cryogenic Propellant Systems, as well as liquid oxygen External Tank Gaseous Oxygen Vent Hood/Arm and the Vehicle Assembly Building (VAB) High Bay Cells. The purpose of math modeling is to simulate the ground hardware systems and to provide an environment for testing in a benign mode. This capability allows the engineers to check out application software for loading and launching the vehicle, and to verify the Checkout, Control, & Monitor Subsystem within the Launch Processing System. It is also used to train operators and to predict system response and status in various configurations (normal operations, emergency and contingent operations), including untried configurations or those too dangerous to try under real conditions, i.e., failure modes.

  4. Modeling Students' Mathematics Using Steffe's Fraction Schemes

    ERIC Educational Resources Information Center

    Norton, Anderson H.; McCloskey, Andrea V.

    2008-01-01

    Each year, more teachers learn about the successful intervention program known as Math Recovery (USMRC 2008; Wright 2003). The program uses Steffe's whole-number schemes to model, understand, and support children's development of whole-number reasoning. Readers are probably less familiar with Steffe's fraction schemes, which have proven similarly…

  5. Using Archeological Data to Model Mathematics

    ERIC Educational Resources Information Center

    Yanik, H. Bahadir; Kurz, Terri L.; Memis, Yasin

    2014-01-01

    The purpose of this investigation is to describe an implementation of a modeling task using mock data from an ancient archeological find. Students discover the relationship between the height of a person and his or her stride length. Qualitative data from student discussions document thinking and reasoning.

  6. Mathematical Modelling of the Infusion Test

    NASA Astrophysics Data System (ADS)

    Cieslicki, Krzysztof

    2007-01-01

    The objective of this paper was to improve the well established in clinical practice Marmarou model for intracranial volume-pressure compensation by adding the pulsatile components. It was demonstrated that complicated pulsation and growth in intracranial pressure during infusion test could be successfully modeled by the relatively simple analytical expression derived in this paper. The CSF dynamics were tested in 25 patients with clinical symptoms of hydrocephalus. Basing on the frequency spectrum of the patient's baseline pressure and identified parameters of CSF dynamic, for each patient an "ideal" infusion test curve free from artefacts and slow waves was simulated. The degree of correlation between simulated and real curves obtained from clinical observations gave insight into the adequacy of assumptions of Marmarou model. The proposed method of infusion tests analysis designates more exactly the value of the reference pressure, which is usually treated as a secondary and of uncertain significance. The properly identified value of the reference pressure decides on the degree of pulsation amplitude growth during IT, as well as on the value of elastance coefficient. The artificially generated tests with various pulsation components were also applied to examine the correctness of the used algorithm of identification of the original Marmarou model parameters.

  7. Mathematical modelling of avascular-tumour growth.

    PubMed

    Ward, J P; King, J R

    1997-03-01

    A system of nonlinear partial differential equations is proposed as a model for the growth of an avascular-tumour spheroid. The model assumes a continuum of cells in two states, living or dead, and, depending on the concentration of a generic nutrient, the live cells may reproduce (expanding the tumour) or die (causing contraction). These volume changes resulting from cell birth and death generate a velocity field within the spheroid. Numerical solutions of the model reveal that after a period of time the variables settle to a constant profile propagating at a fixed speed. The travelling-wave limit is formulated and analytical solutions are found for a particular case. Numerical results for more general parameters compare well with these analytical solutions. Asymptotic techniques are applied to the physically relevant case of a small death rate, revealing two phases of growth retardation from the initial exponential growth, the first of which is due to nutrient-diffusion limitations and the second to contraction during necrosis. In this limit, maximal and "linear' phase growth speeds can be evaluated in terms of the model parameters.

  8. Innovative mathematical modeling in environmental remediation

    SciTech Connect

    Yeh, Gour T.; Gwo, Jin Ping; Siegel, Malcolm D.; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steven B.

    2013-05-01

    There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g.,Ni, Cr, Co).The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport models

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

    PubMed Central

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

    2016-01-01

    Key points 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. Abstract 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

  10. Mathematical modeling of isotope labeling experiments for metabolic flux analysis.

    PubMed

    Nargund, Shilpa; Sriram, Ganesh

    2014-01-01

    Isotope labeling experiments (ILEs) offer a powerful methodology to perform metabolic flux analysis. However, the task of interpreting data from these experiments to evaluate flux values requires significant mathematical modeling skills. Toward this, this chapter provides background information and examples to enable the reader to (1) model metabolic networks, (2) simulate ILEs, and (3) understand the optimization and statistical methods commonly used for flux evaluation. A compartmentalized model of plant glycolysis and pentose phosphate pathway illustrates the reconstruction of a typical metabolic network, whereas a simpler example network illustrates the underlying metabolite and isotopomer balancing techniques. We also discuss the salient features of commonly used flux estimation software 13CFLUX2, Metran, NMR2Flux+, FiatFlux, and OpenFLUX. Furthermore, we briefly discuss methods to improve flux estimates. A graphical checklist at the end of the chapter provides a reader a quick reference to the mathematical modeling concepts and resources.

  11. Development of a mathematical model of the human circulatory system.

    PubMed

    Conlon, Martin J; Russell, Donald L; Mussivand, Tofy

    2006-09-01

    A mathematical lumped parameter model of the human circulatory system (HCS) has been developed to complement in vitro testing of ventricular assist devices. Components included in this model represent the major parts of the systemic HCS loop, with all component parameters based on physiological data available in the literature. Two model configurations are presented in this paper, the first featuring elements with purely linear constitutive relations, and the second featuring nonlinear constitutive relations for the larger vessels. Three different aortic compliance functions are presented, and a pressure-dependent venous flow resistance is used to simulate venous collapse. The mathematical model produces reasonable systemic pressure and flow behaviour, and graphs of this data are included.

  12. Physical and mathematical modeling of antimicrobial photodynamic therapy

    NASA Astrophysics Data System (ADS)

    Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

    2014-07-01

    Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

  13. On the treatment of airline travelers in mathematical models.

    PubMed

    Johansson, Michael A; Arana-Vizcarrondo, Neysarí; Biggerstaff, Brad J; Staples, J Erin; Gallagher, Nancy; Marano, Nina

    2011-01-01

    The global spread of infectious diseases is facilitated by the ability of infected humans to travel thousands of miles in short time spans, rapidly transporting pathogens to distant locations. Mathematical models of the actual and potential spread of specific pathogens can assist public health planning in the case of such an event. Models should generally be parsimonious, but must consider all potentially important components of the system to the greatest extent possible. We demonstrate and discuss important assumptions relative to the parameterization and structural treatment of airline travel in mathematical models. Among other findings, we show that the most common structural treatment of travelers leads to underestimation of the speed of spread and that connecting travel is critical to a realistic spread pattern. Models involving travelers can be improved significantly by relatively simple structural changes but also may require further attention to details of parameterization.

  14. Generalized mathematical models in design optimization

    NASA Technical Reports Server (NTRS)

    Papalambros, Panos Y.; Rao, J. R. Jagannatha

    1989-01-01

    The theory of optimality conditions of extremal problems can be extended to problems continuously deformed by an input vector. The connection between the sensitivity, well-posedness, stability and approximation of optimization problems is steadily emerging. The authors believe that the important realization here is that the underlying basis of all such work is still the study of point-to-set maps and of small perturbations, yet what has been identified previously as being just related to solution procedures is now being extended to study modeling itself in its own right. Many important studies related to the theoretical issues of parametric programming and large deformation in nonlinear programming have been reported in the last few years, and the challenge now seems to be in devising effective computational tools for solving these generalized design optimization models.

