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Sample records for abstract mathematical models

  1. 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…

  2. Mathematical Abstraction through Scaffolding

    ERIC Educational Resources Information Center

    Ozmantar, Mehmet Fatih; Roper, Tom

    2004-01-01

    This paper examines the role of scaffolding in the process of abstraction. An activity-theoretic approach to abstraction in context is taken. This examination is carried out with reference to verbal protocols of two 17 year-old students working together on a task connected to sketching the graph of |f|x|)|. Examination of the data suggests that…

  3. R-Models: a mathematical framework for capturing notions of abstraction and assistance in reproductive systems.

    PubMed

    Webster, Matt; Malcolm, Grant

    2012-11-01

    R-Models are an approach to capturing notions of assistance and abstraction in reproductive systems, based on labelled transition systems and Gibson's theory of affordances. R-Models incorporate a labelled transition system that describes how a reproductive system changes over the course of reproduction. The actors in the system are represented by a set of entities together with a relation describing the states in which those entities are present, and an affordance-modelling function mapping actions to sets of entities which enable those actions to be performed. We show how R-models can be classified based on whether the reproducer is assisted or unassisted in reproduction, and whether or not the reproducer is active during reproduction. We prove that all assisted and unassisted R-models have a related R-model which has the opposite classification. We discuss the relevance to the field of artificial life, give a potential application to the fields of computer virology, and demonstrate reproduction modelling and classification in action using examples.

  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. A dialectical approach to the formation of mathematical abstractions

    NASA Astrophysics Data System (ADS)

    Ozmantar, Mehmet Fatih; Monaghan, John

    2007-09-01

    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 context. This model constitutes the basis of the second section where we describe an empirical study designed to investigate mathematical abstraction in socially rich (e.g., peer-interacted and tutor-assisted) environments. We then present data on two students working with the help of a tutor on tasks concerned with graphs of absolute value functions. On the basis of these data, we discuss four particular themes which are relevant to the purpose of this special issue and are important in the discussion of mathematical abstraction: human and artefact mediation, tutor interventions in assisting the formation of mathematical abstractions, implications of a dialectical view on student development, and the things that are abstracted.

  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. Abstract Models of Probability

    NASA Astrophysics Data System (ADS)

    Maximov, V. M.

    2001-12-01

    Probability theory presents a mathematical formalization of intuitive ideas of independent events and a probability as a measure of randomness. It is based on axioms 1-5 of A.N. Kolmogorov 1 and their generalizations 2. Different formalized refinements were proposed for such notions as events, independence, random value etc., 2,3, whereas the measure of randomness, i.e. numbers from [0,1], remained unchanged. To be precise we mention some attempts of generalization of the probability theory with negative probabilities 4. From another side the physicists tryed to use the negative and even complex values of probability to explain some paradoxes in quantum mechanics 5,6,7. Only recently, the necessity of formalization of quantum mechanics and their foundations 8 led to the construction of p-adic probabilities 9,10,11, which essentially extended our concept of probability and randomness. Therefore, a natural question arises how to describe algebraic structures whose elements can be used as a measure of randomness. As consequence, a necessity arises to define the types of randomness corresponding to every such algebraic structure. Possibly, this leads to another concept of randomness that has another nature different from combinatorical - metric conception of Kolmogorov. Apparenly, discrepancy of real type of randomness corresponding to some experimental data lead to paradoxes, if we use another model of randomness for data processing 12. Algebraic structure whose elements can be used to estimate some randomness will be called a probability set Φ. Naturally, the elements of Φ are the probabilities.

  8. 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 that…

  9. Dissertation Abstracts: Scientific Evidence Related to Teaching and Learning Mathematics

    ERIC Educational Resources Information Center

    Cicmanec, Karen B.

    2008-01-01

    This categorical analysis explores the mathematics education doctoral dissertations archived in UMI "Digital Dissertations" (1991-2005) and 115 abstracts of doctoral dissertations from 46 institutions offering doctoral degrees in 2004. The goal of this study is to a) index changes in the numbers of mathematics education doctoral candidates and b)…

  10. 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…

  11. Modelling Metamorphism by Abstract Interpretation

    NASA Astrophysics Data System (ADS)

    Dalla Preda, Mila; Giacobazzi, Roberto; Debray, Saumya; Coogan, Kevin; Townsend, Gregg M.

    Metamorphic malware apply semantics-preserving transformations to their own code in order to foil detection systems based on signature matching. In this paper we consider the problem of automatically extract metamorphic signatures from these malware. We introduce a semantics for self-modifying code, later called phase semantics, and prove its correctness by showing that it is an abstract interpretation of the standard trace semantics. Phase semantics precisely models the metamorphic code behavior by providing a set of traces of programs which correspond to the possible evolutions of the metamorphic code during execution. We show that metamorphic signatures can be automatically extracted by abstract interpretation of the phase semantics, and that regular metamorphism can be modelled as finite state automata abstraction of the phase semantics.

  12. 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

  13. 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.

  14. 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…

  15. 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…

  16. 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…

  17. Abstracted model for ceramic coating

    SciTech Connect

    Farmer, J C; Stockman, C

    1998-11-14

    Engineers are exploring several mechanisms to delay corrosive attack of the CAM (corrosion allowance material) by dripping water, including drip shields and ceramic coatings. Ceramic coatings deposited with high-velocity oxyfuels (HVOF's) have exhibited a porosity of only 2% at a thickness of 0.15 cm. The primary goal of this document is to provide a detailed description of an abstracted process-level model for Total System Performance Assessment (TSPA) that has been developed to account for the inhibition of corrosion by protective ceramic coatings. A second goal was to address as many of the issues raised during a recent peer review as possible (direct reaction of liquid water with carbon steel, stress corrosion cracking of the ceramic coating, bending stresses in coatings of finite thickness, limitations of simple correction factors, etc.). During the periods of dry oxidation (T ≥ 100°C) and humid-air corrosion (T ≤ 100°C & RH < 8O%), it is assumed that the growth rate of oxide on the surface is diminished in proportion to the surface covered by solid ceramic. The mass transfer impedance imposed by a ceramic coating with gas-filled pores is assumed to be negligible. During the period of aqueous phase corrosion (T ≤ 100°C & RH ≥ 80%), it is assumed that the overall mass transfer resistance governing the corrosion rate is due to the combined resistance of ceramic coating & interfacial corrosion products. Two porosity models (simple cylinder & cylinder-sphere chain) are considered in estimation of the mass transfer resistance of the ceramic coating. It is evident that substantial impedance to 0₂ transport is encountered if pores are filled with liquid water. It may be possible to use a sealant to eliminate porosity. Spallation (rupture) of the ceramic coating is assumed to occur if the stress introduced by the expanding corrosion products at the ceramic- CAM interface exceeds fracture stress. Since this model does not account for the possibility of

  18. 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

  19. The Assessment of Mathematical Logic: Abstract Patterns and Familiar Contexts

    ERIC Educational Resources Information Center

    Teppo, Anne R.; Esty, Warren W.; Kirkpatrick, Kay

    2003-01-01

    Undergraduate students' written exams were analyzed from a freshman-level mathematics course that emphasized, among other topics, the study of mathematical logic. Findings indicate that on questions related to the negation of a conditional sentence, students performed much better when given natural-language contexts than they did on questions…

  20. New Light on Old Horizon: Constructing Mathematical Concepts, Underlying Abstraction Processes, and Sense Making Strategies

    ERIC Educational Resources Information Center

    Scheiner, Thorsten

    2016-01-01

    The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical…

  1. Mathematical Modelling: A New Approach to Teaching Applied Mathematics.

    ERIC Educational Resources Information Center

    Burghes, D. N.; Borrie, M. S.

    1979-01-01

    Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)

  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. Mathematical models of hysteresis

    SciTech Connect

    1998-08-01

    The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.

  4. Mathematical model of sarcoidosis

    PubMed Central

    Hao, Wenrui; Crouser, Elliott D.; Friedman, Avner

    2014-01-01

    Sarcoidosis is a disease involving abnormal collection of inflammatory cells forming nodules, called granulomas. Such granulomas occur in the lung and the mediastinal lymph nodes, in the heart, and in other vital and nonvital organs. The origin of the disease is unknown, and there are only limited clinical data on lung tissue of patients. No current model of sarcoidosis exists. In this paper we develop a mathematical model on the dynamics of the disease in the lung and use patients’ lung tissue data to validate the model. The model is used to explore potential treatments. PMID:25349384

  5. 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,…

  6. 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…

  7. 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…

  8. 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…

  9. 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…

  10. 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…

  11. 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.

  12. Integrating model abstraction into monitoring strategies

    Technology Transfer Automated Retrieval System (TEKTRAN)

    This study was designed and performed to investigate the opportunities and benefits of integrating model abstraction techniques into monitoring strategies. The study focused on future applications of modeling to contingency planning and management of potential and actual contaminant release sites wi...

  13. SATURATED ZONE FLOW AND TRANSPORT MODEL ABSTRACTION

    SciTech Connect

    B.W. ARNOLD

    2004-10-27

    The purpose of the saturated zone (SZ) flow and transport model abstraction task is to provide radionuclide-transport simulation results for use in the total system performance assessment (TSPA) for license application (LA) calculations. This task includes assessment of uncertainty in parameters that pertain to both groundwater flow and radionuclide transport in the models used for this purpose. This model report documents the following: (1) The SZ transport abstraction model, which consists of a set of radionuclide breakthrough curves at the accessible environment for use in the TSPA-LA simulations of radionuclide releases into the biosphere. These radionuclide breakthrough curves contain information on radionuclide-transport times through the SZ. (2) The SZ one-dimensional (I-D) transport model, which is incorporated in the TSPA-LA model to simulate the transport, decay, and ingrowth of radionuclide decay chains in the SZ. (3) The analysis of uncertainty in groundwater-flow and radionuclide-transport input parameters for the SZ transport abstraction model and the SZ 1-D transport model. (4) The analysis of the background concentration of alpha-emitting species in the groundwater of the SZ.

  14. 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…

  15. 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…

  16. Solicited abstract: Global hydrological modeling and models

    NASA Astrophysics Data System (ADS)

    Xu, Chong-Yu

    2010-05-01

    The origins of rainfall-runoff modeling in the broad sense can be found in the middle of the 19th century arising in response to three types of engineering problems: (1) urban sewer design, (2) land reclamation drainage systems design, and (3) reservoir spillway design. Since then numerous empirical, conceptual and physically-based models are developed including event based models using unit hydrograph concept, Nash's linear reservoir models, HBV model, TOPMODEL, SHE model, etc. From the late 1980s, the evolution of global and continental-scale hydrology has placed new demands on hydrologic modellers. The macro-scale hydrological (global and regional scale) models were developed on the basis of the following motivations (Arenll, 1999). First, for a variety of operational and planning purposes, water resource managers responsible for large regions need to estimate the spatial variability of resources over large areas, at a spatial resolution finer than can be provided by observed data alone. Second, hydrologists and water managers are interested in the effects of land-use and climate variability and change over a large geographic domain. Third, there is an increasing need of using hydrologic models as a base to estimate point and non-point sources of pollution loading to streams. Fourth, hydrologists and atmospheric modellers have perceived weaknesses in the representation of hydrological processes in regional and global climate models, and developed global hydrological models to overcome the weaknesses of global climate models. Considerable progress in the development and application of global hydrological models has been achieved to date, however, large uncertainties still exist considering the model structure including large scale flow routing, parameterization, input data, etc. This presentation will focus on the global hydrological models, and the discussion includes (1) types of global hydrological models, (2) procedure of global hydrological model development

  17. 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…

  18. Mathematical Models for Elastic Structures

    NASA Astrophysics Data System (ADS)

    Villaggio, Piero

    1997-10-01

    During the seventeenth century, several useful theories of elastic structures emerged, with applications to civil and mechanical engineering problems. Recent and improved mathematical tools have extended applications into new areas such as mathematical physics, geomechanics, and biomechanics. This book offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures that are used to solve practical problems with particular emphasis on nonlinear problems.

  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. 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.

  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 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.

  3. Mathematical Models of Waiting Time.

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.; Gordon, Florence S.

    1990-01-01

    Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)

  4. 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.

  5. 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…

  6. 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…

  7. Bridging the Gap Between Common Sense and Mathematical Models

    ERIC Educational Resources Information Center

    Press, Laurence

    1975-01-01

    Describes a four-phase method of helping students who are mathematically unsophisticated and have difficulty relating their common sense, English-language understanding of a system to an abstract, mathematical description. The approach uses interactive simulation models. (Author/IRT)

  8. 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…

  9. 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.

  10. 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…

  11. 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…

  12. 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…

  13. 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.

  14. 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.

  15. 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).

  16. 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…

  17. 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…

  18. 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…

  19. 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…

  20. Mathematical Models for Somite Formation

    PubMed Central

    Baker, Ruth E.; Schnell, Santiago; Maini, Philip K.

    2009-01-01

    Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area. PMID:18023728

  1. 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…

  2. Physical and mathematical cochlear models

    NASA Astrophysics Data System (ADS)

    Lim, Kian-Meng

    2000-10-01

    The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity

  3. 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…

  4. 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…

  5. 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.

  6. The Nature of Mathematical Modeling

    NASA Astrophysics Data System (ADS)

    Gershenfeld, Neil

    2011-06-01

    Preface; 1. Introduction; Part I. Analytical Models: 2. Ordinary differential and difference equations; 3. Partial differential equations; 4. Variational principles; 5. Random systems; Part II. Numerical Models: 6. Finite differences: ordinary difference equations; 7. Finite differences: partial differential equations; 8. Finite elements; 9. Cellular automata and lattice gases; Part III. Observational Models: 10. Function fitting; 11. Transforms; 12. Architectures; 13. Optimization and search; 14. Clustering and density estimation; 15. Filtering and state estimation; 16. Linear and nonlinear time series; Appendix 1. Graphical and mathematical software; Appendix 2. Network programming; Appendix 3. Benchmarking; Appendix 4. Problem solutions; Bibliography.

  7. 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…

  8. 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.

  9. What Is Mathematical Modelling? Exploring Prospective Teachers' Use of Experiments to Connect Mathematics to the Study of Motion

    ERIC Educational Resources Information Center

    Carrejo, David J.; Marshall, Jill

    2007-01-01

    This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…

  10. Mathematical modeling of kidney transport.

    PubMed

    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.

  11. 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.

  12. 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'…

  13. 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.

  14. 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).

  15. 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.

  16. A Generative Model of Mathematics Learning

    ERIC Educational Resources Information Center

    Wittrock, M. C.

    1974-01-01

    The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

  17. On Fences, Forms and Mathematical Modeling

    ERIC Educational Resources Information Center

    Lege, Jerry

    2009-01-01

    The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

  18. Mathematical Modeling in the Secondary School Curriculum.

    ERIC Educational Resources Information Center

    Swetz, Frank, Ed.; Hartzler, J. S., Ed.

    Over the past 10 years, national conferences and committees investigating the state of American mathematics education have advocated an increased emphasis on problem solving and mathematical modeling situations in the secondary school curriculum. However, little effort has been made to prepare secondary school teachers to use mathematical modeling…

  19. 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.

  20. 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…

  1. Mathematical Modeling of Electronic Devices and Circuits

    NASA Astrophysics Data System (ADS)

    Singh, B. P.; Singh, Meena; Roy, Sanjay Kumar

    2010-11-01

    The necessity of modeling lies in the nature of technology and its advancement. The modeling minimizes time and cost of the process involved. The mathematical model provides an insight into the behavior of the physical system that reduces the problem to its essential characteristics. The floating admittance matrix (FAM) approach is an elegant method of mathematical modeling of electronic devices and circuits.

  2. A Model for Teaching College Remedial Mathematics.

    ERIC Educational Resources Information Center

    Friedman, Mordechai

    1986-01-01

    A model for teaching college remedial mathematics is presented, with information on the background, the development of the model, and the model itself, as well as a discussion of how the model is used. (MNS)

  3. 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.

  4. Mathematical model for bone mineralization

    PubMed Central

    Komarova, Svetlana V.; Safranek, Lee; Gopalakrishnan, Jay; Ou, Miao-jung Yvonne; McKee, Marc D.; Murshed, Monzur; Rauch, Frank; Zuhr, Erica

    2015-01-01

    Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly nonlinear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology. PMID:26347868

  5. 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…

  6. Mathematical models for exotic wakes

    NASA Astrophysics Data System (ADS)

    Basu, Saikat; Stremler, Mark

    2014-11-01

    Vortex wakes are a common occurrence in the environment around us; the most famous example being the von Kármán vortex street with two vortices being shed by the bluff body in each cycle. However, frequently there can be many other more exotic wake configurations with different vortex arrangements, based on the flow parameters and the bluff body dimensions and/or its oscillation characteristics. Some examples include wakes with periodic shedding of three vortices (`P+S' mode) and four vortices (symmetric `2P' mode, staggered `2P' mode, `2C' mode). We present mathematical models for such wakes assuming two-dimensional potential flows with embedded point vortices. The spatial alignment of the vortices is inspired by the experimentally observed wakes. The idealized system follows a Hamiltonian formalism. Model-based analysis reveals a rich dynamics pertaining to the relative vortex motion in the mid-wake region. Downstream evolution of the vortices, as predicted from the model results, also show good correspondence with wake-shedding experiments performed on flowing soap films.

  7. 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…

  8. Mathematical Modeling of Cellular Metabolism.

    PubMed

    Berndt, Nikolaus; Holzhütter, Hermann-Georg

    2016-01-01

    Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research. PMID:27557541

  9. Mathematical Modeling of Cellular Metabolism.

    PubMed

    Berndt, Nikolaus; Holzhütter, Hermann-Georg

    2016-01-01

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

  10. 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…

  11. 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…

  12. 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…

  13. 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…

  14. 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.

  15. 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.

  16. 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…

  17. 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.

  18. 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)

  19. Model abstraction results using state-space system identifications

    NASA Astrophysics Data System (ADS)

    Popken, Douglas A.

    2000-06-01

    In this paper we report on state-space system identification approaches to dynamic behavioral abstraction of military simulation models. Two stochastic simulation models were identified under a variety of scenarios. The `Attrition Simulation' is a model of two opposing forces with multiple weapon system types. The `Mission Simulation' is a model of a squadron of aircraft performing battlefield air interdiction. Four system identification techniques: Maximum Entropy, Compartmental Models, Canonical State-Space Models, and Hidden Markov Models (HMM), were applied to these simulation models. The system identification techniques were evaluated on how well their resulting abstractions replicated the distributions of the simulation states as well as the decision outputs. Encouraging results were achieved by the HMM technique applied to the Attrition Simulation--and by the Maximum Entropy technique applied to the Mission Simulation.

