WorldWideScience

Sample records for mechanistic mathematical models

  1. Mechanistic Mathematical Modeling Tests Hypotheses of the Neurovascular Coupling in fMRI.

    Directory of Open Access Journals (Sweden)

    Karin Lundengård

    2016-06-01

    Full Text Available Functional magnetic resonance imaging (fMRI measures brain activity by detecting the blood-oxygen-level dependent (BOLD response to neural activity. The BOLD response depends on the neurovascular coupling, which connects cerebral blood flow, cerebral blood volume, and deoxyhemoglobin level to neuronal activity. The exact mechanisms behind this neurovascular coupling are not yet fully investigated. There are at least three different ways in which these mechanisms are being discussed. Firstly, mathematical models involving the so-called Balloon model describes the relation between oxygen metabolism, cerebral blood volume, and cerebral blood flow. However, the Balloon model does not describe cellular and biochemical mechanisms. Secondly, the metabolic feedback hypothesis, which is based on experimental findings on metabolism associated with brain activation, and thirdly, the neurotransmitter feed-forward hypothesis which describes intracellular pathways leading to vasoactive substance release. Both the metabolic feedback and the neurotransmitter feed-forward hypotheses have been extensively studied, but only experimentally. These two hypotheses have never been implemented as mathematical models. Here we investigate these two hypotheses by mechanistic mathematical modeling using a systems biology approach; these methods have been used in biological research for many years but never been applied to the BOLD response in fMRI. In the current work, model structures describing the metabolic feedback and the neurotransmitter feed-forward hypotheses were applied to measured BOLD responses in the visual cortex of 12 healthy volunteers. Evaluating each hypothesis separately shows that neither hypothesis alone can describe the data in a biologically plausible way. However, by adding metabolism to the neurotransmitter feed-forward model structure, we obtained a new model structure which is able to fit the estimation data and successfully predict new

  2. Mathematical Description and Mechanistic Reasoning: A Pathway toward STEM Integration

    Science.gov (United States)

    Weinberg, Paul J.

    2017-01-01

    Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith's…

  3. Conceptual models for waste tank mechanistic analysis

    International Nuclear Information System (INIS)

    Allemann, R.T.; Antoniak, Z.I.; Eyler, L.L.; Liljegren, L.M.; Roberts, J.S.

    1992-02-01

    Pacific Northwest Laboratory (PNL) is conducting a study for Westinghouse Hanford Company (Westinghouse Hanford), a contractor for the US Department of Energy (DOE). The purpose of the work is to study possible mechanisms and fluid dynamics contributing to the periodic release of gases from double-shell waste storage tanks at the Hanford Site in Richland, Washington. This interim report emphasizing the modeling work follows two other interim reports, Mechanistic Analysis of Double-Shell Tank Gas Release Progress Report -- November 1990 and Collection and Analysis of Existing Data for Waste Tank Mechanistic Analysis Progress Report -- December 1990, that emphasized data correlation and mechanisms. The approach in this study has been to assemble and compile data that are pertinent to the mechanisms, analyze the data, evaluate physical properties and parameters, evaluate hypothetical mechanisms, and develop mathematical models of mechanisms

  4. Modeling systems-level dynamics: Understanding without mechanistic explanation in integrative systems biology.

    Science.gov (United States)

    MacLeod, Miles; Nersessian, Nancy J

    2015-02-01

    In this paper we draw upon rich ethnographic data of two systems biology labs to explore the roles of explanation and understanding in large-scale systems modeling. We illustrate practices that depart from the goal of dynamic mechanistic explanation for the sake of more limited modeling goals. These processes use abstract mathematical formulations of bio-molecular interactions and data fitting techniques which we call top-down abstraction to trade away accurate mechanistic accounts of large-scale systems for specific information about aspects of those systems. We characterize these practices as pragmatic responses to the constraints many modelers of large-scale systems face, which in turn generate more limited pragmatic non-mechanistic forms of understanding of systems. These forms aim at knowledge of how to predict system responses in order to manipulate and control some aspects of them. We propose that this analysis of understanding provides a way to interpret what many systems biologists are aiming for in practice when they talk about the objective of a "systems-level understanding." Copyright © 2014 Elsevier Ltd. All rights reserved.

  5. Mechanistic Oral Absorption Modeling and Simulation for Formulation Development and Bioequivalence Evaluation: Report of an FDA Public Workshop.

    Science.gov (United States)

    Zhang, X; Duan, J; Kesisoglou, F; Novakovic, J; Amidon, G L; Jamei, M; Lukacova, V; Eissing, T; Tsakalozou, E; Zhao, L; Lionberger, R

    2017-08-01

    On May 19, 2016, the US Food and Drug Administration (FDA) hosted a public workshop, entitled "Mechanistic Oral Absorption Modeling and Simulation for Formulation Development and Bioequivalence Evaluation." The topic of mechanistic oral absorption modeling, which is one of the major applications of physiologically based pharmacokinetic (PBPK) modeling and simulation, focuses on predicting oral absorption by mechanistically integrating gastrointestinal transit, dissolution, and permeation processes, incorporating systems, active pharmaceutical ingredient (API), and the drug product information, into a systemic mathematical whole-body framework. © 2017 The Authors CPT: Pharmacometrics & Systems Pharmacology published by Wiley Periodicals, Inc. on behalf of American Society for Clinical Pharmacology and Therapeutics.

  6. Conceptual models for waste tank mechanistic analysis. Status report, January 1991

    Energy Technology Data Exchange (ETDEWEB)

    Allemann, R. T.; Antoniak, Z. I.; Eyler, L. L.; Liljegren, L. M.; Roberts, J. S.

    1992-02-01

    Pacific Northwest Laboratory (PNL) is conducting a study for Westinghouse Hanford Company (Westinghouse Hanford), a contractor for the US Department of Energy (DOE). The purpose of the work is to study possible mechanisms and fluid dynamics contributing to the periodic release of gases from double-shell waste storage tanks at the Hanford Site in Richland, Washington. This interim report emphasizing the modeling work follows two other interim reports, Mechanistic Analysis of Double-Shell Tank Gas Release Progress Report -- November 1990 and Collection and Analysis of Existing Data for Waste Tank Mechanistic Analysis Progress Report -- December 1990, that emphasized data correlation and mechanisms. The approach in this study has been to assemble and compile data that are pertinent to the mechanisms, analyze the data, evaluate physical properties and parameters, evaluate hypothetical mechanisms, and develop mathematical models of mechanisms.

  7. Assessing uncertainty in mechanistic models

    Science.gov (United States)

    Edwin J. Green; David W. MacFarlane; Harry T. Valentine

    2000-01-01

    Concern over potential global change has led to increased interest in the use of mechanistic models for predicting forest growth. The rationale for this interest is that empirical models may be of limited usefulness if environmental conditions change. Intuitively, we expect that mechanistic models, grounded as far as possible in an understanding of the biology of tree...

  8. Mechanistic modelling of cancer: some reflections from software engineering and philosophy of science.

    Science.gov (United States)

    Cañete-Valdeón, José M; Wieringa, Roel; Smallbone, Kieran

    2012-12-01

    There is a growing interest in mathematical mechanistic modelling as a promising strategy for understanding tumour progression. This approach is accompanied by a methodological change of making research, in which models help to actively generate hypotheses instead of waiting for general principles to become apparent once sufficient data are accumulated. This paper applies recent research from philosophy of science to uncover three important problems of mechanistic modelling which may compromise its mainstream application, namely: the dilemma of formal and informal descriptions, the need to express degrees of confidence and the need of an argumentation framework. We report experience and research on similar problems from software engineering and provide evidence that the solutions adopted there can be transferred to the biological domain. We hope this paper can provoke new opportunities for further and profitable interdisciplinary research in the field.

  9. Recent advances in mathematical modeling of developmental abnormalities using mechanistic information.

    Science.gov (United States)

    Kavlock, R J

    1997-01-01

    During the last several years, significant changes in the risk assessment process for developmental toxicity of environmental contaminants have begun to emerge. The first of these changes is the development and beginning use of statistically based dose-response models [the benchmark dose (BMD) approach] that better utilize data derived from existing testing approaches. Accompanying this change is the greater emphasis placed on understanding and using mechanistic information to yield more accurate, reliable, and less uncertain risk assessments. The next stage in the evolution of risk assessment will be the use of biologically based dose-response (BBDR) models that begin to build into the statistically based models factors related to the underlying kinetic, biochemical, and/or physiologic processes perturbed by a toxicant. Such models are now emerging from several research laboratories. The introduction of quantitative models and the incorporation of biologic information into them has pointed to the need for even more sophisticated modifications for which we offer the term embryologically based dose-response (EBDR) models. Because these models would be based upon the understanding of normal morphogenesis, they represent a quantum leap in our thinking, but their complexity presents daunting challenges both to the developmental biologist and the developmental toxicologist. Implementation of these models will require extensive communication between developmental toxicologists, molecular embryologists, and biomathematicians. The remarkable progress in the understanding of mammalian embryonic development at the molecular level that has occurred over the last decade combined with advances in computing power and computational models should eventually enable these as yet hypothetical models to be brought into use.

  10. Supporting Mechanistic Reasoning in Domain-Specific Contexts

    Science.gov (United States)

    Weinberg, Paul J.

    2017-01-01

    Mechanistic reasoning is an epistemic practice central within science, technology, engineering, and mathematics disciplines. Although there has been some work on mechanistic reasoning in the research literature and standards documents, much of this work targets domain-general characterizations of mechanistic reasoning; this study provides…

  11. Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.

    Science.gov (United States)

    Yates, James W T

    2008-07-03

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

  12. Testing mechanistic models of growth in insects.

    Science.gov (United States)

    Maino, James L; Kearney, Michael R

    2015-11-22

    Insects are typified by their small size, large numbers, impressive reproductive output and rapid growth. However, insect growth is not simply rapid; rather, insects follow a qualitatively distinct trajectory to many other animals. Here we present a mechanistic growth model for insects and show that increasing specific assimilation during the growth phase can explain the near-exponential growth trajectory of insects. The presented model is tested against growth data on 50 insects, and compared against other mechanistic growth models. Unlike the other mechanistic models, our growth model predicts energy reserves per biomass to increase with age, which implies a higher production efficiency and energy density of biomass in later instars. These predictions are tested against data compiled from the literature whereby it is confirmed that insects increase their production efficiency (by 24 percentage points) and energy density (by 4 J mg(-1)) between hatching and the attainment of full size. The model suggests that insects achieve greater production efficiencies and enhanced growth rates by increasing specific assimilation and increasing energy reserves per biomass, which are less costly to maintain than structural biomass. Our findings illustrate how the explanatory and predictive power of mechanistic growth models comes from their grounding in underlying biological processes. © 2015 The Author(s).

  13. Mathematical modeling of drug release from lipid dosage forms.

    Science.gov (United States)

    Siepmann, J; Siepmann, F

    2011-10-10

    Lipid dosage forms provide an interesting potential for controlled drug delivery. In contrast to frequently used poly(ester) based devices for parenteral administration, they do not lead to acidification upon degradation and potential drug inactivation, especially in the case of protein drugs and other acid-labile active agents. The aim of this article is to give an overview on the current state of the art of mathematical modeling of drug release from this type of advanced drug delivery systems. Empirical and semi-empirical models are described as well as mechanistic theories, considering diffusional mass transport, potentially limited drug solubility and the leaching of other, water-soluble excipients into the surrounding bulk fluid. Various practical examples are given, including lipid microparticles, beads and implants, which can successfully be used to control the release of an incorporated drug during periods ranging from a few hours up to several years. The great benefit of mechanistic mathematical theories is the possibility to quantitatively predict the effects of different formulation parameters and device dimensions on the resulting drug release kinetics. Thus, in silico simulations can significantly speed up product optimization. This is particularly useful if long release periods (e.g., several months) are targeted, since experimental trial-and-error studies are highly time-consuming in these cases. In the future it would be highly desirable to combine mechanistic theories with the quantitative description of the drug fate in vivo, ideally including the pharmacodynamic efficacy of the treatments. Copyright © 2011 Elsevier B.V. All rights reserved.

  14. Numerical simulation in steam injection process by a mechanistic approach

    Energy Technology Data Exchange (ETDEWEB)

    De Souza, J.C.Jr.; Campos, W.; Lopes, D.; Moura, L.S.S. [Petrobras, Rio de Janeiro (Brazil)

    2008-10-15

    Steam injection is a common thermal recovery method used in very viscous oil reservoirs. The method involves the injection of heat to reduce viscosity and mobilize oil. A steam generation and injection system consists primarily of a steam source, distribution lines, injection wells and a discarding tank. In order to optimize injection and improve the oil recovery factor, one must determine the parameters of steam flow such as pressure, temperature and steam quality. This study focused on developing a unified mathematical model by means of a mechanistic approach for two-phase steam flow in pipelines and wells. The hydrodynamic and heat transfer mechanistic model was implemented in a computer simulator to model the parameters of steam injection while trying to avoid the use of empirical correlations. A marching algorithm was used to determine the distribution of pressure and temperature along the pipelines and wellbores. The mathematical model for steam flow in injection systems, developed by a mechanistic approach (VapMec) performed well when the simulated values of pressures and temperatures were compared with the values measured during field tests. The newly developed VapMec model was incorporated in the LinVap-3 simulator that constitutes an engineering supporting tool for steam injection wells operated by Petrobras. 23 refs., 7 tabs., 6 figs.

  15. LASSIM-A network inference toolbox for genome-wide mechanistic modeling.

    Directory of Open Access Journals (Sweden)

    Rasmus Magnusson

    2017-06-01

    Full Text Available Recent technological advancements have made time-resolved, quantitative, multi-omics data available for many model systems, which could be integrated for systems pharmacokinetic use. Here, we present large-scale simulation modeling (LASSIM, which is a novel mathematical tool for performing large-scale inference using mechanistically defined ordinary differential equations (ODE for gene regulatory networks (GRNs. LASSIM integrates structural knowledge about regulatory interactions and non-linear equations with multiple steady state and dynamic response expression datasets. The rationale behind LASSIM is that biological GRNs can be simplified using a limited subset of core genes that are assumed to regulate all other gene transcription events in the network. The LASSIM method is implemented as a general-purpose toolbox using the PyGMO Python package to make the most of multicore computers and high performance clusters, and is available at https://gitlab.com/Gustafsson-lab/lassim. As a method, LASSIM works in two steps, where it first infers a non-linear ODE system of the pre-specified core gene expression. Second, LASSIM in parallel optimizes the parameters that model the regulation of peripheral genes by core system genes. We showed the usefulness of this method by applying LASSIM to infer a large-scale non-linear model of naïve Th2 cell differentiation, made possible by integrating Th2 specific bindings, time-series together with six public and six novel siRNA-mediated knock-down experiments. ChIP-seq showed significant overlap for all tested transcription factors. Next, we performed novel time-series measurements of total T-cells during differentiation towards Th2 and verified that our LASSIM model could monitor those data significantly better than comparable models that used the same Th2 bindings. In summary, the LASSIM toolbox opens the door to a new type of model-based data analysis that combines the strengths of reliable mechanistic models

  16. Appropriateness of mechanistic and non-mechanistic models for the application of ultrafiltration to mixed waste

    International Nuclear Information System (INIS)

    Foust, Henry; Ghosehajra, Malay

    2007-01-01

    This study asks two questions: (1) How appropriate is the use of a basic filtration equation to the application of ultrafiltration of mixed waste, and (2) How appropriate are non-parametric models for permeate rates (volumes)? To answer these questions, mechanistic and non-mechanistic approaches are developed for permeate rates and volumes associated with an ultrafiltration/mixed waste system in dia-filtration mode. The mechanistic approach is based on a filtration equation which states that t/V vs. V is a linear relationship. The coefficients associated with this linear regression are composed of physical/chemical parameters of the system and based the mass balance equation associated with the membrane and associated developing cake layer. For several sets of data, a high correlation is shown that supports the assertion that t/V vs. V is a linear relationship. It is also shown that non-mechanistic approaches, i.e., the use of regression models to are not appropriate. One models considered is Q(p) = a*ln(Cb)+b. Regression models are inappropriate because the scale-up from a bench scale (pilot scale) study to full-scale for permeate rates (volumes) is not simply the ratio of the two membrane surface areas. (authors)

  17. Mathematical modelling

    DEFF Research Database (Denmark)

    Blomhøj, Morten

    2004-01-01

    Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

  18. Application of mechanistic models to fermentation and biocatalysis for next-generation processes

    DEFF Research Database (Denmark)

    Gernaey, Krist; Eliasson Lantz, Anna; Tufvesson, Pär

    2010-01-01

    of variables required for measurement, control and process design. In the near future, mechanistic models with a higher degree of detail will play key roles in the development of efficient next-generation fermentation and biocatalytic processes. Moreover, mechanistic models will be used increasingly......Mechanistic models are based on deterministic principles, and recently, interest in them has grown substantially. Herein we present an overview of mechanistic models and their applications in biotechnology, including future perspectives. Model utility is highlighted with respect to selection...

  19. Mechanistic species distribution modelling as a link between physiology and conservation.

    Science.gov (United States)

    Evans, Tyler G; Diamond, Sarah E; Kelly, Morgan W

    2015-01-01

    Climate change conservation planning relies heavily on correlative species distribution models that estimate future areas of occupancy based on environmental conditions encountered in present-day ranges. The approach benefits from rapid assessment of vulnerability over a large number of organisms, but can have poor predictive power when transposed to novel environments and reveals little in the way of causal mechanisms that define changes in species distribution or abundance. Having conservation planning rely largely on this single approach also increases the risk of policy failure. Mechanistic models that are parameterized with physiological information are expected to be more robust when extrapolating distributions to future environmental conditions and can identify physiological processes that set range boundaries. Implementation of mechanistic species distribution models requires knowledge of how environmental change influences physiological performance, and because this information is currently restricted to a comparatively small number of well-studied organisms, use of mechanistic modelling in the context of climate change conservation is limited. In this review, we propose that the need to develop mechanistic models that incorporate physiological data presents an opportunity for physiologists to contribute more directly to climate change conservation and advance the field of conservation physiology. We begin by describing the prevalence of species distribution modelling in climate change conservation, highlighting the benefits and drawbacks of both mechanistic and correlative approaches. Next, we emphasize the need to expand mechanistic models and discuss potential metrics of physiological performance suitable for integration into mechanistic models. We conclude by summarizing other factors, such as the need to consider demography, limiting broader application of mechanistic models in climate change conservation. Ideally, modellers, physiologists and

  20. Mechanistic movement models to understand epidemic spread.

    Science.gov (United States)

    Fofana, Abdou Moutalab; Hurford, Amy

    2017-05-05

    An overlooked aspect of disease ecology is considering how and why animals come into contact with one and other resulting in disease transmission. Mathematical models of disease spread frequently assume mass-action transmission, justified by stating that susceptible and infectious hosts mix readily, and foregoing any detailed description of host movement. Numerous recent studies have recorded, analysed and modelled animal movement. These movement models describe how animals move with respect to resources, conspecifics and previous movement directions and have been used to understand the conditions for the occurrence and the spread of infectious diseases when hosts perform a type of movement. Here, we summarize the effect of the different types of movement on the threshold conditions for disease spread. We identify gaps in the literature and suggest several promising directions for future research. The mechanistic inclusion of movement in epidemic models may be beneficial for the following two reasons. Firstly, the estimation of the transmission coefficient in an epidemic model is possible because animal movement data can be used to estimate the rate of contacts between conspecifics. Secondly, unsuccessful transmission events, where a susceptible host contacts an infectious host but does not become infected can be quantified. Following an outbreak, this enables disease ecologists to identify 'near misses' and to explore possible alternative epidemic outcomes given shifts in ecological or immunological parameters.This article is part of the themed issue 'Opening the black box: re-examining the ecology and evolution of parasite transmission'. © 2017 The Author(s).