  15. Mathematical Model of an Air Cushion Vehicle

    DTIC Science & Technology

    1975-05-01

    otion, cushion dynamics, control and machinery dynamics and water wave effects are mwdeled. DD IJ එ 1473 EOITION OF I NOV 6 IS OBSOLETE U...cushion pressure model, the calculations are based on scanty experimental and analytical evidence that should not be taken for more than what it is...updates are readily incorporated. Many of the forces acting on the vehicle are curve fits to experimental4data obtained by Bell Aerospace and used in their

  16. Mathematical model of induced flow on the airplane vertical tail

    NASA Astrophysics Data System (ADS)

    Rotaru, Constantin; Cîrciu, Ionicǎ; Edu, Raluca Ioana

    2016-06-01

    In this paper is presented a mathematical model of the flow around the vertical tail of an airplane, based on the general elements of the aerodynamic design, with details leading to the separate formulation of the Fourier coefficients in the series solution of the Prandtl's lifting-line equation. Numerical results are obtained in Maple soft environment, for a standard configuration of an airplane geometry. The results include the discussion of the vortex model for the sidewash gradient on the vertical stabilizer.

  17. A mathematical model for late term cancer chemotherapy

    NASA Astrophysics Data System (ADS)

    Izard, Zac; Hirschbeck, Sarah; Volk, Christian; Shojania Feizabadi, Mitra

    2006-03-01

    A mathematical model for cancer treated with the ``on-off'' type where the drug is either active or inactive and when the chemotherapeutic treatment only affects the cycling cells is presented. This model is considered for late term chemotherapy when the total population of cells doesn't show a significant change. The size of the cycling cells as a function of time has been investigated.

  18. Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.

    PubMed

    Clément, Frédérique

    2016-07-01

    Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of

  19. Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling

    SciTech Connect

    Du, Qiang

    2014-11-12

    The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of which is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next

  20. A mathematical model of lung parenchyma.

    PubMed

    Karakaplan, A D; Bieniek, M P; Skalak, R

    1980-05-01

    The geometry of the proposed model of the parenchyma of a mammalian lung reproduces a cluster of alveoli arranged around a lowest-level air duct. The alveolar walls are assumed to be nonlinear elastic membranes, whose properties are described in terms of a strain energy function which reflects the hardening character of the stress-strain curve. The effect of the surfactant is included in terms of a variable (area-dependent) surface tension. Analyses of various mechanical processes in the parenchyma are performed with the aid of the finite element method, with the geometric and physical nonlinearities of the problem taken into account.

  1. Mathematical modeling of solid oxide fuel cells

    NASA Technical Reports Server (NTRS)

    Lu, Cheng-Yi; Maloney, Thomas M.

    1988-01-01

    Development of predictive techniques, with regard to cell behavior, under various operating conditions is needed to improve cell performance, increase energy density, reduce manufacturing cost, and to broaden utilization of various fuels. Such technology would be especially beneficial for the solid oxide fuel cells (SOFC) at it early demonstration stage. The development of computer models to calculate the temperature, CD, reactant distributions in the tubular and monolithic SOFCs. Results indicate that problems of nonuniform heat generation and fuel gas depletion in the tubular cell module, and of size limitions in the monolithic (MOD 0) design may be encountered during FC operation.

  2. A novel mathematical model for controllable near-field electrospinning

    NASA Astrophysics Data System (ADS)

    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.

  3. A novel mathematical model for controllable near-field electrospinning

    SciTech Connect

    Ru, Changhai E-mail: luojun@shu.edu.cn; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun E-mail: luojun@shu.edu.cn

    2014-01-15

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

  4. Mathematical modelling of carbohydrate degradation by human colonic microbiota.

    PubMed

    Muñoz-Tamayo, Rafael; Laroche, Béatrice; Walter, Eric; Doré, Joël; Leclerc, Marion

    2010-09-07

    The human colon is an anaerobic ecosystem that remains largely unexplored as a result of its limited accessibility and its complexity. Mathematical models can play a central role for a better insight into its dynamics. In this context, this paper presents the development of a mathematical model of carbohydrate degradation. Our aim was to provide an in silico approach to contribute to a better understanding of the fermentation patterns in such an ecosystem. Our mathematical model is knowledge-based, derived by writing down mass-balance equations. It incorporates physiology of the intestine, metabolic reactions and transport phenomena. The model was used to study various nutritional scenarios and to assess the role of the mucus on the system behavior. Model simulations provided an adequate qualitative representation of the human colon. Our model is complementary to experimental studies on human colonic fermentation, which, of course, is not meant to replace. It may be helpful to gain insight on questions that are still difficult to elucidate by experimentation and suggest future experiments.

  5. Tibia Fracture Healing Prediction Using First-Order Mathematical Model

    PubMed Central

    Sridevi, M.; Prakasam, P.; Kumaravel, S.; Madhava Sarma, P.

    2015-01-01

    The prediction of healing period of a tibia fracture in humans across limb using first-order mathematical model is demonstrated. At present, fracture healing is diagnosed using X-rays. Recent studies have demonstrated electric stimulation as a diagnostic tool in fracture healing. A DC electric voltage of 0.7 V was applied across the fracture and stabilized with Teflon coated carbon rings and the data was recorded at different time intervals until the fracture heals. The experimental data fitted a first-order plus dead time zero model (FOPDTZ) that coincided with the mathematical model of electrical simulated tibia fracture limb. Fracture healing diagnosis was proposed using model parameter process gain. Current stabilization in terms of process gain parameter becoming constant indicates that the healing of fracture is a new finding in the work. An error analysis was performed and it was observed that the measured data correlated to the FOPDTZ model with an error of less than 2 percent. Prediction of fracture healing period was done by one of the identified model parameters, namely, process gain. Moreover, mathematically, it is justified that once the fracture is completely united there is no capacitance present across the fracture site, which is a novelty of the work. PMID:26495032

  6. On a Mathematical Model of Brain Activities

    SciTech Connect

    Fichtner, K.-H.; Fichtner, L.; Freudenberg, W.; Ohya, M.

    2007-12-03

    The procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an 'expexted view of the world'. Then the brain compares a signal arising from our senses with the signal chosen from the memory leading to a change of the state of both signals. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from 'excited' to 'nonexcited'. For that reason a statistical model of the recognition process should reflect both--the change of the signals and the loss of excited neurons. A first attempt to explain the process of recognition in terms of quantum statistics was given. In the present note it is not possible to present this approach in detail. In lieu we will sketch roughly a few of the basic ideas and structures of the proposed model of the recognition process (Section). Further, we introduce the basic spaces and justify the choice of spaces used in this approach. A more elaborate presentation including all proofs will be given in a series of some forthcoming papers. In this series also the procedures of creation of signals from the memory, amplification, accumulation and transformation of input signals, and measurements like EEG and MEG will be treated in detail.

  7. Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis

    DOE PAGES

    Yan, Ruqiang; Chen, Xuefeng; Li, Weihua; ...

    2014-12-18

    Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less

  8. Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis

    SciTech Connect

    Yan, Ruqiang; Chen, Xuefeng; Li, Weihua; Sheng, Shuangwen

    2014-12-18

    Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issue is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.

  9. Aspects of Mathematical Modelling of Pressure Retarded Osmosis.

    PubMed

    Anissimov, Yuri G

    2016-02-03

    In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed.

  10. Aspects of Mathematical Modelling of Pressure Retarded Osmosis

    PubMed Central

    Anissimov, Yuri G.

    2016-01-01

    In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696

  11. Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

    SciTech Connect

    Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.; Konopka, Allan

    2014-10-17

    Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can be potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.