  20. Mathematical modeling of radio systems and devices

    NASA Astrophysics Data System (ADS)

    Borisov, Iu. P.; Tsvetnov, V. V.

    Methods for developing mathematical models of radio systems and devices are presented with emphasis on the functional approach to the modeling of radio systems. In particular, attention is given to the formal description of radio systems, computer-aided modeling of radio systems, a classification of methods of radio system modeling, and methods of mathematical description of signals and noise. Specific methods discussed include the carrier method, the complex envelope method, the method of statistical equivalents, and the information parameter method.

  1. The mathematics of cancer: integrating quantitative models.

    PubMed

    Altrock, Philipp M; Liu, Lin L; Michor, Franziska

    2015-12-01

    Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

  2. Mathematical models of regulatory mechanisms of sleep-wake rhythms.

    PubMed

    Nakao, M; Karashima, A; Katayama, N

    2007-05-01

    Studies of regulatory mechanisms of sleep-wake rhythms have benefited greatly from mathematical modeling. There are two major frameworks of modeling: one integrates homeostatic and circadian regulations and the other consists of multiple interacting oscillators. In this article, model constructions based on these respective frameworks and their characteristics are reviewed. The two-process model and the multioscillator model are explained in detail. An appropriate mathematical abstraction is also shown to provide a viewpoint unifying the model structures, which might seem to be distinct. Recently acquired knowledge of neural regulatory mechanisms of sleep-wake rhythm has prompted modeling at the neural network level. Such a detailed model is also reviewed, and could be used to explore a possible neural mechanism underlying a pathological state of sleep-wake rhythm. PMID:17364138

  3. Mathematical Models for Library Systems Analysis.

    ERIC Educational Resources Information Center

    Leimkuhler, F. F.

    1967-01-01

    The paper reviews the research on design and operation of research libraries sponsored by the Purdue University Libraries and the Purdue School of Industrial Engineering. The use of mathematical models in library operations research is discussed. Among the mathematical methods discussed are marginal analysis or cost minimization, computer…

  4. Mathematical Programming Models in Educational Planning.

    ERIC Educational Resources Information Center

    McNamara, James F.

    This document begins by defining and discussing educational planning. A brief overview of mathematical programing with an explanation of the general linear programing model is then provided. Some recent applications of mathematical programing techniques to educational planning problems are reviewed, and their implications for educational research…

  5. 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,…

  6. 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…

  7. Mathematical modelling of cucumber (cucumis sativus) drying

    NASA Astrophysics Data System (ADS)

    Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.

    2014-07-01

    This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.

  8. 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.

  9. 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)

  10. Mathematical models of behavior of individual animals.

    PubMed

    Tsibulsky, Vladimir L; Norman, Andrew B

    2007-01-01

    This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.

  11. 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.

  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. 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…

  14. 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…

  15. 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.

  16. 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…

  17. Tutorial: Mathematical Modeling of Library Systems.

    ERIC Educational Resources Information Center

    Rouse, William B.

    1979-01-01

    Discusses the purpose of mathematical models and reviews the phases of the modeling process--defining performance, representing the problem, predicting performance, estimating parameters, defining optimization criterion, determining solution, and implementing results. Reviews of book-use, resource allocation, and library network models are…

  18. 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…

  19. 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.

  20. Abstracts of the symposium on unsaturated flow and transport modeling

    SciTech Connect

    Not Available

    1982-03-01

    Abstract titles are: Recent developments in modeling variably saturated flow and transport; Unsaturated flow modeling as applied to field problems; Coupled heat and moisture transport in unsaturated soils; Influence of climatic parameters on movement of radionuclides in a multilayered saturated-unsaturated media; Modeling water and solute transport in soil containing roots; Simulation of consolidation in partially saturated soil materials; modeling of water and solute transport in unsaturated heterogeneous fields; Fluid dynamics and mass transfer in variably-saturated porous media; Solute transport through soils; One-dimensional analytical transport modeling; Convective transport of ideal tracers in unsaturated soils; Chemical transport in macropore-mesopore media under partially saturated conditions; Influence of the tension-saturated zone on contaminant migration in shallow water regimes; Influence of the spatial distribution of velocities in porous media on the form of solute transport; Stochastic vs deterministic models for solute movement in the field; and Stochastic analysis of flow and solute transport. (DMC)

  1. 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

  2. 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.

  3. 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…

  4. 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.

  5. Situation models, mental simulations, and abstract concepts in discourse comprehension.

    PubMed

    Zwaan, Rolf A

    2016-08-01

    This article sets out to examine the role of symbolic and sensorimotor representations in discourse comprehension. It starts out with a review of the literature on situation models, showing how mental representations are constrained by linguistic and situational factors. These ideas are then extended to more explicitly include sensorimotor representations. Following Zwaan and Madden (2005), the author argues that sensorimotor and symbolic representations mutually constrain each other in discourse comprehension. These ideas are then developed further to propose two roles for abstract concepts in discourse comprehension. It is argued that they serve as pointers in memory, used (1) cataphorically to integrate upcoming information into a sensorimotor simulation, or (2) anaphorically integrate previously presented information into a sensorimotor simulation. In either case, the sensorimotor representation is a specific instantiation of the abstract concept.

  6. 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.

  7. 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.

  8. 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.

  9. 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

  10. 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…

  11. 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

  12. 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.

  13. The Abstract Machine Model for Transaction-based System Control

    SciTech Connect

    Chassin, David P.

    2003-01-31

    Recent work applying statistical mechanics to economic modeling has demonstrated the effectiveness of using thermodynamic theory to address the complexities of large scale economic systems. Transaction-based control systems depend on the conjecture that when control of thermodynamic systems is based on price-mediated strategies (e.g., auctions, markets), the optimal allocation of resources in a market-based control system results in an emergent optimal control of the thermodynamic system. This paper proposes an abstract machine model as the necessary precursor for demonstrating this conjecture and establishes the dynamic laws as the basis for a special theory of emergence applied to the global behavior and control of complex adaptive systems. The abstract machine in a large system amounts to the analog of a particle in thermodynamic theory. The permit the establishment of a theory dynamic control of complex system behavior based on statistical mechanics. Thus we may be better able to engineer a few simple control laws for a very small number of devices types, which when deployed in very large numbers and operated as a system of many interacting markets yields the stable and optimal control of the thermodynamic system.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. Some mathematical tools for a modeller's workbench

    NASA Technical Reports Server (NTRS)

    Cohen, E.

    1984-01-01

    The development of a mathematical software tools in workbench environment to model related objects more straightforward is outlined. A computer model from informal drawings and a plastic model of a helicopter is discussed. Lofting was the predominant, characteristic modelling technique. Ships and airplane designs use lofting as a technique because they have defined surfaces, (hulls and fuselages) from vertical station cuts perpendicular to the vertical center plane defining the major axis of reflective symmetry. A turbine blade from a jet engine was modelled in this way. The aerodynamic portion and the root comes from different paradigms. The union of these two parts into a coherent model is shown.

  19. 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…

  20. Mathematical challenges in glacier modeling (Invited)

    NASA Astrophysics Data System (ADS)

    jouvet, G.

    2013-12-01

    Many of Earth's glaciers are currently shrinking and it is expected that this trend will continue as global warming progresses. To virtually reproduce the evolution of glaciers and finally to predict their future, one needs to couple models of different disciplines and scales. Indeed, the slow motion of ice is described by fluid mechanics equations while the daily snow precipitations and melting are described by hydrological and climatic models. Less visible, applied mathematics are essential to run such a coupling at two different levels: by solving numerically the underlying equations and by seeking parameters using optimisation methods. This talk aims to make visible the role of mathematics in this area. I will first present a short educational film I have made for the "Mathematics of Planet Earth 2013", which is an introduction to the topic. To go further, solving the mechanical model of ice poses several mathematical challenges due to the complexity of the equations and geometries of glaciers. Then, I will describe some strategies to deal with such difficulties and design robust simulation tools. Finally, I will present some simulations of the largest glacier of the European Alps, the Aletsch glacier. As a less unexpected application, I will show how these results allowed us to make a major advance in a police investigation started in 1926.

  1. Seeking Diversity in Mathematics Education: Mathematical Modeling in the Practice of Biologists and Mathematicians

    NASA Astrophysics Data System (ADS)

    Smith, Erick; Haarer, Shawn; Confrey, Jere

    Although reform efforts in mathematics education have called for more diverse views of mathematics, there have been few studies of how mathematics is used and takes form in practices outside of mathematics itself. Thus legitimate diverse models have largely been missing in education. This study attempts to broaden our understanding of mathematics by investigating how applied mathematicians and biologists, working together to construct dynamic population models, understand these models within the framework of their perspective practices, that is how these models take on a role as ''boundary objects'' between the two practices. By coming to understand how these models function within the practice of biology, the paper suggests that mathematics educators have the opportunity both to reevaluate their own assumptions about modeling and to build an understanding of the dialectic process necessary for these models to develop an epistemological basis that is shared across practices. Investigating this dialectic process is both important and missing in most mathematical classrooms.1

  2. 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.

  3. Mathematical model for citric acid fermentation.

    PubMed

    Hu, J; Wu, P

    1993-01-01

    The kinetics for biomass proliferation, medium consumption and citric acid production in the course of citric acid fermentation were studied, and the mathematical models describing the course of citric acid fermentation were obtained in this paper. Based on the statistical data of experiment, the model was verified, and the model parameters were estimated with the results of the experiment. The results showed that the curves obtained by model calculation fitted with the ones determined by the experiments well, and the models described correctly the course of the citric acid fermentation. This is important for computer application to control the course of fermentation and realize the optimum of fermentation process.

  4. 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

  5. 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.

  6. 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.

  7. The stability of colorectal cancer mathematical models

    NASA Astrophysics Data System (ADS)

    Khairudin, Nur Izzati; Abdullah, Farah Aini

    2013-04-01

    Colorectal cancer is one of the most common types of cancer. To better understand about the kinetics of cancer growth, mathematical models are used to provide insight into the progression of this natural process which enables physicians and oncologists to determine optimal radiation and chemotherapy schedules and develop a prognosis, both of which are indispensable for treating cancer. This thesis investigates the stability of colorectal cancer mathematical models. We found that continuous saturating feedback is the best available model of colorectal cancer growth. We also performed stability analysis. The result shows that cancer progress in sequence of genetic mutations or epigenetic which lead to a very large number of cells population until become unbounded. The cell population growth initiate and its saturating feedback is overcome when mutation changes causing the net per-capita growth rate of stem or transit cells exceed critical threshold.

  8. 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)

  9. 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.…

  10. 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.…

  11. Computing Linear Mathematical Models Of Aircraft

    NASA Technical Reports Server (NTRS)

    Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

    1991-01-01

    Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.

  12. Editorial: Mathematical modelling of infectious diseases.

    PubMed

    Fenton, Andy

    2016-06-01

    The field of disease ecology - the study of the spread and impact of parasites and pathogens within their host populations and communities - has a long history of using mathematical models. Dating back over 100 years, researchers have used mathematics to describe the spread of disease-causing agents, understand the relationship between host density and transmission and plan control strategies. The use of mathematical modelling in disease ecology exploded in the late 1970s and early 1980s through the work of Anderson and May (Anderson and May, 1978, 1981, 1992; May and Anderson, 1978), who developed the fundamental frameworks for studying microparasite (e.g. viruses, bacteria and protozoa) and macroparasite (e.g. helminth) dynamics, emphasizing the importance of understanding features such as the parasite's basic reproduction number (R 0) and critical community size that form the basis of disease ecology research to this day. Since the initial models of disease population dynamics, which primarily focused on human diseases, theoretical disease research has expanded hugely to encompass livestock and wildlife disease systems, and also to explore evolutionary questions such as the evolution of parasite virulence or drug resistance. More recently there have been efforts to broaden the field still further, to move beyond the standard 'one-host-one-parasite' paradigm of the original models, to incorporate many aspects of complexity of natural systems, including multiple potential host species and interactions among multiple parasite species. PMID:27027318

  13. 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)

  14. 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…

  15. "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…

  16. 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…

  17. 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. PMID:25765193

  18. 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.

  19. Basic Perforator Flap Hemodynamic Mathematical Model

    PubMed Central

    Tao, Youlun; Ding, Maochao; Wang, Aiguo; Zhuang, Yuehong; Chang, Shi-Min; Mei, Jin; Hallock, Geoffrey G.

    2016-01-01

    Background: A mathematical model to help explain the hemodynamic characteristics of perforator flaps based on blood flow resistance systems within the flap will serve as a theoretical guide for the future study and clinical applications of these flaps. Methods: There are 3 major blood flow resistance network systems of a perforator flap. These were defined as the blood flow resistance of an anastomosis between artery and artery of adjacent perforasomes, between artery and vein within a perforasome, and then between vein and vein corresponding to the outflow of that perforasome. From this, a calculation could be made of the number of such blood flow resistance network systems that must be crossed for all perforasomes within a perforator flap to predict whether that arrangement would be viable. Results: The summation of blood flow resistance networks from each perforasome in a given perforator flap could predict which portions would likely survive. This mathematical model shows how this is directly dependent on the location of the vascular pedicle to the flap and whether supercharging or superdrainage maneuvers have been added. These configurations will give an estimate of the hemodynamic characteristics for the given flap design. Conclusions: This basic mathematical model can (1) conveniently determine the degree of difficulty for each perforasome within a perforator flap to survive; (2) semiquantitatively allow the calculation of basic hemodynamic parameters; and (3) allow the assessment of the pros and cons expected for each pattern of perforasomes encountered clinically based on predictable hemodynamic observations. PMID:27579238

  20. 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…

  1. Mathematical models of breast and ovarian cancers.

    PubMed

    Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron

    2016-07-01

    Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review, we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, as answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. WIREs Syst Biol Med 2016, 8:337-362. doi: 10.1002/wsbm.1343 For further resources related to this article, please visit the WIREs website. PMID:27259061

  2. Mathematical analysis of a muscle architecture model.

    PubMed

    Navallas, Javier; Malanda, Armando; Gila, Luis; Rodríguez, Javier; Rodríguez, Ignacio

    2009-01-01

    Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area; and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition, a considerable 'edge effect' is present in the outer zone of the muscle cross-section, making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size.

  3. A Review of Mathematical Models for Leukemia and Lymphoma

    PubMed Central

    Clapp, Geoffrey; Levy, Doron

    2014-01-01

    Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

  4. 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.

  5. 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.

  6. 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.

  7. Mathematical and computational models of plasma flows

    NASA Astrophysics Data System (ADS)

    Brushlinsky, K. V.

    Investigations of plasma flows are of interest, firstly, due to numerous applications, and secondly, because of their general principles, which form a special branch of physics: the plasma dynamics. Numerical simulation and computation, together with theoretic and experimental methods, play an important part in these investigations. Speaking on flows, a relatively dense plasma is mentioned, so its mathematical models appertain to the fluid mechanics, i.e., they are based on the magnetohydrodynamic description of plasma. Time dependent two dimensional models of plasma flows of two wide-spread types are considered: the flows across the magnetic field and those in the magnetic field plane.

  8. 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.

  9. Mathematical model on a desalination process

    SciTech Connect

    Al-Samawi, A.A. )

    1994-05-01

    Mathematical models on the desalination of brackish water using EDR process are formulated. The product desalinated water variable is hypothesized as being dependent upon the following independent variables: total dissolved solids of the feed water, total dissolved solids of the product water, the rate of feed water, the temperature of feed water, the number of stages of membranes, and the energy consumption. The final model which is selected on statistical basis is considered appropriated for both prediction purposes and for the purpose of quantifying the separate effects of each significant variable upon the rate of production of desalted water variable. Results of the analysis are reported herein. 6 refs., 4 figs., 5 tabs.

  10. A mathematical model for the dynamics and synchronization of cows

    NASA Astrophysics Data System (ADS)

    Sun, Jie; Bollt, Erik M.; Porter, Mason A.; Dawkins, Marian S.

    2011-09-01

    We formulate a mathematical model for the daily activities of a cow (eating, lying down, and standing) in terms of a piecewise linear dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow “oscillators” together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop biological predictions. In particular, our model illustrates that it is possible for cows to synchronize less when the coupling is increased.

  11. Seeking Diversity in Mathematics Education: Mathematical Modeling in the Practice of Biologists and Mathematicians.

    ERIC Educational Resources Information Center

    Smith, Erick; Haarer, Shawn; Confrey, Jere

    1997-01-01

    Provides details of a study that attempts to broaden the understanding of mathematics by investigating how applied mathematicians and biologists collaborate in developing dynamic population models. (DDR)

  12. 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.

  13. Declarative Representation of Uncertainty in Mathematical Models

    PubMed Central

    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. PMID:22802941

  14. 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…

  15. 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…

  16. 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.

  17. Mathematical model to predict drivers' reaction speeds.

    PubMed

    Long, Benjamin L; Gillespie, A Isabella; Tanaka, Martin L

    2012-02-01

    Mental distractions and physical impairments can increase the risk of accidents by affecting a driver's ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers' performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers' reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers' reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions. PMID:22431214

  18. Mathematical model to predict drivers' reaction speeds.

    PubMed

    Long, Benjamin L; Gillespie, A Isabella; Tanaka, Martin L

    2012-02-01

    Mental distractions and physical impairments can increase the risk of accidents by affecting a driver's ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers' performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers' reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers' reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions.

  19. 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

  20. Mathematical modeling of the coating process.

    PubMed

    Toschkoff, Gregor; Khinast, Johannes G

    2013-12-01

    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.

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. A Mathematical Model of Idiopathic Pulmonary Fibrosis

    PubMed Central

    Hao, Wenrui; Marsh, Clay; Friedman, Avner

    2015-01-01

    Idiopathic pulmonary fibrosis (IPF) is a disease of unknown etiology, and life expectancy of 3-5 years after diagnosis. The incidence rate in the United States is estimated as high as 15 per 100,000 persons per year. The disease is characterized by repeated injury to the alveolar epithelium, resulting in inflammation and deregulated repair, leading to scarring of the lung tissue, resulting in progressive dyspnea and hypoxemia. The disease has no cure, although new drugs are in clinical trials and two agents have been approved for use by the FDA. In the present paper we develop a mathematical model based on the interactions among cells and proteins that are involved in the progression of the disease. The model simulations are shown to be in agreement with available lung tissue data of human patients. The model can be used to explore the efficacy of potential drugs. PMID:26348490

  6. 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.