  1. Mathematical Modeling and Pure Mathematics

    Science.gov (United States)

    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…

  2. Bridging Mechanistic and Phenomenological Models of Complex Biological Systems.

    Science.gov (United States)

    Transtrum, Mark K; Qiu, Peng

    2016-05-01

    The inherent complexity of biological systems gives rise to complicated mechanistic models with a large number of parameters. On the other hand, the collective behavior of these systems can often be characterized by a relatively small number of phenomenological parameters. We use the Manifold Boundary Approximation Method (MBAM) as a tool for deriving simple phenomenological models from complicated mechanistic models. The resulting models are not black boxes, but remain expressed in terms of the microscopic parameters. In this way, we explicitly connect the macroscopic and microscopic descriptions, characterize the equivalence class of distinct systems exhibiting the same range of collective behavior, and identify the combinations of components that function as tunable control knobs for the behavior. We demonstrate the procedure for adaptation behavior exhibited by the EGFR pathway. From a 48 parameter mechanistic model, the system can be effectively described by a single adaptation parameter τ characterizing the ratio of time scales for the initial response and recovery time of the system which can in turn be expressed as a combination of microscopic reaction rates, Michaelis-Menten constants, and biochemical concentrations. The situation is not unlike modeling in physics in which microscopically complex processes can often be renormalized into simple phenomenological models with only a few effective parameters. The proposed method additionally provides a mechanistic explanation for non-universal features of the behavior.

  3. Mathematical Modelling Approach in Mathematics Education

    Science.gov (United States)

    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…

  4. Mathematical modeling of gonadotropin-releasing hormone signaling.

    Science.gov (United States)

    Pratap, Amitesh; Garner, Kathryn L; Voliotis, Margaritis; Tsaneva-Atanasova, Krasimira; McArdle, Craig A

    2017-07-05

    Gonadotropin-releasing hormone (GnRH) acts via G-protein coupled receptors on pituitary gonadotropes to control reproduction. These are G q -coupled receptors that mediate acute effects of GnRH on the exocytotic secretion of luteinizing hormone (LH) and follicle-stimulating hormone (FSH), as well as the chronic regulation of their synthesis. GnRH is secreted in short pulses and GnRH effects on its target cells are dependent upon the dynamics of these pulses. Here we overview GnRH receptors and their signaling network, placing emphasis on pulsatile signaling, and how mechanistic mathematical models and an information theoretic approach have helped further this field. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

  5. Mathematical modelling

    CERN Document Server

    2016-01-01

    This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

  6. Malaria's Missing Number: Calculating the Human Component of R0 by a Within-Host Mechanistic Model of Plasmodium falciparum Infection and Transmission

    OpenAIRE

    Johnston, Geoffrey L.; Smith, David L.; Fidock, David A.

    2013-01-01

    Human infection by malarial parasites of the genus Plasmodium begins with the bite of an infected Anopheles mosquito. Current estimates place malaria mortality at over 650,000 individuals each year, mostly in African children. Efforts to reduce disease burden can benefit from the development of mathematical models of disease transmission. To date, however, comprehensive modeling of the parameters defining human infectivity to mosquitoes has remained elusive. Here, we describe a mechanistic wi...

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

    Science.gov (United States)

    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…

  8. Evaluation of mechanistic DNB models using HCLWR CHF data

    International Nuclear Information System (INIS)

    Iwamura, Takamichi; Watanabe, Hironori; Okubo, Tsutomu; Araya, Fumimasa; Murao, Yoshio.

    1992-03-01

    An onset of departure from nucleate boiling (DNB) in light water reactor (LWR) has been generally predicted with empirical correlations. Since these correlations have less physical bases and contain adjustable empirical constants determined by best fitting of test data, applicable geometries and flow conditions are limited within the original experiment ranges. In order to obtain more universal prediction method, several mechanistic DNB models based on physical approaches have been proposed in recent years. However, the predictive capabilities of mechanistic DNB models have not been verified successfully especially for advanced LWR design purposes. In this report, typical DNB mechanistic models are reviewed and compared with critical heat flux (CHF) data for high conversion light water reactor (HCLWR). The experiments were performed using triangular 7-rods array with non-uniform axial heat flux distribution. Test pressure was 16 MPa, mass velocities ranged from 800 t0 3100 kg/s·m 2 and exit qualities from -0.07 to 0.19. The evaluated models are: 1) Wisman-Pei, 2) Chang-Lee, 3) Lee-Mudawwar, 4) Lin-Lee-Pei, and 5) Katto. The first two models are based on near-wall bubble crowding model and the other three models on sublayer dryout model. The comparison with experimental data indicated that the Weisman-Pei model agreed relatively well with the CHF data. Effects of empirical constants in each model on CHF calculation were clarified by sensitivity studies. It was also found that the magnitudes of physical quantities obtained in the course of calculation were significantly different for each model. Therefore, microscopic observation of the onset of DNB on heated surface is essential to clarify the DNB mechanism and establish a general DNB mechanistic model based on physical phenomenon. (author)

  9. Specialists without spirit: limitations of the mechanistic biomedical model.

    Science.gov (United States)

    Hewa, S; Hetherington, R W

    1995-06-01

    This paper examines the origin and the development of the mechanistic model of the human body and health in terms of Max Weber's theory of rationalization. It is argued that the development of Western scientific medicine is a part of the broad process of rationalization that began in sixteenth century Europe as a result of the Reformation. The development of the mechanistic view of the human body in Western medicine is consistent with the ideas of calculability, predictability, and control-the major tenets of the process of rationalization as described by Weber. In recent years, however, the limitations of the mechanistic model have been the topic of many discussions. George Engel, a leading advocate of general systems theory, is one of the leading proponents of a new medical model which includes the general quality of life, clean environment, and psychological, or spiritual stability of life. The paper concludes with consideration of the potential of Engel's proposed new model in the context of the current state of rationalization in modern industrialized society.

  10. Mechanistic Fermentation Models for Process Design, Monitoring, and Control

    DEFF Research Database (Denmark)

    Mears, Lisa; Stocks, Stuart M.; Albæk, Mads Orla

    2017-01-01

    Mechanistic models require a significant investment of time and resources, but their application to multiple stages of fermentation process development and operation can make this investment highly valuable. This Opinion article discusses how an established fermentation model may be adapted...... for application to different stages of fermentation process development: planning, process design, monitoring, and control. Although a longer development time is required for such modeling methods in comparison to purely data-based model techniques, the wide range of applications makes them a highly valuable tool...... for fermentation research and development. In addition, in a research environment, where collaboration is important, developing mechanistic models provides a platform for knowledge sharing and consolidation of existing process understanding....

  11. The epistemology of mathematical and statistical modeling: a quiet methodological revolution.

    Science.gov (United States)

    Rodgers, Joseph Lee

    2010-01-01

    A quiet methodological revolution, a modeling revolution, has occurred over the past several decades, almost without discussion. In contrast, the 20th century ended with contentious argument over the utility of null hypothesis significance testing (NHST). The NHST controversy may have been at least partially irrelevant, because in certain ways the modeling revolution obviated the NHST argument. I begin with a history of NHST and modeling and their relation to one another. Next, I define and illustrate principles involved in developing and evaluating mathematical models. Following, I discuss the difference between using statistical procedures within a rule-based framework and building mathematical models from a scientific epistemology. Only the former is treated carefully in most psychology graduate training. The pedagogical implications of this imbalance and the revised pedagogy required to account for the modeling revolution are described. To conclude, I discuss how attention to modeling implies shifting statistical practice in certain progressive ways. The epistemological basis of statistics has moved away from being a set of procedures, applied mechanistically, and moved toward building and evaluating statistical and scientific models. Copyrigiht 2009 APA, all rights reserved.

  12. Chemical kinetic mechanistic models to investigate cancer biology and impact cancer medicine

    International Nuclear Information System (INIS)

    Stites, Edward C

    2013-01-01

    Traditional experimental biology has provided a mechanistic understanding of cancer in which the malignancy develops through the acquisition of mutations that disrupt cellular processes. Several drugs developed to target such mutations have now demonstrated clinical value. These advances are unequivocal testaments to the value of traditional cellular and molecular biology. However, several features of cancer may limit the pace of progress that can be made with established experimental approaches alone. The mutated genes (and resultant mutant proteins) function within large biochemical networks. Biochemical networks typically have a large number of component molecules and are characterized by a large number of quantitative properties. Responses to a stimulus or perturbation are typically nonlinear and can display qualitative changes that depend upon the specific values of variable system properties. Features such as these can complicate the interpretation of experimental data and the formulation of logical hypotheses that drive further research. Mathematical models based upon the molecular reactions that define these networks combined with computational studies have the potential to deal with these obstacles and to enable currently available information to be more completely utilized. Many of the pressing problems in cancer biology and cancer medicine may benefit from a mathematical treatment. As work in this area advances, one can envision a future where such models may meaningfully contribute to the clinical management of cancer patients. (paper)

  13. Mechanistic model for microbial growth on hydrocarbons

    Energy Technology Data Exchange (ETDEWEB)

    Mallee, F M; Blanch, H W

    1977-12-01

    Based on available information describing the transport and consumption of insoluble alkanes, a mechanistic model is proposed for microbial growth on hydrocarbons. The model describes the atypical growth kinetics observed, and has implications in the design of large scale equipment for single cell protein (SCP) manufacture from hydrocarbons. The model presents a framework for comparison of the previously published experimental kinetic data.

  14. Mathematical modeling

    CERN Document Server

    Eck, Christof; Knabner, Peter

    2017-01-01

    Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

  15. Study of n-Butyl Acrylate Self-Initiation Reaction Experimentally and via Macroscopic Mechanistic Modeling

    Directory of Open Access Journals (Sweden)

    Ahmad Arabi Shamsabadi

    2016-04-01

    Full Text Available This paper presents an experimental study of the self-initiation reaction of n-butyl acrylate (n-BA in free-radical polymerization. For the first time, the frequency factor and activation energy of the monomer self-initiation reaction are estimated from measurements of n-BA conversion in free-radical homo-polymerization initiated only by the monomer. The estimation was carried out using a macroscopic mechanistic mathematical model of the reactor. In addition to already-known reactions that contribute to the polymerization, the model considers a n-BA self-initiation reaction mechanism that is based on our previous electronic-level first-principles theoretical study of the self-initiation reaction. Reaction rate equations are derived using the method of moments. The reaction-rate parameter estimates obtained from conversion measurements agree well with estimates obtained via our purely-theoretical quantum chemical calculations.

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

    Science.gov (United States)

    Clément, Frédérique

    2016-07-01

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

  17. Teaching Mathematical Modeling in Mathematics Education

    Science.gov (United States)

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

    Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

  18. Mathematical modelling techniques

    CERN Document Server

    Aris, Rutherford

    1995-01-01

    ""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode

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

    Science.gov (United States)

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

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

    Science.gov (United States)

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

  1. Mechanistic modeling analysis of micro-evolutive responses from a Caenorhabditis elegans population exposed to a radioactive metallic stress

    International Nuclear Information System (INIS)

    Goussen, Benoit

    2013-01-01

    The evolution of toxic effects at a relevant scale is an important challenge for the ecosystem protection. Indeed, pollutants may impact populations over long-term and represent a new evolutionary force which can be adding itself to the natural selection forces. Thereby, it is necessary to acquire knowledge on the phenotypics and genetics changes that may appear in populations submitted to stress over several generations. Usually statistical analyses are performed to analyse such multi-generational studies. The use of a mechanistic mathematical model may provide a way to fully understand the impact of pollutants on the populations' dynamics. Such kind of model allows the integration of biological and toxic processes into the analysis of eco-toxicological data and the assessment of interactions between these processes. The aim of this Ph.D. project was to assess the contributions of the mechanistic modelling to the analysis of evolutionary experiment assessing long-term exposure. To do so, a three step strategy has been developed. Foremost, a multi-generational study was performed to assess the evolution of two populations of the ubiquitous nematode Caenorhabditis elegans in control conditions or exposed to 1.1 mM of uranium. Several generations were selected to assess growth, reproduction, and dose-responses relationships, through exposure to a range of concentrations (from 0 to 1.2 mM U) with all endpoints measured daily. A first statistical analysis was then performed. In a second step, a bio-energetic model adapted to the assessment of eco-toxicological data (DEBtox) was developed on C. elegans. Its numerical behaviour was analysed. Finally, this model was applied to all the selected generations in order to infer parameters values for the two populations and to assess their evolutions. Results highlighted an impact of the uranium starting from 0.4 mM U on both C. elegans' growth and reproduction. Results from the mechanistic analysis indicate this effect is due

  2. MATHEMATICAL MODEL MANIPULATOR ROBOTS

    Directory of Open Access Journals (Sweden)

    O. N. Krakhmalev

    2015-12-01

    Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.

  3. Developing mathematical modelling competence

    DEFF Research Database (Denmark)

    Blomhøj, Morten; Jensen, Tomas Højgaard

    2003-01-01

    In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....

  4. Advanced reach tool (ART) : Development of the mechanistic model

    NARCIS (Netherlands)

    Fransman, W.; Tongeren, M. van; Cherrie, J.W.; Tischer, M.; Schneider, T.; Schinkel, J.; Kromhout, H.; Warren, N.; Goede, H.; Tielemans, E.

    2011-01-01

    This paper describes the development of the mechanistic model within a collaborative project, referred to as the Advanced REACH Tool (ART) project, to develop a tool to model inhalation exposure for workers sharing similar operational conditions across different industries and locations in Europe.

  5. Higher plant modelling for life support applications: first results of a simple mechanistic model

    Science.gov (United States)

    Hezard, Pauline; Dussap, Claude-Gilles; Sasidharan L, Swathy

    2012-07-01

    In the case of closed ecological life support systems, the air and water regeneration and food production are performed using microorganisms and higher plants. Wheat, rice, soybean, lettuce, tomato or other types of eatable annual plants produce fresh food while recycling CO2 into breathable oxygen. Additionally, they evaporate a large quantity of water, which can be condensed and used as potable water. This shows that recycling functions of air revitalization and food production are completely linked. Consequently, the control of a growth chamber for higher plant production has to be performed with efficient mechanistic models, in order to ensure a realistic prediction of plant behaviour, water and gas recycling whatever the environmental conditions. Purely mechanistic models of plant production in controlled environments are not available yet. This is the reason why new models must be developed and validated. This work concerns the design and test of a simplified version of a mathematical model coupling plant architecture and mass balance purposes in order to compare its results with available data of lettuce grown in closed and controlled chambers. The carbon exchange rate, water absorption and evaporation rate, biomass fresh weight as well as leaf surface are modelled and compared with available data. The model consists of four modules. The first one evaluates plant architecture, like total leaf surface, leaf area index and stem length data. The second one calculates the rate of matter and energy exchange depending on architectural and environmental data: light absorption in the canopy, CO2 uptake or release, water uptake and evapotranspiration. The third module evaluates which of the previous rates is limiting overall biomass growth; and the last one calculates biomass growth rate depending on matter exchange rates, using a global stoichiometric equation. All these rates are a set of differential equations, which are integrated with time in order to provide

  6. Descriptive and mechanistic models of crop–weed competition

    NARCIS (Netherlands)

    Bastiaans, L.; Storkey, J.

    2017-01-01

    Crop-weed competitive relations are an important element of agroecosystems. Quantifying and understanding them helps to design appropriate weed management at operational, tactical and strategic level. This chapter presents and discusses simple descriptive and more mechanistic models for crop-weed

  7. Requirements on mechanistic NPP models used in CSS for diagnostics and predictions

    International Nuclear Information System (INIS)

    Juslin, K.

    1996-01-01

    Mechanistic models have for several years with good experience been used for operators' support in electric power dispatching centres. Some models of limited scope have already been in use at nuclear power plants. It is considered that also advanced mechanistic models in combination with present computer technology with preference could be used in Computerized Support Systems (CSS) for the assistance of Nuclear Power Plant (NPP) operators. Requirements with respect to accuracy, validity range, speed flexibility and level of detail on the models used for such purposes are discussed. Quality Assurance, Verification and Validation efforts are considered. A long term commitment in the field of mechanistic modelling and real time simulation is considered as the key to successful implementations. The Advanced PROcess Simulation (APROS) code system and simulation environment developed at the Technical Research Centre of Finland (VTT) is intended also for CSS applications in NPP control rooms. (author). 4 refs

  8. Mechanistic Models for Process Development and Optimization of Fed-batch Fermentation Systems

    DEFF Research Database (Denmark)

    Mears, Lisa; Stocks, Stuart M.; Albæk, Mads O.

    2016-01-01

    This work discusses the application of mechanistic models to pilot scale filamentous fungal fermentation systems operated at Novozymes A/S. For on-line applications, a state estimator model is developed based on a stoichiometric balance in order to predict the biomass and product concentration....... This is based on on-line gas measurements and ammonia addition flow rate measurements. Additionally, a mechanistic model is applied offline as a tool for batch planning, based on definition of the process back pressure, aeration rate and stirrer speed. This allows the batch starting fill to be planned, taking...... into account the oxygen transfer conditions, as well as the evaporation rates of the system. Mechanistic models are valuable tools which are applicable for both process development and optimization. The state estimator described will be a valuable tool for future work as part of control strategy development...

  9. Mathematical Modeling Using MATLAB

    National Research Council Canada - National Science Library

    Phillips, Donovan

    1998-01-01

    .... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...

  10. Mathematical Modeling: A Structured Process

    Science.gov (United States)

    Anhalt, Cynthia Oropesa; Cortez, Ricardo

    2015-01-01

    Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

  11. A Physics-Inspired Mechanistic Model of Migratory Movement Patterns in Birds.

    Science.gov (United States)

    Revell, Christopher; Somveille, Marius

    2017-08-29

    In this paper, we introduce a mechanistic model of migratory movement patterns in birds, inspired by ideas and methods from physics. Previous studies have shed light on the factors influencing bird migration but have mainly relied on statistical correlative analysis of tracking data. Our novel method offers a bottom up explanation of population-level migratory movement patterns. It differs from previous mechanistic models of animal migration and enables predictions of pathways and destinations from a given starting location. We define an environmental potential landscape from environmental data and simulate bird movement within this landscape based on simple decision rules drawn from statistical mechanics. We explore the capacity of the model by qualitatively comparing simulation results to the non-breeding migration patterns of a seabird species, the Black-browed Albatross (Thalassarche melanophris). This minimal, two-parameter model was able to capture remarkably well the previously documented migration patterns of the Black-browed Albatross, with the best combination of parameter values conserved across multiple geographically separate populations. Our physics-inspired mechanistic model could be applied to other bird and highly-mobile species, improving our understanding of the relative importance of various factors driving migration and making predictions that could be useful for conservation.

  12. Mathematical modeling of sleep state dynamics in a rodent model of shift work

    Directory of Open Access Journals (Sweden)

    Michael J. Rempe

    2018-06-01

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

  13. Fuel swelling importance in PCI mechanistic modelling

    International Nuclear Information System (INIS)

    Arimescu, V.I.

    2005-01-01

    Under certain conditions, fuel pellet swelling is the most important factor in determining the intensity of the pellet-to-cladding mechanical interaction (PCMI). This is especially true during power ramps, which lead to a temperature increase to a higher terminal plateau that is maintained for hours. The time-dependent gaseous swelling is proportional to temperature and is also enhanced by the increased gas atom migration to the grain boundary during the power ramp. On the other hand, gaseous swelling is inhibited by a compressive hydrostatic stress in the pellet. Therefore, PCMI is the net result of combining gaseous swelling and pellet thermal expansion with the opposing feedback from the cladding mechanical reaction. The coupling of the thermal and mechanical processes, mentioned above, with various feedback loops is best simulated by a mechanistic fuel code. This paper discusses a mechanistic swelling model that is coupled with a fission gas release model as well as a mechanical model of the fuel pellet. The role of fuel swelling is demonstrated for typical power ramps at different burn-ups. Also, fuel swelling plays a significant role in avoiding the thermal instability for larger gap fuel rods, by limiting the potentially exponentially increasing gap due to the positive feedback loop effect of increasing fission gas release and the associated over-pressure inside the cladding. (author)

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

    Science.gov (United States)

    Karali, Diren; Durmus, Soner

    2015-01-01

    The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

  15. Profiling the biological activity of oxide nanomaterials with mechanistic models

    NARCIS (Netherlands)

    Burello, E.