  12. The Effects of Mathematical Modeling on Creative Production Ability and Self-Directed Learning Attitude

    ERIC Educational Resources Information Center

    Kim, Sun Hee; Kim, Soojin

    2010-01-01

    What should we do to educate the mathematically gifted and how should we do it? In this research, to satisfy diverse mathematical and cognitive demands of the gifted who have excellent learning ability and task tenacity in mathematics, we sought to apply mathematical modeling. One of the objectives of the gifted education in Korea is cultivating…

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

    ERIC Educational Resources Information Center

    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.…

  14. Modeling School Mathematics Teaching in Initial Teacher Training Colleges for Multilingual Classrooms

    ERIC Educational Resources Information Center

    Chitera, Nancy

    2011-01-01

    In this article, the author presents a discussion of how mathematics teacher educators model school mathematics teaching in initial teacher training colleges, as they prepare the student teachers to teach mathematics in multilingual classrooms in Malawi. In particular, the article examines the instructional practices that mathematics teacher…

  15. Modelling the sensitivity of river reaches to water abstraction: RAPHSA- a hydroecology tool for environmental managers

    NASA Astrophysics Data System (ADS)

    Klaar, Megan; Laize, Cedric; Maddock, Ian; Acreman, Mike; Tanner, Kath; Peet, Sarah

    2014-05-01

    A key challenge for environmental managers is the determination of environmental flows which allow a maximum yield of water resources to be taken from surface and sub-surface sources, whilst ensuring sufficient water remains in the environment to support biota and habitats. It has long been known that sensitivity to changes in water levels resulting from river and groundwater abstractions varies between rivers. Whilst assessment at the catchment scale is ideal for determining broad pressures on water resources and ecosystems, assessment of the sensitivity of reaches to changes in flow has previously been done on a site-by-site basis, often with the application of detailed but time consuming techniques (e.g. PHABSIM). While this is appropriate for a limited number of sites, it is costly in terms of money and time resources and therefore not appropriate for application at a national level required by responsible licensing authorities. To address this need, the Environment Agency (England) is developing an operational tool to predict relationships between physical habitat and flow which may be applied by field staff to rapidly determine the sensitivity of physical habitat to flow alteration for use in water resource management planning. An initial model of river sensitivity to abstraction (defined as the change in physical habitat related to changes in river discharge) was developed using site characteristics and data from 66 individual PHABSIM surveys throughout the UK (Booker & Acreman, 2008). By applying a multivariate multiple linear regression analysis to the data to define habitat availability-flow curves using resource intensity as predictor variables, the model (known as RAPHSA- Rapid Assessment of Physical Habitat Sensitivity to Abstraction) is able to take a risk-based approach to modeled certainty. Site specific information gathered using desk-based, or a variable amount of field work can be used to predict the shape of the habitat- flow curves, with the

  16. Mathematical modeling is also physics—interdisciplinary teaching between mathematics and physics in Danish upper secondary education

    NASA Astrophysics Data System (ADS)

    Michelsen, Claus

    2015-07-01

    Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students’ achievement and attitude in both physics and mathematics. But although there are overwhelming amounts of literature on modeling in science and mathematics education, the interdisciplinary position is seldom addressed explicitly. Furthermore, there has been a striking lack of exposure of the question of how future teachers, who are largely educated in a mono-disciplinary fashion, can best become equipped to introduce genuinely interdisciplinary teaching activities to their future pupils. This paper presents some preliminary reflections upon a graduate course, which aims to prepare future physics and mathematics teachers for interdisciplinary teaching, and which has been designed on the basis of influential theoretical expositions of the concept of interdisciplinarity.

  17. Mathematical modelling of the growth of human fetus anatomical structures.

    PubMed

    Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

    2016-07-08

    The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

  18. Mathematical models of continuous flow electrophoresis: Electrophoresis technology

    NASA Technical Reports Server (NTRS)

    Saville, Dudley A.

    1986-01-01

    Two aspects of continuous flow electrophoresis were studied: (1) the structure of the flow field in continuous flow devices; and (2) the electrokinetic properties of suspended particles relevant to electrophoretic separations. Mathematical models were developed to describe flow structure and stability, with particular emphasis on effects due to buoyancy. To describe the fractionation of an arbitrary particulate sample by continuous flow electrophoresis, a general mathematical model was constructed. In this model, chamber dimensions, field strength, buffer composition, and other design variables can be altered at will to study their effects on resolution and throughput. All these mathematical models were implemented on a digital computer and the codes are available for general use. Experimental and theoretical work with particulate samples probed how particle mobility is related to buffer composition. It was found that ions on the surface of small particles are mobile, contrary to the widely accepted view. This influences particle mobility and suspension conductivity. A novel technique was used to measure the mobility of particles in concentrated suspensions.

  19. Mathematical and computer modeling of component surface shaping

    NASA Astrophysics Data System (ADS)

    Lyashkov, A.

    2016-04-01

    The process of shaping technical surfaces is an interaction of a tool (a shape element) and a component (a formable element or a workpiece) in their relative movements. It was established that the main objects of formation are: 1) a discriminant of a surfaces family, formed by the movement of the shape element relatively the workpiece; 2) an enveloping model of the real component surface obtained after machining, including transition curves and undercut lines; 3) The model of cut-off layers obtained in the process of shaping. When modeling shaping objects there are a lot of insufficiently solved or unsolved issues that make up a single scientific problem - a problem of qualitative shaping of the surface of the tool and then the component surface produced by this tool. The improvement of known metal-cutting tools, intensive development of systems of their computer-aided design requires further improvement of the methods of shaping the mating surfaces. In this regard, an important role is played by the study of the processes of shaping of technical surfaces with the use of the positive aspects of analytical and numerical mathematical methods and techniques associated with the use of mathematical and computer modeling. The author of the paper has posed and has solved the problem of development of mathematical, geometric and algorithmic support of computer-aided design of cutting tools based on computer simulation of the shaping process of surfaces.

  20. Mathematical modelling to support traceable dynamic calibration of pressure sensors

    NASA Astrophysics Data System (ADS)

    Matthews, C.; Pennecchi, F.; Eichstädt, S.; Malengo, A.; Esward, T.; Smith, I.; Elster, C.; Knott, A.; Arrhén, F.; Lakka, A.

    2014-06-01

    This paper focuses on the mathematical modelling required to support the development of new primary standard systems for traceable calibration of dynamic pressure sensors. We address two fundamentally different approaches to realizing primary standards, specifically the shock tube method and the drop-weight method. Focusing on the shock tube method, the paper presents first results of system identification and discusses future experimental work that is required to improve the mathematical and statistical models. We use simulations to identify differences between the shock tube and drop-weight methods, to investigate sources of uncertainty in the system identification process and to assist experimentalists in designing the required measuring systems. We demonstrate the identification method on experimental results and draw conclusions.

  1. The force-frequency relationship: insights from mathematical modeling.

    PubMed

    Puglisi, Jose L; Negroni, Jorge A; Chen-Izu, Ye; Bers, Donald M

    2013-03-01

    The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by β-adrenergic stimulation, and, in a coordinated way, the neurohumoral state alters both frequency (acting on the sinoatrial node) as well as force generation (modifying ventricular myocytes). This synchronized tuning is needed to meet new metabolic demands. Cardiac modelers have already linked mechanical and electrical activity in their formulations and showed how those activities feedback on each other. However, now it is necessary to include neurological control to have a complete description of heart performance, especially when changes in frequency are involved. Study of arrhythmias (or antiarrhythmic drugs) based on mathematical models should incorporate this effect to make useful predictions or point out potential pharmaceutical targets.

  2. Information system based on the mathematical model of the EPS

    NASA Astrophysics Data System (ADS)

    Kalimoldayev, Maksat N.; Abdildayeva, Assel A.; Mamyrbayev, Orken Zh.; Akhmetzhanov, Maksat

    2016-11-01

    This article discusses the structure of an information system, the mathematical and information models of electric power systems. Currently, the major application areas include system relaying data communication systems and automation, automated dispatching and technological management of electric power facilities, as well as computer-aided calculation of energy resources. Automatic control of excitation (ARV) synchronous machines is one of the most effective ways to ensure the stability of power systems. However, the variety of possible options and modes even in a single grid pose significant obstacles to the development of the best means of ensuring sustainability. Thus, the use of ARVs to ensure stability in some cases may not be sufficient. Therefore, there is a need to develop an information system based on a mathematical model.