  7. Mathematical modelling of eukaryotic DNA replication.

    PubMed

    Hyrien, Olivier; Goldar, Arach

    2010-01-01

    Eukaryotic DNA replication is a complex process. Replication starts at thousand origins that are activated at different times in S phase and terminates when converging replication forks meet. Potential origins are much more abundant than actually fire within a given S phase. The choice of replication origins and their time of activation is never exactly the same in any two cells. Individual origins show different efficiencies and different firing time probability distributions, conferring stochasticity to the DNA replication process. High-throughput microarray and sequencing techniques are providing increasingly huge datasets on the population-averaged spatiotemporal patterns of DNA replication in several organisms. On the other hand, single-molecule replication mapping techniques such as DNA combing provide unique information about cell-to-cell variability in DNA replication patterns. Mathematical modelling is required to fully comprehend the complexity of the chromosome replication process and to correctly interpret these data. Mathematical analysis and computer simulations have been recently used to model and interpret genome-wide replication data in the yeast Saccharomyces cerevisiae and Schizosaccharomyces pombe, in Xenopus egg extracts and in mammalian cells. These works reveal how stochasticity in origin usage confers robustness and reliability to the DNA replication process. PMID:20205354

  8. Building Mathematics Achievement Models in Four Countries Using TIMSS 2003

    ERIC Educational Resources Information Center

    Wang, Ze; Osterlind, Steven J.; Bergin, David A.

    2012-01-01

    Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries…

  9. 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.…

  10. Computer-Assisted Mathematics--A Model Approach.

    ERIC Educational Resources Information Center

    Bitter, Gary G.

    1987-01-01

    Discussion of need for improved mathematics education of preservice teachers focuses on a model program, the Mathematics Fitness Project, that includes a computer-generated testing system, management system, and remediation system. Use of the system to improve mathematics skills and attitudes of college students and post high school adults is…

  11. 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…

  12. Middle School Mathematics Clinic: A Theoretical Model.

    ERIC Educational Resources Information Center

    Gore, Ethel V.

    This paper describes a middle school mathematics clinic in the District of Columbia Public Schools, which was designed to aid students in the transition from mathematics in the primary grades to high school mathematics courses. It is intended to provide the low achiever with effective diagnostic and corrective instruction by the best trained…

  13. Mathematical modeling of a rotary hearth calciner

    SciTech Connect

    Meisingset, H.C.; Balchen, J.G.; Fernandez, R.

    1996-10-01

    Calcination of petroleum coke is a thermal process where green petroleum coke is heat-treated to a pre-determined temperature. During heat treatment the associated moisture is removed and the volatile combustible matter (VCM) is released. The VCM is burned in the gas phase giving the energy to sustain the process. In addition, structural changes take place. The combination of the final calcination temperature and the residence time determine the final real density of the calcined coke. Depending on its further use, different real density requirements may arise. It is important to control the dynamics of the calcination process so that the specified final quality is achieved. A dynamic mathematical model of a Rotary Hearth Calciner is presented. The model is based on physicochemical laws involving the most important phenomena taking place and the relevant calcination parameters. The temperature profile in the coke bed is predicted which in terms is related to the real density of the coke.

  14. Mathematical model of renal interstitial fibrosis

    PubMed Central

    Hao, Wenrui; Rovin, Brad H.; Friedman, Avner

    2014-01-01

    Lupus nephritis (LN) is an autoimmune disease that occurs when autoantibodies complex with self-antigen and form immune complexes that accumulate in the glomeruli. These immune complexes initiate an inflammatory response resulting in glomerular injury. LN often concomitantly affects the tubulointerstitial compartment of the kidney, leading first to interstitial inflammation and subsequently to interstitial fibrosis and atrophy of the renal tubules if not appropriately treated. Presently the only way to assess interstitial inflammation and fibrosis is through kidney biopsy, which is invasive and cannot be repeated frequently. Hence, monitoring of disease progression and response to therapy is suboptimal. In this paper we describe a mathematical model of the progress from tubulointerstitial inflammation to fibrosis. We demonstrate how the model can be used to monitor treatments for interstitial fibrosis in LN with drugs currently being developed or used for nonrenal fibrosis. PMID:25225370

  15. 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.

  16. Mathematical Modeling of the Auditory Periphery.

    NASA Astrophysics Data System (ADS)

    Koshigoe, Shozo

    The auditory periphery is conventionally divided into three parts, namely, the outer, middle, and inner ear (or cochlea). Mathematical modeling of the auditory periphery has been used for increasing our understanding of its mechanics via the simulation of experimental results, and for estimating unknown parameters. The various techniques used in this study for modeling the auditory periphery are: (1) Green function methods for investigation of the external ear directional filter functions; (2) finite difference methods in cochlear mechanical model calculations; (3) dispersion relation tests of the consistency of model calculations; (4) dispersion relation checks of experimental cochlear response data for approximate consistency with the implications of causality, linearity, time translation invariance, and minimum phase behavior; (5) dispersion relation tests of the stability of the linear cochlear models with active elements; (6) the introduction of viscosity effects in cochlear mechanics in order to account for data on the low frequency cochlear input impedance; and (7) the incorporation of a non-linear feedback outer-hair-cell model into a cochlear model in order to account for the physiological and psychological data (such as spontaneous and induced acoustic emissions from human ears and their active non-linear interactions with external stimuli).

  17. 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

  18. Mathematical modeling of acid-base physiology.

    PubMed

    Occhipinti, Rossana; Boron, Walter F

    2015-01-01

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

  19. 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.

  20. Incorporating neurophysiological concepts in mathematical thermoregulation models.

    PubMed

    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.

  1. Mathematical Model of Evolution of Brain Parcellation.

    PubMed

    Ferrante, Daniel D; Wei, Yi; Koulakov, Alexei A

    2016-01-01

    We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals. PMID:27378859

  2. Mathematical Model of Evolution of Brain Parcellation

    PubMed Central

    Ferrante, Daniel D.; Wei, Yi; Koulakov, Alexei A.

    2016-01-01

    We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals. PMID:27378859

  3. Mathematical model of tumor-immune surveillance.

    PubMed

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

    2016-09-01

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

  4. 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.

  5. 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…

  6. 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…

  7. A Proposal for Improving Students' Mathematical Attitude Based on Mathematical Modelling

    ERIC Educational Resources Information Center

    Falsetti, Marcela C.; Rodriguez, Mabel A.

    2005-01-01

    On the occasion of having to design an introductory course of mathematics for the University (UNGS, Buenos Aires, Argentina) we took into account the perspective of mathematical modelling. In this article we present the theoretical framework that we elaborated on to design our course. This framework allowed us to adapt the generic perspectives of…

  8. Mathematical model for contemplative amoeboid locomotion.

    PubMed

    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.

  9. 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.

  10. Mathematical modelling of autothermal thermophilic aerobic digesters.

    PubMed

    Gomez, J; de Gracia, M; Ayesa, E; Garcia-Heras, J L

    2007-03-01

    This paper presents a new mathematical model for Autothermal Thermophilic Aerobic Digesters. The reactor has been modelled as two completely mixed volumes to separately predict the behaviour of the liquid and gaseous phases as well as the interrelation between them. The model includes biochemical transformations based on the standard Activated Sludge Models of IWA, as well as physico-chemical transformations associated with the chemical equilibria and the mass transfer between the liquid and the gaseous phases similar to those proposed in the ADM1 of IWA. An energy balance has also been included in the model in order to predict the temperature of the system. This thermal balance takes into account all those biochemical and physico-chemical transformations that entail the most relevant heat interchanges. Reactor performance has been explored by simulation in two different scenarios: in the first where it acts as the initial stage in a Dual system, and in the second where it acts as a single-stage treatment. Each scenario enabled the identification of the relevance of the different parameters. PMID:17258787

  11. 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.

  12. 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.

  13. 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

  14. 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.

  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. PMID:25387532

  16. Mathematical modeling plasma transport in tokamaks

    SciTech Connect

    Quiang, Ji

    1995-12-31

    In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10{sup 20}/m{sup 3} with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%.

  17. 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.

  18. 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. PMID:20030966

  19. 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

  20. 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.

  1. 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.

  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. 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

  4. 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.

  5. 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.

  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 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.

  8. Mathematical Modeling of the Transmission and Control of Foodborne Pathogens and Antimicrobial Resistance at Preharvest

    PubMed Central

    Lu, Zhao; Gröhn, Yrjo T.

    2011-01-01

    Abstract Foodborne diseases are a significant health-care and economic burden. Most foodborne pathogens are enteric pathogens harbored in the gastrointestinal tract of farm animals. Understanding the transmission of foodborne pathogens and the dissemination of antimicrobial resistance at the farm level is necessary to design effective control strategies at preharvest. Mathematical models improve our understanding of pathogen dynamics by providing a theoretical framework in which factors affecting transmission and control of the pathogens can be explicitly considered. In this review, we aim to present the principles underlying the mathematical modeling of foodborne pathogens and antimicrobial resistance at the farm level to a broader audience. PMID:21043837

  9. (abstract) Simple Spreadsheet Thermal Models for Cryogenic Applications

    NASA Technical Reports Server (NTRS)

    Nash, A. E.

    1994-01-01

    Self consistent circuit analog thermal models, that can be run in commercial spreadsheet programs on personal computers, have been created to calculate the cooldown and steady state performance of cryogen cooled Dewars. The models include temperature dependent conduction and radiation effects. The outputs of the models provide temperature distribution and Dewar performance information. These models have been used to analyze the Cryogenic Telescope Test Facility (CTTF). The facility will be on line in early 1995 for its first user, the Infrared Telescope Technology Testbed (ITTT), for the Space Infrared Telescope Facility (SIRTF) at JPL. The model algorithm as well as a comparison of the model predictions and actual performance of this facility will be presented.

  10. 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.

  11. 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. PMID:26983919

  12. Modelling Mathematical Argumentation: The Importance of Qualification

    ERIC Educational Resources Information Center

    Inglis, Matthew; Mejia-Ramos, Juan; Simpson, Adrian

    2007-01-01

    In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…

  13. Mathematics Teacher TPACK Standards and Development Model

    ERIC Educational Resources Information Center

    Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis

    2009-01-01

    What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…

  14. 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…

  15. Some Models of Mathematics Teachers' Centres.

    ERIC Educational Resources Information Center

    Seiferth, Berniece B.

    There are two types of teacher centres in Great Britain, multi-purpose centres designed for all subjects of the curriculum, and topical centres which deal specifically with one area of subject matter such as mathematics, English, etc. In this paper, the five mathematics centres in London are analyzed for purpose, materials available, and…

  16. 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

  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. RAFFS: Model Checking a Robust Abstract Flash File Store

    NASA Astrophysics Data System (ADS)

    Taverne, Paul; Pronk, C. (Kees)

    This paper presents a case study in modeling and verifying a POSIX-like file store for Flash memory. This work fits in the context of Hoare's verification challenge and, in particular, Joshi and Holzmann's mini-challenge to build a verifiable file store. We have designed a simple robust file store and implemented it in the form of a Promela model. A test harness is used to exercise the file store in a number of ways. Model checking technology has been extensively used to verify the correctness of our implementation. A distinguishing feature of our approach is the (bounded) exhaustive verification of power loss recovery.

  19. 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…

  20. 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…

  1. 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…

  2. 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

  3. 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. PMID:23459865

  4. Mathematical modeling of biomass fuels formation process.

    PubMed

    Gaska, Krzysztof; Wandrasz, Andrzej J

    2008-01-01

    The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task.

  5. A mathematical model of a computational problem solving system

    NASA Astrophysics Data System (ADS)

    Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan

    2015-05-01

    This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.

  6. Abstracting the principles of development using imaging and modeling

    PubMed Central

    Xiong, Fengzhu; Megason, Sean G.

    2015-01-01

    Summary Here we look at modern developmental biology with a focus on the relationship between different approaches of investigation. We argue that direct imaging is a powerful approach not only for obtaining descriptive information but also for model generation and testing that lead to mechanistic insights. Modeling, on the other hand, conceptualizes imaging data and provides guidance to perturbations. The inquiry progresses most efficiently when a trinity of approaches—quantitative imaging (measurement), modeling (theory) and perturbation (test) —are pursued in concert, but not when one approach is dominant. Using recent studies of the zebrafish system, we show how this combination has effectively advanced classic topics in developmental biology compared to a perturbation-centric approach. Finally, we show that interdisciplinary expertise and perhaps specialization are necessary for carrying out a systematic approach, and discuss the technical hurdles. PMID:25946995

  7. An Introduction to Groups. Abstract Algebra. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 461.

    ERIC Educational Resources Information Center

    Rosenberg, Nancy S.

    A group is viewed to be one of the simplest and most interesting algebraic structures. The theory of groups has been applied to many branches of mathematics as well as to crystallography, coding theory, quantum mechanics, and the physics of elementary particles. This material is designed to help the user: 1) understand what groups are and why they…

  8. 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.

  9. Mathematical modeling and simulation of seated stability.

    PubMed

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

    2010-03-22

    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.

  10. 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

  11. 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)

  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. Physical vs. Mathematical Models in Rock Mechanics

    NASA Astrophysics Data System (ADS)

    Morozov, I. B.; Deng, W.

    2013-12-01

    One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an

  14. 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…

  15. 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…

  16. 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…

  17. 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…

  18. 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…

  19. 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

  20. Mathematical modeling of efficient protocols to control glioma growth.

    PubMed

    Branco, J R; Ferreira, J A; de Oliveira, Paula

    2014-09-01

    In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included.

  1. 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

  2. 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

  3. 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

  4. Mathematical modeling of urea transport in the kidney.

    PubMed

    Layton, Anita T

    2014-01-01

    Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.

  5. 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.

  6. [Mathematical model of value of population].

    PubMed

    Sha, J; Wang, S

    1983-09-29

    The authors define the value of population as an economic concept and present mathematical formulas for calculating this value. Included in this theoretical discussion are different kinds of surplus value of population and the social significance of population value. PMID:12279805

  7. 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…

  8. 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,…

  9. Pragmatism, mathematical models, and the scientific ideal of prediction and control.

    PubMed

    Moore, J

    2015-05-01

    Mathematical models are often held to be valuable, if not necessary, for theories and explanations in the quantitative analysis of behavior. The present review suggests that mathematical models primarily derived from the observation of functional relations do indeed contribute to the scientific value of theories and explanations, even though the final form of the models appears to be highly abstract. However, mathematical models not primarily so derived risk being essentialist in character, based on a particular view of formal causation. Such models invite less effective and frequently mentalistic theories and explanations of behavior. Models may be evaluated in terms of both (a) the verbal processes responsible for their origin and development and (b) the prediction and control engendered by the theories and explanations that incorporate the models, however indirect or abstract that prediction and control may be. Overall, the present review suggests that technological application and theoretical contemplation may be usefully viewed as continuous and overlapping forms of scientific activity, rather than dichotomous and mutually exclusive.

  10. Pragmatism, mathematical models, and the scientific ideal of prediction and control.

    PubMed

    Moore, J

    2015-05-01

    Mathematical models are often held to be valuable, if not necessary, for theories and explanations in the quantitative analysis of behavior. The present review suggests that mathematical models primarily derived from the observation of functional relations do indeed contribute to the scientific value of theories and explanations, even though the final form of the models appears to be highly abstract. However, mathematical models not primarily so derived risk being essentialist in character, based on a particular view of formal causation. Such models invite less effective and frequently mentalistic theories and explanations of behavior. Models may be evaluated in terms of both (a) the verbal processes responsible for their origin and development and (b) the prediction and control engendered by the theories and explanations that incorporate the models, however indirect or abstract that prediction and control may be. Overall, the present review suggests that technological application and theoretical contemplation may be usefully viewed as continuous and overlapping forms of scientific activity, rather than dichotomous and mutually exclusive. PMID:25596451

  11. 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.

  12. Classical and Weak Solutions for Two Models in Mathematical Finance

    NASA Astrophysics Data System (ADS)

    Gyulov, Tihomir B.; Valkov, Radoslav L.

    2011-12-01

    We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.

  13. 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.)

  14. 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…

  15. 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…

  16. 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…

  17. Evaluation of Limb Load Asymmetry Using Two New Mathematical Models

    PubMed Central

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

    2015-01-01

    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. PMID:25716372

  18. Mathematical Modeling of the Induced Mutation Process in Bacterial Cells

    NASA Astrophysics Data System (ADS)

    Belov, Oleg V.; Krasavin, Evgeny A.; Parkhomenko, Alexander Yu.

    2010-01-01

    A mathematical model of the ultraviolet (UV) irradiation-induced mutation process in bacterial cells Escherichia coli is developed. Using mathematical approaches, the whole chain of events is tracked from a cell exposure to the damaging factor to mutation formation in the DNA chain. An account of the key special features of the regulation of this genetic network allows predicting the effects induced by the cell exposure to certain UV energy fluence.

  19. Mathematical modeling and physical reality in noncovalent interactions.

    PubMed

    Politzer, Peter; Murray, Jane S; Clark, Timothy

    2015-03-01

    The Hellmann-Feynman theorem provides a straightforward interpretation of noncovalent bonding in terms of Coulombic interactions, which encompass polarization (and accordingly include dispersion). Exchange, Pauli repulsion, orbitals, etc., are part of the mathematics of obtaining the system's wave function and subsequently its electronic density. They do not correspond to physical forces. Charge transfer, in the context of noncovalent interactions, is equivalent to polarization. The key point is that mathematical models must not be confused with physical reality. PMID:25697332

  20. Mathematical Modeling and the Redesign of a Teaching Ambulatory Clinic

    ERIC Educational Resources Information Center

    Baker, Duke H.; Mamlin, Joseph

    1976-01-01

    Mathematical modeling was utilized in the planning and decision-making process involved in reorganizing a teaching clinic to effect continuity of care. The model interrelated physicians, time, and space, facilitating value judgments and decisions. The reorganization was successful and the outcomes remarkably similar to model predictions.…

  1. Mathematical Modelling in Physics and Engineering--Part 2.

    ERIC Educational Resources Information Center

    Oke, K. H.; Jones, A. L.