    2013-01-01

    In this study we present three mechanistic models for profiling the potential biological and toxicological effects of oxide nanomaterials. The models attempt to describe the reactivity, protein adsorption and membrane adhesion processes of a large range of oxide materials and are based on properties

  16. Finite mathematics models and applications

    CERN Document Server

    Morris, Carla C

    2015-01-01

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

  17. The 24-Hour Mathematical Modeling Challenge

    Science.gov (United States)

    Galluzzo, Benjamin J.; Wendt, Theodore J.

    2015-01-01

    Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

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

    Science.gov (United States)

    Suppes, Patrick

    This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

  19. A mechanistic model on methane oxidation in the rice rhizosphere

    NARCIS (Netherlands)

    Bodegom, van P.M.; Leffelaar, P.A.; Goudriaan, J.

    2001-01-01

    A mechanistic model is presented on the processes leading to methane oxidation in rice rhizosphere. The model is driven by oxygen release from a rice root into anaerobic rice soil. Oxygen is consumed by heterotrophic and methanotrophic respiration, described by double Monod kinetics, and by iron

  20. Mathematical Modeling and Experimental Validation of Nanoemulsion-Based Drug Transport across Cellular Barriers.

    Science.gov (United States)

    Kadakia, Ekta; Shah, Lipa; Amiji, Mansoor M

    2017-07-01

    Nanoemulsions have shown potential in delivering drug across epithelial and endothelial cell barriers, which express efflux transporters. However, their transport mechanisms are not entirely understood. Our goal was to investigate the cellular permeability of nanoemulsion-encapsulated drugs and apply mathematical modeling to elucidate transport mechanisms and sensitive nanoemulsion attributes. Transport studies were performed in Caco-2 cells, using fish oil nanoemulsions and a model substrate, rhodamine-123. Permeability data was modeled using a semi-mechanistic approach, capturing the following cellular processes: endocytotic uptake of the nanoemulsion, release of rhodamine-123 from the nanoemulsion, efflux and passive permeability of rhodamine-123 in aqueous solution. Nanoemulsions not only improved the permeability of rhodamine-123, but were also less sensitive to efflux transporters. The model captured bidirectional permeability results and identified sensitive processes, such as the release of the nanoemulsion-encapsulated drug and cellular uptake of the nanoemulsion. Mathematical description of cellular processes, improved our understanding of transport mechanisms, such as nanoemulsions don't inhibit efflux to improve drug permeability. Instead, their endocytotic uptake, results in higher intracellular drug concentrations, thereby increasing the concentration gradient and transcellular permeability across biological barriers. Modeling results indicated optimizing nanoemulsion attributes like the droplet size and intracellular drug release rate, may further improve drug permeability.

  1. Polymerization kinetics of wheat gluten upon thermosetting. A mechanistic model.

    Science.gov (United States)

    Domenek, Sandra; Morel, Marie-Hélène; Bonicel, Joëlle; Guilbert, Stéphane

    2002-10-09

    Size exclusion high-performance liquid chromatography analysis was carried out on wheat gluten-glycerol blends subjected to different heat treatments. The elution profiles were analyzed in order to follow the solubility loss of protein fractions with specific molecular size. Owing to the known biochemical changes involved during the heat denaturation of gluten, a mechanistic mathematical model was developed, which divided the protein denaturation into two distinct reaction steps: (i) reversible change in protein conformation and (ii) protein precipitation through disulfide bonding between initially SDS-soluble and SDS-insoluble reaction partners. Activation energies of gluten unfolding, refolding, and precipitation were calculated with the Arrhenius law to 53.9 kJ x mol(-1), 29.5 kJ x mol(-1), and 172 kJ x mol(-1), respectively. The rate of protein solubility loss decreased as the cross-linking reaction proceeded, which may be attributed to the formation of a three-dimensional network progressively hindering the reaction. The enhanced susceptibility to aggregation of large molecules was assigned to a risen reaction probability due to their higher number of cysteine residues and to the increased percentage of unfolded and thereby activated proteins as complete protein refolding seemed to be an anticooperative process.

  2. Mathematical problems in meteorological modelling

    CERN Document Server

    Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella

    2016-01-01

    This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...

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

    Science.gov (United States)

    Thrasher, Emily Plunkett

    2016-01-01

    The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

  4. An improved mechanistic critical heat flux model for subcooled flow boiling

    Energy Technology Data Exchange (ETDEWEB)

    Kwon, Young Min [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Chang, Soon Heung [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

    1998-12-31

    Based on the bubble coalescence adjacent to the heated wall as a flow structure for CHF condition, Chang and Lee developed a mechanistic critical heat flux (CHF) model for subcooled flow boiling. In this paper, improvements of Chang-Lee model are implemented with more solid theoretical bases for subcooled and low-quality flow boiling in tubes. Nedderman-Shearer`s equations for the skin friction factor and universal velocity profile models are employed. Slip effect of movable bubbly layer is implemented to improve the predictability of low mass flow. Also, mechanistic subcooled flow boiling model is used to predict the flow quality and void fraction. The performance of the present model is verified using the KAIST CHF database of water in uniformly heated tubes. It is found that the present model can give a satisfactory agreement with experimental data within less than 9% RMS error. 9 refs., 5 figs. (Author)

  5. An improved mechanistic critical heat flux model for subcooled flow boiling

    Energy Technology Data Exchange (ETDEWEB)

    Kwon, Young Min [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Chang, Soon Heung [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

    1997-12-31

    Based on the bubble coalescence adjacent to the heated wall as a flow structure for CHF condition, Chang and Lee developed a mechanistic critical heat flux (CHF) model for subcooled flow boiling. In this paper, improvements of Chang-Lee model are implemented with more solid theoretical bases for subcooled and low-quality flow boiling in tubes. Nedderman-Shearer`s equations for the skin friction factor and universal velocity profile models are employed. Slip effect of movable bubbly layer is implemented to improve the predictability of low mass flow. Also, mechanistic subcooled flow boiling model is used to predict the flow quality and void fraction. The performance of the present model is verified using the KAIST CHF database of water in uniformly heated tubes. It is found that the present model can give a satisfactory agreement with experimental data within less than 9% RMS error. 9 refs., 5 figs. (Author)

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

    Science.gov (United States)

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

    2017-01-01

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

  7. Mathematical modeling with multidisciplinary applications

    CERN Document Server

    Yang, Xin-She

    2013-01-01

    Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the

  8. Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

    Science.gov (United States)

    Lowe, James; Carter, Merilyn; Cooper, Tom

    2018-01-01

    Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

  9. Applied impulsive mathematical models

    CERN Document Server

    Stamova, Ivanka

    2016-01-01

    Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

  10. A Primer for Mathematical Modeling

    Science.gov (United States)

    Sole, Marla

    2013-01-01

    With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

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

    Science.gov (United States)

    Czocher, Jennifer A.

    2016-01-01

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

  12. Mathematical modelling of membrane separation

    DEFF Research Database (Denmark)

    Vinther, Frank

    This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...

  13. Mechanistic effect modeling for ecological risk assessment: where to go from here?

    Science.gov (United States)

    Grimm, Volker; Martin, Benjamin T

    2013-07-01

    Mechanistic effect models (MEMs) consider the mechanisms of how chemicals affect individuals and ecological systems such as populations and communities. There is an increasing awareness that MEMs have high potential to make risk assessment of chemicals more ecologically relevant than current standard practice. Here we discuss what kinds of MEMs are needed to improve scientific and regulatory aspects of risk assessment. To make valid predictions for a wide range of environmental conditions, MEMs need to include a sufficient amount of emergence, for example, population dynamics emerging from what individual organisms do. We present 1 example where the life cycle of individuals is described using Dynamic Energy Budget theory. The resulting individual-based population model is thus parameterized at the individual level but correctly predicts multiple patterns at the population level. This is the case for both control and treated populations. We conclude that the state-of-the-art in mechanistic effect modeling has reached a level where MEMs are robust and predictive enough to be used in regulatory risk assessment. Mechanistic effect models will thus be used to advance the scientific basis of current standard practice and will, if their development follows Good Modeling Practice, be included in a standardized way in future regulatory risk assessments. Copyright © 2013 SETAC.

  14. Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

    Science.gov (United States)

    Wickstrom, Megan H.

    2017-01-01

    This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

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

    Science.gov (United States)

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

    2014-01-01

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

  16. An introduction to mathematical modeling

    CERN Document Server

    Bender, Edward A

    2000-01-01

    Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The

  17. Mechanistic modeling of reactive soil nitrogen emissions across agricultural management practices

    Science.gov (United States)

    Rasool, Q. Z.; Miller, D. J.; Bash, J. O.; Venterea, R. T.; Cooter, E. J.; Hastings, M. G.; Cohan, D. S.

    2017-12-01

    The global reactive nitrogen (N) budget has increased by a factor of 2-3 from pre-industrial levels. This increase is especially pronounced in highly N fertilized agricultural regions in summer. The reactive N emissions from soil to atmosphere can be in reduced (NH3) or oxidized (NO, HONO, N2O) forms, depending on complex biogeochemical transformations of soil N reservoirs. Air quality models like CMAQ typically neglect soil emissions of HONO and N2O. Previously, soil NO emissions estimated by models like CMAQ remained parametric and inconsistent with soil NH3 emissions. Thus, there is a need to more mechanistically and consistently represent the soil N processes that lead to reactive N emissions to the atmosphere. Our updated approach estimates soil NO, HONO and N2O emissions by incorporating detailed agricultural fertilizer inputs from EPIC, and CMAQ-modeled N deposition, into the soil N pool. EPIC addresses the nitrification, denitrification and volatilization rates along with soil N pools for agricultural soils. Suitable updates to account for factors like nitrite (NO2-) accumulation not addressed in EPIC, will also be made. The NO and N2O emissions from nitrification and denitrification are computed mechanistically using the N sub-model of DAYCENT. These mechanistic definitions use soil water content, temperature, NH4+ and NO3- concentrations, gas diffusivity and labile C availability as dependent parameters at various soil layers. Soil HONO emissions found to be most probable under high NO2- availability will be based on observed ratios of HONO to NO emissions under different soil moistures, pH and soil types. The updated scheme will utilize field-specific soil properties and N inputs across differing manure management practices such as tillage. Comparison of the modeled soil NO emission rates from the new mechanistic and existing schemes against field measurements will be discussed. Our updated framework will help to predict the diurnal and daily variability

  18. Mathematical Modeling in the Undergraduate Curriculum

    Science.gov (United States)

    Toews, Carl

    2012-01-01

    Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

  19. Teachers' Conceptions of Mathematical Modeling

    Science.gov (United States)

    Gould, Heather

    2013-01-01

    The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

  20. Mathematical Modelling of Predatory Prokaryotes

    NARCIS (Netherlands)

    Wilkinson, Michael H.F.

    2006-01-01

    Predator–prey models have a long history in mathematical modelling of ecosystem dynamics and evolution. In this chapter an introduction to the methodology of mathematical modelling is given, with emphasis on microbial predator–prey systems, followed by a description of variants of the basic

  1. Mechanistic species distribution modeling reveals a niche shift during invasion.

    Science.gov (United States)

    Chapman, Daniel S; Scalone, Romain; Štefanić, Edita; Bullock, James M

    2017-06-01

    Niche shifts of nonnative plants can occur when they colonize novel climatic conditions. However, the mechanistic basis for niche shifts during invasion is poorly understood and has rarely been captured within species distribution models. We quantified the consequence of between-population variation in phenology for invasion of common ragweed (Ambrosia artemisiifolia L.) across Europe. Ragweed is of serious concern because of its harmful effects as a crop weed and because of its impact on public health as a major aeroallergen. We developed a forward mechanistic species distribution model based on responses of ragweed development rates to temperature and photoperiod. The model was parameterized and validated from the literature and by reanalyzing data from a reciprocal common garden experiment in which native and invasive populations were grown within and beyond the current invaded range. It could therefore accommodate between-population variation in the physiological requirements for flowering, and predict the potentially invaded ranges of individual populations. Northern-origin populations that were established outside the generally accepted climate envelope of the species had lower thermal requirements for bud development, suggesting local adaptation of phenology had occurred during the invasion. The model predicts that this will extend the potentially invaded range northward and increase the average suitability across Europe by 90% in the current climate and 20% in the future climate. Therefore, trait variation observed at the population scale can trigger a climatic niche shift at the biogeographic scale. For ragweed, earlier flowering phenology in established northern populations could allow the species to spread beyond its current invasive range, substantially increasing its risk to agriculture and public health. Mechanistic species distribution models offer the possibility to represent niche shifts by varying the traits and niche responses of individual

  2. Development of a mechanistically based computer simulation of nitrogen oxide absorption in packed towers

    International Nuclear Information System (INIS)

    Counce, R.M.

    1981-01-01

    A computer simulation for nitrogen oxide (NO/sub x/) scrubbing in packed towers was developed for use in process design and process control. This simulation implements a mechanistically based mathematical model, which was formulated from (1) an exhaustive literature review; (2) previous NO/sub x/ scrubbing experience with sieve-plate towers; and (3) comparisons of sequential sets of experiments. Nitrogen oxide scrubbing is characterized by simultaneous absorption and desorption phenomena: the model development is based on experiments designed to feature these two phenomena. The model was then successfully tested in experiments designed to put it in jeopardy

  3. Mathematical Modeling: A Bridge to STEM Education

    Science.gov (United States)

    Kertil, Mahmut; Gurel, Cem

    2016-01-01

    The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

  4. Wind tunnel modeling of roadways: Comparison with mathematical models

    International Nuclear Information System (INIS)

    Heidorn, K.; Davies, A.E.; Murphy, M.C.

    1991-01-01

    The assessment of air quality impacts from roadways is a major concern to urban planners. In order to assess future road and building configurations, a number of techniques have been developed including mathematical models, which simulate traffic emissions and atmospheric dispersion through a series of mathematical relationships and physical models. The latter models simulate emissions and dispersion through scaling of these processes in a wind tunnel. Two roadway mathematical models, HIWAY-2 and CALINE-4, were applied to a proposed development in a large urban area. Physical modeling procedures developed by Rowan Williams Davies and Irwin Inc. (RWDI) in the form of line source simulators were also applied, and the resulting carbon monoxide concentrations were compared. The results indicated a factor of two agreement between the mathematical and physical models. The physical model, however, reacted to change in building massing and configuration. The mathematical models did not, since no provision for such changes was included in the mathematical models. In general, the RWDI model resulted in higher concentrations than either HIWAY-2 or CALINE-4. Where there was underprediction, it was often due to shielding of the receptor by surrounding buildings. Comparison of these three models with the CALTRANS Tracer Dispersion Experiment showed good results although concentrations were consistently underpredicted

  5. Mathematical models for plant-herbivore interactions

    Science.gov (United States)

    Feng, Zhilan; DeAngelis, Donald L.

    2017-01-01

    Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

  6. The coefficient of restitution of pressurized balls: a mechanistic model

    Science.gov (United States)

    Georgallas, Alex; Landry, Gaëtan

    2016-01-01

    Pressurized, inflated balls used in professional sports are regulated so that their behaviour upon impact can be anticipated and allow the game to have its distinctive character. However, the dynamics governing the impacts of such balls, even on stationary hard surfaces, can be extremely complex. The energy transformations, which arise from the compression of the gas within the ball and from the shear forces associated with the deformation of the wall, are examined in this paper. We develop a simple mechanistic model of the dependence of the coefficient of restitution, e, upon both the gauge pressure, P_G, of the gas and the shear modulus, G, of the wall. The model is validated using the results from a simple series of experiments using three different sports balls. The fits to the data are extremely good for P_G > 25 kPa and consistent values are obtained for the value of G for the wall material. As far as the authors can tell, this simple, mechanistic model of the pressure dependence of the coefficient of restitution is the first in the literature. *%K Coefficient of Restitution, Dynamics, Inflated Balls, Pressure, Impact Model

  7. Mechanistic modeling of CHF in forced-convection subcooled boiling

    International Nuclear Information System (INIS)

    Podowski, M.Z.; Alajbegovic, A.; Kurul, N.; Drew, D.A.; Lahey, R.T. Jr.

    1997-05-01

    Because of the complexity of phenomena governing boiling heat transfer, the approach to solve practical problems has traditionally been based on experimental correlations rather than mechanistic models. The recent progress in computational fluid dynamics (CFD), combined with improved experimental techniques in two-phase flow and heat transfer, makes the use of rigorous physically-based models a realistic alternative to the current simplistic phenomenological approach. The objective of this paper is to present a new CFD model for critical heat flux (CHF) in low quality (in particular, in subcooled boiling) forced-convection flows in heated channels

  8. Development of Improved Mechanistic Deterioration Models for Flexible Pavements

    DEFF Research Database (Denmark)

    Ullidtz, Per; Ertman, Hans Larsen

    1998-01-01

    The paper describes a pilot study in Denmark with the main objective of developing improved mechanistic deterioration models for flexible pavements based on an accelerated full scale test on an instrumented pavement in the Danish Road Tessting Machine. The study was the first in "International...... Pavement Subgrade Performance Study" sponsored by the Federal Highway Administration (FHWA), USA. The paper describes in detail the data analysis and the resulting models for rutting, roughness, and a model for the plastic strain in the subgrade.The reader will get an understanding of the work needed...

  9. Mathematical modeling of climate change and malaria transmission dynamics: a historical review.

    Science.gov (United States)

    Eikenberry, Steffen E; Gumel, Abba B

    2018-04-24

    Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics. A wide variety of process-based (or mechanistic) mathematical models have thus been proposed for the complex, highly nonlinear weather-driven Anopheles lifecycle and malaria transmission dynamics, but have reached somewhat disparate conclusions as to optimum temperatures for transmission, and the possible effect of increasing temperatures upon (potential) malaria distribution, with some projecting a large increase in the area at risk for malaria, but others predicting primarily a shift in the disease's geographic range. More generally, both global and local environmental changes drove the initial emergence of P. falciparum as a major human pathogen in tropical Africa some 10,000 years ago, and the disease has a long and deep history through the present. It is the goal of this paper to review major aspects of malaria biology, methods for formalizing these into mathematical forms, uncertainties and controversies in proper modeling methodology, and to provide a timeline of some major modeling efforts from the classical works of Sir Ronald Ross and George Macdonald through recent climate-focused modeling studies. Finally, we attempt to place such mathematical work within a broader historical context for the "million-murdering Death" of malaria.

  10. Calibrating mechanistic-empirical pavement performance models with an expert matrix

    Energy Technology Data Exchange (ETDEWEB)

    Tighe, S.; AlAssar, R.; Haas, R. [Waterloo Univ., ON (Canada). Dept. of Civil Engineering; Zhiwei, H. [Stantec Consulting Ltd., Cambridge, ON (Canada)

    2001-07-01

    Proper management of pavement infrastructure requires pavement performance modelling. For the past 20 years, the Ontario Ministry of Transportation has used the Ontario Pavement Analysis of Costs (OPAC) system for pavement design. Pavement needs, however, have changed substantially during that time. To address this need, a new research contract is underway to enhance the model and verify the predictions, particularly at extreme points such as low and high traffic volume pavement design. This initiative included a complete evaluation of the existing OPAC pavement design method, the construction of a new set of pavement performance prediction models, and the development of the flexible pavement design procedure that incorporates reliability analysis. The design was also expanded to include rigid pavement designs and modification of the existing life cycle cost analysis procedure which includes both the agency cost and road user cost. Performance prediction and life-cycle costs were developed based on several factors, including material properties, traffic loads and climate. Construction and maintenance schedules were also considered. The methodology for the calibration and validation of a mechanistic-empirical flexible pavement performance model was described. Mechanistic-empirical design methods combine theory based design such as calculated stresses, strains or deflections with empirical methods, where a measured response is associated with thickness and pavement performance. Elastic layer analysis was used to determine pavement response to determine the most effective design using cumulative Equivalent Single Axle Loads (ESALs), below grade type and layer thickness.The new mechanistic-empirical model separates the environment and traffic effects on performance. This makes it possible to quantify regional differences between Southern and Northern Ontario. In addition, roughness can be calculated in terms of the International Roughness Index or Riding comfort Index

  11. Causal Bayes Model of Mathematical Competence in Kindergarten

    Directory of Open Access Journals (Sweden)

    Božidar Tepeš

    2016-06-01

    Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.