  3. Mathematical modeling and simulation of a thermal system

    NASA Astrophysics Data System (ADS)

    Toropoc, Mirela; Gavrila, Camelia; Frunzulica, Rodica; Toma, Petrica D.

    2016-12-01

    The aim of the present paper is the conception of a mathematical model and simulation of a system formed by a heatexchanger for domestic hot water preparation, a storage tank for hot water and a radiator, starting from the mathematical equations describing this system and developed using Scilab-Xcos program. The model helps to determine the evolution in time for the hot water temperature, for the return temperature in the primary circuit of the heat exchanger, for the supply temperature in the secondary circuit, the thermal power for heating and for hot water preparation to the consumer respectively. In heating systems, heat-exchangers have an important role and their performances influence the energy efficiency of the systems. In the meantime, it is very important to follow the behavior of such systems in dynamic regimes. Scilab-Xcos program can be utilized to follow the important parameters of the systems in different functioning scenarios.

  4. Mathematical Modelling of Bacterial Populations in Bio-remediation Processes

    NASA Astrophysics Data System (ADS)

    Vasiliadou, Ioanna A.; Vayenas, Dimitris V.; Chrysikopoulos, Constantinos V.

    2011-09-01

    An understanding of bacterial behaviour concerns many field applications, such as the enhancement of water, wastewater and subsurface bio-remediation, the prevention of environmental pollution and the protection of human health. Numerous microorganisms have been identified to be able to degrade chemical pollutants, thus, a variety of bacteria are known that can be used in bio-remediation processes. In this study the development of mathematical models capable of describing bacterial behaviour considered in bio-augmentation plans, such as bacterial growth, consumption of nutrients, removal of pollutants, bacterial transport and attachment in porous media, is presented. The mathematical models may be used as a guide in designing and assessing the conditions under which areas contaminated with pollutants can be better remediated.

  5. An inverse problem for a mathematical model of aquaponic agriculture

    NASA Astrophysics Data System (ADS)

    Bobak, Carly; Kunze, Herb

    2017-01-01

    Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.

  6. Using mathematical modeling as a resource in clinical trials.

    PubMed

    Afenya, Evans K

    2005-07-01

    In light of recent clinical developments, the importance of mathematical modeling in cancer prevention and treatment is discussed. An exist- ing model of cancer chemotherapy is reintroduced and placed within current investigative frameworks regarding approaches to treatment optimization. Areas of commonality between the model predictions and the clinical findings are investigated as a way of further validating the model predictions and also establishing mathematical foundations for the clinical studies. The model predictions are used to propose additional ways that treatment optimization could enhance the clinical processes. Arising out of these, an expanded model of cancer is proposed and a treatment model is subsequently obtained. These models predict that malignant cells in the marrow and peripheral blood exhibit the tendency to evolve toward population levels that enable them to replace normal cells in these compartments in the untreated case. In the case of dose-dense treatment along with recombinant hematopoietic growth factors, the models predict a situation in which normal and abnormal cells in the marrow and peripheral blood are obliterated by drug action, while the normal cells regain their growth capabilities through growth-factor stimulation.

  7. A Mathematical Model for Simulating Infrared Images of Ships

    DTIC Science & Technology

    1986-12-01

    DEFENCE RESEARCH CENTRE SALISBURY SOUTH AUSTRALIA TECHNICAL REPORT ER L-0396-TR A MATHEMATICAL MODEL FOR SIMULATING INFRARED IMAGES OF SHIPS OS SCO1T...lli,wlng purposes: Reports documents prepared for maneagrial purposes, Technical recodAs of scientific end technical work of a permanent value Intended...They are Memoranda usually tentative in nature and reflec the personal views of the author, 3j, . A ~ ~ ~ ,~tu’~’ ’. . . UNCLASSIFIED AR-004.885

  8. Mathematical Model of the Jet Engine Fuel System

    NASA Astrophysics Data System (ADS)

    Klimko, Marek

    2015-05-01

    The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor) engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator) will be described, with respect to advanced predetermined simplifications.

  9. The mathematical model of the chevron-arch gearing transmitter

    NASA Astrophysics Data System (ADS)

    Bubenchikov, Aleksey; Bubenchikov, Mikhail; Matvienko, Oleg; Shcherbakov, Nikolay

    2016-01-01

    The teeth of herringbone transmission wheels are obtained by docking two helical wheels with an opposite arrangement of teeth, which can solve the problem of the axial force. The mathematical model of coupling chevron teeth of the driving wheel in the area of their docking using the arch tooth fragment is developed. The conjugacy area surface of the driven wheel chevron teeth is obtained as the envelope of the surfaces family formed by the arched tooth during the process of the parts motion.

  10. Mathematical modeling of DNA's transcription process for the cancer study

    NASA Astrophysics Data System (ADS)

    Morales-Peñaloza, A.; Meza-López, C. D.; Godina-Nava, J. J.

    2012-10-01

    The cancer is a phenomenon caused by an anomaly in the DNA's transcription process, therefore it is necessary to known how such anomaly is generated in order to implement alternative therapies to combat it. We propose to use mathematical modeling to treat the problem. Is implemented a simulation of the process of transcription and are studied the transport properties in the heterogeneous case using nonlinear dynamics.

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

    ERIC Educational Resources Information Center

    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…

  12. A Mathematical Model Coupling Tumor Growth and Angiogenesis

    PubMed Central

    Gomez, Hector

    2016-01-01

    We present a mathematical model for vascular tumor growth. We use phase fields to model cellular growth and reaction-diffusion equations for the dynamics of angiogenic factors and nutrients. The model naturally predicts the shift from avascular to vascular growth at realistic scales. Our computations indicate that the negative regulation of the Delta-like ligand 4 signaling pathway slows down tumor growth by producing a larger density of non-functional capillaries. Our results show good quantitative agreement with experiments. PMID:26891163

  13. Mathematical modeling of a class of multibody flexible spacecraft structures

    NASA Technical Reports Server (NTRS)

    Kelkar, Atul, G.

    1994-01-01

    A mathematical model for a general multibody flexible spacecraft is obtained. The generic spacecraft considered consists of a flexible central body to which a number of flexible multibody structures are attached. The coordinate systems used in the derivation allow effective decoupling of the translational motion of the entire spacecraft from its rotational motion about its center of mass. The derivation assumes that the deformations in the bodies are only due to elastic motions. The dynamic model derived is a closed-form vector-matrix differential equation. The model developed can be used for analysis and simulation of many realistic spacecraft configurations.

  14. A Mathematical Model of the Thermo-Anemometric Flowmeter

    PubMed Central

    Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

    2015-01-01

    A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed. PMID:26378535

  15. Mathematical model of a lithium/polypyrrole cell

    NASA Technical Reports Server (NTRS)

    Yeu, Taewhan; White, Ralph E.

    1990-01-01

    A mathematical model to simulate the charge/discharge behavior of a lithium/lithium perchlorate-propylene carbonate/polypyrrole secondary battery cell is presented. The model can be used to gain a better understanding of the behavior of this cell and to provide guidance toward the design of new secondary batteries which utilize an electronically conductive polymer such as polypyrrole as the cathode. The model includes the capability of handling charge and discharge behavior and is used to study the effect of various design parameters on the performance of the cell.

  16. Transmission dynamics of cholera: Mathematical modeling and control strategies

    NASA Astrophysics Data System (ADS)

    Sun, Gui-Quan; Xie, Jun-Hui; Huang, Sheng-He; Jin, Zhen; Li, Ming-Tao; Liu, Liqun

    2017-04-01

    Cholera, as an endemic disease around the world, has generated great threat to human society and caused enormous morbidity and mortality with weak surveillance system. In this paper, we propose a mathematical model to describe the transmission of Cholera. Moreover, basic reproduction number and the global dynamics of the dynamical model are obtained. Then we apply our model to characterize the transmission process of Cholera in China. It was found that, in order to avoid its outbreak in China, it may be better to increase immunization coverage rate and make effort to improve environmental management especially for drinking water. Our results may provide some new insights for elimination of Cholera.