    1982-01-01

    Mathematical modelling and an example used with undergraduates were presented in part 1 (v17, n5, p212-18, 1982). A second example, Power from Windmills, is provided which has considerable potential for development both as a model and as a series of modelling experiences of increasing difficulty for students with different backgrounds. (Author/JN)

  2. An Introduction to Mathematical Modelling for Ecologists and Environmental Scientists.

    ERIC Educational Resources Information Center

    Smith, I. R.; Henderson-Sellers, B.

    1981-01-01

    Describes the basic philosophy, nomenclature, and techniques used in mathematical modelling to enable biologists, engineers, land managers, and others to understand the concepts and usefulness of models. Contrasts conceptual and empirical approaches, using ecosystem models as an example of the former. (DC)

  3. A survey of mathematics-based equivalent-circuit and electrochemical battery models for hybrid and electric vehicle simulation

    NASA Astrophysics Data System (ADS)

    Seaman, Aden; Dao, Thanh-Son; McPhee, John

    2014-06-01

    In this paper, we survey two kinds of mathematics-based battery models intended for use in hybrid and electric vehicle simulation. The first is circuit-based, which is founded upon the electrical behaviour of the battery, and abstracts away the electrochemistry into equivalent electrical components. The second is chemistry-based, which is founded upon the electrochemical equations of the battery chemistry.

  4. 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.

  5. 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.

  6. A Review on Mathematical Modeling for Textile Processes

    NASA Astrophysics Data System (ADS)

    Chattopadhyay, R.

    2015-10-01

    Mathematical model is a powerful tool in engineering for studying variety of problems related to design and development of products and processes, optimization of manufacturing process, understanding a phenomenon and predicting product's behaviour in actual use. An insight of the process and use of appropriate mathematical tools are necessary for developing models. In the present paper, a review of types of model, procedure followed in developing them and their limitations have been discussed. Modeling techniques being used in few textile processes available in the literature have been cited as examples.

  7. 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.

  8. A Mathematical Model for Evolution and SETI

    NASA Astrophysics Data System (ADS)

    Maccone, Claudio

    2011-12-01

    Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl 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 fl 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.

  9. 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. PMID:22139521

  10. 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.

  11. 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

  12. An agent-based mathematical model about carp aggregation

    NASA Astrophysics Data System (ADS)

    Liang, Yu; Wu, Chao

    2005-05-01

    This work presents an agent-based mathematical model to simulate the aggregation of carp, a harmful fish in North America. The referred mathematical model is derived from the following assumptions: (1) instead of the consensus among every carps involved in the aggregation, the aggregation of carp is completely a random and spontaneous physical behavior of numerous of independent carp; (2) carp aggregation is a collective effect of inter-carp and carp-environment interaction; (3) the inter-carp interaction can be derived from the statistical analytics about large-scale observed data. The proposed mathematical model is mainly based on empirical inter-carp force field, whose effect is featured with repulsion, parallel orientation, attraction, out-of-perception zone, and blind. Based on above mathematical model, the aggregation behavior of carp is formulated and preliminary simulation results about the aggregation of small number of carps within simple environment are provided. Further experiment-based validation about the mathematical model will be made in our future work.

  13. Redundancy management of electrohydraulic servoactuators by mathematical model referencing

    NASA Technical Reports Server (NTRS)

    Campbell, R. A.

    1971-01-01

    A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.

  14. Dependability breakeven point mathematical model for production - quality strategy support

    NASA Astrophysics Data System (ADS)

    Vilcu, Adrian; Verzea, Ion; Chaib, Rachid

    2016-08-01

    This paper connects the field of dependability system with the production-quality strategies through a new mathematical model based on breakeven points. The novelties consist in the identification of the parameters of dependability system which, in safety control, represents the degree to which an item is capable of performing its required function at any randomly chosen time during its specified operating period disregarding non-operation related influences, as well as the analysis of the production-quality strategies, defining a mathematical model based on a new concept - dependability breakeven points, model validation on datasets and shows the practical applicability of this new approach.

  15. 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…

  16. 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.

  17. 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…

  18. Mathematical models of ABE fermentation: review and analysis.

    PubMed

    Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S

    2013-12-01

    Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities. PMID:23072615

  19. Mathematical models of ABE fermentation: review and analysis.

    PubMed

    Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S

    2013-12-01

    Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.

  20. Metaphors and Models in Translation between College and Workplace Mathematics

    ERIC Educational Resources Information Center

    Williams, Julian; Wake, Geoff

    2007-01-01

    We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…

  1. Mitochondrial DNA damage and efficiency of ATP biosynthesis: mathematical model.

    PubMed

    Beregovskaya, N; Maiboroda, R

    1995-01-21

    The role of mitochondrial DNA (mtDNA) damage in ageing processes and in malignant transformation of a cell is discussed. A mathematical model of the mtDNA population in a cell and in tissue is constructed. The model describes the effects of mtDNA damages accumulated during ageing and some features of malignant transformation and regeneration.

  2. PARCC Model Content Frameworks: Mathematics--Grades 3-11

    ERIC Educational Resources Information Center

    Partnership for Assessment of Readiness for College and Careers (NJ1), 2011

    2011-01-01

    As part of its proposal to the U.S. Department of Education, the Partnership for Assessment of Readiness for College and Careers (PARCC) committed to developing model content frameworks for mathematics to serve as a bridge between the Common Core State Standards and the PARCC assessments. The PARCC Model Content Frameworks were developed through a…

  3. 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…

  4. 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.

  5. 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.

  6. Rationale and resources for teaching the mathematical modeling of athletic training and performance.

    PubMed

    Clarke, David C; Skiba, Philip F

    2013-06-01

    A number of professions rely on exercise prescription to improve health or athletic performance, including coaching, fitness/personal training, rehabilitation, and exercise physiology. It is therefore advisable that the professionals involved learn the various tools available for designing effective training programs. Mathematical modeling of athletic training and performance, which we henceforth call "performance modeling," is one such tool. Two models, the critical power (CP) model and the Banister impulse-response (IR) model, offer complementary information. The CP model describes the relationship between work rates and the durations for which an individual can sustain them during constant-work-rate or intermittent exercise. The IR model describes the dynamics by which an individual's performance capacity changes over time as a function of training. Both models elegantly abstract the underlying physiology, and both can accurately fit performance data, such that educating exercise practitioners in the science of performance modeling offers both pedagogical and practical benefits. In addition, performance modeling offers an avenue for introducing mathematical modeling skills to exercise physiology researchers. A principal limitation to the adoption of performance modeling is a lack of education. The goal of this report is therefore to encourage educators of exercise physiology practitioners and researchers to incorporate the science of performance modeling in their curricula and to serve as a resource to support this effort. The resources include a comprehensive review of the concepts associated with the development and use of the models, software to enable hands-on computer exercises, and strategies for teaching the models to different audiences.

  7. 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.

  8. 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.

  9. Mathematical model of the SH-3G helicopter

    NASA Technical Reports Server (NTRS)

    Phillips, J. D.

    1982-01-01

    A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.

  10. Mathematical modelling of undrained clay behavior

    NASA Technical Reports Server (NTRS)

    Prevost, J. H.; Noeg, K.

    1976-01-01

    The proposed general analytical model describes the anisotropic, elastoplastic, path-dependent, stress-strain properties of inviscid saturated clays under undrained conditions. Model parameters are determined by using results from strain-controlled simple shear tests on a saturated clay. The model's accuracy is evaluated by applying it to predict the results of other tests on the same clay, including monotonic and cyclic loading. The model explains the very anisotropic shear strength behavior observed for weak marine clays.

  11. Mathematical models of magnetite desliming for automated quality control systems

    NASA Astrophysics Data System (ADS)

    Olevska, Yu.; Mishchenko, V.; Olevskyi, V.

    2016-10-01

    The aim of the study is to provide multifactor mathematical models suitable for use in automatic control systems of desliming process. For this purpose we described the motion of a two-phase environment regard to the shape the desliming machine and technological parameters of the enrichment process. We created the method for preparation of dependences of the enrichment process quality from the technological and design parameters. To automate the process we constructed mathematical models to justify intensive technological modes and optimal parameters for design of desliming machine.

  12. Asymmetrical passive intermodulation distortions of memristors with mathematical behavior models

    NASA Astrophysics Data System (ADS)

    Wu, Yongle; Jin, Qiuyan; Wang, Weimin; Liu, Yuanan

    2016-10-01

    A rigorous mathematical explanation and accurate numerical prediction for asymmetrical passive intermodulation (PIM) distortions of memristors are investigated in this article. This theoretical explanation is based on behavior models of memristors representing the interrelation between terminated voltages and currents. The simulated single-tone and two-tone signal spectrums for extremely low-frequency (Hz) and microwave (GHz) applications verify our proposed mathematical approach and the new discovery of asymmetrical PIM distortions. This presented method provides an innovative choice to model and simulate the external performance of circuits and systems with asymmetrical PIM distortions in the future.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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

  18. An applied mathematics perspective on stochastic modelling for climate.

    PubMed

    Majda, Andrew J; Franzke, Christian; Khouider, Boualem

    2008-07-28

    Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new low-dimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here. PMID:18445572

  19. On correct mathematical models of ecological LSS of high closure

    NASA Astrophysics Data System (ADS)

    Bartsev, S. I.

    Usually mathematical models of natural ecological systems are implicitly based on the assumption of stoichiometrically rigid metabolism In most cases such assumption is applicable but in the case of ecological systems of high closure it can cause errors of forecast For completely closed ecological system the assumption of rigid metabolism results in completely incorrect forecast Since CELSS for long-duration missions have to be of high closure then using adequate mathematical description is of great importance for successfulness of a space mission Possible variants of non-rigid metabolism applicable to different type of biological components of CELSS are considered in the paper It is shown non-rigid models of metabolism not only eliminate incorrectness of mathematical description but as well allow to obtain more adequate estimation of stability of closed ecological systems

  20. 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.

  1. 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.

  2. 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

  3. 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…

  4. A Mathematical Model for Segmenting ECG Signals

    NASA Astrophysics Data System (ADS)

    Feier, Horea; Roşu, Doina; Falniţǎ, Lucian; Roşu, Şerban; Pater, Liana

    2010-09-01

    This paper deals with the behavior of the modulus of the continuous wavelet transform (CWT) for some known mother wavelets like the Morlet wavelet and the Mexican Hat. By exploiting these properties, the models presented can behave as a segmentation/ recognition signal processing tool by modeling the temporal structure of the observed surface ECG.

  5. 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.

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

    PubMed

    Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

    2015-07-22

    A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform. PMID:26120897

  7. 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.

  8. 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.

  9. 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

  10. 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.

  11. Automatic mathematical modeling for real time simulation system

    NASA Technical Reports Server (NTRS)

    Wang, Caroline; Purinton, Steve

    1988-01-01

    A methodology for automatic mathematical modeling and generating simulation models is described. The models will be verified by running in a test environment using standard profiles with the results compared against known results. The major objective is to create a user friendly environment for engineers to design, maintain, and verify their model and also automatically convert the mathematical model into conventional code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine Simulation. It is written in LISP and MACSYMA and runs on a Symbolic 3670 Lisp Machine. The program provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. It 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. The system is then able to automatically generate the model and FORTRAN code. The future goal which is under construction is to download the FORTRAN code to VAX/VMS system for conventional computation. The SSME mathematical model will be verified in a test environment and the solution compared with the real data profile. The use of artificial intelligence techniques has shown that the process of the simulation modeling can be simplified.

  12. Physical and Mathematical Modeling in Experimental Papers.

    PubMed

    Möbius, Wolfram; Laan, Liedewij

    2015-12-17

    An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations.

  13. Physical and Mathematical Modeling in Experimental Papers.

    PubMed

    Möbius, Wolfram; Laan, Liedewij

    2015-12-17

    An increasing number of publications include modeling. Often, such studies help us to gain a deeper insight into the phenomena studied and break down barriers between experimental and theoretical communities. However, combining experimental and theoretical work is challenging for authors, reviewers, and readers. To help maximize the usefulness and impact of combined theoretical and experimental research, this Primer describes the purpose, usefulness, and different types of models and addresses the practical aspect of integrated publications by outlining characteristics of good modeling, presentation, and fruitful collaborations. PMID:26687351

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

    PubMed

    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.

  15. 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.

  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. System and mathematical modeling of quadrotor dynamics

    NASA Astrophysics Data System (ADS)

    Goodman, Jacob M.; Kim, Jinho; Gadsden, S. Andrew; Wilkerson, Stephen A.

    2015-05-01

    Unmanned aerial systems (UAS) are becoming increasingly visible in our daily lives; and range in operation from search and rescue, monitoring hazardous environments, and to the delivery of goods. One of the most popular UAS are based on a quad-rotor design. These are typically small devices that rely on four propellers for lift and movement. Quad-rotors are inherently unstable, and rely on advanced control methodologies to keep them operating safely and behaving in a predictable and desirable manner. The control of these devices can be enhanced and improved by making use of an accurate dynamic model. In this paper, we examine a simple quadrotor model, and note some of the additional dynamic considerations that were left out. We then compare simulation results of the simple model with that of another comprehensive model.

  18. Discrete mathematical physics and particle modeling

    NASA Astrophysics Data System (ADS)

    Greenspan, D.

    The theory and application of the arithmetic approach to the foundations of both Newtonian and special relativistic mechanics are explored. Using only arithmetic, a reformulation of the Newtonian approach is given for: gravity; particle modeling of solids, liquids, and gases; conservative modeling of laminar and turbulent fluid flow, heat conduction, and elastic vibration; and nonconservative modeling of heat convection, shock-wave generation, the liquid drop problem, porous flow, the interface motion of a melting solid, soap films, string vibrations, and solitons. An arithmetic reformulation of special relativistic mechanics is given for theory in one space dimension, relativistic harmonic oscillation, and theory in three space dimensions. A speculative quantum mechanical model of vibrations in the water molecule is also discussed.

  19. Some mathematical models of intermolecular autophosphorylation.

    PubMed

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

    2015-04-01

    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.

  20. Mathematical Model For Engineering Analysis And Optimization

    NASA Technical Reports Server (NTRS)

    Sobieski, Jaroslaw

    1992-01-01

    Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.

  1. 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…

  2. Mathematical modeling of clearing liquid drop diffusion after intradermal injection

    NASA Astrophysics Data System (ADS)

    Stolnitz, Mikhail M.; Bashkatov, Alexey N.; Genina, Elina A.; Tuchin, Valery V.

    2007-05-01

    The mathematical model of clearing agent diffusion after intradermal injection has been developed. Skin was presented as multilayer medium, but one layer with proper boundary conditions is considered. Analytical solution of the boundary problem for small and large time intervals is obtained.

  3. Mathematical model of single-photon emission computed tomography

    SciTech Connect

    Clough, A.V.

    1986-01-01

    Single-photon emission computed tomography (SPECT) is a nuclear-medicine imaging technique that has been shown to provide clinically useful images of radionuclide distributions within the body. The problem of quantitative determination of tomographic activity images from a projection data set leads to a mathematical inverse problem which is formulated as an integral equation. The solution of this problem then depends on an accurate mathematical model as well as a reliable and efficient inversion algorithm. The effects of attenuation and Compton scatter within the body have been incorporated into the model in the hopes of providing a more physically realistic mathematical model. The attenuated Radon transform is the mathematical basis of SPECT. In this work, the case of constant attenuation is reviewed and a new proof of the Tretiak-Metz algorithm is presented. A space-domain version of the inverse attenuated Radon transform is derived. A special case of this transform that is applicable when the object is rotationally symmetric, and attenuated Abel transform is derived, and its inverse is found. A numerical algorithm for the implementation of the inverse attenuated Radon transform with constant attenuation is described and computer simulations are performed to demonstrate the results of the inversion procedure. With the use of the single-scatter approximation and an energy-windowed detector, the effects of Compton scatter are incorporated into the model. The data are then taken to be the sum of primary photons and single-scattered photons.

  4. Fibrin polymerization as a phase transition wave: A mathematical model

    NASA Astrophysics Data System (ADS)

    Lobanov, A. I.

    2016-06-01

    A mathematical model of fibrin polymerization is described. The problem of the propagation of phase transition wave is reduced to a nonlinear Stefan problem. A one-dimensional discontinuity fitting difference scheme is described, and the results of one-dimensional computations are presented.

  5. Optimization of a new mathematical model for bacterial growth

    Technology Transfer Automated Retrieval System (TEKTRAN)

    The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...

  6. 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. PMID:27561265

  7. A mathematical model concerning reflectance from a row crop

    NASA Technical Reports Server (NTRS)

    Jaggi, R. K.

    1972-01-01

    The recent work of Allen, Gayle, and Richardson (1970) and Suits (1972) has been extended to compute directional reflectance from a crop row. A model is constructed which takes into account edge effects and aids in discriminating crops with leaf orientation in preferred directions. This report only contains the development of the mathematical equations. Numerical results will be published in a forthcoming report.

  8. Lesson Study: A Professional Development Model for Mathematics Reform

    ERIC Educational Resources Information Center

    Taylor, Ann R.; Anderson, Shari; Meyer, Karen; Wagner, Mary Kay; West, Christine

    2005-01-01

    In this action research report 4 teachers and 1 teacher educator use the Japanese lesson study model of professional development for 15 months in rural Carlinville, Illinois. In March 2001, 4 teachers identified a goal to improve their students' understanding of two step word problems in 2nd grade elementary mathematics. Teachers completed three…

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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…

  14. 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…

  15. Mathematical Models in Educational Planning. Education and Development, Technical Reports.

    ERIC Educational Resources Information Center

    Organisation for Economic Cooperation and Development, Paris (France).

    This volume contains papers, presented at a 1966 OECD meeting, on the possibilities of applying a number of related techniques such as mathematical model building, simulation, and systematic control theory to the problems of educational planning. The authors and their papers are (1) Richard Stone, "A View of the Conference," (2) Hector Correa, "A…

  16. 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

  17. Mathematical models for biodegradation of chlorinated solvents. 1: Model framework

    SciTech Connect

    Zhang, X.; Banerji, S.; Bajpai, R.