  12. INCORPORATION OF MECHANISTIC INFORMATION IN THE ARSENIC PBPK MODEL DEVELOPMENT PROCESS

    Science.gov (United States)

    INCORPORATING MECHANISTIC INSIGHTS IN A PBPK MODEL FOR ARSENICElaina M. Kenyon, Michael F. Hughes, Marina V. Evans, David J. Thomas, U.S. EPA; Miroslav Styblo, University of North Carolina; Michael Easterling, Analytical Sciences, Inc.A physiologically based phar...

  13. Mechanistic models for the evaluation of biocatalytic reaction conditions and biosensor design optimization

    DEFF Research Database (Denmark)

    Semenova, Daria

    . In the first case study a mechanistic model was developed to describe the enzymatic reaction of glucose oxidase and glucose in the presence of catalase inside a commercial microfluidic platform with integrated oxygen sensor spots. The simplicity of the proposed model allowed an easy calibration of the reaction...... the microfluidic device. In the second case study the flexible microfluidic platform with integrated amperometric glucose biosensors was developed for continuous monitoring of glucose consumption rates. The integration of the mixing chamber inside the platform allowed performing sample dilutions which subsequently......BRs. In the third case study the mechanistic model of the cyclic voltammetry response of the first generation glucose biosensors was developed and applied for the biosensor design optimization. Furthermore the obtained qualitative and quantitative dependencies between the model output and experimental results were...

  14. Mathematical models in medicine: Diseases and epidemics

    International Nuclear Information System (INIS)

    Witten, M.

    1987-01-01

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

  15. The use of mechanistic descriptions of algal growth and zooplankton grazing in an estuarine eutrophication model

    Science.gov (United States)

    Baird, M. E.; Walker, S. J.; Wallace, B. B.; Webster, I. T.; Parslow, J. S.

    2003-03-01

    A simple model of estuarine eutrophication is built on biomechanical (or mechanistic) descriptions of a number of the key ecological processes in estuaries. Mechanistically described processes include the nutrient uptake and light capture of planktonic and benthic autotrophs, and the encounter rates of planktonic predators and prey. Other more complex processes, such as sediment biogeochemistry, detrital processes and phosphate dynamics, are modelled using empirical descriptions from the Port Phillip Bay Environmental Study (PPBES) ecological model. A comparison is made between the mechanistically determined rates of ecological processes and the analogous empirically determined rates in the PPBES ecological model. The rates generally agree, with a few significant exceptions. Model simulations were run at a range of estuarine depths and nutrient loads, with outputs presented as the annually averaged biomass of autotrophs. The simulations followed a simple conceptual model of eutrophication, suggesting a simple biomechanical understanding of estuarine processes can provide a predictive tool for ecological processes in a wide range of estuarine ecosystems.

  16. Mathematical Modeling and Computational Thinking

    Science.gov (United States)

    Sanford, John F.; Naidu, Jaideep T.

    2017-01-01

    The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

  17. Summer Camp of Mathematical Modeling in China

    Science.gov (United States)

    Tian, Xiaoxi; Xie, Jinxing

    2013-01-01

    The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

  18. Strategies to Support Students' Mathematical Modeling

    Science.gov (United States)

    Jung, Hyunyi

    2015-01-01

    An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

  19. Explorations in Elementary Mathematical Modeling

    Science.gov (United States)

    Shahin, Mazen

    2010-01-01

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

  20. Mathematical Modeling of Diverse Phenomena

    Science.gov (United States)

    Howard, J. C.

    1979-01-01

    Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

  1. LEARNING AND THOUGHT PROCESSES IN REALISTIC MATHEMATICS INSTRUCTION

    NARCIS (Netherlands)

    Nelissen, J.; Tomic, W.

    2008-01-01

    This article deals with the various different approaches to mathematics and the influence that these approaches have had on the teaching of this subject. In addition to the three generally known schools of mathematics instruction - the mechanistic, the structuralistic and the empirical - the article

  2. An introduction to mathematical modeling of infectious diseases

    CERN Document Server

    Li, Michael Y

    2018-01-01

    This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies.  The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis.  Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases.  Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

  3. Principles of mathematical modeling

    CERN Document Server

    Dym, Clive

    2004-01-01

    Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

  4. INTEGRATION OF QSAR AND SAR METHODS FOR THE MECHANISTIC INTERPRETATION OF PREDICTIVE MODELS FOR CARCINOGENICITY

    Directory of Open Access Journals (Sweden)

    Natalja Fjodorova

    2012-07-01

    Full Text Available The knowledge-based Toxtree expert system (SAR approach was integrated with the statistically based counter propagation artificial neural network (CP ANN model (QSAR approach to contribute to a better mechanistic understanding of a carcinogenicity model for non-congeneric chemicals using Dragon descriptors and carcinogenic potency for rats as a response. The transparency of the CP ANN algorithm was demonstrated using intrinsic mapping technique specifically Kohonen maps. Chemical structures were represented by Dragon descriptors that express the structural and electronic features of molecules such as their shape and electronic surrounding related to reactivity of molecules. It was illustrated how the descriptors are correlated with particular structural alerts (SAs for carcinogenicity with recognized mechanistic link to carcinogenic activity. Moreover, the Kohonen mapping technique enables one to examine the separation of carcinogens and non-carcinogens (for rats within a family of chemicals with a particular SA for carcinogenicity. The mechanistic interpretation of models is important for the evaluation of safety of chemicals.

  5. The Role of Aggregates of Therapeutic Protein Products in Immunogenicity: An Evaluation by Mathematical Modeling

    Directory of Open Access Journals (Sweden)

    Liusong Yin

    2015-01-01

    Full Text Available Therapeutic protein products (TPP have been widely used to treat a variety of human diseases, including cancer, hemophilia, and autoimmune diseases. However, TPP can induce unwanted immune responses that can impact both drug efficacy and patient safety. The presence of aggregates is of particular concern as they have been implicated in inducing both T cell-independent and T cell-dependent immune responses. We used mathematical modeling to evaluate several mechanisms through which aggregates of TPP could contribute to the development of immunogenicity. Modeling interactions between aggregates and B cell receptors demonstrated that aggregates are unlikely to induce T cell-independent immune responses by cross-linking B cell receptors because the amount of signal transducing complex that can form under physiologically relevant conditions is limited. We systematically evaluate the role of aggregates in inducing T cell-dependent immune responses using a recently developed multiscale mechanistic mathematical model. Our analysis indicates that aggregates could contribute to T cell-dependent immune response by inducing high affinity epitopes which may not be present in the nonaggregated TPP and/or by enhancing danger signals to break tolerance. In summary, our computational analysis is suggestive of novel insights into the mechanisms underlying aggregate-induced immunogenicity, which could be used to develop mitigation strategies.

  6. Concepts of mathematical modeling

    CERN Document Server

    Meyer, Walter J

    2004-01-01

    Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

  7. The Combined Use of Correlative and Mechanistic Species Distribution Models Benefits Low Conservation Status Species.

    Directory of Open Access Journals (Sweden)

    Thibaud Rougier

    Full Text Available Species can respond to climate change by tracking appropriate environmental conditions in space, resulting in a range shift. Species Distribution Models (SDMs can help forecast such range shift responses. For few species, both correlative and mechanistic SDMs were built, but allis shad (Alosa alosa, an endangered anadromous fish species, is one of them. The main purpose of this study was to provide a framework for joint analyses of correlative and mechanistic SDMs projections in order to strengthen conservation measures for species of conservation concern. Guidelines for joint representation and subsequent interpretation of models outputs were defined and applied. The present joint analysis was based on the novel mechanistic model GR3D (Global Repositioning Dynamics of Diadromous fish Distribution which was parameterized on allis shad and then used to predict its future distribution along the European Atlantic coast under different climate change scenarios (RCP 4.5 and RCP 8.5. We then used a correlative SDM for this species to forecast its distribution across the same geographic area and under the same climate change scenarios. First, projections from correlative and mechanistic models provided congruent trends in probability of habitat suitability and population dynamics. This agreement was preferentially interpreted as referring to the species vulnerability to climate change. Climate change could not be accordingly listed as a major threat for allis shad. The congruence in predicted range limits between SDMs projections was the next point of interest. The difference, when noticed, required to deepen our understanding of the niche modelled by each approach. In this respect, the relative position of the northern range limit between the two methods strongly suggested here that a key biological process related to intraspecific variability was potentially lacking in the mechanistic SDM. Based on our knowledge, we hypothesized that local

  8. Teaching mathematical modelling through project work

    DEFF Research Database (Denmark)

    Blomhøj, Morten; Kjeldsen, Tinne Hoff

    2006-01-01

    are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...

  9. Mathematical modelling of scour: A review

    DEFF Research Database (Denmark)

    Sumer, B. Mutlu

    2007-01-01

    A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...

  10. Mathematical modeling a chemical engineer's perspective

    CERN Document Server

    Rutherford, Aris

    1999-01-01

    Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus

  11. Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

    Science.gov (United States)

    Tutak, Tayfun; Güder, Yunus

    2013-01-01

    The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…

  12. Mechanistic model for void distribution in flashing flow

    International Nuclear Information System (INIS)

    Riznic, J.; Ishii, M.; Afgan, N.

    1987-01-01

    A problem of discharging of an initially subcooled liquid from a high pressure condition into a low pressure environment is quite important in several industrial systems such as nuclear reactors and chemical reactors. A new model for the flashing process is proposed here based on the wall nucleation theory, bubble growth model and drift-flux bubble transport model. In order to calculate the bubble number density, the bubble number transport equation with a distributed source from the wall nucleation sites is used. The model predictions in terms of the void fraction are compared to Moby Dick and BNL experimental data. It shows that satisfactory agreements could be obtained from the present model without any floating parameter to be adjusted with data. This result indicates that, at least for the experimental conditions considered here, the mechanistic prediction of the flashing phenomenon is possible based on the present wall nucleation based model. 43 refs., 4 figs

  13. Specific Type of Knowledge Map: Mathematical Model

    OpenAIRE

    Milan, Houška; Martina, Beránková

    2005-01-01

    The article deals with relationships between mathematical models and knowledge maps. The goal of the article is to suggest how to use the mathematical model as a knowledge map and/or as a part (esp. the inference mechanism) of the knowledge system. The results are demonstrated on the case study, when the knowledge from a story is expressed by mathematical model. The model is used for both knowledge warehousing and inferencing new artificially derived knowledge.

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

    Science.gov (United States)

    Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

    2016-01-01

    Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

  15. Mechanistic modeling of heat transfer process governing pressure tube-to-calandria tube contact and fuel channel failure

    International Nuclear Information System (INIS)

    Luxat, J.C.

    2002-01-01

    Heat transfer behaviour and phenomena associated with ballooning deformation of a pressure tube into contact with a calandria tube have been analyzed and mechanistic models have been developed to describe the heat transfer and thermal-mechanical processes. These mechanistic models are applied to analyze experiments performed in various COG funded Contact Boiling Test series. Particular attention is given in the modeling to characterization of the conditions for which fuel channel failure may occur. Mechanistic models describing the governing heat transfer and thermal-mechanical processes are presented. The technical basis for characterizing parameters of the models from the general heat transfer literature is described. The validity of the models is demonstrated by comparison with experimental data. Fuel channel integrity criteria are proposed which are based upon three necessary and sequential mechanisms: Onset of CHF and local drypatch formation at contact; sustained film boiling in the post-contact period; and creep strain to failure of the calandria tube while in sustained film boiling. (author)

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

    Science.gov (United States)

    Zbiek, Rose Mary; Conner, Annamarie

    2006-01-01

    Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

  17. A mechanistic model for electricity consumption on dairy farms: Definition, validation, and demonstration

    NARCIS (Netherlands)

    Upton, J.R.; Murphy, M.; Shallo, L.; Groot Koerkamp, P.W.G.; Boer, de I.J.M.

    2014-01-01

    Our objective was to define and demonstrate a mechanistic model that enables dairy farmers to explore the impact of a technical or managerial innovation on electricity consumption, associated CO2 emissions, and electricity costs. We, therefore, (1) defined a model for electricity consumption on

  18. A mathematical model of sentimental dynamics accounting for marital dissolution.

    Science.gov (United States)

    Rey, José-Manuel

    2010-03-31

    Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

  19. A mathematical model of sentimental dynamics accounting for marital dissolution.

    Directory of Open Access Journals (Sweden)

    José-Manuel Rey

    Full Text Available BACKGROUND: Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. METHODOLOGY/PRINCIPAL FINDINGS: Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. CONCLUSIONS/SIGNIFICANCE: These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

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

    Science.gov (United States)

    Khusna, H.; Heryaningsih, N. Y.

    2018-01-01

    The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

  1. Mathematical Modelling as a Professional Task

    Science.gov (United States)

    Frejd, Peter; Bergsten, Christer

    2016-01-01

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

  2. Mathematical models of hysteresis

    International Nuclear Information System (INIS)

    1998-01-01

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

  3. Mathematical models of hysteresis

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1998-08-01

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

  4. Mathematical modelling of metabolism

    DEFF Research Database (Denmark)

    Gombert, Andreas Karoly; Nielsen, Jens

    2000-01-01

    Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...

  5. Using Covariation Reasoning to Support Mathematical Modeling

    Science.gov (United States)

    Jacobson, Erik

    2014-01-01

    For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

  6. The many faces of the mathematical modeling cycle

    NARCIS (Netherlands)

    Perrenet, J.C.; Zwaneveld, B.

    2012-01-01

    In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been

  7. Mathematical models in radiogeochronology

    International Nuclear Information System (INIS)

    Abril, J.M.; Garcia Leon, M.

    1991-01-01

    The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

  8. Validation of a mathematical model of the bovine estrous cycle for cows with different estrous cycle characteristics.

    Science.gov (United States)

    Boer, H M T; Butler, S T; Stötzel, C; Te Pas, M F W; Veerkamp, R F; Woelders, H

    2017-11-01

    A recently developed mechanistic mathematical model of the bovine estrous cycle was parameterized to fit empirical data sets collected during one estrous cycle of 31 individual cows, with the main objective to further validate the model. The a priori criteria for validation were (1) the resulting model can simulate the measured data correctly (i.e. goodness of fit), and (2) this is achieved without needing extreme, probably non-physiological parameter values. We used a least squares optimization procedure to identify parameter configurations for the mathematical model to fit the empirical in vivo measurements of follicle and corpus luteum sizes, and the plasma concentrations of progesterone, estradiol, FSH and LH for each cow. The model was capable of accommodating normal variation in estrous cycle characteristics of individual cows. With the parameter sets estimated for the individual cows, the model behavior changed for 21 cows, with improved fit of the simulated output curves for 18 of these 21 cows. Moreover, the number of follicular waves was predicted correctly for 18 of the 25 two-wave and three-wave cows, without extreme parameter value changes. Estimation of specific parameters confirmed results of previous model simulations indicating that parameters involved in luteolytic signaling are very important for regulation of general estrous cycle characteristics, and are likely responsible for differences in estrous cycle characteristics between cows.

  9. Mathematical modelling a case studies approach

    CERN Document Server

    Illner, Reinhard; McCollum, Samantha; Roode, Thea van

    2004-01-01

    Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; oth...

  10. Mechanistic model of mass-specific basal metabolic rate: evaluation in healthy young adults.

    Science.gov (United States)

    Wang, Z; Bosy-Westphal, A; Schautz, B; Müller, M

    2011-12-01

    Mass-specific basal metabolic rate (mass-specific BMR), defined as the resting energy expenditure per unit body mass per day, is an important parameter in energy metabolism research. However, a mechanistic explanation for magnitude of mass-specific BMR remains lacking. The objective of the present study was to validate the applicability of a proposed mass-specific BMR model in healthy adults. A mechanistic model was developed at the organ-tissue level, mass-specific BMR = Σ( K i × F i ), where Fi is the fraction of body mass as individual organs and tissues, and K i is the specific resting metabolic rate of major organs and tissues. The Fi values were measured by multiple MRI scans and the K i values were suggested by Elia in 1992. A database of healthy non-elderly non-obese adults (age 20 - 49 yrs, BMI BMR of all subjects was 21.6 ± 1.9 (mean ± SD) and 21.7 ± 1.6 kcal/kg per day, respectively. The measured mass-specific BMR was correlated with the predicted mass-specific BMR (r = 0.82, P BMR, versus the average of measured and predicted mass-specific BMR. In conclusion, the proposed mechanistic model was validated in non-elderly non-obese adults and can help to understand the inherent relationship between mass-specific BMR and body composition.

  11. Quantitative assessment of biological impact using transcriptomic data and mechanistic network models

    International Nuclear Information System (INIS)

    Thomson, Ty M.; Sewer, Alain; Martin, Florian; Belcastro, Vincenzo; Frushour, Brian P.; Gebel, Stephan; Park, Jennifer; Schlage, Walter K.; Talikka, Marja; Vasilyev, Dmitry M.; Westra, Jurjen W.; Hoeng, Julia; Peitsch, Manuel C.

    2013-01-01

    Exposure to biologically active substances such as therapeutic drugs or environmental toxicants can impact biological systems at various levels, affecting individual molecules, signaling pathways, and overall cellular processes. The ability to derive mechanistic insights from the resulting system responses requires the integration of experimental measures with a priori knowledge about the system and the interacting molecules therein. We developed a novel systems biology-based methodology that leverages mechanistic network models and transcriptomic data to quantitatively assess the biological impact of exposures to active substances. Hierarchically organized network models were first constructed to provide a coherent framework for investigating the impact of exposures at the molecular, pathway and process levels. We then validated our methodology using novel and previously published experiments. For both in vitro systems with simple exposure and in vivo systems with complex exposures, our methodology was able to recapitulate known biological responses matching expected or measured phenotypes. In addition, the quantitative results were in agreement with experimental endpoint data for many of the mechanistic effects that were assessed, providing further objective confirmation of the approach. We conclude that our methodology evaluates the biological impact of exposures in an objective, systematic, and quantifiable manner, enabling the computation of a systems-wide and pan-mechanistic biological impact measure for a given active substance or mixture. Our results suggest that various fields of human disease research, from drug development to consumer product testing and environmental impact analysis, could benefit from using this methodology. - Highlights: • The impact of biologically active substances is quantified at multiple levels. • The systems-level impact integrates the perturbations of individual networks. • The networks capture the relationships between

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

    Directory of Open Access Journals (Sweden)

    Jennifer M. Suh

    2017-06-01

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

  13. SITE-94. Adaptation of mechanistic sorption models for performance assessment calculations

    International Nuclear Information System (INIS)

    Arthur, R.C.