  17. Mathematical modelling of the composting process: a review.

    PubMed

    Mason, I G

    2006-01-01

    In this paper mathematical models of the composting process are examined and their performance evaluated. Mathematical models of the composting process have been derived from both energy and mass balance considerations, with solutions typically derived in time, and in some cases, spatially. Both lumped and distributed parameter models have been reported, with lumped parameter models presently predominating in the literature. Biological energy production functions within the models included first-order, Monod-type or empirical expressions, and these have predicted volatile solids degradation, oxygen consumption or carbon dioxide production, with heat generation derived using heat quotient factors. Rate coefficient correction functions for temperature, moisture, oxygen and/or free air space have been incorporated in a number of the first-order and Monod-type expressions. The most successful models in predicting temperature profiles were those which incorporated either empirical kinetic expressions for volatile solids degradation or CO2 production, or which utilised a first-order model for volatile solids degradation, with empirical corrections for temperature and moisture variations. Models incorporating Monod-type kinetic expressions were less successful. No models were able to predict maximum, average and peak temperatures to within criteria of 5, 2 and 2 degrees C, respectively, or to predict the times to reach peak temperatures to within 8 h. Limitations included the modelling of forced aeration systems only and the generation of temperature validation data for relatively short time periods in relation to those used in full-scale composting practice. Moisture and solids profiles were well predicted by two models, but oxygen and carbon dioxide profiles were generally poorly modelled. Further research to obtain more extensive substrate degradation data, develop improved first-order biological heat production models, investigate mechanistically-based moisture

  18. Mathematical models of wound healing and closure: a comprehensive review.

    PubMed

    Jorgensen, Stephanie N; Sanders, Jonathan R

    2016-09-01

    Wound healing is a complex process comprised of overlapping phases and events that work to construct a new, functioning tissue. Mathematical models describe these events and yield understanding about the overall process of wound healing. Generally, these models are focused on only one phase (or a few phases) to explain healing for a specific system. A review of the literature reveals insights as reported on herein regarding the variety of overlapping inputs and outputs for any given type of model. Specifically, these models have been characterized with respect to the phases of healing and their mathematical/physical basis in an effort to shed light on new opportunities for model development. Though all phases of wound healing have been modeled, previous work has focused mostly on the proliferation and related contraction phases of healing with fewer results presented regarding other phases. As an example, a gap in the literature has been identified regarding models to describe facilitated wound closure techniques (e.g., suturing and its effect on resultant scarring). Thus, an opportunity exists to create models that tie the transient processes of wound healing, such as cell migration, to resultant scarring when considering tension applied to skin with given suturing techniques.

  19. Mathematical and Numerical Techniques in Energy and Environmental Modeling

    NASA Astrophysics Data System (ADS)

    Chen, Z.; Ewing, R. E.

    Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

  20. Developing the Roots of Modelling Conceptions: "Mathematical Modelling Is the Life of the World"

    ERIC Educational Resources Information Center

    Brown, Jill Patricia; Stillman, Gloria Ann

    2017-01-01

    A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…

  1. Abstractive dissociation of oxygen over Al(111): a nonadiabatic quantum model.

    PubMed

    Katz, Gil; Kosloff, Ronnie; Zeiri, Yehuda

    2004-02-22

    The dissociation of oxygen on a clean aluminum surface is studied theoretically. A nonadiabatic quantum dynamical model is used, based on four electronically distinct potential energy surfaces characterized by the extent of charge transfer from the metal to the adsorbate. A flat surface approximation is used to reduce the computation complexity. The conservation of the helicopter angular momentum allows Boltzmann averaging of the outcome of the propagation of a three degrees of freedom wave function. The dissociation event is simulated by solving the time-dependent Schrödinger equation for a period of 30 femtoseconds. As a function of incident kinetic energy, the dissociation yield follows the experimental trend. An attempt at simulation employing only the lowest adiabatic surface failed, qualitatively disagreeing with both experiment and nonadiabatic calculations. The final products, adsorptive dissociation and abstractive dissociation, are obtained by carrying out a semiclassical molecular dynamics simulation with surface hopping which describes the back charge transfer from an oxygen atom negative ion to the surface. The final adsorbed oxygen pair distribution compares well with experiment. By running the dynamical events backward in time, a correlation is established between the products and the initial conditions which lead to their production. Qualitative agreement is thus obtained with recent experiments that show suppression of abstraction by rotational excitation.

  2. Viscoelasticity in Polymers: Phenomenological to Molecular Mathematical Modelling

    DTIC Science & Technology

    2006-12-14

    of his 80th birthday. Abstract We report on two recent advances in the modelling of viscoelastic polymers: (i) a new constitutive model which combines...the virtual stick-slip continuum “molecular-based” ideas of Johnson and Stacer with the Rouse bead chain ideas; (ii) a two-dimensional version of a ...also loosely re- ferred to as hysteresis) in materials using ideas from elasticity has attracted the attention of a large number of investigators over

  3. Mathematical and Computational Modeling in Complex Biological Systems

    PubMed Central

    Li, Wenyang; Zhu, Xiaoliang

    2017-01-01

    The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology. PMID:28386558

  4. Mathematical modeling of the neuron morphology using two dimensional images.

    PubMed

    Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja

    2016-02-07

    In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.

  5. Assessment of mathematical models for the flow in directional solidification

    NASA Astrophysics Data System (ADS)

    Lu, Jay W.; Chen, Falin

    1997-02-01

    In a binary solution unidirectionally solidified from below, the bulk melt and the eutectic solid is separated by a dendritic mushy zone. The mathematical formulation governing the fluid motion shall thus consist of the equations in the bulk melt and the mushy zone and the associated boundary conditions. In the bulk melt, assuming that the melt is a Newtonian fluid, the governing equations are the continuity equation, the Navier-Stokes equations, the heat conservation equation, and the solute conservation equation. In the mushy layer, however, the formulation of the momentum equation and the associated boundary conditions are diversified in previous investigations. In this paper, we discuss three mathematical models, which had been previously applied to study the flow induced by the solidification of binary solutions cooling from below. The assessment is given on the bases of the stability characteristics of the convective flow and the comparison between the numerical and experimental results.

  6. An alternate mathematical model for single-wall carbon nanotubes

    NASA Astrophysics Data System (ADS)

    Cotfas, Nicolae

    2005-09-01

    The positions of atoms forming a carbon nanotube are usually described by using a system of generators of the symmetry group. Each atomic position corresponds to an element of the set Z×{0,1,…,n}×{0,1}, where n is a natural number depending on the considered nanotube. We obtain an alternate rather different description by starting from a description of the honeycomb lattice in terms of Miller indices. In our mathematical model which is a factor space defined by an equivalence relation in the set {(v0,v1,v2)∈Z|v0+v1+v2∈{0,1}} the neighbours of an atomic position can be described in a simpler way, and the mathematical objects with geometric or physical significance have a simpler and more symmetric form.