    1996-12-31

    Complete mineralization of chlorinated solvents by microbial action has been demonstrated under aerobic as well as anaerobic conditions. In most of the cases, it is believed that the biodegradation is initiated by broad-specificity enzymes involved in metabolism of a primary substrate. Under aerobic conditions, some of the primary carbon and energy substrates are methane, propane, toluene, phenol, and ammonia; under anaerobic conditions, glucose, sucrose, acetate, propionate, isopropanol, methanol, and even natural organics act as the carbon source. Published biochemical studies suggest that the limiting step is often the initial part of the biodegradation pathway within the microbial system. For aerobic systems, the limiting step is thought to be the reaction catalyzed by mono- and dioxygenases which are induced by most primary substrates, although some constitutive strains have been reported. Other critical features of the biodegradative pathway include: (1) activity losses of critical enzyme(s) through the action of metabolic byproducts, (2) energetic needs of contaminant biodegradation which must be met by catabolism of the primary substrates, (3) changes in metabolic patterns in mixed cultures found in nature depending on the availability of electron acceptors, and (4) the associated accumulation and disappearance of metabolic intermediates. Often, the contaminant pool itself consists of several chlorinated solvents with separate and interactive biochemical needs. The existing models address some of the issues mentioned above. However, their ability to successfully predict biological fate of chlorinated solvents in nature is severely limited due to the existing mathematical models. Limiting step(s), inactivation of critical enzymes, recovery action, energetics, and a framework for multiple degradative pathways will be presented as a comprehensive model. 91 refs.

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

    NASA Astrophysics Data System (ADS)

    Chupin, Laurent

    2016-07-01

    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.

  19. A mathematical model for predicting the viability of airborne viruses.

    PubMed

    Posada, J A; Redrow, J; Celik, I

    2010-03-01

    A mathematical model was developed to predict the viability of airborne viruses. The model uses water activity as the primary independent variable and an exponential decay function for the viability of the virus. This model was tested using published experimental data obtained by different investigators for influenza, Langat and polio viruses. The aerosolized media were modelled as a binary solution of water and sodium chloride. The water activity is related directly to the solute concentration in the binary solution. The minimum viability usually occurred just above the efflorescence point, which is the relative humidity at which the solution crystallizes. The relationship between water activity and relative humidity is based on the Köhler theory, whereby the Kelvin term was taken into account. Physical explanations are provided on the variation of viral viability at different relative humidity levels. The predictions obtained by the proposed mathematical model compare well with most of the published experimental data.

  20. 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.

  1. Making the abstract concrete: the role of norms and values in experimental modeling.

    PubMed

    Peschard, Isabelle F; van Fraassen, Bas C

    2014-06-01

    Experimental modeling is the construction of theoretical models hand in hand with experimental activity. As explained in Section 1, experimental modeling starts with claims about phenomena that use abstract concepts, concepts whose conditions of realization are not yet specified; and it ends with a concrete model of the phenomenon, a model that can be tested against data. This paper argues that this process from abstract concepts to concrete models involves judgments of relevance, which are irreducibly normative. In Section 2, we show, on the basis of several case studies, how these judgments contribute to the determination of the conditions of realization of the abstract concepts and, at the same time, of the quantities that characterize the phenomenon under study. Then, in Section 3, we compare this view on modeling with other approaches that also have acknowledged the role of relevance judgments in science. To conclude, in Section 4, we discuss the possibility of a plurality of relevance judgments and introduce a distinction between locally and generally relevant factors.

  2. 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.

  3. 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.

  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 Continuous Biotechnological Processes

    ERIC Educational Resources Information Center

    Pencheva, T.; Hristozov, I.; Shannon, A. G.

    2003-01-01

    Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

  7. 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.

  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. [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.

  10. Mathematical modelling of triple arterial stenoses.

    PubMed

    Ang, K C; Mazumdar, J

    1995-06-01

    This paper examines the effects of triple stenoses (ie. three stenoses in series) in a reasonably large artery. The model developed is axi-symmetric and blood is assumed to be a Newtonian fluid. The governing equations are the Navier-Stokes equations and the continuity equation. These equations are solved using the Finite Element Method and the FIDAP computational fluid dynamics (C.F.D.) package. Various combinations of differing degrees of stenosis in the triplet are considered. Pressure drop profiles and streamline plots of the solutions to these models show that the effects of milder stenoses are diminished in the presence of more severe ones. Also, a pressure recovery is observed whenever a mild stenosis follows a more severe stenosis in multiply stenosed arteries.

  11. 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.

  12. Mathematical modeling of pathogenicity of Cryptococcus neoformans

    PubMed Central

    Garcia, Jacqueline; Shea, John; Alvarez-Vasquez, Fernando; Qureshi, Asfia; Luberto, Chiara; Voit, Eberhard O; Del Poeta, Maurizio

    2008-01-01

    Cryptococcus neoformans (Cn) is the most common cause of fungal meningitis worldwide. In infected patients, growth of the fungus can occur within the phagolysosome of phagocytic cells, especially in non-activated macrophages of immunocompromised subjects. Since this environment is characteristically acidic, Cn must adapt to low pH to survive and efficiently cause disease. In the present work, we designed, tested, and experimentally validated a theoretical model of the sphingolipid biochemical pathway in Cn under acidic conditions. Simulations of metabolic fluxes and enzyme deletions or downregulation led to predictions that show good agreement with experimental results generated post hoc and reconcile intuitively puzzling results. This study demonstrates how biochemical modeling can yield testable predictions and aid our understanding of fungal pathogenesis through the design and computational simulation of hypothetical experiments. PMID:18414484

  13. 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.

  14. On the Treatment of Airline Travelers in Mathematical Models

    PubMed Central

    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. PMID:21799782

  15. 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…

  16. 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.

  17. Mathematical models for the EPIC code

    SciTech Connect

    Buchanan, H.L.

    1981-06-03

    EPIC is a fluid/envelope type computer code designed to study the energetics and dynamics of a high energy, high current electron beam passing through a gas. The code is essentially two dimensional (x, r, t) and assumes an axisymmetric beam whose r.m.s. radius is governed by an envelope model. Electromagnetic fields, background gas chemistry, and gas hydrodynamics (density channel evolution) are all calculated self-consistently as functions of r, x, and t. The code is a collection of five major subroutines, each of which is described in some detail in this report.

  18. 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. PMID:6893348

  19. 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.

  20. Mathematical Reliability Model of Building Components by Rayleigh

    NASA Astrophysics Data System (ADS)

    Nowogońska, Beata

    2015-03-01

    The patterns of process situations play an important role in the monitoring of diagnostic processes. The adaptation of mathematical models describing the degradation processes in mechanical and electronic devices creates opportunities to develop diagnostic standards for buildings erected in traditional technology. This article presents a proposal for the prediction of building operational reliability, which is a prognostic process model within the full period of its use.

  1. 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.

  2. On a Mathematical Model of Brain Activities

    NASA Astrophysics Data System (ADS)

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

    2007-12-01

    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 [1]. 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 [2, 3]. 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.

  3. 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

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

    PubMed

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

    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

  5. 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.

  6. Mathematical analysis of intermittent gas injection model in oil production

    NASA Astrophysics Data System (ADS)

    Tasmi, Silvya, D. R.; Pudjo, S.; Leksono, M.; Edy, S.

    2016-02-01

    Intermittent gas injection is a method to help oil production process. Gas is injected through choke in surface and then gas into tubing. Gas forms three areas in tubing: gas column area, film area and slug area. Gas column is used to propel slug area until surface. A mathematical model of intermittent gas injection is developed in gas column area, film area and slug area. Model is expanding based on mass and momentum conservation. Using assume film thickness constant in tubing, model has been developed by Tasmi et. al. [14]. Model consists of 10 ordinary differential equations. In this paper, assumption of pressure in gas column is uniform. Model consist of 9 ordinary differential equations. Connection of several variables can be obtained from this model. Therefore, dynamics of all variables that affect to intermittent gas lift process can be seen from four equations. To study the behavior of variables can be analyzed numerically and mathematically. In this paper, simple mathematically analysis approach is used to study behavior of the variables. Variables that affect to intermittent gas injection are pressure in upstream valve and in gas column. Pressure in upstream valve will decrease when gas mass in valve greater than gas mass in choke. Dynamic of the pressure in the gas column will decrease and increase depending on pressure in upstream valve.

  7. Mathematical modeling of near-critical convection

    SciTech Connect

    Cox, B.L.; Pruess, K.; McKibbin, R.

    1988-01-01

    Fluid and heat flow at temperatures approaching or exceeding that at the critical point (374ºC for pure water, higher for saline fluids) may be encountered in deep zones of geothermal systems and above cooling intrusives. Laboratory experiments have demonstrated strong enhancements in heat transfer at near-critical conditions (Dunn and Hardee, 1981). We have developed special numerical techniques for modeling porous flow at near-critical conditions, which can handle the extreme non-linearities in water properties near the critical point. Our numerical experiments show strong enhancements of convective heat transfer at near-critical conditions; however, the heat transfer rates obtained in the numerical simulations are considerably smaller than those seen in the laboratory experiments by Dunn and Hardee. We discuss possible reasons for this discrepancy and develop suggestions for additional laboratory experiments.

  8. Uncovering protein interaction in abstracts and text using a novel linear model and word proximity networks

    PubMed Central

    Abi-Haidar, Alaa; Kaur, Jasleen; Maguitman, Ana; Radivojac, Predrag; Rechtsteiner, Andreas; Verspoor, Karin; Wang, Zhiping; Rocha, Luis M

    2008-01-01

    Background: We participated in three of the protein-protein interaction subtasks of the Second BioCreative Challenge: classification of abstracts relevant for protein-protein interaction (interaction article subtask [IAS]), discovery of protein pairs (interaction pair subtask [IPS]), and identification of text passages characterizing protein interaction (interaction sentences subtask [ISS]) in full-text documents. We approached the abstract classification task with a novel, lightweight linear model inspired by spam detection techniques, as well as an uncertainty-based integration scheme. We also used a support vector machine and singular value decomposition on the same features for comparison purposes. Our approach to the full-text subtasks (protein pair and passage identification) includes a feature expansion method based on word proximity networks. Results: Our approach to the abstract classification task (IAS) was among the top submissions for this task in terms of measures of performance used in the challenge evaluation (accuracy, F-score, and area under the receiver operating characteristic curve). We also report on a web tool that we produced using our approach: the Protein Interaction Abstract Relevance Evaluator (PIARE). Our approach to the full-text tasks resulted in one of the highest recall rates as well as mean reciprocal rank of correct passages. Conclusion: Our approach to abstract classification shows that a simple linear model, using relatively few features, can generalize and uncover the conceptual nature of protein-protein interactions from the bibliome. Because the novel approach is based on a rather lightweight linear model, it can easily be ported and applied to similar problems. In full-text problems, the expansion of word features with word proximity networks is shown to be useful, although the need for some improvements is discussed. PMID:18834489

  9. 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.

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

    DOE PAGES

    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 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

  11. Mathematical model for wound healing following autologous keratinocyte transplantation.

    PubMed

    Renner, Regina; Teuwen, Isabell; Gebhardt, Carl; Simon, Jan C

    2008-06-01

    In times of increasing economical pressure on the health care systems, it is important to optimise the outpatient treatment of chronic wounds. Another aim of wound healing research is to discover agents to accelerate healing. Wound healing trajectories or healing velocities can provide information to demonstrate the endpoints for wound healing. A great problem in clinical trials is to specify these parameters. Therefore, we developed a mathematical model for more transparency. In this initial project, we observed 19 wounds to construct the wound healing trajectories after transplantation of autologous keratinocytes, and the results are so encouraging that investigation in this area will continue. The developed mathematical model describes the clinical observed healing process. It was possible to find parameters to distinguish between old and young patients, retrospectively or prospectively calculate the healing rates and to determine exactly the endpoint of healing. Therefore, our model might be very useful in practices or for studies.

  12. 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

  13. 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.

  14. 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.

  15. A mathematical model of the sleep/wake cycle.

    PubMed

    Rempe, Michael J; Best, Janet; Terman, David

    2010-05-01

    We present a biologically-based mathematical model that accounts for several features of the human sleep/wake cycle. These features include the timing of sleep and wakefulness under normal and sleep-deprived conditions, ultradian rhythms, more frequent switching between sleep and wakefulness due to the loss of orexin and the circadian dependence of several sleep measures. The model demonstrates how these features depend on interactions between a circadian pacemaker and a sleep homeostat and provides a biological basis for the two-process model for sleep regulation. The model is based on previous "flip-flop" conceptual models for sleep/wake and REM/NREM and we explore whether the neuronal components in these flip-flop models, with the inclusion of a sleep-homeostatic process and the circadian pacemaker, are sufficient to account for the features of the sleep/wake cycle listed above. The model is minimal in the sense that, besides the sleep homeostat and constant cortical drives, the model includes only those nuclei described in the flip-flop models. Each of the cell groups is modeled by at most two differential equations for the evolution of the total population activity, and the synaptic connections are consistent with those described in the flip-flop models. A detailed analysis of the model leads to an understanding of the mathematical mechanisms, as well as insights into the biological mechanisms, underlying sleep/wake dynamics.

  16. 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

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

    PubMed

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

    2012-06-01

    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

  18. 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.…

  19. The Academic Merits of Modelling in Higher Mathematics Education: A Case Study

    ERIC Educational Resources Information Center

    Perrenet, Jacob; Adan, Ivo

    2010-01-01

    Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge…

  20. 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…

  1. 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.

  2. 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.

  3. Modeling the meaning of words: neural correlates of abstract and concrete noun processing.

    PubMed

    Mårtensson, Frida; Roll, Mikael; Apt, Pia; Horne, Merle

    2011-01-01

    We present a model relating analysis of abstract and concrete word meaning in terms of semantic features and contextual frames within a general framework of neurocognitive information processing. The approach taken here assumes concrete noun meanings to be intimately related to sensory feature constellations. These features are processed by posterior sensory regions of the brain, e.g. the occipital lobe, which handles visual information. The interpretation of abstract nouns, however, is likely to be more dependent on semantic frames and linguistic context. A greater involvement of more anteriorly located, perisylvian brain areas has previously been found for the processing of abstract words. In the present study, a word association test was carried out in order to compare semantic processing in healthy subjects (n=12) with subjects with aphasia due to perisylvian lesions (n=3) and occipital lesions (n=1). The word associations were coded into different categories depending on their semantic content. A double dissociation was found, where, compared to the controls, the perisylvian aphasic subjects had problems associating to abstract nouns and produced fewer semantic framebased associations, whereas the occipital aphasic subject showed disturbances in concrete noun processing and made fewer semantic feature based associations.

  4. Preventing clonal evolutionary processes in cancer: Insights from mathematical models.

    PubMed

    Rodriguez-Brenes, Ignacio A; Wodarz, Dominik

    2015-07-21

    Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.

  5. 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.

  6. 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.

  7. 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

  8. Kinetic modeling of α-hydrogen abstractions from unsaturated and saturated oxygenate compounds by hydrogen atoms.

    PubMed

    Paraskevas, Paschalis D; Sabbe, Maarten K; Reyniers, Marie-Françoise; Papayannakos, Nikos G; Marin, Guy B

    2014-10-01

    Hydrogen-abstraction reactions play a significant role in thermal biomass conversion processes, as well as regular gasification, pyrolysis, or combustion. In this work, a group additivity model is constructed that allows prediction of reaction rates and Arrhenius parameters of hydrogen abstractions by hydrogen atoms from alcohols, ethers, esters, peroxides, ketones, aldehydes, acids, and diketones in a broad temperature range (300-2000 K). A training set of 60 reactions was developed with rate coefficients and Arrhenius parameters calculated by the CBS-QB3 method in the high-pressure limit with tunneling corrections using Eckart tunneling coefficients. From this set of reactions, 15 group additive values were derived for the forward and the reverse reaction, 4 referring to primary and 11 to secondary contributions. The accuracy of the model is validated upon an ab initio and an experimental validation set of 19 and 21 reaction rates, respectively, showing that reaction rates can be predicted with a mean factor of deviation of 2 for the ab initio and 3 for the experimental values. Hence, this work illustrates that the developed group additive model can be reliably applied for the accurate prediction of kinetics of α-hydrogen abstractions by hydrogen atoms from a broad range of oxygenates. PMID:25209711

  9. 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.

  10. Mathematical modeling for a thermionic-AMTEC cascade system

    SciTech Connect

    Lodhi, M.A.; Schuller, M.; Hausgen, P.

    1996-03-01

    A mathematical modeling of a system consisting of a cascade of a thermionic energy conversion (TIEC) device and an alkali metal thermal to electrical conversion (AMTEC) device has been performed. The TIEC is heated by electron bombardment which converts heat partially into electricity and rejects the remaining. The AMTEC utilizes this reject heat of the TIEC. A mathematical thermal model of the cascade converter has been developed to analyze effects of key parameters such as power level, heat fluxes, temperatures, cascade geometry, etc. In this effort, a 9-node system of nonlinear simultaneous equations has been constructed which is solved by MATHCAD predicting the temperatures of the principal components and the heat flow. Through this study, a better understanding of the thermal coupling of the two converters was gained which helps to produce a more efficient cascade. {copyright} {ital 1996 American Institute of Physics.}

  11. [Dolphin's flukes: A mathematical model of rigid wing].

    PubMed

    Romanenko, E V; Pushkov, S G; Lopatin, V N

    2015-01-01

    New analytical method is used to estimate hydrodynamic forces produced by dolphin's flukes. A mathematical model is proposed that describes dolphin's flukes as a flat rigid rectangular wing whose pitch axis location varies, heaving and pitching amplitudes are sufficiently large, and the phase angle shift for the combined oscillations can change arbitrarily. The dolphin's flukes kinematic parameters are obtained and used to estimate hydrodynamic forces.

  12. Mathematical modeling of a nickel-cadmium battery

    NASA Technical Reports Server (NTRS)

    Fan, Deyuan; White, Ralph E.

    1991-01-01

    Extensions are presented for a mathematical model of an Ni-CD cell (Fan and White, 1991). These extensions consist of intercalation thermodynamics for the nickel electrode and oxygen generation and reduction reactions during charge and overcharge. The simulated results indicate that intercalation may be important in the nickel electrode and that including the oxygen reactions provides a means of predicting the efficiency of the cell on charge and discharge.

  13. 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.

  14. 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.

  15. Mathematical analysis techniques for modeling the space network activities

    NASA Technical Reports Server (NTRS)

    Foster, Lisa M.

    1992-01-01

    The objective of the present work was to explore and identify mathematical analysis techniques, and in particular, the use of linear programming. This topic was then applied to the Tracking and Data Relay Satellite System (TDRSS) in order to understand the space network better. Finally, a small scale version of the system was modeled, variables were identified, data was gathered, and comparisons were made between actual and theoretical data.

  16. [Dolphin's flukes: A mathematical model of rigid wing].