    1996-10-01

    Sorption is considered in most predictive models of radionuclide transport in geologic systems. Most models simulate the effects of sorption in terms of empirical parameters, which however can be criticized because the data are only strictly valid under the experimental conditions at which they were measured. An alternative is to adopt a more mechanistic modeling framework based on recent advances in understanding the electrical properties of oxide mineral-water interfaces. It has recently been proposed that these 'surface-complexation' models may be directly applicable to natural systems. A possible approach for adapting mechanistic sorption models for use in performance assessments, using this 'surface-film' concept, is described in this report. Surface-acidity parameters in the Generalized Two-Layer surface complexation model are combined with surface-complexation constants for Np(V) sorption ob hydrous ferric oxide to derive an analytical model enabling direct calculation of corresponding intrinsic distribution coefficients as a function of pH, and Ca 2+ , Cl - , and HCO 3 - concentrations. The surface film concept is then used to calculate whole-rock distribution coefficients for Np(V) sorption by altered granitic rocks coexisting with a hypothetical, oxidized Aespoe groundwater. The calculated results suggest that the distribution coefficients for Np adsorption on these rocks could range from 10 to 100 ml/g. Independent estimates of K d for Np sorption in similar systems, based on an extensive review of experimental data, are consistent, though slightly conservative, with respect to the calculated values. 31 refs

  14. Mechanistic CHF modeling for natural circulation applications in SMR

    Energy Technology Data Exchange (ETDEWEB)

    Luitjens, Jeffrey [Department of Nuclear Engineering and Radiation Health Physics, Oregon State University, 3451 SW Jefferson Way, Corvallis, OR 97331 (United States); Wu, Qiao, E-mail: qiao.wu@oregonstate.edu [Department of Nuclear Engineering and Radiation Health Physics, Oregon State University, 3451 SW Jefferson Way, Corvallis, OR 97331 (United States); Greenwood, Scott; Corradini, Michael [Department of Engineering Physics, University of Wisconsin, 1415 Engineering Drive, Madison, WI 53706 (United States)

    2016-12-15

    A mechanistic critical heat flux correlation has been developed for a wide range of operating conditions which include low mass fluxes of 540–890 kg/m{sup 2}-s, high pressures of 12–13 MPa, and critical heat fluxes of 835–1100 kW/m{sup 2}. Eleven experimental data points have been collected over these conditions to inform the development of the model using bundle geometry. Errors of within 15% have been obtained with the proposed model for predicting the critical heat flux value, location, and critical pin power for a non-uniform heat flux applied to a 2 × 2 bundle configuration.

  15. Mathematical Modeling in the High School Curriculum

    Science.gov (United States)

    Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary

    2016-01-01

    In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

  16. Mechanistic curiosity will not kill the Bayesian cat

    NARCIS (Netherlands)

    Borsboom, D.; Wagenmakers, E.-J.; Romeijn, J.-W.

    2011-01-01

    Jones & Love (J&L) suggest that Bayesian approaches to the explanation of human behavior should be constrained by mechanistic theories. We argue that their proposal misconstrues the relation between process models, such as the Bayesian model, and mechanisms. While mechanistic theories can answer

  17. Mechanistic curiosity will not kill the Bayesian cat

    NARCIS (Netherlands)

    Borsboom, Denny; Wagenmakers, Eric-Jan; Romeijn, Jan-Willem

    Jones & Love (J&L) suggest that Bayesian approaches to the explanation of human behavior should be constrained by mechanistic theories. We argue that their proposal misconstrues the relation between process models, such as the Bayesian model, and mechanisms. While mechanistic theories can answer

  18. Understanding apparently non-exponential outbreaks Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

    Science.gov (United States)

    Champredon, David; Earn, David J. D.

    2016-09-01

    Mechanistic mathematical modelling of the population dynamics of infectious diseases has advanced tremendously over the last few decades [1-6]. Transmission models have been applied to countless diseases of public health importance, including seasonal and pandemic influenza [7], childhood diseases such as measles [8,9] and whooping cough [10], vector transmitted diseases such as malaria [11] and dengue [12], and waterborne diseases such as cholera [13-15]. Much attention in recent years has been directed to emergent diseases such as SARS [16], new subtypes of influenza [17,18], Ebola [19,20], and Zika [21], for which an understanding of early outbreak dynamics is critical.

  19. Mathematical Modeling Approaches in Plant Metabolomics.

    Science.gov (United States)

    Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas

    2018-01-01

    The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

  20. Students’ mathematical learning in modelling activities

    DEFF Research Database (Denmark)

    Kjeldsen, Tinne Hoff; Blomhøj, Morten

    2013-01-01

    Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts i...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....

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

    Science.gov (United States)

    Stohlmann, Micah S.

    2017-01-01

    Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

  2. Mutagenesis and mathematics: The allure of numbers

    International Nuclear Information System (INIS)

    Haynes, R.H.

    1989-01-01

    This paper sets out the formal, empirical, and mechanistic equations that my colleagues and I have developed for the description and analysis of dose-response data on the lethal and genetic effects of mutagens in microorganisms. These three types of equations are interrelated inasmuch as they are all based ultimately on the use of the Poisson distribution in the formal definition of lethal and mutational hit functions. Explicit mathematical expressions for these functions can be written down in either empirical or mechanistic terms. The empirical equations are obtained simply by writing the hit functions as finite polynomials with adjustable coefficients. The mechanistic equations are based on the assumptions of the DNA damage-repair hypothesis. The mathematical formulation of this hypothesis entails an important change in the definition of the word hit from that used in the classical hit/target theory of radiation biology. The theoretical and practical applications of these various equations in mutation research are summarized briefly and their merits are assessed in light of recent advances in our understanding of the biochemical basis of mutagenesis

  3. An Emphasis on Perception: Teaching Image Formation Using a Mechanistic Model of Vision.

    Science.gov (United States)

    Allen, Sue; And Others

    An effective way to teach the concept of image is to give students a model of human vision which incorporates a simple mechanism of depth perception. In this study two almost identical versions of a curriculum in geometrical optics were created. One used a mechanistic, interpretive eye model, and in the other the eye was modeled as a passive,…

  4. Mathematical modelling of fracture hydrology

    International Nuclear Information System (INIS)

    Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

    1985-01-01

    This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments

  5. Mathematical modeling of laser lipolysis

    Directory of Open Access Journals (Sweden)

    Reynaud Jean

    2008-02-01

    Full Text Available Abstract Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc. The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s give similar skin surface temperature (max: 41°C. These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction

  6. Modeling of the pyruvate production with Escherichia coli: comparison of mechanistic and neural networks-based models.

    Science.gov (United States)

    Zelić, B; Bolf, N; Vasić-Racki, D

    2006-06-01

    Three different models: the unstructured mechanistic black-box model, the input-output neural network-based model and the externally recurrent neural network model were used to describe the pyruvate production process from glucose and acetate using the genetically modified Escherichia coli YYC202 ldhA::Kan strain. The experimental data were used from the recently described batch and fed-batch experiments [ Zelić B, Study of the process development for Escherichia coli-based pyruvate production. PhD Thesis, University of Zagreb, Faculty of Chemical Engineering and Technology, Zagreb, Croatia, July 2003. (In English); Zelić et al. Bioproc Biosyst Eng 26:249-258 (2004); Zelić et al. Eng Life Sci 3:299-305 (2003); Zelić et al Biotechnol Bioeng 85:638-646 (2004)]. The neural networks were built out of the experimental data obtained in the fed-batch pyruvate production experiments with the constant glucose feed rate. The model validation was performed using the experimental results obtained from the batch and fed-batch pyruvate production experiments with the constant acetate feed rate. Dynamics of the substrate and product concentration changes was estimated using two neural network-based models for biomass and pyruvate. It was shown that neural networks could be used for the modeling of complex microbial fermentation processes, even in conditions in which mechanistic unstructured models cannot be applied.

  7. Improving Predictive Modeling in Pediatric Drug Development: Pharmacokinetics, Pharmacodynamics, and Mechanistic Modeling

    Energy Technology Data Exchange (ETDEWEB)

    Slikker, William; Young, John F.; Corley, Rick A.; Dorman, David C.; Conolly, Rory B.; Knudsen, Thomas; Erstad, Brian L.; Luecke, Richard H.; Faustman, Elaine M.; Timchalk, Chuck; Mattison, Donald R.

    2005-07-26

    A workshop was conducted on November 18?19, 2004, to address the issue of improving predictive models for drug delivery to developing humans. Although considerable progress has been made for adult humans, large gaps remain for predicting pharmacokinetic/pharmacodynamic (PK/PD) outcome in children because most adult models have not been tested during development. The goals of the meeting included a description of when, during development, infants/children become adultlike in handling drugs. The issue of incorporating the most recent advances into the predictive models was also addressed: both the use of imaging approaches and genomic information were considered. Disease state, as exemplified by obesity, was addressed as a modifier of drug pharmacokinetics and pharmacodynamics during development. Issues addressed in this workshop should be considered in the development of new predictive and mechanistic models of drug kinetics and dynamics in the developing human.

  8. Exploring Yellowstone National Park with Mathematical Modeling

    Science.gov (United States)

    Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

    2017-01-01

    Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

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

    Directory of Open Access Journals (Sweden)

    Nita Delima

    2017-03-01

    Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa.    Kata Kunci: Comprehensive

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

    Science.gov (United States)

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

    2016-01-01

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

  11. Mathematical modeling courses for Media technology students

    DEFF Research Database (Denmark)

    Timcenko, Olga

    2009-01-01

    This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...

  12. Teaching Mathematical Modelling for Earth Sciences via Case Studies

    Science.gov (United States)

    Yang, Xin-She

    2010-05-01

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

  13. Rival approaches to mathematical modelling in immunology

    Science.gov (United States)

    Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.

    2007-08-01

    In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.

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

    Science.gov (United States)

    Jungck, John R; Gaff, Holly; Weisstein, Anton E

    2010-01-01

    Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

  15. Modeling Bird Migration under Climate Change: A Mechanistic Approach

    Science.gov (United States)

    Smith, James A.

    2009-01-01

    How will migrating birds respond to changes in the environment under climate change? What are the implications for migratory success under the various accelerated climate change scenarios as forecast by the Intergovernmental Panel on Climate Change? How will reductions or increased variability in the number or quality of wetland stop-over sites affect migratory bird species? The answers to these questions have important ramifications for conservation biology and wildlife management. Here, we describe the use of continental scale simulation modeling to explore how spatio-temporal changes along migratory flyways affect en-route migration success. We use an individually based, biophysical, mechanistic, bird migration model to simulate the movement of shorebirds in North America as a tool to study how such factors as drought and wetland loss may impact migratory success and modify migration patterns. Our model is driven by remote sensing and climate data and incorporates important landscape variables. The energy budget components of the model include resting, foraging, and flight, but presently predation is ignored. Results/Conclusions We illustrate our model by studying the spring migration of sandpipers through the Great Plains to their Arctic breeding grounds. Why many species of shorebirds have shown significant declines remains a puzzle. Shorebirds are sensitive to stop-over quality and spacing because of their need for frequent refueling stops and their opportunistic feeding patterns. We predict bird "hydrographs that is, stop-over frequency with latitude, that are in agreement with the literature. Mean stop-over durations predicted from our model for nominal cases also are consistent with the limited, but available data. For the shorebird species simulated, our model predicts that shorebirds exhibit significant plasticity and are able to shift their migration patterns in response to changing drought conditions. However, the question remains as to whether this

  16. Malaria's missing number: calculating the human component of R0 by a within-host mechanistic model of Plasmodium falciparum infection and transmission.

    Directory of Open Access Journals (Sweden)

    Geoffrey L Johnston

    2013-04-01

    Full Text Available Human infection by malarial parasites of the genus Plasmodium begins with the bite of an infected Anopheles mosquito. Current estimates place malaria mortality at over 650,000 individuals each year, mostly in African children. Efforts to reduce disease burden can benefit from the development of mathematical models of disease transmission. To date, however, comprehensive modeling of the parameters defining human infectivity to mosquitoes has remained elusive. Here, we describe a mechanistic within-host model of Plasmodium falciparum infection in humans and pathogen transmission to the mosquito vector. Our model incorporates the entire parasite lifecycle, including the intra-erythrocytic asexual forms responsible for disease, the onset of symptoms, the development and maturation of intra-erythrocytic gametocytes that are transmissible to Anopheles mosquitoes, and human-to-mosquito infectivity. These model components were parameterized from malaria therapy data and other studies to simulate individual infections, and the ensemble of outputs was found to reproduce the full range of patient responses to infection. Using this model, we assessed human infectivity over the course of untreated infections and examined the effects in relation to transmission intensity, expressed by the basic reproduction number R0 (defined as the number of secondary cases produced by a single typical infection in a completely susceptible population. Our studies predict that net human-to-mosquito infectivity from a single non-immune individual is on average equal to 32 fully infectious days. This estimate of mean infectivity is equivalent to calculating the human component of malarial R0 . We also predict that mean daily infectivity exceeds five percent for approximately 138 days. The mechanistic framework described herein, made available as stand-alone software, will enable investigators to conduct detailed studies into theories of malaria control, including the effects of

  17. Assessment of Primary 5 Students' Mathematical Modelling Competencies

    Science.gov (United States)

    Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia

    2012-01-01

    Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…

  18. Behavioural Procedural Models – a multipurpose mechanistic account

    Directory of Open Access Journals (Sweden)

    Leonardo Ivarola

    2012-05-01

    Full Text Available In this paper we outline an epistemological defence of what wecall Behavioural Procedural Models (BPMs, which represent the processes of individual decisions that lead to relevant economic patterns as psychologically (rather than rationally driven. Their general structure, and the way in which they may be incorporated to a multipurpose view of models, where the representational and interventionist goals are combined, is shown. It is argued that BPMs may provide “mechanistic-based explanations” in the sense defended by Hedström and Ylikoski (2010, which involve invariant regularities in Woodward’s sense. Such mechanisms provide a causal sort of explanation of anomalous economic patterns, which allow for extra marketintervention and manipulability in order to correct and improve some key individual decisions. This capability sets the basis for the so called libertarian paternalism (Sunstein and Thaler 2003.

  19. A mechanistic modelling and data assimilation approach to estimate the carbon/chlorophyll and carbon/nitrogen ratios in a coupled hydrodynamical-biological model

    Directory of Open Access Journals (Sweden)

    B. Faugeras

    2004-01-01

    Full Text Available The principal objective of hydrodynamical-biological models is to provide estimates of the main carbon fluxes such as total and export oceanic production. These models are nitrogen based, that is to say that the variables are expressed in terms of their nitrogen content. Moreover models are calibrated using chlorophyll data sets. Therefore carbon to chlorophyll (C:Chl and carbon to nitrogen (C:N ratios have to be assumed. This paper addresses the problem of the representation of these ratios. In a 1D framework at the DYFAMED station (NW Mediterranean Sea we propose a model which enables the estimation of the basic biogeochemical fluxes and in which the spatio-temporal variability of the C:Chl and C:N ratios is fully represented in a mechanical way. This is achieved through the introduction of new state variables coming from the embedding of a phytoplankton growth model in a more classical Redfieldian NNPZD-DOM model (in which the C:N ratio is assumed to be a constant. Following this modelling step, the parameters of the model are estimated using the adjoint data assimilation method which enables the assimilation of chlorophyll and nitrate data sets collected at DYFAMED in 1997.Comparing the predictions of the new Mechanistic model with those of the classical Redfieldian NNPZD-DOM model which was calibrated with the same data sets, we find that both models reproduce the reference data in a comparable manner. Both fluxes and stocks can be equally well predicted by either model. However if the models are coinciding on an average basis, they are diverging from a variability prediction point of view. In the Mechanistic model biology adapts much faster to its environment giving rise to higher short term variations. Moreover the seasonal variability in total production differs from the Redfieldian NNPZD-DOM model to the Mechanistic model. In summer the Mechanistic model predicts higher production values in carbon unit than the Redfieldian NNPZD

  20. Mathematical modeling and computational intelligence in engineering applications

    CERN Document Server

    Silva Neto, Antônio José da; Silva, Geraldo Nunes

    2016-01-01

    This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.

  1. The (Mathematical) Modeling Process in Biosciences.

    Science.gov (United States)

    Torres, Nestor V; Santos, Guido

    2015-01-01

    In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

  2. A mechanistic Eulerian-Lagrangian model for dispersed flow film boiling

    International Nuclear Information System (INIS)

    Andreani, M.; Yadigaroglu, G.

    1991-01-01

    In this paper a new mechanistic model of heat transfer in the dispersed flow regime is presented. The usual assumptions that render most of the available models unsuitable for the analysis of the reflooding phase of the LOCA are discussed, and a two-dimensional time-independent numerical model is developed. The gas temperature field is solved in a fixed-grid (Eulerian) mesh, with the droplets behaving as mass and energy sources. The histories of a large number of computational droplets are followed in a Lagrangian frame, considering evaporation, break-up and interactions with the vapor and with the wall. comparisons of calculated wall and vapor temperatures with experimental data are shown for two reflooding tests

  3. Mechanistic variables can enhance predictive models of endotherm distributions: The American pika under current, past, and future climates

    Science.gov (United States)

    Mathewson, Paul; Moyer-Horner, Lucas; Beever, Erik; Briscoe, Natalie; Kearney, Michael T.; Yahn, Jeremiah; Porter, Warren P.

    2017-01-01

    How climate constrains species’ distributions through time and space is an important question in the context of conservation planning for climate change. Despite increasing awareness of the need to incorporate mechanism into species distribution models (SDMs), mechanistic modeling of endotherm distributions remains limited in this literature. Using the American pika (Ochotona princeps) as an example, we present a framework whereby mechanism can be incorporated into endotherm SDMs. Pika distribution has repeatedly been found to be constrained by warm temperatures, so we used Niche Mapper, a mechanistic heat-balance model, to convert macroclimate data to pika-specific surface activity time in summer across the western United States. We then explored the difference between using a macroclimate predictor (summer temperature) and using a mechanistic predictor (predicted surface activity time) in SDMs. Both approaches accurately predicted pika presences in current and past climate regimes. However, the activity models predicted 8–19% less habitat loss in response to annual temperature increases of ~3–5 °C predicted in the region by 2070, suggesting that pikas may be able to buffer some climate change effects through behavioral thermoregulation that can be captured by mechanistic modeling. Incorporating mechanism added value to the modeling by providing increased confidence in areas where different modeling approaches agreed and providing a range of outcomes in areas of disagreement. It also provided a more proximate variable relating animal distribution to climate, allowing investigations into how unique habitat characteristics and intraspecific phenotypic variation may allow pikas to exist in areas outside those predicted by generic SDMs. Only a small number of easily obtainable data are required to parameterize this mechanistic model for any endotherm, and its use can improve SDM predictions by explicitly modeling a widely applicable direct physiological effect

  4. Mechanistic variables can enhance predictive models of endotherm distributions: the American pika under current, past, and future climates.

    Science.gov (United States)

    Mathewson, Paul D; Moyer-Horner, Lucas; Beever, Erik A; Briscoe, Natalie J; Kearney, Michael; Yahn, Jeremiah M; Porter, Warren P

    2017-03-01

    How climate constrains species' distributions through time and space is an important question in the context of conservation planning for climate change. Despite increasing awareness of the need to incorporate mechanism into species distribution models (SDMs), mechanistic modeling of endotherm distributions remains limited in this literature. Using the American pika (Ochotona princeps) as an example, we present a framework whereby mechanism can be incorporated into endotherm SDMs. Pika distribution has repeatedly been found to be constrained by warm temperatures, so we used Niche Mapper, a mechanistic heat-balance model, to convert macroclimate data to pika-specific surface activity time in summer across the western United States. We then explored the difference between using a macroclimate predictor (summer temperature) and using a mechanistic predictor (predicted surface activity time) in SDMs. Both approaches accurately predicted pika presences in current and past climate regimes. However, the activity models predicted 8-19% less habitat loss in response to annual temperature increases of ~3-5 °C predicted in the region by 2070, suggesting that pikas may be able to buffer some climate change effects through behavioral thermoregulation that can be captured by mechanistic modeling. Incorporating mechanism added value to the modeling by providing increased confidence in areas where different modeling approaches agreed and providing a range of outcomes in areas of disagreement. It also provided a more proximate variable relating animal distribution to climate, allowing investigations into how unique habitat characteristics and intraspecific phenotypic variation may allow pikas to exist in areas outside those predicted by generic SDMs. Only a small number of easily obtainable data are required to parameterize this mechanistic model for any endotherm, and its use can improve SDM predictions by explicitly modeling a widely applicable direct physiological effect

  5. Continuum mechanics the birthplace of mathematical models

    CERN Document Server

    Allen, Myron B

    2015-01-01

    Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer.  This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe

  6. Mathematical models in marketing a collection of abstracts

    CERN Document Server

    Funke, Ursula H

    1976-01-01

    Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe­ matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...