  7. A Cellular Automata-Based Mathematical Model for Thymocyte Development

    PubMed Central

    Souza-e-Silva, Hallan; Savino, Wilson; Feijóo, Raúl A.; Vasconcelos, Ana Tereza Ribeiro

    2009-01-01

    Intrathymic T cell development is an important process necessary for the normal formation of cell-mediated immune responses. Importantly, such a process depends on interactions of developing thymocytes with cellular and extracellular elements of the thymic microenvironment. Additionally, it includes a series of oriented and tunely regulated migration events, ultimately allowing mature cells to cross endothelial barriers and leave the organ. Herein we built a cellular automata-based mathematical model for thymocyte migration and development. The rules comprised in this model take into account the main stages of thymocyte development, two-dimensional sections of the normal thymic microenvironmental network, as well as the chemokines involved in intrathymic cell migration. Parameters of our computer simulations with further adjusted to results derived from previous experimental data using sub-lethally irradiated mice, in which thymus recovery can be evaluated. The model fitted with the increasing numbers of each CD4/CD8-defined thymocyte subset. It was further validated since it fitted with the times of permanence experimentally ascertained in each CD4/CD8-defined differentiation stage. Importantly, correlations using the whole mean volume of young normal adult mice revealed that the numbers of cells generated in silico with the mathematical model fall within the range of total thymocyte numbers seen in these animals. Furthermore, simulations made with a human thymic epithelial network using the same mathematical model generated similar profiles for temporal evolution of thymocyte developmental stages. Lastly, we provided in silico evidence that the thymus architecture is important in the thymocyte development, since changes in the epithelial network result in different theoretical profiles for T cell development/migration. This model likely can be used to predict thymocyte evolution following therapeutic strategies designed for recovery of the thymus in diseases

  8. Mathematical model of frost heave and thaw settlement in pavements

    NASA Astrophysics Data System (ADS)

    Guymon, Gary L.; Berg, Richard L.; Hromadka, Theodore V.

    1993-04-01

    Since 1975 the U.S. Army Corps of Engineers, the Federal Highway Administration and the Federal Aviation Administration have been working cooperatively to develop a mathematical model to estimate frost heave and thaw weakening under various environmental conditions and for various pavement designs. A model has been developed. It is a one-dimensional representation of vertical heat and moisture flux. It is based on a numerical solution technique termed the nodal domain integration method, and it estimates frost heave and frost penetration reasonably well for a variety of situations. The model is now ready for additional field evaluation and implementation in appropriate cases. The main objectives of this report are: (1) to describe the model, FROST, including modeling uncertainties and errors; (2) to summarize recent comparisons between measured and computed values for frost heave and frost penetration; and (3) to describe parameters necessary for input into the model.

  9. Tumor Angiogenesis and Vascular Patterning: A Mathematical Model

    PubMed Central

    Travasso, Rui D. M.; Corvera Poiré, Eugenia; Castro, Mario; Rodrguez-Manzaneque, Juan Carlos; Hernández-Machado, A.

    2011-01-01

    Understanding tumor induced angiogenesis is a challenging problem with important consequences for diagnosis and treatment of cancer. Recently, strong evidences suggest the dual role of endothelial cells on the migrating tips and on the proliferating body of blood vessels, in consonance with further events behind lumen formation and vascular patterning. In this paper we present a multi-scale phase-field model that combines the benefits of continuum physics description and the capability of tracking individual cells. The model allows us to discuss the role of the endothelial cells' chemotactic response and proliferation rate as key factors that tailor the neovascular network. Importantly, we also test the predictions of our theoretical model against relevant experimental approaches in mice that displayed distinctive vascular patterns. The model reproduces the in vivo patterns of newly formed vascular networks, providing quantitative and qualitative results for branch density and vessel diameter on the order of the ones measured experimentally in mouse retinas. Our results highlight the ability of mathematical models to suggest relevant hypotheses with respect to the role of different parameters in this process, hence underlining the necessary collaboration between mathematical modeling, in vivo imaging and molecular biology techniques to improve current diagnostic and therapeutic tools. PMID:21637756

  10. Mathematical modeling the radiation effects on humoral immunity

    NASA Astrophysics Data System (ADS)

    Smirnova, O. A.

    A mathematical model of humoral immune response in nonirradiated and irradiated mammals is developed. It is based on conventional theories and experimental facts in this field. The model is a system of nonlinear differential equations which describe the dynamics of concentrations of antibody and antigen molecules, immunocompetent B lymphocytes, and the rest blood lymphocytes, as well as the bone-marrow lymphocyte precursors. The interaction of antigen molecules with antibodies and with antibody-like receptors on immunocompetent cells is also incorporated. The model quantitatively reproduces the dynamics of the humoral immune response to the T-independent antigen (capsular antigen of plague microbe) in nonirradiated mammals (CBA mice). It describes the peculiarities of the humoral immune response in CBA mice exposed to acute radiation before or after introducing antigen. The model predicts an adaptation of humoral immune system to low dose rate chronic irradiation in the result of which the intensity of immune response relaxes to a new, lower than normal, stable level. The mechanisms of this phenomenon are revealed. The results obtained show that the developed model, after the appropriate identification, can be used to predict the effects of acute and low-level long-term irradiation on the system of humoral immunity in humans. Employment of the mathematical model identified in the proper way should be important in estimating the radiation risk for cosmonauts and astronauts on long space missions such as a voyage to Mars or a lunar colony.

  11. Mathematical model of a flexible space shuttle vehicle

    NASA Technical Reports Server (NTRS)

    Harvey, C. A.

    1972-01-01

    The development of a mathematical model of the lateral motion of a flexible space shuttle vehicle during ascent is described. The model was developed to perform control system synthesis using stochastic constrained optimization techniques. The goals of the control system synthesis are to demonstrate the applicability of the techniques and to discover any problems peculiar to the flexible nature of a shuttle vehicle. The equations of motion are derived. A brief description of the generation of numerical data is given. Explicit definitions and numerical values of trajectory data and coefficients appearing in the equations of motion are included.

  12. Mathematical model of one-man air revitalization system

    NASA Technical Reports Server (NTRS)

    1976-01-01

    A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

  13. Mathematical Model Of Curing Behavior Of A Polymer

    NASA Technical Reports Server (NTRS)

    Loomis, Willard C.; Beyer, Rodney B.; Liu, Edmund K. S.

    1995-01-01

    Mathematical model predicts selected aspects of chemical, thermal and mechanical responses of polymeric liner and propellant materials during curing process. Predictions made both prior to processing and during process in quasi-real time. Developed specifically for use in designing and analyzing process in which bondline materials (including polymeric liners) and propellant cast and cured in rocket motor. With modifications, model applicable to curing of other polymeric materials. Further development may provide direct "in-line" program for calculations, including comparisons, in real time. This will constitute basis for more sophisticated control of process.

  14. Mathematical model of depolarization mechanism of conducted vasoreactivity

    NASA Astrophysics Data System (ADS)

    Neganova, Anastasiia Y.; Stiukhina, Elena S.; Postnov, Dmitry E.

    2015-03-01

    We address the problem of conducted vasodilation, the phenomenon which is also known as functional hyperemia. Specifically, we test the mechanism of nondecremental propagation of electric signals along endothelial cell layer recently hypothesized by Figueroa et al. By means of functional modeling we focus on possible nonlinear mechanisms that can underlie such regenerative pulse transmission (RPT). Since endothelial cells (EC) are generally known as electrically inexcitable, the possible role of ECs in RPT mechanisms is not evident. By means of mathematical modeling we check the dynamical self-consistency of Figueroa's hypothesis, as well as estimate the possible contribution of specific ionic currents to the suggested RPT mechanism.

  15. A mathematical model for the doubly fed wound rotor generator

    NASA Technical Reports Server (NTRS)

    Brady, F. J.

    1983-01-01

    A mathematical analysis of a doubly-fed wound rotor machine used as a constant frequency generator is presented. The purpose of this analysis is to derive a consistent set of circuit equations which produce constant stator frequency and constant stator voltage. Starting with instantaneous circuit equations, the necessary rotor voltages and currents are derived. The model, thus obtained, is assumed to be valid, since the resulting relationships between mechanical power and active volt-amperes agrees with the results of others. In addition, the model allows for a new interpretation of the power flow in the doubly-fed generator.