    PubMed

    Romanenko, E V; Pushkov, S G; Lopatin, V N

    2015-01-01

    New analytical method is used to estimate hydrodynamic forces produced by dolphin's flukes. A mathematical model is proposed that describes dolphin's flukes as a flat rigid rectangular wing whose pitch axis location varies, heaving and pitching amplitudes are sufficiently large, and the phase angle shift for the combined oscillations can change arbitrarily. The dolphin's flukes kinematic parameters are obtained and used to estimate hydrodynamic forces. PMID:26852573

  17. A Mathematical Model of Cancer Treatment by Radiotherapy

    PubMed Central

    Yang, Chenxue

    2014-01-01

    A periodic mathematical model of cancer treatment by radiotherapy is presented and studied in this paper. Conditions on the coexistence of the healthy and cancer cells are obtained. Furthermore, sufficient conditions on the existence and globally asymptotic stability of the positive periodic solution, the cancer eradication periodic solution, and the cancer win periodic solution are established. Some numerical examples are shown to verify the validity of the results. A discussion is presented for further study. PMID:25478002

  18. Mathematical modeling of stormwater pollution in a tidal embayment

    SciTech Connect

    Najjar, K.F.

    1989-01-01

    It has been recognized for many years that stormwater runoff provides a transport mechanism for non-point pollutants into the nation's waterways. As more watershed areas continue to urbanize, greater increases in pollutant loadings will continue to impact the water quality of the receiving water bodies. In many instances, the pollutant impact exceeds the assimilative capacity of the receiving water. To estimate the potential impacts of stormwater pollution, mathematical models are constructed. In this dissertation, mathematical models have been constructed to estimate the non-point pollutant loadings from an urbanizing area as well as to model the assimilative capacity of the receiving tidal embayment system. The models are capable of simulating the hydrologic aspects as well as the water quality cycles of the system as a function of urbanization. In determining the response of the receiving water system to stormwater loadings, the change in receiving water quality is modeled spatially as well as temporally. The overall model is composed of three subsystem models: a stormwater model, a hydrodynamic tidal model, and a receiving water quality model. Construction of the stormwater model is based on STORM (Storage, Treatment, Overflow, Runoff Model) by the US Army Corps of Engineers. A ground water component to the model has been added to adjust the model for application to the study area, Lakes Bay, New Jersey. The tidal model is developed from a pseudo two-dimensional approach. The methodology utilizes the link-node concept to simulate the embayment system. Solutions to equations of motion and continuity are solved using a finite difference method. The receiving water quality model is a two-dimensional time variable water quality model which is based in a finite segment approach.

  19. 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

  20. 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.

  1. The limitations of mathematical modeling in high school physics education

    NASA Astrophysics Data System (ADS)

    Forjan, Matej

    The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems

  2. 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

  3. Mathematical Model of a Thermostating Coating with a Thermoelectric Module

    NASA Astrophysics Data System (ADS)

    Zarubin, V. S.; Kuvyrkin, G. N.; Savel‧eva, I. Yu.

    2015-11-01

    On the basis of a variational formulation of the problem of stationary heat conduction in a heterogeneous solid, a mathematical model of a fragment of a flat heat-insulating layer containing a thermoelectric module has been constructed. This model has been used to establish conditions under which, when fulfilled, the heat-insulating layer can serve as a thermostating coating for an object with a given fixed temperature under convective-radiative heat exchange on the outer surface of the fragment under consideration. The results of the qualitative analysis of the proposed model are presented.

  4. Generalized Mathematical Model Predicting the Mechanical Processing Topography

    NASA Astrophysics Data System (ADS)

    Leonov, S. L.; Markov, A. M.; Belov, A. B.; Sczygol, N.

    2016-04-01

    We propose a unified approach for the construction of mathematical models for the formation of surface topography and calculation of its roughness parameters for different methods of machining processes. The approach is based on a process of geometric copy tool in the material which superimposes plastico-elastic deformation, oscillatory occurrences in processing and random components of the profile. The unified approach makes it possible to reduce the time forcreation of simulated stochastic model for a specific type of processing and guarantee the accuracy of geometric parameters calculation of the surface. We make an application example of generalized model for calculation of roughness density distribution Ra in external sharpening.

  5. 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…

  6. Mathematical Modelling of Cation Transport and Regulation in Yeast.

    PubMed

    Kahm, Matthiasé; Kschischo, Maik

    2016-01-01

    Mathematical modelling of ion transport is a strategy to understand the complex interplay between various ionic species and their transporters. Such models should provide new insights and suggest new interesting experiments. Two essential variables in models for ion transport and control are the membrane potential and the intracellular pH, which generates an additional layer of complexity absent from many other models of biochemical reaction pathways. The aim of this text is to introduce the reader to the basic principles and assumptions of modelling in this field. A simplified model of potassium transport will be used as an example and will be derived in a step by step manner. This forms the basis for understanding the advantages and limitations of more complex models. These are briefly reviewed at the end of this chapter.

  7. A three-dimensional mathematical model of electromagnetic casting and testing against a physical model: Part I. The mathematical model

    NASA Astrophysics Data System (ADS)

    Cook, D. P.; Evans, J. W.

    1995-02-01

    This first of two related articles describes a mathematical model for electromagnetic casting in three dimensions, i.e., where the dependent variables are functions of all three spatial coordinates. It is shown how the method of inductances can be extended to three dimensions in order to solve Maxwell's equations for the electromagnetic field in and around the caster. The principal task here is the calculation of the inductances between loops of irregular shape, and the method by which this is done is described. The computations are self-consistent ones in that the free surface of the molten metal is adjusted in response to the supporting electromagnetic forces which are themselves dependent on the shape of that surface. The computed electromagnetic forces are input into a second phase of the calculation where melt flow is computed in three dimensions using the finite element package FIDAP.

  8. The abstract geometry modeling language (AgML): experience and road map toward eRHIC

    NASA Astrophysics Data System (ADS)

    Webb, Jason; Lauret, Jerome; Perevoztchikov, Victor

    2014-06-01

    The STAR experiment has adopted an Abstract Geometry Modeling Language (AgML) as the primary description of our geometry model. AgML establishes a level of abstraction, decoupling the definition of the detector from the software libraries used to create the concrete geometry model. Thus, AgML allows us to support both our legacy GEANT 3 simulation application and our ROOT/TGeo based reconstruction software from a single source, which is demonstrably self- consistent. While AgML was developed primarily as a tool to migrate away from our legacy FORTRAN-era geometry codes, it also provides a rich syntax geared towards the rapid development of detector models. AgML has been successfully employed by users to quickly develop and integrate the descriptions of several new detectors in the RHIC/STAR experiment including the Forward GEM Tracker (FGT) and Heavy Flavor Tracker (HFT) upgrades installed in STAR for the 2012 and 2013 runs. AgML has furthermore been heavily utilized to study future upgrades to the STAR detector as it prepares for the eRHIC era. With its track record of practical use in a live experiment in mind, we present the status, lessons learned and future of the AgML language as well as our experience in bringing the code into our production and development environments. We will discuss the path toward eRHIC and pushing the current model to accommodate for detector miss-alignment and high precision physics.

  9. 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

    2016-02-01

    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.

  10. Analyzing electrical activities of pancreatic β cells using mathematical models.

    PubMed

    Cha, Chae Young; Powell, Trevor; Noma, Akinori

    2011-11-01

    Bursts of repetitive action potentials are closely related to the regulation of glucose-induced insulin secretion in pancreatic β cells. Mathematical studies with simple β-cell models have established the central principle that the burst-interburst events are generated by the interaction between fast membrane excitation and slow cytosolic components. Recently, a number of detailed models have been developed to simulate more realistic β cell activity based on expanded findings on biophysical characteristics of cellular components. However, their complex structures hinder our intuitive understanding of the underlying mechanisms, and it is becoming more difficult to dissect the role of a specific component out of the complex network. We have recently developed a new detailed model by incorporating most of ion channels and transporters recorded experimentally (the Cha-Noma model), yet the model satisfies the charge conservation law and reversible responses to physiological stimuli. Here, we review the mechanisms underlying bursting activity by applying mathematical analysis tools to representative simple and detailed models. These analyses include time-based simulation, bifurcation analysis and lead potential analysis. In addition, we introduce a new steady-state I-V (ssI-V) curve analysis. We also discuss differences in electrical signals recorded from isolated single cells or from cells maintaining electrical connections within multi-cell preparations. Towards this end, we perform simulations with our detailed pancreatic β-cell model.

  11. Mathematical modeling of MCFC cells/stacks and networks

    NASA Astrophysics Data System (ADS)

    Williams, M. C.; Wimer, J.; Sudhoff, F.; Archer, D.

    In this paper, various molten carbonate fuel cell (MCFC) cell/stack, network, and system models available in the public domain are discussed. Parametric and phenomenological fuel cell mathematical models are being used to simulate individual MCFC cell/stack performance. With initial demonstration of full-area, full-height 250-kW to 2-MW MCFC power plants, the spatial configuration of the MCFC stacks into networks in the fuel cell power plant takes on new importance. MCFC network and power plant system flowsheet performance is being modeled using the ASPEN system model. ASPEN is a tear and iterate flowsheet simulator in the public domain. ASPEN is suitable for MCFC network simulation since it has strong systems and property database capabilities. With emergence of larger MCFC power plant system demonstrations, system modeling of MCFC power plants is now essential. DOE routinely uses MCFC models in making performance comparisons and in decision making.

  12. 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.

  13. Analysis of unstable modes distinguishes mathematical models of flagellar motion

    PubMed Central

    Bayly, P. V.; Wilson, K. S.

    2015-01-01

    The mechanisms underlying the coordinated beating of cilia and flagella remain incompletely understood despite the fundamental importance of these organelles. The axoneme (the cytoskeletal structure of cilia and flagella) consists of microtubule doublets connected by passive and active elements. The motor protein dynein is known to drive active bending, but dynein activity must be regulated to generate oscillatory, propulsive waveforms. Mathematical models of flagellar motion generate quantitative predictions that can be analysed to test hypotheses concerning dynein regulation. One approach has been to seek periodic solutions to the linearized equations of motion. However, models may simultaneously exhibit both periodic and unstable modes. Here, we investigate the emergence and coexistence of unstable and periodic modes in three mathematical models of flagellar motion, each based on a different dynein regulation hypothesis: (i) sliding control; (ii) curvature control and (iii) control by interdoublet separation (the ‘geometric clutch’ (GC)). The unstable modes predicted by each model are used to critically evaluate the underlying hypothesis. In particular, models of flagella with ‘sliding-controlled’ dynein activity admit unstable modes with non-propulsive, retrograde (tip-to-base) propagation, sometimes at the same parameter values that lead to periodic, propulsive modes. In the presence of these retrograde unstable modes, stable or periodic modes have little influence. In contrast, unstable modes of the GC model exhibit switching at the base and propulsive base-to-tip propagation. PMID:25833248

  14. Mathematical models for predicting indoor air quality from smoking activity.

    PubMed Central

    Ott, W R

    1999-01-01

    Much progress has been made over four decades in developing, testing, and evaluating the performance of mathematical models for predicting pollutant concentrations from smoking in indoor settings. Although largely overlooked by the regulatory community, these models provide regulators and risk assessors with practical tools for quantitatively estimating the exposure level that people receive indoors for a given level of smoking activity. This article reviews the development of the mass balance model and its application to predicting indoor pollutant concentrations from cigarette smoke and derives the time-averaged version of the model from the basic laws of conservation of mass. A simple table is provided of computed respirable particulate concentrations for any indoor location for which the active smoking count, volume, and concentration decay rate (deposition rate combined with air exchange rate) are known. Using the indoor ventilatory air exchange rate causes slightly higher indoor concentrations and therefore errs on the side of protecting health, since it excludes particle deposition effects, whereas using the observed particle decay rate gives a more accurate prediction of indoor concentrations. This table permits easy comparisons of indoor concentrations with air quality guidelines and indoor standards for different combinations of active smoking counts and air exchange rates. The published literature on mathematical models of environmental tobacco smoke also is reviewed and indicates that these models generally give good agreement between predicted concentrations and actual indoor measurements. PMID:10350523

  15. 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…

  16. 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.

  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. PMID:26925235

  19. 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.

  20. A Mathematical Learning Model Including Interactions among Different Learnings

    NASA Astrophysics Data System (ADS)

    Nariyuki, Yasuhiro; Yamaguchi, Norikazu

    2015-03-01

    The mathematical learning model reported by Nitta [Phys. Rev. ST Phys. Educ. Res. 6, 020105 (2010)], which describes the transition from pre test score (fraction of the correct answer) to the post score, is extended to include interactions among different learnings. Numerical solutions of the model suggest that the effects of loss due to the different learnings possibly conceal interactive learnings from observational data.

  1. 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.

  2. Impulsive mathematical modeling of ascorbic acid metabolism in healthy subjects.

    PubMed

    Bachar, Mostafa; Raimann, Jochen G; Kotanko, Peter

    2016-03-01

    In this work, we develop an impulsive mathematical model of Vitamin C (ascorbic acid) metabolism in healthy subjects for daily intake over a long period of time. The model includes the dynamics of ascorbic acid plasma concentration, the ascorbic acid absorption in the intestines and a novel approach to quantify the glomerular excretion of ascorbic acid. We investigate qualitative and quantitative dynamics. We show the existence and uniqueness of the global asymptotic stability of the periodic solution. We also perform a numerical simulation for the entire time period based on published data reporting parameters reflecting ascorbic acid metabolism at different oral doses of ascorbic acid.

  3. 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.

  4. Mathematical model of the electric arc furnace. Final report

    SciTech Connect

    Szekely, J.

    1982-07-01

    Electric Arc Furnace Steelmaking is responsible for some 25% of the steel produced in the US and this proportion is likely to grow in the future. This operation consumes some 1.4 x 10/sup 10/ kWh annually at an overall process efficiency of about 60 to 75%. The purpose of this program has been to develop a mathematical model representing the energy transfer in electric arc furnaces with the objective of defining means for the optimization of the system, such that the energy consumption is reduced. Through the statement of the appropriate transport equations, subject to certain simplifying assumptions, a mathematical model has been developed to represent heat and fluid flow phenomena in the arc, the interaction of the arc with the bath, and bath circulation in electric arc furnaces. While there is a paucity of reliable information for the critical testing of the model as a description of industrial scale arc furnaces, there is enough data on plasmas, arcs and some industrial units to prove that the basic premises of the modelling effort are sound; indeed the predictions based on the model were found to be consistent with industrial scale measurements.

  5. A mathematical model for simulating noise suppression of lined ejectors

    NASA Technical Reports Server (NTRS)

    Watson, Willie R.

    1994-01-01

    A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

  6. A mathematical model of a sealed nickel-cadmium battery

    NASA Technical Reports Server (NTRS)

    Fan, Deyuan; White, Ralph E.

    1991-01-01

    A mathematical model for the charge and discharge of a sealed nickel-cadmium (Ni-Cd) battery is presented. The model is used to study the effect of transport properties of the electrolyte and kinetic parameters of the electrode reactions on the cell performance during the charge and discharge period. The model can also be used to demonstrate the changes of cell performance during cycling. Some comparisons between model predictions and experimental results indicate that the model predictions appear to fit the experimental data well. Sensitivity analyses illustrate that the sealed nickel-cadmium battery operates under activation control. It is also shown theoretically that oxygen generated on the positive electrode during charge is reduced electrochemically on the negative electrode.

  7. Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics

    NASA Astrophysics Data System (ADS)

    Agoshkov, V. I.; Zalesny, V. B.

    2012-03-01

    Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of Numerical Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and space coordinates. Numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples. These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean dynamics model with an observed data assimilation procedure.

  8. 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.

  9. Mathematical modeling of a hydrophilic cylinder floating on water.

    PubMed

    Mao, Zai-Sha; Yang, Chao; Chen, Jiayong

    2012-07-01

    In this paper, a hydrostatic model of the surface profile anchored to the upper edge of a vertical cylinder is proposed to explain why coins can float on water surface. The sharp edge of a cylinder is thus modeled as a round smooth surface on which the contact line may be anchored at a position according to the weight of the cylinder. The mathematical model of the surface profile is established based on the hydrostatics and a third order ordinary differential equation is resulted. Numerical solution of the model demonstrates under practical conditions the existence of the surface profiles that provide reasonable uplifting force at the contact line so that the force is available for floating coins on water surface. The proposed model explains the obviously enlarged apparent contact angle and the edge effect in the literature. The numerical simulation is found in very good agreement with the experimental data in the literature. PMID:22520711

  10. 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…

  11. 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…

  12. 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.

  13. 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

  14. Grade 3 Students' Mathematization through Modeling: Situation Models and Solution Models with Mutli-Digit Subtraction Problem Solving

    ERIC Educational Resources Information Center

    Murata, Aki; Kattubadi, Sailaja

    2012-01-01

    In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…

  15. Mathematical Modeling of Spreading Cortical Depression: Spiral and Reverberating Waves

    NASA Astrophysics Data System (ADS)

    Tuckwell, Henry C.

    2008-07-01

    Mathematical models of spreading depression are considered in the form of reaction-diffusion systems in two space dimensions. The systems are solved numerically. In the two component model with potassium and calcium ion concentrations, we demonstrate, using updated parameter values, travelling solitary waves of increased potassium and decreased calcium. These have circular wavefronts emanating from a region of application of potassium chloride. The collision of two such waves does not, as in one space dimension, result in annihilation but the formation of a unified wave with a large wavefront. For the first time we show that the mathematical model reproduces the actual properties of spreading depression waves in cortical structures. With attention to geometry, timing and location of stimuli we have succeeded in finding reverberating waves matching experiment. By simulating the technique of anodal block, spiral waves have also been demonstrated which parallel those found experimentally. The six-component model, which contains additionally sodium, chloride, glutamate and GABA, is also investigated in 2 space dimensions, including an experimentally based exchange pump for sodium and potassium. Solutions are obtained without (amplitude 29 mM external K+) and with action potentials (amplitude 44 mM external K+) with speeds of propagation, allowing for tortuosity, of 1.4 mm/minute and 2.7 mm/minute, respectively. When action potentials are included a somewhat higher pump strength is required to ensure the return to resting state.

  16. Mathematical model for estimation of meteoroid dark flight trajectory

    NASA Astrophysics Data System (ADS)

    Vinnikov, V. V.; Gritsevich, M. I.; Turchak, L. I.