  7. Semi-mechanistic Model Applied to the Search for Economically Optimal Conditions and Blending of Gasoline Feedstock for Steam-cracking Process

    Directory of Open Access Journals (Sweden)

    Karaba Adam

    2016-01-01

    Full Text Available Steam-cracking is energetically intensive large-scaled process which transforms a wide range of hydrocarbons feedstock to petrochemical products. The dependence of products yields on feedstock composition and reaction conditions has been successfully described by mathematical models which are very useful tools for the optimization of cracker operation. Remaining problem is to formulate objective function for such an optimization. Quantitative criterion based on the process economy is proposed in this paper. Previously developed and verified industrial steam-cracking semi-mechanistic model is utilized as supporting tool for economic evaluation of selected gasoline feedstock. Economic criterion is established as the difference between value of products obtained by cracking of studied feedstock under given conditions and the value of products obtained by cracking of reference feedstock under reference conditions. As an example of method utilization, optimal reaction conditions were searched for each of selected feedstock. Potential benefit of individual cracking and cracking of grouped feedstocks in the contrast to cracking under the middle of optimums is evaluated and also compared to cracking under usual conditions.

  8. Modelling and Optimizing Mathematics Learning in Children

    Science.gov (United States)

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

    2013-01-01

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

  9. Rational and Mechanistic Perspectives on Reinforcement Learning

    Science.gov (United States)

    Chater, Nick

    2009-01-01

    This special issue describes important recent developments in applying reinforcement learning models to capture neural and cognitive function. But reinforcement learning, as a theoretical framework, can apply at two very different levels of description: "mechanistic" and "rational." Reinforcement learning is often viewed in mechanistic terms--as…

  10. Mathematical modeling of a process the rolling delivery

    Science.gov (United States)

    Stepanov, Mikhail A.; Korolev, Andrey A.

    2018-03-01

    An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.

  11. Mechanistic Systems Modeling to Improve Understanding and Prediction of Cardiotoxicity Caused by Targeted Cancer Therapeutics

    Directory of Open Access Journals (Sweden)

    Jaehee V. Shim

    2017-09-01

    Full Text Available Tyrosine kinase inhibitors (TKIs are highly potent cancer therapeutics that have been linked with serious cardiotoxicity, including left ventricular dysfunction, heart failure, and QT prolongation. TKI-induced cardiotoxicity is thought to result from interference with tyrosine kinase activity in cardiomyocytes, where these signaling pathways help to control critical processes such as survival signaling, energy homeostasis, and excitation–contraction coupling. However, mechanistic understanding is limited at present due to the complexities of tyrosine kinase signaling, and the wide range of targets inhibited by TKIs. Here, we review the use of TKIs in cancer and the cardiotoxicities that have been reported, discuss potential mechanisms underlying cardiotoxicity, and describe recent progress in achieving a more systematic understanding of cardiotoxicity via the use of mechanistic models. In particular, we argue that future advances are likely to be enabled by studies that combine large-scale experimental measurements with Quantitative Systems Pharmacology (QSP models describing biological mechanisms and dynamics. As such approaches have proven extremely valuable for understanding and predicting other drug toxicities, it is likely that QSP modeling can be successfully applied to cardiotoxicity induced by TKIs. We conclude by discussing a potential strategy for integrating genome-wide expression measurements with models, illustrate initial advances in applying this approach to cardiotoxicity, and describe challenges that must be overcome to truly develop a mechanistic and systematic understanding of cardiotoxicity caused by TKIs.

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

    Science.gov (United States)

    Fasni, N.; Turmudi, T.; Kusnandi, K.

    2017-09-01

    This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

  13. Simulating the Risk of Liver Fluke Infection using a Mechanistic Hydro-epidemiological Model

    Science.gov (United States)

    Beltrame, Ludovica; Dunne, Toby; Rose, Hannah; Walker, Josephine; Morgan, Eric; Vickerman, Peter; Wagener, Thorsten

    2016-04-01

    Liver Fluke (Fasciola hepatica) is a common parasite found in livestock and responsible for considerable economic losses throughout the world. Risk of infection is strongly influenced by climatic and hydrological conditions, which characterise the host environment for parasite development and transmission. Despite on-going control efforts, increases in fluke outbreaks have been reported in recent years in the UK, and have been often attributed to climate change. Currently used fluke risk models are based on empirical relationships derived between historical climate and incidence data. However, hydro-climate conditions are becoming increasingly non-stationary due to climate change and direct anthropogenic impacts such as land use change, making empirical models unsuitable for simulating future risk. In this study we introduce a mechanistic hydro-epidemiological model for Liver Fluke, which explicitly simulates habitat suitability for disease development in space and time, representing the parasite life cycle in connection with key environmental conditions. The model is used to assess patterns of Liver Fluke risk for two catchments in the UK under current and potential future climate conditions. Comparisons are made with a widely used empirical model employing different datasets, including data from regional veterinary laboratories. Results suggest that mechanistic models can achieve adequate predictive ability and support adaptive fluke control strategies under climate change scenarios.

  14. A tissue-engineered gastric cancer model for mechanistic study of anti-tumor drugs

    International Nuclear Information System (INIS)

    Gao, Ming; Cai, Yiting; Wu, Wei; Shi, Yazhou; Fei, Zhewei

    2013-01-01

    The use of the traditional xenograft subcutaneous tumor model has been contested because of its limitations, such as a slow tumorigenesis, inconsistent chemotherapeutic results, etc. In light of these challenges, we aim to revamp the traditional model by employing an electrospun scaffold composed of polydioxanone, gelatin and elastin to boost the tumorigenesis. The scaffold featured a highly porous microstructure and successfully supported the growth of tumor cells in vitro without provoking apoptosis. In vivo studies showed that in the scaffold model the tumor volume increased by 43.27% and the weight by 75.58%, respectively, within a 12-week period. In addition, the scaffold model saw an increase of CD24 + and CD44 + cells in the tumor mass by 42% and 313%, respectively. The scaffolding materials did not lead to phenotypic changes during the tumorigenesis. Thereafter, in the scaffold model, we found that the chemotherapeutic regimen of docetaxel, cisplatin and fluorouracil unleashed a stronger capability than the regimen comprising cisplatin and fluorouracil to deplete the CD44 + subpopulation. This discovery sheds mechanistic lights on the role of docetaxel for its future chemotherapeutic applications. This revamped model affords cancer scientists a convenient and reliable platform to mechanistically investigate the chemotherapeutic drugs on gastric cancer stem cells. (paper)

  15. Mathematical modelling of two-phase flows

    International Nuclear Information System (INIS)

    Komen, E.M.J.; Stoop, P.M.

    1992-11-01

    A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs

  16. Comparison of Two-Phase Pipe Flow in OpenFOAM with a Mechanistic Model

    Science.gov (United States)

    Shuard, Adrian M.; Mahmud, Hisham B.; King, Andrew J.

    2016-03-01

    Two-phase pipe flow is a common occurrence in many industrial applications such as power generation and oil and gas transportation. Accurate prediction of liquid holdup and pressure drop is of vast importance to ensure effective design and operation of fluid transport systems. In this paper, a Computational Fluid Dynamics (CFD) study of a two-phase flow of air and water is performed using OpenFOAM. The two-phase solver, interFoam is used to identify flow patterns and generate values of liquid holdup and pressure drop, which are compared to results obtained from a two-phase mechanistic model developed by Petalas and Aziz (2002). A total of 60 simulations have been performed at three separate pipe inclinations of 0°, +10° and -10° respectively. A three dimensional, 0.052m diameter pipe of 4m length is used with the Shear Stress Transport (SST) k - ɷ turbulence model to solve the turbulent mixtures of air and water. Results show that the flow pattern behaviour and numerical values of liquid holdup and pressure drop compare reasonably well to the mechanistic model.

  17. Modelling Mathematical Reasoning in Physics Education

    Science.gov (United States)

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

    2012-04-01

    Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

  18. An introduction to mathematical modeling a course in mechanics

    CERN Document Server

    Oden, Tinsley J

    2011-01-01

    A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

  19. A mechanistic model for the evolution of multicellularity

    Science.gov (United States)

    Amado, André; Batista, Carlos; Campos, Paulo R. A.

    2018-02-01

    Through a mechanistic approach we investigate the formation of aggregates of variable sizes, accounting mechanisms of aggregation, dissociation, death and reproduction. In our model, cells can produce two metabolites, but the simultaneous production of both metabolites is costly in terms of fitness. Thus, the formation of larger groups can favor the aggregates to evolve to a configuration where division of labor arises. It is assumed that the states of the cells in a group are those that maximize organismal fitness. In the model it is considered that the groups can grow linearly, forming a chain, or compactly keeping a roughly spherical shape. Starting from a population consisting of single-celled organisms, we observe the formation of groups with variable sizes and usually much larger than two-cell aggregates. Natural selection can favor the formation of large groups, which allows the system to achieve new and larger fitness maxima.

  20. Mathematical models and accuracy of radioisotope gauges

    International Nuclear Information System (INIS)

    Urbanski, P.

    1989-01-01

    Mathematical expressions relating the variance and mean value of the intrinsic error with the parameters of one and multi-dimensional mathematical models of radioisotope gauges are given. Variance of the intrinsic error at the model's output is considered as a sum of the variances of the random error which is created in the first stages of the measuring chain and the random error of calibration procedure. The mean value of the intrinsic error (systematic error) appears always for nonlinear models. It was found that the optimal model of calibration procedure not always corresponds to the minimal value of the intrinsic error. The derived expressions are applied for the assessment of the mathematical models of some of the existing gauges (radioisotope belt weigher, XRF analyzer and coating thickness gauge). 7 refs., 5 figs., 1 tab. (author)

  1. Leading Undergraduate Research Projects in Mathematical Modeling

    Science.gov (United States)

    Seshaiyer, Padmanabhan

    2017-01-01

    In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

  2. Scaffolding Mathematical Modelling with a Solution Plan

    Science.gov (United States)

    Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

    2015-01-01

    In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

  3. A dynamic and mechanistic model of PCB bioaccumulation in the European hake ( Merluccius merluccius)

    Science.gov (United States)

    Bodiguel, Xavier; Maury, Olivier; Mellon-Duval, Capucine; Roupsard, François; Le Guellec, Anne-Marie; Loizeau, Véronique

    2009-08-01

    Bioaccumulation is difficult to document because responses differ among chemical compounds, with environmental conditions, and physiological processes characteristic of each species. We use a mechanistic model, based on the Dynamic Energy Budget (DEB) theory, to take into account this complexity and study factors impacting accumulation of organic pollutants in fish through ontogeny. The bioaccumulation model proposed is a comprehensive approach that relates evolution of hake PCB contamination to physiological information about the fish, such as diet, metabolism, reserve and reproduction status. The species studied is the European hake ( Merluccius merluccius, L. 1758). The model is applied to study the total concentration and the lipid normalised concentration of 4 PCB congeners in male and female hakes from the Gulf of Lions (NW Mediterranean sea) and the Bay of Biscay (NE Atlantic ocean). Outputs of the model compare consistently to measurements over the life span of fish. Simulation results clearly demonstrate the relative effects of food contamination, growth and reproduction on the PCB bioaccumulation in hake. The same species living in different habitats and exposed to different PCB prey concentrations exhibit marked difference in the body accumulation of PCBs. At the adult stage, female hakes have a lower PCB concentration compared to males for a given length. We successfully simulated these sex-specific PCB concentrations by considering two mechanisms: a higher energy allocation to growth for females and a transfer of PCBs from the female to its eggs when allocating lipids from reserve to eggs. Finally, by its mechanistic description of physiological processes, the model is relevant for other species and sets the stage for a mechanistic understanding of toxicity and ecological effects of organic contaminants in marine organisms.

  4. Modeling interdisciplinary activities involving Mathematics

    DEFF Research Database (Denmark)

    Iversen, Steffen Møllegaard

    2006-01-01

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

  5. The Spectrum of Mathematical Models.

    Science.gov (United States)

    Karplus, Walter J.

    1983-01-01

    Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…

  6. Mathematical model in economic environmental problems

    Energy Technology Data Exchange (ETDEWEB)

    Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)

    1996-12-31

    The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.

  7. Secondary clarifier hybrid model calibration in full scale pulp and paper activated sludge wastewater treatment

    Energy Technology Data Exchange (ETDEWEB)

    Sreckovic, G.; Hall, E.R. [British Columbia Univ., Dept. of Civil Engineering, Vancouver, BC (Canada); Thibault, J. [Laval Univ., Dept. of Chemical Engineering, Ste-Foy, PQ (Canada); Savic, D. [Exeter Univ., School of Engineering, Exeter (United Kingdom)

    1999-05-01

    The issue of proper model calibration techniques applied to mechanistic mathematical models relating to activated sludge systems was discussed. Such calibrations are complex because of the non-linearity and multi-model objective functions of the process. This paper presents a hybrid model which was developed using two techniques to model and calibrate secondary clarifier parts of an activated sludge system. Genetic algorithms were used to successfully calibrate the settler mechanistic model, and neural networks were used to reduce the error between the mechanistic model output and real world data. Results of the modelling study show that the long term response of a one-dimensional settler mechanistic model calibrated by genetic algorithms and compared to full scale plant data can be improved by coupling the calibrated mechanistic model to as black-box model, such as a neural network. 11 refs., 2 figs.

  8. Development of a Multidisciplinary Middle School Mathematics Infusion Model

    Science.gov (United States)

    Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

    2011-01-01

    The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

  9. Mathematical models in biology bringing mathematics to life

    CERN Document Server

    Ferraro, Maria; Guarracino, Mario

    2015-01-01

    This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy.  The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...

  10. Ocular hemodynamics and glaucoma: the role of mathematical modeling.

    Science.gov (United States)

    Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

    2013-01-01

    To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

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

    Science.gov (United States)

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

    2017-12-01

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

  12. Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

    Science.gov (United States)

    Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.

    2011-01-01

    We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

  13. Incorporation of lysosomal sequestration in the mechanistic model for prediction of tissue distribution of basic drugs.

    Science.gov (United States)

    Assmus, Frauke; Houston, J Brian; Galetin, Aleksandra

    2017-11-15

    The prediction of tissue-to-plasma water partition coefficients (Kpu) from in vitro and in silico data using the tissue-composition based model (Rodgers & Rowland, J Pharm Sci. 2005, 94(6):1237-48.) is well established. However, distribution of basic drugs, in particular into lysosome-rich lung tissue, tends to be under-predicted by this approach. The aim of this study was to develop an extended mechanistic model for the prediction of Kpu which accounts for lysosomal sequestration and the contribution of different cell types in the tissue of interest. The extended model is based on compound-specific physicochemical properties and tissue composition data to describe drug ionization, distribution into tissue water and drug binding to neutral lipids, neutral phospholipids and acidic phospholipids in tissues, including lysosomes. Physiological data on the types of cells contributing to lung, kidney and liver, their lysosomal content and lysosomal pH were collated from the literature. The predictive power of the extended mechanistic model was evaluated using a dataset of 28 basic drugs (pK a ≥7.8, 17 β-blockers, 11 structurally diverse drugs) for which experimentally determined Kpu data in rat tissue have been reported. Accounting for the lysosomal sequestration in the extended mechanistic model improved the accuracy of Kpu predictions in lung compared to the original Rodgers model (56% drugs within 2-fold or 88% within 3-fold of observed values). Reduction in the extent of Kpu under-prediction was also evident in liver and kidney. However, consideration of lysosomal sequestration increased the occurrence of over-predictions, yielding overall comparable model performances for kidney and liver, with 68% and 54% of Kpu values within 2-fold error, respectively. High lysosomal concentration ratios relative to cytosol (>1000-fold) were predicted for the drugs investigated; the extent differed depending on the lysosomal pH and concentration of acidic phospholipids among

  14. Mathematical models for therapeutic approaches to control HIV disease transmission

    CERN Document Server

    Roy, Priti Kumar

    2015-01-01

    The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...

  15. Mathematical Modelling of Surfactant Self-assembly at Interfaces

    KAUST Repository

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

    2015-01-01

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

  16. a Discrete Mathematical Model to Simulate Malware Spreading

    Science.gov (United States)

    Del Rey, A. Martin; Sánchez, G. Rodriguez

    2012-10-01

    With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

  17. Use of mathematical modeling in nuclear measurements projects

    International Nuclear Information System (INIS)

    Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.

    2011-01-01

    Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)

  18. Mechanistic modelling of the drying behaviour of single pharmaceutical granules

    DEFF Research Database (Denmark)

    Thérèse F.C. Mortier, Séverine; Beer, Thomas De; Gernaey, Krist

    2012-01-01

    The trend to move towards continuous production processes in pharmaceutical applications enhances the necessity to develop mechanistic models to understand and control these processes. This work focuses on the drying behaviour of a single wet granule before tabletting, using a six...... phase (submodel 2), the water inside the granule evaporates. The second submodel contains an empirical power coefficient, b. A sensitivity analysis was performed to study the influence of parameters on the moisture content of single pharmaceutical granules, which clearly points towards the importance...

  19. Mechanistic link between uptake of sulfonamides and bacteriostatic effect: model development and application to experimental data from two soil microorganisms.

    Science.gov (United States)

    Focks, Andreas; Klasmeier, Jörg; Matthies, Michael

    2010-07-01

    Sulfonamides (SA) are antibiotic compounds that are widely used as human and veterinary pharmaceuticals. They are not rapidly biodegradable and have been detected in various environmental compartments. Effects of sulfonamides on microbial endpoints in soil have been reported from laboratory incubation studies. Sulfonamides inhibit the growth of sensitive microorganisms by competitive binding to the dihydropteroate-synthase (DHPS) enzyme of folic acid production. A mathematical model was developed that relates the extracellular SA concentration to the inhibition of the relative bacterial growth rate. Two factors--the anionic accumulation factor (AAF) and the cellular affinity factor (CAF)--determine the effective concentration of an SA. The AAF describes the SA uptake into bacterial cells and varies with both the extra- and intracellular pH values and with the acidic pKa value of an SA. The CAF subsumes relevant cellular and enzyme properties, and is directly proportional to the DHPS affinity constant for an SA. Based on the model, a mechanistic dose-response relationship is developed and evaluated against previously published data, where differences in the responses of Pseudomonas aeruginosa and Panthoea agglomerans toward changing medium pH values were found, most likely as a result of their diverse pH regulation. The derived dose-response relationship explains the pH and pKa dependency of mean effective concentration values (EC50) of eight SA and two soil bacteria based on AAF and CAF values. The mathematical model can be used to extrapolate sulfonamide effects to other pH values and to calculate the CAF as a pH-independent measure for the SA effects on microbial growth. Copyright (c) 2010 SETAC.

  20. Mathematical modelling of fracture hydrology

    International Nuclear Information System (INIS)

    Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

    1985-06-01

    This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)

  1. Mathematical Modelling Plant Signalling Networks

    KAUST Repository

    Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.