  16. Mathematical model for light scanning system based on circular laser

    NASA Astrophysics Data System (ADS)

    Xu, Peiquan; Yao, Shun; Lu, Fenggui; Tang, Xinhua; Zhang, Wei

    2005-11-01

    A novel light scanning system based on circular laser trajectory for welding robot is developed. With the help of image processing technique, intelligent laser welding could be realized. According to laser triangulation algorithm and Scheimpflug condition, mathematical model for circular laser vision is built. This scanning system projects circular laser onto welded seams and recovers the depth of the welded seams, escapes from shortcomings of less information, explains ambiguity and single tracking direction inherent in "spot" or "line" type laser trajectory. Three-dimensional (3D) model for welded seams could be recognized after depth recovery. The imaging error is investigated also.

  17. Mathematical modeling of bent-axis hydraulic piston motors

    NASA Technical Reports Server (NTRS)

    Bartos, R. D.

    1992-01-01

    Each of the DSN 70-m antennas uses 16 bent-axis hydraulic piston motors as part of the antenna drive system. On each of the two antenna axes, four motors are used to drive the antenna and four motors provide counter torque to remove the backlash in the antenna drive train. This article presents a mathematical model for bent-axis hydraulic piston motors. The model was developed to understand the influence of the hydraulic motors on the performance of the DSN 70-m antennas' servo control system.

  18. A review on mathematical models for estimating indoor radon concentrations.

    PubMed

    Park, Ji Hyun; Kang, Dae Ryong; Kim, Jinheum

    2016-01-01

    Radiation from natural sources is one of causes of the environmental diseases. Radon is the leading environmental cause of lung cancer next to smoking. To investigate the relationship between indoor radon concentrations and lung cancer, researchers must be able to estimate an individual's cumulative level of indoor radon exposure and to do so, one must first be able to assess indoor radon concentrations. In this article, we outline factors affecting indoor radon concentrations and review related mathematical models based on the mass balance equation and the differential equations. Furthermore, we suggest the necessities of applying time-dependent functions for indoor radon concentrations and developing stochastic models.

  19. A 6DOF mathematical model of parachute in Mars EDL

    NASA Astrophysics Data System (ADS)

    Shen, Ganghui; Xia, Yuanqing; Sun, Haoran

    2015-04-01

    The base of the dynamics characteristic research on the parachute and vehicle system is to establish a dynamics model, during the parachute descent phase, which can accurately display the relationship among the velocity, altitude and attitude angles as well as the variation of time. This paper starts with a new tracking law - ADRC in Mars entry guidance, which affects the initial states of the parachute deployment point and determines precision landing capability. Then, the influence of unsteady resistance to the parachute in Martian air is considered as the added mass, and a 6DOF nonlinear mathematical model of the parachute and vehicle system is established.

  20. Mathematical modelling at secondary school: the MACSI-Clongowes Wood College experience

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

    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. Participants developed simple mathematical models for everyday life problems with an open-ended answer. The format and content of the workshop are described and feedback from both students and participating teachers is provided. For nearly all participants, this workshop was an enjoyable experience which showed mathematics and other STEM components in a very positive way.

  1. Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics

    PubMed Central

    Noecker, Cecilia; Schaefer, Krista; Zaccheo, Kelly; Yang, Yiding; Day, Judy; Ganusov, Vitaly V.

    2015-01-01

    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 dose. These results

  2. Secondary Teachers' Conceptions and Practices of Assessment Models: The Case for Mathematics Teachers in Jordan

    ERIC Educational Resources Information Center

    Al Duwairi, Ahmed

    2013-01-01

    This study aimed at investigating the extent to which secondary schools mathematics teachers practice to assessment models in their mathematics teaching and learning. Definitely, the study aimed at answering the following questions: (1) To what extent do secondary schools mathematics teachers practice each of the assessment models in their…

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

    ERIC Educational Resources Information Center

    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…

  4. On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population

    NASA Astrophysics Data System (ADS)

    Boulanouar, Mohamed

    2013-04-01

    In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.

  5. Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

    ERIC Educational Resources Information Center

    Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

    2017-01-01

    The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

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

    ERIC Educational Resources Information Center

    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…

  7. On problems in defining abstract and metaphysical concepts--emergence of a new model.

    PubMed

    Nahod, Bruno; Nahod, Perina Vukša

    2014-12-01

    Basic anthropological terminology is the first project covering terms from the domain of the social sciences under the Croatian Special Field Terminology program (Struna). Problems that have been sporadically noticed or whose existence could have been presumed during the processing of terms mainly from technical fields and sciences have finally emerged in "anthropology". The principles of the General Theory of Terminology (GTT), which are followed in Struna, were put to a truly exacting test, and sometimes stretched beyond their limits when applied to concepts that do not necessarily have references in the physical world; namely, abstract and metaphysical concepts. We are currently developing a new terminographical model based on Idealized Cognitive Models (ICM), which will hopefully ensure a better cross-filed implementation of various types of concepts and their relations. The goal of this paper is to introduce the theoretical bases of our model. Additionally, we will present a pilot study of the series of experiments in which we are trying to investigate the nature of conceptual categorization in special languages and its proposed difference form categorization in general language.

  8. Comparison of two different surfaces for 3d model abstraction in support of remote sensing simulations

    SciTech Connect

    Pope, Paul A; Ranken, Doug M

    2010-01-01

    A method for abstracting a 3D model by shrinking a triangular mesh, defined upon a best fitting ellipsoid surrounding the model, onto the model's surface has been previously described. This ''shrinkwrap'' process enables a semi-regular mesh to be defined upon an object's surface. This creates a useful data structure for conducting remote sensing simulations and image processing. However, using a best fitting ellipsoid having a graticule-based tessellation to seed the shrinkwrap process suffers from a mesh which is too dense at the poles. To achieve a more regular mesh, the use of a best fitting, subdivided icosahedron was tested. By subdividing each of the twenty facets of the icosahedron into regular triangles of a predetermined size, arbitrarily dense, highly-regular starting meshes can be created. Comparisons of the meshes resulting from these two seed surfaces are described. Use of a best fitting icosahedron-based mesh as the seed surface in the shrinkwrap process is preferable to using a best fitting ellipsoid. The impacts to remote sensing simulations, specifically generation of synthetic imagery, is illustrated.

  9. Mathematical modeling of the West Africa Ebola epidemic

    PubMed Central

    Chretien, Jean-Paul; Riley, Steven; George, Dylan B

    2015-01-01

    As of November 2015, the Ebola virus disease (EVD) epidemic that began in West Africa in late 2013 is waning. The human toll includes more than 28,000 EVD cases and 11,000 deaths in Guinea, Liberia, and Sierra Leone, the most heavily-affected countries. We reviewed 66 mathematical modeling studies of the EVD epidemic published in the peer-reviewed literature to assess the key uncertainties models addressed, data used for modeling, public sharing of data and results, and model performance. Based on the review, we suggest steps to improve the use of modeling in future public health emergencies. DOI: http://dx.doi.org/10.7554/eLife.09186.001 PMID:26646185

  10. A mathematical model of the UH-60 helicopter

    NASA Technical Reports Server (NTRS)

    Hilbert, K. B.

    1984-01-01

    This report documents the revisions made to a ten-degree-of-freedom, full-flight envelope, generic helicopter mathematical model to represent the UH-60 helicopter accurately. The major modifications to the model include fuselage aerodynamic force and moment equations specific to the UH-60, a canted tail rotor, a horizontal stabilator with variable incidence, and a pitch bias actuator (PBA). In addition, this report presents a full set of parameters and numerical values which describe the helicopter configuration and physical characteristics. Model validation was accomplished by comparison of trim and stability derivative data generated from the UH-60 math model with data generated from a similar total force and moment math model.

  11. (abstract) Modeling Protein Families and Human Genes: Hidden Markov Models and a Little Beyond

    NASA Technical Reports Server (NTRS)

    Baldi, Pierre

    1994-01-01

    We will first give a brief overview of Hidden Markov Models (HMMs) and their use in Computational Molecular Biology. In particular, we will describe a detailed application of HMMs to the G-Protein-Coupled-Receptor Superfamily. We will also describe a number of analytical results on HMMs that can be used in discrimination tests and database mining. We will then discuss the limitations of HMMs and some new directions of research. We will conclude with some recent results on the application of HMMs to human gene modeling and parsing.