    2016-10-01

    This paper is concerned with mathematical model for numerical simulation of meteoroid dynamics. The simulations of bolide ballistics are carried out via hard sphere approximation. System of differential equations for movement and heat transfer is solved in Lagrange variables via Runge-Kutta methods. The drag force of atmospheric air is computed via Henderson formula, valid for wide ranges of Reynolds and Mach numbers. The parameters of surrounding gas are obtained from standard atmosphere model. The impact pressure is computed taking into account entropy jump through bow head shockwave and consequent isentropic deceleration of the flow in the vicinity of streamlined sphere. Meteoroid fragmentation is modeled as sequential division of parent body into two parts using random weighting coefficient for parent mass. The condition for fragmentation event occur when the hemisphere-averaged value of impact pressure exceeds the threshold of relative body strength, which nonlinearly depends on ration of initial meteoroid mass to current mass of considered fragment. To compute trajectory divergence for newly-formed splinters we introduce the repulsive force, dependent on impact pressure, cross sectional areas of mutually repulsing bodies and distances between them. The set of mathematical models is implemented as the program complex. Preliminary computational results show that fragmentation altitude, terminal velocities and maximum splinter masses are in good agreement with corresponding observations and measurements.

  17. 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

  18. 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

  19. Melatonin in Epilepsy: A New Mathematical Model of Diurnal Secretion

    PubMed Central

    Kijonka, Marek; Pęcka, Marcin; Sokół, Maria

    2016-01-01

    Purpose. The main objective of the study was to create a mathematical model that describes the melatonin circadian secretion and, then the functionality of the model was tested by a comparison of the melatonin secretions in children with and without epilepsy. Material and Methods. The patients were divided into the epilepsy group (EG, n = 52) and the comparison group (CG, n = 30). The melatonin level was assessed by a radioimmunoassay method. The diurnal melatonin secretion was described using a nonlinear least squares method. Spearman's rank correlation coefficient was chosen to estimate the dependence of the acquired data. The model reproduces blood concentration profiles and its parameters were statistically analyzed using the Mann-Whitney-Wilcoxon test and logistic regression. Results. The correlation analysis performed for the EG and CG groups showed moderate correlations between age and the melatonin secretion model parameters. Patients with epilepsy are characterized by an increased phase shift of melatonin release. PMID:27478439

  20. Pulmonary fluid flow challenges for experimental and mathematical modeling.

    PubMed

    Levy, Rachel; Hill, David B; Forest, M Gregory; Grotberg, James B

    2014-12-01

    Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many challenges. The complex rheology of the fluids, interaction between fluids and structures, and complicated multi-scale geometry all add to the complexity of the problem. We provide a brief overview of approaches used to model three aspects of pulmonary fluid and flow: the surfactant layer in the deep branches of the lung, the mucus layer in the upper airway branches, and closure/reopening of the airway. We discuss models of each aspect, the potential to capture biological and therapeutic information, and open questions worthy of further investigation. We hope to promote multi-disciplinary collaboration by providing insights into mathematical descriptions of fluid-mechanics in the lung and the kinds of predictions these models can make. PMID:25096289

  1. Pulmonary Fluid Flow Challenges for Experimental and Mathematical Modeling

    PubMed Central

    Levy, Rachel; Hill, David B.; Forest, M. Gregory; Grotberg, James B.

    2014-01-01

    Modeling the flow of fluid in the lungs, even under baseline healthy conditions, presents many challenges. The complex rheology of the fluids, interaction between fluids and structures, and complicated multi-scale geometry all add to the complexity of the problem. We provide a brief overview of approaches used to model three aspects of pulmonary fluid and flow: the surfactant layer in the deep branches of the lung, the mucus layer in the upper airway branches, and closure/reopening of the airway. We discuss models of each aspect, the potential to capture biological and therapeutic information, and open questions worthy of further investigation. We hope to promote multi-disciplinary collaboration by providing insights into mathematical descriptions of fluid-mechanics in the lung and the kinds of predictions these models can make. PMID:25096289

  2. Melatonin in Epilepsy: A New Mathematical Model of Diurnal Secretion.

    PubMed

    Paprocka, Justyna; Kijonka, Marek; Pęcka, Marcin; Sokół, Maria

    2016-01-01

    Purpose. The main objective of the study was to create a mathematical model that describes the melatonin circadian secretion and, then the functionality of the model was tested by a comparison of the melatonin secretions in children with and without epilepsy. Material and Methods. The patients were divided into the epilepsy group (EG, n = 52) and the comparison group (CG, n = 30). The melatonin level was assessed by a radioimmunoassay method. The diurnal melatonin secretion was described using a nonlinear least squares method. Spearman's rank correlation coefficient was chosen to estimate the dependence of the acquired data. The model reproduces blood concentration profiles and its parameters were statistically analyzed using the Mann-Whitney-Wilcoxon test and logistic regression. Results. The correlation analysis performed for the EG and CG groups showed moderate correlations between age and the melatonin secretion model parameters. Patients with epilepsy are characterized by an increased phase shift of melatonin release. PMID:27478439

  3. Pattern formation in stromatolites: insights from mathematical modelling

    PubMed Central

    Cuerno, R.; Escudero, C.; García-Ruiz, J. M.; Herrero, M. A.

    2012-01-01

    To this day, computer models for stromatolite formation have made substantial use of the Kardar–Parisi–Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means of a KPZ-based model. What can be shown, however, is that whatever their (biotic or abiotic) origin might be, some morphologies found in actual stromatolite structures (e.g. overhangs) cannot be formed as a consequence of a process modelled exclusively in terms of the KPZ equation and acting over sufficiently large times. This suggests the need to search for alternative mathematical approaches to model these structures, some of which are discussed in this paper. PMID:21993008

  4. Mathematical modeling of spinning elastic bodies for modal analysis.

    NASA Technical Reports Server (NTRS)

    Likins, P. W.; Barbera, F. J.; Baddeley, V.

    1973-01-01

    The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

  5. The prototype effect revisited: Evidence for an abstract feature model of face recognition.

    PubMed

    Wallis, Guy; Siebeck, Ulrike E; Swann, Kellie; Blanz, Volker; Bülthoff, Heinrich H

    2008-01-01

    Humans typically have a remarkable memory for faces. Nonetheless, in some cases they can be fooled. Experiments described in this paper provide new evidence for an effect in which observers falsely "recognize" a face that they have never seen before. The face is a chimera (prototype) built from parts extracted from previously viewed faces. It is known that faces of this kind can be confused with truly familiar faces, a result referred to as the prototype effect. However, recent studies have failed to find evidence for a full effect, one in which the prototype is regarded not only as familiar, but as more familiar than faces which have been seen before. This study sought to reinvestigate the effect. In a pair of experiments, evidence is reported for the full effect based on both an old/new discrimination task and a familiarity ranking task. The results are shown to be consistent with a recognition model in which faces are represented as combinations of reusable, abstract features. In a final experiment, novel predictions of the model are verified by comparing the size of the prototype effect for upright and upside-down faces. Despite the fundamentally piecewise nature of the model, an explanation is provided as to how it can also account for the sensitivity of observers to configural and holistic cues. This discussion is backed up with the use of an unsupervised network model. Overall, the paper describes how an abstract feature-based model can reconcile a range of results in the face recognition literature and, in turn, lessen currently perceived differences between the representation of faces and other objects. PMID:18484826

  6. Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation.

    PubMed

    Andasari, Vivi; Gerisch, Alf; Lolas, Georgios; South, Andrew P; Chaplain, Mark A J

    2011-07-01

    The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.

  7. Mathematical modeling of the magnetization transfer effect in tissues

    NASA Astrophysics Data System (ADS)

    Yarnykh, V.

    2016-02-01

    The term magnetization transfer (MT) describes a group of molecular processes causing incoherent exchange of magnetic energy between water and macromolecules in biological objects. Magnetic resonance imaging (MRI) can be sensitized to the MT effect using various magnetization preparation techniques. Since its introduction in early 90s, MT MRI has been used in various applications as a tool for quantitative or semi-quantitative tissue characterization and modification of tissue contrast. This review article provides an overview of biophysical mechanisms of MT in tissues, in-depth mathematical consideration of the widely used two-pool model of MT, and a summary of experimental methods used to study MT phenomena.

  8. [Reparative and neoplastic spheroid cellular structures and their mathematical model].

    PubMed

    Kogan, E A; Namiot, V A; Demura, T A; Faĭzullina, N M; Sukhikh, G T

    2014-01-01

    Spheroid cell structures in the cell cultures have been described and are used for studying cell-cell and cell- matrix interactions. At the same time, spheroid cell structure participation in the repair and development of cancer in vivo remains unexplored. The aim of this study was to investigate the cellular composition of spherical structures and their functional significance in the repair of squamous epithelium in human papilloma virus-associated cervical pathology--chronic cervicitis and cervical intraepithelial neoplasia 1-3 degree, and also construct a mathematical model to explain the development and behavior of such spheroid cell structure.

  9. Mathematical modeling of heat transfer problems in the permafrost

    NASA Astrophysics Data System (ADS)

    Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.

    2014-11-01

    In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.

  10. A mathematical model on the optimal timing of offspring desertion.

    PubMed

    Seno, Hiromi; Endo, Hiromi

    2007-06-01

    We consider the offspring desertion as the optimal strategy for the deserter parent, analyzing a mathematical model for its expected reproductive success. It is shown that the optimality of the offspring desertion significantly depends on the offsprings' birth timing in the mating season, and on the other ecological parameters characterizing the innate nature of considered animals. Especially, the desertion is less likely to occur for the offsprings born in the later period of mating season. It is also implied that the offspring desertion after a partially biparental care would be observable only with a specific condition.

  11. A mathematical model of carbon dioxide flooding with hydrate formation

    NASA Astrophysics Data System (ADS)

    Tsypkin, G. G.

    2014-10-01

    The injection of carbon dioxide into a reservoir that contains methane and water in a free state is investigated. A mathematical model of this process is proposed that suggests the formation of the CO2 hydrate on the surface of the phase transition separating regions of methane and carbon dioxide. The conditions on the interface are derived, and an asymptotic solution of the problem is found. Critical diagrams are obtained that define parameter ranges in which there is full or partial transition of gaseous carbon dioxide to a hydrate state.

  12. A mathematical model for voigt poro-visco-plastic deformation

    NASA Astrophysics Data System (ADS)

    Yang, Xin-She

    2002-03-01

    A mathematical model for poro-visco-plastic compaction and pressure solution in porous sediments has been formulated using the Voigt-type rheological constitutive relation as derived from experimental data. The governing equations reduce to a nonlinear hyperbolic heat conduction equation in the case of slow deformation where permeability is relatively high and the pore fluid pressure is nearly hydrostatic, while travelling wave exists in the opposite limit where overpressuring occurs and the pore fluid pressure is almost quasi-lithostatic. Full numerical simulation using a finite element method agree well with the approximate analytical solutions.

  13. A mathematical model on the optimal timing of offspring desertion.

    PubMed

    Seno, Hiromi; Endo, Hiromi

    2007-06-01

    We consider the offspring desertion as the optimal strategy for the deserter parent, analyzing a mathematical model for its expected reproductive success. It is shown that the optimality of the offspring desertion significantly depends on the offsprings' birth timing in the mating season, and on the other ecological parameters characterizing the innate nature of considered animals. Especially, the desertion is less likely to occur for the offsprings born in the later period of mating season. It is also implied that the offspring desertion after a partially biparental care would be observable only with a specific condition. PMID:17328918

  14. Mathematical modeling of a flat-membrane-controlled release device

    SciTech Connect

    Ramraj, R.; Farrell, S.; Loney, N.W.

    1999-08-01

    The closed form solution to a mathematical model of a flat membrane device successfully predicts the release profile of benzoic acid. Physically, the device consists of a given concentration of benzoic acid in octanol (reservoir) bounded by a microporous flat film (Cellgard 2400) with water-filled pores. The prediction shows excellent agreement with the experimentally derived release profile (maximum difference < 10%). Predicted results are obtained from the use of the steady state plus the first term of the transient solution (infinite series) and with the use of the first nonzero eigenvalue.

  15. Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

    NASA Astrophysics Data System (ADS)

    Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

    2015-09-01

    The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity

  16. Control of active sites in selective flocculation: I -- Mathematical model

    SciTech Connect

    Behl, S.; Moudgil, B.M.; Prakash, T.S. . Dept. of Materials Science and Engineering)

    1993-12-01

    Heteroflocculation has been determined to be another major reason for loss in selectivity for flocculation process. In a mathematical model developed earlier, conditions for controlling heteroflocculation were discussed. Blocking active sites to control selective adsorption of a flocculant oil a desirable solid surface is discussed. It has been demonstrated that the lower molecular weight fraction of a flocculant which is incapable of flocculating the particles is an efficient site blocking agent. The major application of selective flocculation has been in mineral processing but many potential uses exist in biological and other colloidal systems. These include purification of ceramic powders, separating hazardous solids from chemical waste, and removal of deleterious components from paper pulp.

  17. Mathematical modeling of electrochemical remediation for soils under galvanostatic conditions.

    PubMed

    Teutli León, M M; Oropeza Guzmán, M T; González, I

    2001-01-01

    This work proposes a mathematical model for the electrochemical remediation of clayey soils based on the total volume concept for a two-phase system. The mathematical formulation was done including contributions from theories for: groundwater, membranes, porous electrodes and environmental soil chemistry. The resulting model accounts for: free and complexed species in the soil matrix and the pore solution; chemical reactions taking place on either phase and/or between phases; a dynamic soil surface charge affected by the ion content of the pore solution; and electroneutrality of the total volume. Soil surface charge was included in a modified Ohm's law (voltage gradient) and in a modified Schlög's law (convective movement). Numerical implementation was done using orthogonal collocation on finite elements for spatial derivatives, and forward finite differences for time derivatives. Visual Fortran supported by IMSL subroutines was used for computer simulation. Model predictions were successfully compared with reported experimental data. Also, an analysis of pH profiles through the soil is provided for conditions when parameters including hydrostatic head, applied current density and initial pH are modified.

  18. Mathematical Modeling of Eukaryotic Cell Migration: Insights Beyond Experiments

    PubMed Central

    Danuser, Gaudenz; Allard, Jun; Mogilner, Alex

    2014-01-01

    A migrating cell is a molecular machine made of tens of thousands of short-lived and interacting parts. Understanding migration means understanding the self-organization of these parts into a system of functional units. This task is one of tackling complexity: First, the system integrates numerous chemical and mechanical component processes. Second, these processes are connected in feedback interactions and over a large range of spatial and temporal scales. Third, many processes are stochastic, which leads to heterogeneous migration behaviors. Early on in the research of cell migration it became evident that this complexity exceeds human intuition. Thus, the cell migration community has led the charge to build mathematical models that could integrate the diverse experimental observations and measurements in consistent frameworks, first in conceptual and more recently in molecularly explicit models. The main goal of this review is to sift through a series of important conceptual and explicit mathematical models of cell migration and to evaluate their contribution to the field in their ability to integrate critical experimental data. PMID:23909278

  19. The development of a mathematical model of a hybrid airship

    NASA Astrophysics Data System (ADS)

    Abdul Ghaffar, Alia Farhana

    The mathematical model of a winged hybrid airship is developed for the analysis of its dynamic stability characteristics. A full nonlinear equation of motion that describes the dynamics of the hybrid airship is determined and for completeness, some of the components in the equations are estimated using the appropriate methods that has been established and used in the past. Adequate assumptions are made in order to apply any relevant computation and estimation methods. While this hybrid airship design is unique, its modeling and stability analysis were done according to the typical procedure of conventional airships and aircrafts. All computations pertaining to the hybrid airship's equation of motion are carried out and any issues related to the integration of the wing to the conventional airship design are discussed in this thesis. The design of the hybrid airship is also slightly modified to suit the demanding requirement of a complete and feasible mathematical model. Then, linearization is performed under a chosen trim condition, and eigenvalue analysis is carried out to determine the general dynamic stability characteristics of the winged hybrid airship. The result shows that the winged hybrid airship possesses dynamic instability in longitudinal pitch motion and lateral-directional slow roll motion. This is due to the strong coupling between the aerostatic lift from the buoyant gas and aerodynamic lift from the wing.

  20. Zoonotic Transmission of Waterborne Disease: A Mathematical Model.

    PubMed

    Waters, Edward K; Hamilton, Andrew J; Sidhu, Harvinder S; Sidhu, Leesa A; Dunbar, Michelle

    2016-01-01

    Waterborne parasites that infect both humans and animals are common causes of diarrhoeal illness, but the relative importance of transmission between humans and animals and vice versa remains poorly understood. Transmission of infection from animals to humans via environmental reservoirs, such as water sources, has attracted attention as a potential source of endemic and epidemic infections, but existing mathematical models of waterborne disease transmission have limitations for studying this phenomenon, as they only consider contamination of environmental reservoirs by humans. This paper develops a mathematical model that represents the transmission of waterborne parasites within and between both animal and human populations. It also improves upon existing models by including animal contamination of water sources explicitly. Linear stability analysis and simulation results, using realistic parameter values to describe Giardia transmission in rural Australia, show that endemic infection of an animal host with zoonotic protozoa can result in endemic infection in human hosts, even in the absence of person-to-person transmission. These results imply that zoonotic transmission via environmental reservoirs is important. PMID:26733222

  1. Mathematical models for Enterococcus faecalis recovery after microwave water disinfection.

    PubMed

    Benjamin, Earl; Reznik, Aron; Benjamin, Ellis; Pramanik, Saroj K; Sowers, Louise; Williams, Arthur L

    2009-12-01

    Microwave water disinfection is a rapid purification technique which can give billions of people access to clean drinking water. However, better understanding of bacterial recovery after microwave heating over time is necessary to determine parameters such as delayed bacterial growth rates and maximum bacterial yields. Mathematical models for Enterococcus faecalis recovery after microwave treatment in optimum growth conditions were developed for times up to 5 minutes using an optical absorbance method. Microwave times below 3 minutes (2,450 MHz, 130W) showed that bacterial recovery maintained a time-dependent sigmoidal form which included a maximum value. At microwave times greater than three minutes, bacterial recovery, with a time-dependent exponential form, significantly decreased and did not reach the maximum value within the interval of observance (0-8 hours). No bacterial growth was found after 6 minutes of microwave treatment. The prepared mathematical models were produced by transforming the given variables to the logistic or exponential functions. We found that time-dependent maximum growth rates and lag times could be approximated with second order polynomial functions. The determined models can be used as a template to illustrate bacterial survival during water purification using microwave irradiation, in both commercial and industrial processes.