    2013-01-01

    methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more

  2. Mathematical modeling and applications in nonlinear dynamics

    CERN Document Server

    Merdan, Hüseyin

    2016-01-01

    The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

  3. Mathematical modelling methodologies in predictive food microbiology: a SWOT analysis.

    Science.gov (United States)

    Ferrer, Jordi; Prats, Clara; López, Daniel; Vives-Rego, Josep

    2009-08-31

    Predictive microbiology is the area of food microbiology that attempts to forecast the quantitative evolution of microbial populations over time. This is achieved to a great extent through models that include the mechanisms governing population dynamics. Traditionally, the models used in predictive microbiology are whole-system continuous models that describe population dynamics by means of equations applied to extensive or averaged variables of the whole system. Many existing models can be classified by specific criteria. We can distinguish between survival and growth models by seeing whether they tackle mortality or cell duplication. We can distinguish between empirical (phenomenological) models, which mathematically describe specific behaviour, and theoretical (mechanistic) models with a biological basis, which search for the underlying mechanisms driving already observed phenomena. We can also distinguish between primary, secondary and tertiary models, by examining their treatment of the effects of external factors and constraints on the microbial community. Recently, the use of spatially explicit Individual-based Models (IbMs) has spread through predictive microbiology, due to the current technological capacity of performing measurements on single individual cells and thanks to the consolidation of computational modelling. Spatially explicit IbMs are bottom-up approaches to microbial communities that build bridges between the description of micro-organisms at the cell level and macroscopic observations at the population level. They provide greater insight into the mesoscale phenomena that link unicellular and population levels. Every model is built in response to a particular question and with different aims. Even so, in this research we conducted a SWOT (Strength, Weaknesses, Opportunities and Threats) analysis of the different approaches (population continuous modelling and Individual-based Modelling), which we hope will be helpful for current and future

  4. A Mechanistic Beta-Binomial Probability Model for mRNA Sequencing Data.

    Science.gov (United States)

    Smith, Gregory R; Birtwistle, Marc R

    2016-01-01

    A main application for mRNA sequencing (mRNAseq) is determining lists of differentially-expressed genes (DEGs) between two or more conditions. Several software packages exist to produce DEGs from mRNAseq data, but they typically yield different DEGs, sometimes markedly so. The underlying probability model used to describe mRNAseq data is central to deriving DEGs, and not surprisingly most softwares use different models and assumptions to analyze mRNAseq data. Here, we propose a mechanistic justification to model mRNAseq as a binomial process, with data from technical replicates given by a binomial distribution, and data from biological replicates well-described by a beta-binomial distribution. We demonstrate good agreement of this model with two large datasets. We show that an emergent feature of the beta-binomial distribution, given parameter regimes typical for mRNAseq experiments, is the well-known quadratic polynomial scaling of variance with the mean. The so-called dispersion parameter controls this scaling, and our analysis suggests that the dispersion parameter is a continually decreasing function of the mean, as opposed to current approaches that impose an asymptotic value to the dispersion parameter at moderate mean read counts. We show how this leads to current approaches overestimating variance for moderately to highly expressed genes, which inflates false negative rates. Describing mRNAseq data with a beta-binomial distribution thus may be preferred since its parameters are relatable to the mechanistic underpinnings of the technique and may improve the consistency of DEG analysis across softwares, particularly for moderately to highly expressed genes.

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

    Science.gov (United States)

    Plotnitsky, Arkady

    2017-06-01

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

  6. Mechanistic modeling of sulfur-deprived photosynthesis and hydrogen production in suspensions of Chlamydomonas reinhardtii.

    Science.gov (United States)

    Williams, C R; Bees, M A

    2014-02-01

    The ability of unicellular green algal species such as Chlamydomonas reinhardtii to produce hydrogen gas via iron-hydrogenase is well known. However, the oxygen-sensitive hydrogenase is closely linked to the photosynthetic chain in such a way that hydrogen and oxygen production need to be separated temporally for sustained photo-production. Under illumination, sulfur-deprivation has been shown to accommodate the production of hydrogen gas by partially-deactivating O2 evolution activity, leading to anaerobiosis in a sealed culture. As these facets are coupled, and the system complex, mathematical approaches potentially are of significant value since they may reveal improved or even optimal schemes for maximizing hydrogen production. Here, a mechanistic model of the system is constructed from consideration of the essential pathways and processes. The role of sulfur in photosynthesis (via PSII) and the storage and catabolism of endogenous substrate, and thus growth and decay of culture density, are explicitly modeled in order to describe and explore the complex interactions that lead to H2 production during sulfur-deprivation. As far as possible, functional forms and parameter values are determined or estimated from experimental data. The model is compared with published experimental studies and, encouragingly, qualitative agreement for trends in hydrogen yield and initiation time are found. It is then employed to probe optimal external sulfur and illumination conditions for hydrogen production, which are found to differ depending on whether a maximum yield of gas or initial production rate is required. The model constitutes a powerful theoretical tool for investigating novel sulfur cycling regimes that may ultimately be used to improve the commercial viability of hydrogen gas production from microorganisms. © 2013 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc.

  7. FEMME, a flexible environment for mathematically modelling the environment

    NARCIS (Netherlands)

    Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.

    2002-01-01

    A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model

  8. mathematical models for estimating radio channels utilization

    African Journals Online (AJOL)

    2017-08-08

    Aug 8, 2017 ... Mathematical models for radio channels utilization assessment by real-time flows transfer in ... data transmission networks application having dynamic topology ..... Journal of Applied Mathematics and Statistics, 56(2): 85–90.

  9. Problems in mechanistic theoretical models for cell transformation by ionizing radiation

    International Nuclear Information System (INIS)

    Chatterjee, Aloke; Holley, W.R.

    1992-01-01

    A mechanistic model based on yields of double strand breaks has been developed to determine the dose response curves for cell transformation frequencies. At its present stage the model is applicable to immortal cell lines and to various qualities (X-rays, Neon and Iron) of ionizing radiation. Presently, we have considered four types of processes which can lead to activation phenomena: (i) point mutation events on a regulatory segment of selected oncogenes, (ii) inactivation of suppressor genes, through point mutation, (iii) deletion of a suppressor gene by a single track, and (iv) deletion of a suppressor gene by two tracks. (author)

  10. Mechanistic modeling for mammography screening risks

    International Nuclear Information System (INIS)

    Bijwaard, Harmen

    2008-01-01

    Full text: Western populations show a very high incidence of breast cancer and in many countries mammography screening programs have been set up for the early detection of these cancers. Through these programs large numbers of women (in the Netherlands, 700.000 per year) are exposed to low but not insignificant X-ray doses. ICRP based risk estimates indicate that the number of breast cancer casualties due to mammography screening can be as high as 50 in the Netherlands per year. The number of lives saved is estimated to be much higher, but for an accurate calculation of the benefits of screening a better estimate of these risks is indispensable. Here it is attempted to better quantify the radiological risks of mammography screening through the application of a biologically based model for breast tumor induction by X-rays. The model is applied to data obtained from the National Institutes of Health in the U.S. These concern epidemiological data of female TB patients who received high X-ray breast doses in the period 1930-1950 through frequent fluoroscopy of their lungs. The mechanistic model that is used to describe the increased breast cancer incidence is based on an earlier study by Moolgavkar et al. (1980), in which the natural background incidence of breast cancer was modeled. The model allows for a more sophisticated extrapolation of risks to the low dose X-ray exposures that are common in mammography screening and to the higher ages that are usually involved. Furthermore, it allows for risk transfer to other (non-western) populations. The results have implications for decisions on the frequency of screening, the number of mammograms taken at each screening, minimum and maximum ages for screening and the transfer to digital equipment. (author)

  11. Mathematical modeling of CA125 kinetics in recurrent ovarian cancer (ROC) patients treated with chemotherapy and predictive value of early modeled kinetic parameters in CALYPSO trial: A GCIG study

    DEFF Research Database (Denmark)

    You, Benoit; Colomban, Olivier; Heywood, Mark

    2011-01-01

    Background: Although CA125 kinetic profiles may be related with relapse risk in ovarian cancer patients treated with chemotherapy, no reliable kinetic parameters have been reported. Mathematical modeling may help describe CA125 decline dynamically and determine parameters predictive of relapse....... Methods: Data from CALYPSO phase III trial data comparing 2 carboplatin-based regimens in ROC patients were analyzed. Based on population kinetic approach (Monolix software), a semi-mechanistic model was used to fit serum log (CA125) concentration-time profiles with following parameters: tumor growth rate...... the first 50 treatment days were tested regarding progression free survival (PFS) against other reported prognostic factors using Cox-models: treatment arm; platinum-free interval (PFI), metastatic site number, largest tumor size, elevated WBC and measurable disease. Results: The CA125 kinetics from 898...

  12. Mathematical modelling in solid mechanics

    CERN Document Server

    Sofonea, Mircea; Steigmann, David

    2017-01-01

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

  13. Comparison of Two-Phase Pipe Flow in OpenFOAM with a Mechanistic Model

    International Nuclear Information System (INIS)

    Shuard, Adrian M; Mahmud, Hisham B; King, Andrew J

    2016-01-01

    Two-phase pipe flow is a common occurrence in many industrial applications such as power generation and oil and gas transportation. Accurate prediction of liquid holdup and pressure drop is of vast importance to ensure effective design and operation of fluid transport systems. In this paper, a Computational Fluid Dynamics (CFD) study of a two-phase flow of air and water is performed using OpenFOAM. The two-phase solver, interFoam is used to identify flow patterns and generate values of liquid holdup and pressure drop, which are compared to results obtained from a two-phase mechanistic model developed by Petalas and Aziz (2002). A total of 60 simulations have been performed at three separate pipe inclinations of 0°, +10° and -10° respectively. A three dimensional, 0.052m diameter pipe of 4m length is used with the Shear Stress Transport (SST) k - ω turbulence model to solve the turbulent mixtures of air and water. Results show that the flow pattern behaviour and numerical values of liquid holdup and pressure drop compare reasonably well to the mechanistic model. (paper)

  14. Interfacial Fluid Mechanics A Mathematical Modeling Approach

    CERN Document Server

    Ajaev, Vladimir S

    2012-01-01

    Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail.  Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also:  Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...

  15. Mathematical Models of Tuberculosis Reactivation and Relapse

    Directory of Open Access Journals (Sweden)

    Robert Steven Wallis

    2016-05-01

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

  16. Exploring the Relationship between Mathematical Modelling and Classroom Discourse

    Science.gov (United States)

    Redmond, Trevor; Sheehy, Joanne; Brown, Raymond

    2010-01-01

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

  17. Mathematical model of compact type evaporator

    Science.gov (United States)

    Borovička, Martin; Hyhlík, Tomáš

    2018-06-01

    In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

  18. Modellus: Learning Physics with Mathematical Modelling

    Science.gov (United States)

    Teodoro, Vitor

    Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

  19. Development and evaluation of a dimensionless mechanistic pan coating model for the prediction of coated tablet appearance.

    Science.gov (United States)

    Niblett, Daniel; Porter, Stuart; Reynolds, Gavin; Morgan, Tomos; Greenamoyer, Jennifer; Hach, Ronald; Sido, Stephanie; Karan, Kapish; Gabbott, Ian

    2017-08-07

    A mathematical, mechanistic tablet film-coating model has been developed for pharmaceutical pan coating systems based on the mechanisms of atomisation, tablet bed movement and droplet drying with the main purpose of predicting tablet appearance quality. Two dimensionless quantities were used to characterise the product properties and operating parameters: the dimensionless Spray Flux (relating to area coverage of the spray droplets) and the Niblett Number (relating to the time available for drying of coating droplets). The Niblett Number is the ratio between the time a droplet needs to dry under given thermodynamic conditions and the time available for the droplet while on the surface of the tablet bed. The time available for drying on the tablet bed surface is critical for appearance quality. These two dimensionless quantities were used to select process parameters for a set of 22 coating experiments, performed over a wide range of multivariate process parameters. The dimensionless Regime Map created can be used to visualise the effect of interacting process parameters on overall tablet appearance quality and defects such as picking and logo bridging. Copyright © 2017 Elsevier B.V. All rights reserved.

  20. On the mathematical modeling of memristors

    KAUST Repository

    Radwan, Ahmed G.

    2012-10-06

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

  1. Mathematical Properties Relevant to Geomagnetic Field Modeling

    DEFF Research Database (Denmark)

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

    2010-01-01

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

  2. Mathematical Properties Relevant to Geomagnetic Field Modeling

    DEFF Research Database (Denmark)

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

    2014-01-01

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

  3. Mechanistic modeling of aberrant energy metabolism in human disease

    Directory of Open Access Journals (Sweden)

    Vineet eSangar

    2012-10-01

    Full Text Available Dysfunction in energy metabolism—including in pathways localized to the mitochondria—has been implicated in the pathogenesis of a wide array of disorders, ranging from cancer to neurodegenerative diseases to type II diabetes. The inherent complexities of energy and mitochondrial metabolism present a significant obstacle in the effort to understand the role that these molecular processes play in the development of disease. To help unravel these complexities, systems biology methods have been applied to develop an array of computational metabolic models, ranging from mitochondria-specific processes to genome-scale cellular networks. These constraint-based models can efficiently simulate aspects of normal and aberrant metabolism in various genetic and environmental conditions. Development of these models leverages—and also provides a powerful means to integrate and interpret—information from a wide range of sources including genomics, proteomics, metabolomics, and enzyme kinetics. Here, we review a variety of mechanistic modeling studies that explore metabolic functions, deficiency disorders, and aberrant biochemical pathways in mitochondria and related regions in the cell.

  4. Mathematical modeling and optimization of complex structures

    CERN Document Server

    Repin, Sergey; Tuovinen, Tero

    2016-01-01

    This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented  on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in  modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include:  * Computer simulation methods in mechanics, physics, and biology;  * Variational problems and methods; minimiz...

  5. Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

    Directory of Open Access Journals (Sweden)

    Zoran Benić

    2016-01-01

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

  6. Mathematical Modeling of Loop Heat Pipes

    Science.gov (United States)

    Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.

    1998-01-01

    The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.

  7. Mathematical Modelling Plant Signalling Networks

    KAUST Repository

    Muraro, D.

    2013-01-01

    During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.

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

    Science.gov (United States)

    Edwards, Thomas

    1995-01-01

    By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

  9. Simple mathematical models of symmetry breaking. Application to particle physics

    International Nuclear Information System (INIS)

    Michel, L.

    1976-01-01

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

  10. Mathematical modeling of dissolved oxygen in fish ponds ...

    African Journals Online (AJOL)

    Mathematical modeling of dissolved oxygen in fish ponds. WJS Mwegoha, ME Kaseva, SMM Sabai. Abstract. A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide and chemical oxygen demand (COD) on Dissolved Oxygen (DO) in fish ponds. The effects ...

  11. Mechanistic modelling of genetic and epigenetic events in radiation carcinogenesis

    International Nuclear Information System (INIS)

    Andreev, S. G.; Eidelman, Y. A.; Salnikov, I. V.; Khvostunov, I. K.

    2006-01-01

    Methodological problems arise on the way of radiation carcinogenesis modelling with the incorporation of radiobiological and cancer biology mechanistic data. The results of biophysical modelling of different endpoints [DNA DSB induction, repair, chromosome aberrations (CA) and cell proliferation] are presented and applied to the analysis of RBE-LET relationships for radiation-induced neoplastic transformation (RINT) of C3H/10T1/2 cells in culture. Predicted values for some endpoints correlate well with the data. It is concluded that slowly repaired DSB clusters, as well as some kind of CA, may be initiating events for RINT. As an alternative interpretation, it is possible that DNA damage can induce RINT indirectly via epigenetic process. A hypothetical epigenetic pathway for RINT is discussed. (authors)

  12. Structured Mathematical Modeling of Industrial Boiler

    Directory of Open Access Journals (Sweden)

    Abdullah Nur Aziz

    2014-04-01

    Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.

  13. Prediction of net hepatic release of glucose using a “hybrid” mechanistic model in ruminants applied to positive energy balance

    OpenAIRE

    Bahloul, Lahlou; Ortigues, Isabelle; Vernet, Jean; Lapierre, Helène; Noziere, Pierre; Sauvant, Daniel

    2013-01-01

    Ruminants depend on hepatic gluconeogenesis to meet most of their metabolic demand for glucose which relies on availability of precursors from diet supply and animal requirements (Loncke et al., 2010). Several mechanistic models of the metabolic fate of nutrients across the liver exist that have been parameterized for dairy cows. They cannot be directly used to predict hepatic gluconeogenesis in all types of ruminants in different physiological status. A hybrid mechanistic model of nutrient f...

  14. The possibilities of a modelling perspective for school mathematics

    Directory of Open Access Journals (Sweden)

    Dirk Wessels

    2009-09-01

    complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has definitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to finding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full benefit of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future. 

  15. A mechanistic model for electricity consumption on dairy farms: Definition, validation, and demonstration

    OpenAIRE

    Upton, J.R.; Murphy, M.; Shallo, L.; Groot Koerkamp, P.W.G.; Boer, de, I.J.M.

    2014-01-01

    Our objective was to define and demonstrate a mechanistic model that enables dairy farmers to explore the impact of a technical or managerial innovation on electricity consumption, associated CO2 emissions, and electricity costs. We, therefore, (1) defined a model for electricity consumption on dairy farms (MECD) capable of simulating total electricity consumption along with related CO2 emissions and electricity costs on dairy farms on a monthly basis; (2) validated the MECD using empirical d...

  16. iSTEM: Promoting Fifth Graders' Mathematical Modeling

    Science.gov (United States)

    Yanik, H. Bahadir; Karabas, Celil

    2014-01-01

    Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…

  17. Mechanistic systems modeling to guide drug discovery and development.

    Science.gov (United States)

    Schmidt, Brian J; Papin, Jason A; Musante, Cynthia J

    2013-02-01

    A crucial question that must be addressed in the drug development process is whether the proposed therapeutic target will yield the desired effect in the clinical population. Pharmaceutical and biotechnology companies place a large investment on research and development, long before confirmatory data are available from human trials. Basic science has greatly expanded the computable knowledge of disease processes, both through the generation of large omics data sets and a compendium of studies assessing cellular and systemic responses to physiologic and pathophysiologic stimuli. Given inherent uncertainties in drug development, mechanistic systems models can better inform target selection and the decision process for advancing compounds through preclinical and clinical research. Copyright © 2012 Elsevier Ltd. All rights reserved.

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

    CERN Document Server

    Rudolph, Lee

    2012-01-01

    In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, in

  19. Mathematical modeling of biological processes

    CERN Document Server

    Friedman, Avner

    2014-01-01

    This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

  20. Refined pipe theory for mechanistic modeling of wood development.

    Science.gov (United States)

    Deckmyn, Gaby; Evans, Sam P; Randle, Tim J

    2006-06-01

    We present a mechanistic model of wood tissue development in response to changes in competition, management and climate. The model is based on a refinement of the pipe theory, where the constant ratio between sapwood and leaf area (pipe theory) is replaced by a ratio between pipe conductivity and leaf area. Simulated pipe conductivity changes with age, stand density and climate in response to changes in allocation or pipe radius, or both. The central equation of the model, which calculates the ratio of carbon (C) allocated to leaves and pipes, can be parameterized to describe the contrasting stem conductivity behavior of different tree species: from constant stem conductivity (functional homeostasis hypothesis) to height-related reduction in stem conductivity with age (hydraulic limitation hypothesis). The model simulates the daily growth of pipes (vessels or tracheids), fibers and parenchyma as well as vessel size and simulates the wood density profile and the earlywood to latewood ratio from these data. Initial runs indicate the model yields realistic seasonal changes in pipe radius (decreasing pipe radius from spring to autumn) and wood density, as well as realistic differences associated with the competitive status of trees (denser wood in suppressed trees).

  1. Applied Mathematics, Modelling and Computational Science

    CERN Document Server

    Kotsireas, Ilias; Makarov, Roman; Melnik, Roderick; Shodiev, Hasan

    2015-01-01

    The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics ...

  2. Multiscale mechanistic modeling in pharmaceutical research and development.

    Science.gov (United States)

    Kuepfer, Lars; Lippert, Jörg; Eissing, Thomas

    2012-01-01

    Discontinuation of drug development projects due to lack of efficacy or adverse events is one of the main cost drivers in pharmaceutical research and development (R&D). Investments have to be written-off and contribute to the total costs of a successful drug candidate receiving marketing authorization and allowing return on invest. A vital risk for pharmaceutical innovator companies is late stage clinical failure since costs for individual clinical trials may exceed the one billion Euro threshold. To guide investment decisions and to safeguard maximum medical benefit and safety for patients recruited in clinical trials, it is therefore essential to understand the clinical consequences of all information and data generated. The complexity of the physiological and pathophysiological processes and the sheer amount of information available overcharge the mental capacity of any human being and prevent a prediction of the success in clinical development. A rigorous integration of knowledge, assumption, and experimental data into computational models promises a significant improvement of the rationalization of decision making in pharmaceutical industry. We here give an overview of the current status of modeling and simulation in pharmaceutical R&D and outline the perspectives of more recent developments in mechanistic modeling. Specific modeling approaches for different biological scales ranging from intracellular processes to whole organism physiology are introduced and an example for integrative multiscale modeling of therapeutic efficiency in clinical oncology trials is showcased.