  12. Mathematics Underground

    ERIC Educational Resources Information Center

    Luther, Kenneth H.

    2012-01-01

    Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

  13. Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review

    PubMed Central

    Moog, Claude H.; Stan, Guy-Bart; Brunet, Cecile; Raffi, François; Ferré, Virginie; Costanza, Vicente; Mhawej, Marie J.; Biafore, Federico; Ouattara, Djomangan A.; Ernst, Damien; Fonteneau, Raphael; Xia, Xiaohua

    2014-01-01

    Abstract This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients. PMID:25371860

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

    ERIC Educational Resources Information Center

    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)…

  15. Mathematical Modelling of Silica Scaling Deposition in Geothermal Wells

    NASA Astrophysics Data System (ADS)

    Nizami, M.; Sutopo

    2016-09-01

    Silica scaling is widely encountered in geothermal wells in which produce two-phase geothermal fluid. Silica scaling could be formed due to chemical reacting by mixing a geothermal fluid with other geothermal fluid in different compositions, or also can be caused by changes in fluid properties due to changes pressure and temperature. One of method to overcome silica scaling which is occurred around geothermal well is by workover operation. Modelling of silica deposition in porous medium has been modeled in previously. However, the growth of silica scaling deposition in geothermal wells has never been modeled. Modelling of silica deposition through geothermal is important aspects to determine depth of silica scaling growth and best placing for workover device to clean silica scaling. This study is attempted to develop mathematical models for predicting silica scaling through geothermal wells. The mathematical model is developed by integrating the solubility-temperature correlation and two-phase pressure drop coupled wellbore fluid temperature correlation in a production well. The coupled model of two-phase pressure drop and wellbore fluid temperature correlation which is used in this paper is Hasan-Kabir correlation. This modelling is divided into two categories: single and two phase fluid model. Modelling of silica deposition is constrained in temperature distribution effect through geothermal wells by solubility correlation for silica. The results of this study are visualizing the growth of silica scaling thickness through geothermal wells in each segment of depth. Sensitivity analysis is applied in several parameters, such as: bottom-hole pressure, temperature, and silica concentrations. Temperature is most impact factor for silica scaling through geothermal wellbore and depth of flash point. In flash point, silica scaling thickness has reached maximum because reducing of mole in liquid portion.

  16. Mathematical Modeling of Intestinal Iron Absorption Using Genetic Programming

    PubMed Central

    Colins, Andrea; Gerdtzen, Ziomara P.; Nuñez, Marco T.; Salgado, J. Cristian

    2017-01-01

    Iron is a trace metal, key for the development of living organisms. Its absorption process is complex and highly regulated at the transcriptional, translational and systemic levels. Recently, the internalization of the DMT1 transporter has been proposed as an additional regulatory mechanism at the intestinal level, associated to the mucosal block phenomenon. The short-term effect of iron exposure in apical uptake and initial absorption rates was studied in Caco-2 cells at different apical iron concentrations, using both an experimental approach and a mathematical modeling framework. This is the first report of short-term studies for this system. A non-linear behavior in the apical uptake dynamics was observed, which does not follow the classic saturation dynamics of traditional biochemical models. We propose a method for developing mathematical models for complex systems, based on a genetic programming algorithm. The algorithm is aimed at obtaining models with a high predictive capacity, and considers an additional parameter fitting stage and an additional Jackknife stage for estimating the generalization error. We developed a model for the iron uptake system with a higher predictive capacity than classic biochemical models. This was observed both with the apical uptake dataset used for generating the model and with an independent initial rates dataset used to test the predictive capacity of the model. The model obtained is a function of time and the initial apical iron concentration, with a linear component that captures the global tendency of the system, and a non-linear component that can be associated to the movement of DMT1 transporters. The model presented in this paper allows the detailed analysis, interpretation of experimental data, and identification of key relevant components for this complex biological process. This general method holds great potential for application to the elucidation of biological mechanisms and their key components in other complex

  17. EBS Radionuclide Transport Abstraction

    SciTech Connect

    J.D. Schreiber

    2005-08-25

    The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in ''Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration'' (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment for the license application (TSPA-LA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA-LA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers

  18. Synthesising 30 Years of Mathematical Modelling of Echinococcus Transmission

    PubMed Central

    Atkinson, Jo-An M.; Williams, Gail M.; Yakob, Laith; Clements, Archie C. A.; Barnes, Tamsin S.; McManus, Donald P.; Yang, Yu Rong; Gray, Darren J.

    2013-01-01

    Background Echinococcosis is a complex zoonosis that has domestic and sylvatic lifecycles, and a range of different intermediate and definitive host species. The complexities of its transmission and the sparse evidence on the effectiveness of control strategies in diverse settings provide significant challenges for the design of effective public health policy against this disease. Mathematical modelling is a useful tool for simulating control packages under locally specific transmission conditions to inform optimal timing and frequency of phased interventions for cost-effective control of echinococcosis. The aims of this review of 30 years of Echinococcus modelling were to discern the epidemiological mechanisms underpinning models of Echinococcus granulosus and E. multilocularis transmission and to establish the need to include a human transmission component in such models. Methodology/Principal Findings A search was conducted of all relevant articles published up until July 2012, identified from the PubMED, Web of Knowledge and Medline databases and review of bibliographies of selected papers. Papers eligible for inclusion were those describing the design of a new model, or modification of an existing mathematical model of E. granulosus or E. multilocularis transmission. A total of 13 eligible papers were identified, five of which described mathematical models of E. granulosus and eight that described E. multilocularis transmission. These models varied primarily on the basis of six key mechanisms that all have the capacity to modulate model dynamics, qualitatively affecting projections. These are: 1) the inclusion of a ‘latent’ class and/or time delay from host exposure to infectiousness; 2) an age structure for animal hosts; 3) the presence of density-dependent constraints; 4) accounting for seasonality; 5) stochastic parameters; and 6) inclusion of spatial and risk structures. Conclusions/Significance This review discusses the conditions under which these

  19. Mathematical models of tumor heterogeneity and drug resistance

    NASA Astrophysics Data System (ADS)

    Greene, James

    In this dissertation we develop mathematical models of tumor heterogeneity and drug resistance in cancer chemotherapy. Resistance to chemotherapy is one of the major causes of the failure of cancer treatment. Furthermore, recent experimental evidence suggests that drug resistance is a complex biological phenomena, with many influences that interact nonlinearly. Here we study the influence of such heterogeneity on treatment outcomes, both in general frameworks and under specific mechanisms. We begin by developing a mathematical framework for describing multi-drug resistance to cancer. Heterogeneity is reflected by a continuous parameter, which can either describe a single resistance mechanism (such as the expression of P-gp in the cellular membrane) or can account for the cumulative effect of several mechanisms and factors. The model is written as a system of integro-differential equations, structured by the continuous "trait," and includes density effects as well as mutations. We study the limiting behavior of the model, both analytically and numerically, and apply it to study treatment protocols. We next study a specific mechanism of tumor heterogeneity and its influence on cell growth: the cell-cycle. We derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations, when the number of cells is large. The model is closely tied to experimental data of cell growth, and includes a novel implementation of

  20. Abstraction through Game Play

    ERIC Educational Resources Information Center

    Avraamidou, Antri; Monaghan, John; Walker, Aisha

    2012-01-01

    This paper examines the computer game play of an 11-year-old boy. In the course of building a virtual house he developed and used, without assistance, an artefact and an accompanying strategy to ensure that his house was symmetric. We argue that the creation and use of this artefact-strategy is a mathematical abstraction. The discussion…