  2. Role of mathematical modeling in bone fracture healing

    PubMed Central

    Pivonka, Peter; Dunstan, Colin R

    2012-01-01

    Bone fracture healing is a complex physiological process commonly described by a four-phase model consisting of an inflammatory phase, two repair phases with soft callus formation followed by hard callus formation, and a remodeling phase, or more recently by an anabolic/catabolic model. Data from humans and animal models have demonstrated crucial environmental conditions for optimal fracture healing, including the mechanical environment, blood supply and availability of mesenchymal stem cells. Fracture healing spans multiple length and time scales, making it difficult to know precisely which factors and/or phases to manipulate in order to obtain optimal fracture-repair outcomes. Deformations resulting from physiological loading or fracture fixation at the organ scale are sensed at the cellular scale by cells inside the fracture callus. These deformations together with autocrine and paracrine signals determine cellular differentiation, proliferation and migration. The local repair activities lead to new bone formation and stabilization of the fracture. Although experimental data are available at different spatial and temporal scales, it is not clear how these data can be linked to provide a holistic view of fracture healing. Mathematical modeling is a powerful tool to quantify conceptual models and to establish the missing links between experimental data obtained at different scales. The objective of this review is to introduce mathematical modeling to readers who are not familiar with this methodology and to demonstrate that once validated, such models can be used for hypothesis testing and to assist in clinical treatment as will be shown for the example of atrophic nonunions. PMID:24228159

  3. Mathematical modelling of microtumour infiltration based on in vitro experiments.

    PubMed

    Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia

    2016-08-01

    The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment

  4. Mathematical modelling of microtumour infiltration based on in vitro experiments.

    PubMed

    Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia

    2016-08-01

    The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment.

  5. A New Model for the Integration of Science and Mathematics: The Balance Model

    ERIC Educational Resources Information Center

    Kiray, S. Ahmet

    2012-01-01

    The aim of this study is to develop an integrated scientific and mathematical model that is suited to the background of Turkish teachers. The dimensions of the model are given and compared to the models which have been previously developed and the findings of earlier studies on the topic. The model is called the balance, reflecting the…

  6. Evolvable mathematical models: A new artificial Intelligence paradigm

    NASA Astrophysics Data System (ADS)

    Grouchy, Paul

    We develop a novel Artificial Intelligence paradigm to generate autonomously artificial agents as mathematical models of behaviour. Agent/environment inputs are mapped to agent outputs via equation trees which are evolved in a manner similar to Symbolic Regression in Genetic Programming. Equations are comprised of only the four basic mathematical operators, addition, subtraction, multiplication and division, as well as input and output variables and constants. From these operations, equations can be constructed that approximate any analytic function. These Evolvable Mathematical Models (EMMs) are tested and compared to their Artificial Neural Network (ANN) counterparts on two benchmarking tasks: the double-pole balancing without velocity information benchmark and the challenging discrete Double-T Maze experiments with homing. The results from these experiments show that EMMs are capable of solving tasks typically solved by ANNs, and that they have the ability to produce agents that demonstrate learning behaviours. To further explore the capabilities of EMMs, as well as to investigate the evolutionary origins of communication, we develop NoiseWorld, an Artificial Life simulation in which interagent communication emerges and evolves from initially noncommunicating EMM-based agents. Agents develop the capability to transmit their x and y position information over a one-dimensional channel via a complex, dialogue-based communication scheme. These evolved communication schemes are analyzed and their evolutionary trajectories examined, yielding significant insight into the emergence and subsequent evolution of cooperative communication. Evolved agents from NoiseWorld are successfully transferred onto physical robots, demonstrating the transferability of EMM-based AIs from simulation into physical reality.

  7. Membrane transport of several ions during peritoneal dialysis: mathematical modeling.

    PubMed

    Galach, Magda; Waniewski, Jacek

    2012-09-01

    Peritoneal dialysis utilizes a complex mass exchange device created by natural permselective membranes of the visceral and abdominal muscle tissues. In mathematical modeling of solute transport during peritoneal dialysis, each solute is typically considered as a neutral, independent particle. However, such mathematical models cannot predict transport parameters for small ions. Therefore, the impact of the electrostatic interactions between ions on the estimated transport parameters needs to be investigated. In this study, transport of sodium, chloride, and a third ion through a permselective membrane with characteristics of the peritoneal transport barrier was described using two models: a model with the Nernst-Planck (NP) equations for a set of interacting ions and a model with combined diffusive and convective transport of each ion separately (DC). Transport parameters for the NP model were calculated using the pore theory, while the parameters for the DC model were estimated by fitting the model to the predictions from the NP model. Solute concentration profiles in the membrane obtained by computer simulations based on these two models were similar, whereas the transport parameters (diffusive mass transport parameters and sieving coefficients) were generally different. The presence of the third ion could substantially modify the values of diffusive mass parameter for sodium and chloride ions estimated using the DC model compared with those predicted by NP. The extent of this modification depended on the molecular mass and concentration of the third ion, and the rate of volumetric flow. Closed formulas for the transport parameters of the DC model in terms of the NP model parameters, ion concentration profiles in the membrane, and volumetric flow across the membrane were derived. Their reliable approximations, which include only boundary ion concentrations instead of spatial intramembrane concentration profiles, were formulated. The precision of this approximation

  8. Kinetic investigation and mathematical modeling of methanogenesis of glucose

    SciTech Connect

    Kalyuzhnyy, S.V.; Sklyar, V.I.; Varfolomeyev, S.D.; Gachok, V.P.

    1991-12-31

    The kinetic regularities of anaerobic conversion of glucose, and intermediates of its decomposition (ethanol, butyrate, and acetate) by a microbial methanogenic association from anaerobic digester were investigated. Kinetic scheme for conversion of glucose is suggested, and the mathematical model based on the scheme is evolved. The model includes growth and metabolism of three kinds of microorganisms-acid producents, and acetate- and hydrogen-utilizing methane producents; of cell lysis with consequent fermentation of {open_quotes}died biomass{close_quotes} to acetate, hydrogen, and carbon dioxide; of induction and repression of the enzyme responsible for decomposition of butyrate, and for a number of regulations depending on the concentrations of intermediates in glucose metabolism. The values of parameters of the model have been calculated, sufficiently describing the experimental regularities. The numerical experiments have enabled us to reveal and describe the principal regulating factors of glucose methanogenesis.

  9. Mathematical modelling of post combustion in Dofasco`s KOBM

    SciTech Connect

    Gou, H.; Irons, G.A.; Lu, W.K.

    1992-12-31

    In the AISI Direct Steelmaking program, trials were undertaken in Dofasco`s 300 Tonne KOBM to examine post combustion. To support this work, a two-dimensional turbulent mathematical model has been developed to describe gas flow, combustion reactions and heat transfer (radiation and convection) in converter-type steelmaking processes. Gaseous flow patterns, temperature and heat flux distributions in the furnace were calculated with this model. Key findings are: The post combustion ratio is determined from the rates of oxygen supply, oxygen used for decarburization and the remainder available for post combustion, i.e. deducible from a mass balance calculation, comparison between the heat transfer fluxes calculated based on the model and those measured industrially indicates that the conventionally defined heat transfer efficiency over-estimates the heat recovered by the bath by about 20%, and the location of the combustion zone can be controlled, to a certain extent, by adjusting the lance practice.

  10. Mathematical modelling of post combustion in Dofasco's KOBM

    SciTech Connect

    Gou, H.; Irons, G.A.; Lu, W.K.

    1992-01-01

    In the AISI Direct Steelmaking program, trials were undertaken in Dofasco's 300 Tonne KOBM to examine post combustion. To support this work, a two-dimensional turbulent mathematical model has been developed to describe gas flow, combustion reactions and heat transfer (radiation and convection) in converter-type steelmaking processes. Gaseous flow patterns, temperature and heat flux distributions in the furnace were calculated with this model. Key findings are: The post combustion ratio is determined from the rates of oxygen supply, oxygen used for decarburization and the remainder available for post combustion, i.e. deducible from a mass balance calculation, comparison between the heat transfer fluxes calculated based on the model and those measured industrially indicates that the conventionally defined heat transfer efficiency over-estimates the heat recovered by the bath by about 20%, and the location of the combustion zone can be controlled, to a certain extent, by adjusting the lance practice.

  11. A mathematical model for jet engine combustor pollutant emissions

    NASA Technical Reports Server (NTRS)

    Boccio, J. L.; Weilerstein, G.; Edelman, R. B.

    1973-01-01

    Mathematical modeling for the description of the origin and disposition of combustion-generated pollutants in gas turbines is presented. A unified model in modular form is proposed which includes kinetics, recirculation, turbulent mixing, multiphase flow effects, swirl and secondary air injection. Subelements of the overall model were applied to data relevant to laboratory reactors and practical combustor configurations. Comparisons between the theory and available data show excellent agreement for basic CO/H2/Air chemical systems. For hydrocarbons the trends are predicted well including higher-than-equilibrium NO levels within the fuel rich regime. Although the need for improved accuracy in fuel rich combustion is indicated, comparisons with actual jet engine data in terms of the effect of combustor-inlet temperature is excellent. In addition, excellent agreement with data is obtained regarding reduced NO emissions with water droplet and steam injection.

  12. Mathematical model of sugar uptake in fermenting yeasted dough.

    PubMed

    Loveday, S M; Winger, R J

    2007-07-25

    Fermentation prior to freezing significantly reduces the shelf life of frozen dough, measured as a decline in proofing power. Changes during fermentation caused by yeast metabolism have previously been described empirically on a dough weight basis and have not been mathematically modeled. In this work, yeast metabolites were quantified in fermenting dough and their concentrations were estimated in the aqueous environment around yeast cells. The osmotic pressure in the aqueous phase increases by 23% during 3 h of fermentation, which depresses the freezing point by 1 degrees C. The rise in osmotic pressure and the accumulation of ethanol may affect phase equilibria in the dough, baking properties, and the shelf life of frozen dough. Predictive modeling equations fitted sugar concentration data accurately. It was found that the preference of baker's yeast for glucose over fructose was stronger in fermenting dough than in liquid fermentations. The usefulness of the model in industrial bakery formulation work was demonstrated. PMID:17595109

  13. Mathematical Model of Oxygen Transport in Tuberculosis Granulomas.

    PubMed

    Datta, Meenal; Via, Laura E; Chen, Wei; Baish, James W; Xu, Lei; Barry, Clifton E; Jain, Rakesh K

    2016-04-01

    Pulmonary granulomas--the hallmark of Mycobacterium tuberculosis (MTB) infection--are dense cellular lesions that often feature regions of hypoxia and necrosis, partially due to limited transport of oxygen. Low oxygen in granulomas can impair the host immune response, while MTB are able to adapt and persist in hypoxic environments. Here, we used a physiologically based mathematical model of oxygen diffusion and consumption to calculate oxygen profiles within the granuloma, assuming Michaelis-Menten kinetics. An approximate analytical solution--using a priori and newly estimated parameters from experimental data in a rabbit model of tuberculosis--was able to predict the size of hypoxic and necrotic regions in agreement with experimental results from the animal model. Such quantitative understanding of transport limitations can inform future tuberculosis therapeutic strategies that may include adjunct host-directed therapies that facilitate oxygen and drug delivery for more effective treatment.

  14. Mathematical model and numerical algorithm for aerodynamical flow

    NASA Astrophysics Data System (ADS)

    Shaydurov, V.; Shchepanovskaya, G.; Yakubovich, M.

    2016-10-01

    In the paper, a mathematical model and a numerical algorithm are proposed for modeling an air flow. The proposed model is based on the time-dependent Navier-Stokes equations for viscous heat-conducting gas. The energy equation and the state equations are modified to account for two kinds of `internal' energy. The first one is the usual translational and rotational energy of molecules which defines the thermodynamical temperature and the pressure. The second one is the subgrid energy of small turbulent eddies. A numerical algorithm is proposed for solving the formulated initial-boundary value problem as a combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. A numerical example illustrates these approaches.

  15. Mathematical Formulation Requirements and Specifications for the Process Models

    SciTech Connect

    Steefel, C.; Moulton, D.; Pau, G.; Lipnikov, K.; Meza, J.; Lichtner, P.; Wolery, T.; Bacon, D.; Spycher, N.; Bell, J.; Moridis, G.; Yabusaki, S.; Sonnenthal, E.; Zyvoloski, G.; Andre, B.; Zheng, L.; Davis, J.

    2010-11-01

    The Advanced Simulation Capability for Environmental Management (ASCEM) is intended to be a state-of-the-art scientific tool and approach for understanding and predicting contaminant fate and transport in natural and engineered systems. The ASCEM program is aimed at addressing critical EM program needs to better understand and quantify flow and contaminant transport behavior in complex geological systems. It will also address the long-term performance of engineered components including cementitious materials in nuclear waste disposal facilities, in order to reduce uncertainties and risks associated with DOE EM's environmental cleanup and closure activities. Building upon national capabilities developed from decades of Research and Development in subsurface geosciences, computational and computer science, modeling and applied mathematics, and environmental remediation, the ASCEM initiative will develop an integrated, open-source, high-performance computer modeling system for multiphase, multicomponent, multiscale subsurface flow and contaminant transport. This integrated modeling system will incorporate capabilities for predicting releases from various waste forms, identifying exposure pathways and performing dose calculations, and conducting systematic uncertainty quantification. The ASCEM approach will be demonstrated on selected sites, and then applied to support the next generation of performance assessments of nuclear waste disposal and facility decommissioning across the EM complex. The Multi-Process High Performance Computing (HPC) Simulator is one of three thrust areas in ASCEM. The other two are the Platform and Integrated Toolsets (dubbed the Platform) and Site Applications. The primary objective of the HPC Simulator is to provide a flexible and extensible computational engine to simulate the coupled processes and flow scenarios described by the conceptual models developed using the ASCEM Platform. The graded and iterative approach to assessments naturally

  16. A mathematical model for apoptotic switch in Drosophila

    NASA Astrophysics Data System (ADS)

    Ziraldo, Riccardo; Ma, Lan

    2015-10-01

    Apoptosis is an evolutionarily-conserved process of autonomous cell death. The molecular switch mechanism underlying the fate decision of apoptosis in mammalian cells has been intensively studied by mathematical modeling. In contrast, the apoptotic switch in invertebrates, with highly conserved signaling proteins and pathway, remains poorly understood mechanistically and calls for theoretical elucidation. In this study, we develop a mathematical model of the apoptosis pathway in Drosophila and compare the switch mechanism to that in mammals. Enumeration of the elementary reactions for the model demonstrates that the molecular interactions among the signaling components are considerably different from their mammalian counterparts. A notable distinction in network organization is that the direct positive feedback from the effector caspase (EC) to the initiator caspase in mammalian pathway is replaced by a double-negative regulation in Drosophila. The model is calibrated by experimental input-output relationship and the simulated trajectories exhibit all-or-none bimodal behavior. Bifurcation diagrams confirm that the model of Drosophila apoptotic switch possesses bistability, a well-recognized feature for an apoptosis system. Since the apoptotic protease activating factor-1 (APAF1) induced irreversible activation of caspase is an essential and beneficial property for the mammalian apoptotic switch, we perform analysis of the bistable caspase activation with respect to the input of DARK protein, the Drosophila homolog of APAF1. Interestingly, this bistable behavior in Drosophila is predicted to be reversible. Further analysis suggests that the mechanism underlying the systems property of reversibility is the double-negative feedback from the EC to the initiator caspase. Using theoretical modeling, our study proposes plausible evolution of the switch mechanism for apoptosis between organisms.

  17. A mathematical model for apoptotic switch in Drosophila.

    PubMed

    Ziraldo, Riccardo; Ma, Lan

    2015-08-20

    Apoptosis is an evolutionarily-conserved process of autonomous cell death. The molecular switch mechanism underlying the fate decision of apoptosis in mammalian cells has been intensively studied by mathematical modeling. In contrast, the apoptotic switch in invertebrates, with highly conserved signaling proteins and pathway, remains poorly understood mechanistically and calls for theoretical elucidation. In this study, we develop a mathematical model of the apoptosis pathway in Drosophila and compare the switch mechanism to that in mammals. Enumeration of the elementary reactions for the model demonstrates that the molecular interactions among the signaling components are considerably different from their mammalian counterparts. A notable distinction in network organization is that the direct positive feedback from the effector caspase (EC) to the initiator caspase in mammalian pathway is replaced by a double-negative regulation in Drosophila. The model is calibrated by experimental input-output relationship and the simulated trajectories exhibit all-or-none bimodal behavior. Bifurcation diagrams confirm that the model of Drosophila apoptotic switch possesses bistability, a well-recognized feature for an apoptosis system. Since the apoptotic protease activating factor-1 (APAF1) induced irreversible activation of caspase is an essential and beneficial property for the mammalian apoptotic switch, we perform analysis of the bistable caspase activation with respect to the input of DARK protein, the Drosophila homolog of APAF1. Interestingly, this bistable behavior in Drosophila is predicted to be reversible. Further analysis suggests that the mechanism underlying the systems property of reversibility is the double-negative feedback from the EC to the initiator caspase. Using theoretical modeling, our study proposes plausible evolution of the switch mechanism for apoptosis between organisms.

  18. Modelling Of Flotation Processes By Classical Mathematical Methods - A Review

    NASA Astrophysics Data System (ADS)

    Jovanović, Ivana; Miljanović, Igor

    2015-12-01

    Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.

  19. 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…

  20. Mathematical model and software for control of commissioning blast furnace

    NASA Astrophysics Data System (ADS)

    Spirin, N. A.; Onorin, O. P.; Shchipanov, K. A.; Lavrov, V. V.

    2016-09-01

    Blowing-in is a starting period of blast furnace operation after construction or major repair. The current approximation methods of blowing-in burden analysis are based on blowing-in practice of previously commissioned blast furnaces. This area is theoretically underexplored; there are no common scientifically based methods for selection of the burden composition and blast parameters. The purpose of this paper is development and scientific substantiation of the methods for selection of the burden composition and blast parameters in the blast furnace during the blowing-in period. Research methods are based on physical regularities of main processes running in the blast furnace, system analysis, and application of modern principles for development and construction of mathematical models, algorithms and software designed for automated control of complex production processes in metallurgy. As consequence of the research made by the authors the following results have been achieved: 1. A set of mathematical models for analysis of burden arrangement throughout the height of the blast furnace and for selection of optimal blast and gas dynamic parameters has been developed. 2. General principles for selection of the blowing-in burden composition and blast and gas dynamic parameters have been set up. 3. The software for the engineering and process staff of the blast furnace has been developed and introduced in the industry.