  3. Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation

    Science.gov (United States)

    Day, Judy D.; Metes, Diana M.; Vodovotz, Yoram

    2015-01-01

    A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient’s (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression. PMID:26441988

  4. Vibratory gyroscopes : identification of mathematical model from test data

    CSIR Research Space (South Africa)

    Shatalov, MY

    2007-05-01

    Full Text Available Simple mathematical model of vibratory gyroscopes imperfections is formulated, which includes anisotropic damping and variation of mass-stiffness parameters and their harmonics. The method of identification of parameters of the mathematical model...

  5. Сontrol systems using mathematical models of technological objects ...

    African Journals Online (AJOL)

    Сontrol systems using mathematical models of technological objects in the control loop. ... Journal of Fundamental and Applied Sciences ... Such mathematical models make it possible to specify the optimal operating modes of the considered ...

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

    Science.gov (United States)

    Dalla Vecchia, Rodrigo

    2015-01-01

    This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…

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

    Science.gov (United States)

    Akgün, Levent

    2015-01-01

    The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…

  8. Mathematical modelling of the process of quality control of construction products

    Directory of Open Access Journals (Sweden)

    Pogorelov Vadim

    2017-01-01

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

  9. Mathematical modeling of rainwater runoff over catchment surface ...

    African Journals Online (AJOL)

    The subject of an article is the mathematical modeling of the rainwater runoff along the surface catchment taking account the transport of pollution which permeates into the water flow from a porous media of soil at the certain areas of this surface. The developed mathematical model consists of two types of equations: the ...

  10. Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

    Science.gov (United States)

    Anhalt, Cynthia Oropesa; Cortez, Ricardo

    2016-01-01

    This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…

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

    Directory of Open Access Journals (Sweden)

    Ednilson Sergio Ramalho de Souza

    2013-06-01

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

  12. A mathematical model for iodine kinetics

    International Nuclear Information System (INIS)

    Silva, E.A.T. da.

    1976-01-01

    A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case [pt

  13. Enhancing Students’ Interest through Mathematics Learning

    Science.gov (United States)

    Azmidar, A.; Darhim, D.; Dahlan, J. A.

    2017-09-01

    A number of previous researchers indicated that students’ mathematics interest still low because most of them have perceived that mathematics is very difficult, boring, not very practical, and have many abstract theorems that were very hard to understand. Another cause is the teaching and learning process used, which is mechanistic without considering students’ needs. Learning is more known as the process of transferring the knowledge to the students. Let students construct their own knowledge with the physical and mental reflection that is done by activity in the new knowledge. This article is literature study. The purpose of this article is to examine the Concrete-Pictorial-Abstract approach in theoretically to improve students’ mathematics interest. The conclusion of this literature study is the Concrete-Pictorial-Abstract approach can be used as an alternative to improve students’ mathematics interest.

  14. Mathematical Modelling of Unmanned Aerial Vehicles

    Directory of Open Access Journals (Sweden)

    Saeed Sarwar

    2013-04-01

    Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV

  15. Mathematical modelling of unmanned aerial vehicles

    International Nuclear Information System (INIS)

    Sarwar, S.; Rehman, S.U.

    2013-01-01

    UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)

  16. Molecular modeling: An open invitation for applied mathematics

    Science.gov (United States)

    Mezey, Paul G.

    2013-10-01

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

  17. Application of mathematical modeling in sustained release delivery systems.

    Science.gov (United States)

    Grassi, Mario; Grassi, Gabriele

    2014-08-01

    This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

  18. Mathematical modeling for novel cancer drug discovery and development.

    Science.gov (United States)

    Zhang, Ping; Brusic, Vladimir

    2014-10-01

    Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

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

    DEFF Research Database (Denmark)

    Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.

    2002-01-01

    Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...... efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available....

  20. Mathematical modeling of swirled flows in industrial applications

    Science.gov (United States)

    Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.

    2018-03-01

    Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.

  1. A mathematical model for postirradiation immunity

    International Nuclear Information System (INIS)

    Smirnova, O.A.

    1988-01-01

    A mathematical model of autoimmune processes in exposed mammals was developed. In terms of this model a study was made of the dependence of the autoimmunity kinetics on radiation dose and radiosensitivity of autologous tissues. The model simulates the experimentally observed dynamics of autoimmune diseases

  2. Mathematical modelling of anaerobic digestion processes: applications and future needs

    DEFF Research Database (Denmark)

    Batstone, Damien J.; Puyol, Daniel; Flores Alsina, Xavier

    2015-01-01

    Anaerobic process modelling is a mature and well-established field, largely guided by a mechanistic model structure that is defined by our understanding of underlying processes. This led to publication of the IWA ADM1, and strong supporting, analytical, and extension research in the 15 years sinc...

  3. Modelling and applications in mathematics education the 14th ICMI study

    CERN Document Server

    Galbraith, Peter L; Niss, Mogens

    2007-01-01

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

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

    International Nuclear Information System (INIS)

    Ghaboussi, J; Kim, J; Elnashai, A

    2010-01-01

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

  5. Mathematics of epidemics on networks from exact to approximate models

    CERN Document Server

    Kiss, István Z; Simon, Péter L

    2017-01-01

    This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...

  6. Mathematical models of natural gas consumption

    International Nuclear Information System (INIS)

    Sabo, Kristian; Scitovski, Rudolf; Vazler, Ivan; Zekic-Susac, Marijana

    2011-01-01

    In this paper we consider the problem of natural gas consumption hourly forecast on the basis of hourly movement of temperature and natural gas consumption in the preceding period. There are various methods and approaches for solving this problem in the literature. Some mathematical models with linear and nonlinear model functions relating to natural gas consumption forecast with the past natural gas consumption data, temperature data and temperature forecast data are mentioned. The methods are tested on concrete examples referring to temperature and natural gas consumption for the area of the city of Osijek (Croatia) from the beginning of the year 2008. The results show that most acceptable forecast is provided by mathematical models in which natural gas consumption and temperature are related explicitly.

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

    Science.gov (United States)

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

    2010-12-01

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

  8. Development of a mechanistic model for release of radionuclides from spent fuel in brines: Salt Repository Project

    International Nuclear Information System (INIS)

    Reimus, P.W.; Windisch, C.F.

    1988-03-01

    At present there are no comprehensive mechanistic models describing the release of radionuclides from spent fuel in brine environments. This report provides a comprehensive review of the various factors that can affect radionuclide release from spent fuel, suggests a modeling approach, and discusses proposed experiments for obtaining a better mechanistic understanding of the radionuclide release processes. Factors affecting radionuclide release include the amount, location, and disposition of radionuclides in the fuel and environmental factors such as redox potential, pH, the presence of complexing anions, temperature, and radiolysis. It is concluded that a model describing the release of radionuclides from spent fuel should contain separate terms for release from the gap, grain boundaries, and grains of the fuel. Possible functional forms for these terms are discussed in the report. Experiments for assessing their validity and obtaining key model parameters are proposed. 71 refs., 4 figs., 6 tabs

  9. Mathematical modeling of reciprocating pump

    International Nuclear Information System (INIS)

    Lee, Jong Kyeom; Jung, Jun Ki; Chai, Jang Bom; Lee, Jin Woo

    2015-01-01

    A new mathematical model is presented for the analysis and diagnosis of a high-pressure reciprocating pump system with three cylinders. The kinematic and hydrodynamic behaviors of the pump system are represented by the piston displacements, volume flow rates and pressures in its components, which are expressed as functions of the crankshaft angle. The flow interaction among the three cylinders, which was overlooked in the previous models, is considered in this model and its effect on the cylinder pressure profiles is investigated. The tuning parameters in the mathematical model are selected, and their values are adjusted to match the simulated and measured cylinder pressure profiles in each cylinder in a normal state. The damage parameter is selected in an abnormal state, and its value is adjusted to match the simulated and ensured pressure profiles under the condition of leakage in a valve. The value of the damage parameter over 300 cycles is calculated, and its probability density function is obtained for diagnosis and prognosis on the basis of the probabilistic feature of valve leakage.

  10. Explorations in Elementary Mathematical Modeling

    Directory of Open Access Journals (Sweden)

    Mazen Shahin

    2010-06-01

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

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

    Science.gov (United States)

    Rash, Agnes M.; Zurbach, E. Peter

    2004-01-01

    The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…

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

    Science.gov (United States)

    Gilbert, Scott F

    2018-01-31

    Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.

  13. Mechanistic Modeling of Water Replenishment Rate of Zeer Refrigerator

    Directory of Open Access Journals (Sweden)

    B. N. Nwankwojike

    2017-06-01

    Full Text Available A model for predicting the water replenishment rate of zeer pot refrigerator was developed in this study using mechanistic modeling approach and evaluated at Obowo, Imo State, Nigeria using six fruits, tomatoes, guava, okra, banana, orange and avocado pear. The developed model confirmed zeer pot water replenishment rate as a function of ambient temperature, relative humidity, wind speed, thermal conductivity of the pot materials and sand, density of air and water vapor, permeability coefficient of clay and heat transfer coefficient of water into air, circumferential length, height of pot, geometrical profile of the pot, heat load of the food preserved, heat flow into the device and gradient at which the pot is placed above ground level. Compared to the conventional approach of water replenishment, performance analysis results revealed 44% to 58% water economy when the zeer pot’s water was replenished based on the model’s prediction; while there was no significant difference in the shelf-life of the fruits preserved with both replenishment methods. Application of the developed water replenishment model facilitates optimal water usage in this system, thereby reducing operational cost of zeer pot refrigerator.

  14. Mathematical model for temperature change of a journal bearing

    Directory of Open Access Journals (Sweden)

    Antunović Ranko

    2018-01-01

    Full Text Available In this work, a representative mathematical model has been developed, which reliably describes the heating and cooling of a journal bearing as a result of its malfunctioning, and the model has been further confirmed on a test bench. The bearing model was validated by using analytical modeling methods, i. e. the experimental results were compared to the data obtained by analytical calculations. The regression and variance analysis techniques were applied to process the recorded data, to test the mathematical model and to define mathematical functions for the heating/cooling of the journal bearing. This investigation shows that a representative model may reliably indicate the change in the thermal field, which may be a consequence of journal bearing damage.

  15. Mechanistic Features of Nanodiamonds in the Lapping of Magnetic Heads

    Directory of Open Access Journals (Sweden)

    Xionghua Jiang

    2014-01-01

    Full Text Available Nanodiamonds, which are the main components of slurry in the precision lapping process of magnetic heads, play an important role in surface quality. This paper studies the mechanistic features of nanodiamond embedment into a Sn plate in the lapping process. This is the first study to develop mathematical models for nanodiamond embedment. Such models can predict the optimum parameters for particle embedment. From the modeling calculations, the embedded pressure satisfies p0=3/2·W/πa2 and the indentation depth satisfies δ=k1P/HV. Calculation results reveal that the largest embedded pressure is 731.48 GPa and the critical indentation depth δ is 7 nm. Atomic force microscopy (AFM, scanning electron microscopy (SEM, and Auger electron spectroscopy (AES were used to carry out surface quality detection and analysis of the disk head. Both the formation of black spots on the surface and the removal rate have an important correlation with the size of nanodiamonds. The results demonstrate that an improved removal rate (21 nm·min−1 can be obtained with 100 nm diamonds embedded in the plate.

  16. Mechanistic features of nanodiamonds in the lapping of magnetic heads.

    Science.gov (United States)

    Jiang, Xionghua; Chen, Zhenxing; Wolfram, Joy; Yang, Zhizhou

    2014-01-01

    Nanodiamonds, which are the main components of slurry in the precision lapping process of magnetic heads, play an important role in surface quality. This paper studies the mechanistic features of nanodiamond embedment into a Sn plate in the lapping process. This is the first study to develop mathematical models for nanodiamond embedment. Such models can predict the optimum parameters for particle embedment. From the modeling calculations, the embedded pressure satisfies p 0 = (3/2) · (W/πa (2)) and the indentation depth satisfies δ = k1√P/HV. Calculation results reveal that the largest embedded pressure is 731.48 GPa and the critical indentation depth δ is 7 nm. Atomic force microscopy (AFM), scanning electron microscopy (SEM), and Auger electron spectroscopy (AES) were used to carry out surface quality detection and analysis of the disk head. Both the formation of black spots on the surface and the removal rate have an important correlation with the size of nanodiamonds. The results demonstrate that an improved removal rate (21 nm · min(-1)) can be obtained with 100 nm diamonds embedded in the plate.

  17. Growth and lipid production of Umbelopsis isabellina on a solid substrate - Mechanistic modeling and validation

    NARCIS (Netherlands)

    Meeuwse, P.; Klok, A.J.; Haemers, S.; Tramper, J.; Rinzema, A.

    2012-01-01

    Microbial lipids are an interesting feedstock for biodiesel. Their production from agricultural waste streams by fungi cultivated in solid-state fermentation may be attractive, but the yield of this process is still quite low. In this article, a mechanistic model is presented that describes growth,

  18. Phenomenological and mechanistic modeling of melt-structure-water interactions in a light water reactor severe accident

    International Nuclear Information System (INIS)

    Bui, V.A.

    1998-01-01

    The objective of this work is to address the modeling of the thermal hydrodynamic phenomena and interactions occurring during the progression of reactor severe accidents. Integrated phenomenological models are developed to describe the accident scenarios, which consist of many processes, while mechanistic modeling, including direct numerical simulation, is carried out to describe separate effects and selected physical phenomena of particular importance

  19. Mathematical Modelling of Involute Spur Gears Manufactured by Rack Cutter

    Directory of Open Access Journals (Sweden)

    Tufan Gürkan YILMAZ

    2016-05-01

    Full Text Available In this study, mathematical modelling of asymmetric involute spur gears was situated in by Litvin approach. In this context, firstly, mathematical expressions of rack cutter which manufacture asymmetric involute spur gear, then mathematical expression of asymmetric involute spur gear were obtained by using differential geometry, coordinate transformation and gear theory. Mathematical expressions were modelled in MATLAB and output files including points of involute spur gear’s teeth were designed automatically thanks to macros.

  20. Rapid Discrimination Among Putative Mechanistic Models of Biochemical Systems.

    Science.gov (United States)

    Lomnitz, Jason G; Savageau, Michael A

    2016-08-31

    An overarching goal in molecular biology is to gain an understanding of the mechanistic basis underlying biochemical systems. Success is critical if we are to predict effectively the outcome of drug treatments and the development of abnormal phenotypes. However, data from most experimental studies is typically noisy and sparse. This allows multiple potential mechanisms to account for experimental observations, and often devising experiments to test each is not feasible. Here, we introduce a novel strategy that discriminates among putative models based on their repertoire of qualitatively distinct phenotypes, without relying on knowledge of specific values for rate constants and binding constants. As an illustration, we apply this strategy to two synthetic gene circuits exhibiting anomalous behaviors. Our results show that the conventional models, based on their well-characterized components, cannot account for the experimental observations. We examine a total of 40 alternative hypotheses and show that only 5 have the potential to reproduce the experimental data, and one can do so with biologically relevant parameter values.

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

    Science.gov (United States)

    Handayani, I.; Januar, R. L.; Purwanto, S. E.

    2018-01-01

    This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.

  2. Mathematical and numerical foundations of turbulence models and applications

    CERN Document Server

    Chacón Rebollo, Tomás

    2014-01-01

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

  3. Mechanistic modelling of the corrosion behaviour of copper nuclear fuel waste containers

    Energy Technology Data Exchange (ETDEWEB)

    King, F; Kolar, M

    1996-10-01

    A mechanistic model has been developed to predict the long-term corrosion behaviour of copper nuclear fuel waste containers in a Canadian disposal vault. The model is based on a detailed description of the electrochemical, chemical, adsorption and mass-transport processes involved in the uniform corrosion of copper, developed from the results of an extensive experimental program. Predictions from the model are compared with the results of some of these experiments and with observations from a bronze cannon submerged in seawater saturated clay sediments. Quantitative comparisons are made between the observed and predicted corrosion potential, corrosion rate and copper concentration profiles adjacent to the corroding surface, as a way of validating the long-term model predictions. (author). 12 refs., 5 figs.

  4. Productivity of "collisions generate heat" for reconciling an energy model with mechanistic reasoning: A case study

    Science.gov (United States)

    Scherr, Rachel E.; Robertson, Amy D.

    2015-06-01

    We observe teachers in professional development courses about energy constructing mechanistic accounts of energy transformations. We analyze a case in which teachers investigating adiabatic compression develop a model of the transformation of kinetic energy to thermal energy. Among their ideas is the idea that thermal energy is generated as a byproduct of individual particle collisions, which is represented in science education research literature as an obstacle to learning. We demonstrate that in this instructional context, the idea that individual particle collisions generate thermal energy is not an obstacle to learning, but instead is productive: it initiates intellectual progress. Specifically, this idea initiates the reconciliation of the teachers' energy model with mechanistic reasoning about adiabatic compression, and leads to a canonically correct model of the transformation of kinetic energy into thermal energy. We claim that the idea's productivity is influenced by features of our particular instructional context, including the instructional goals of the course, the culture of collaborative sense making, and the use of certain representations of energy.

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

    Science.gov (United States)

    Karatas, Ilhan

    2014-01-01

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

  6. Application of computer mathematical modeling in nuclear well-logging industry

    International Nuclear Information System (INIS)

    Cai Shaohui

    1994-01-01

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

  7. Mathematical Modeling Applied to Maritime Security

    OpenAIRE

    Center for Homeland Defense and Security

    2010-01-01

    Center for Homeland Defense and Security, OUT OF THE CLASSROOM Download the paper: Layered Defense: Modeling Terrorist Transfer Threat Networks and Optimizing Network Risk Reduction” Students in Ted Lewis’ Critical Infrastructure Protection course are taught how mathematic modeling can provide...

  8. Authenticity of Mathematical Modeling

    Science.gov (United States)

    Tran, Dung; Dougherty, Barbara J.

    2014-01-01

    Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

  9. How to Introduce Mathematic Modeling in Industrial Design Education

    NARCIS (Netherlands)

    Langereis, G.R.; Hu, J.; Feijs, L.M.G.; Stillmann, G.A.; Kaiser, G.; Blum, W.B.; Brown, J.P.

    2013-01-01

    With competency based learning in a project driven environment, we are facing a different perspective of how students perceive mathematical modelling. In this chapter, a model is proposed where conventional education is seen as a process from mathematics to design, while competency driven approaches

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

    Science.gov (United States)

    Schwerdtfeger, Sara

    2017-01-01

    This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

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

    Science.gov (United States)

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

    2015-01-01

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

  12. The mathematics of models for climatology and environment. Proceedings

    Energy Technology Data Exchange (ETDEWEB)

    Ildefonso Diaz, J. [ed.] [Universidad Complutense de Madrid (Spain). Facultad de Ciencas Matematicas

    1997-12-31

    This book presents a coherent survey of modelling in climatology and the environment and the mathematical treatment of those problems. It is divided into 4 parts containing a total of 16 chapters. Parts I, II and III are devoted to general models and part IV to models related to some local problems. Most of the mathematical models considered here involve systems of nonlinear partial differential equations.

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

    Science.gov (United States)

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

    2013-12-01

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

  14. Experimental and mathematical modeling methods for the investigation of toxicological interactions

    International Nuclear Information System (INIS)

    El-Masri, Hisham A.

    2007-01-01

    While procedures have been developed and used for many years to assess risk and determine acceptable exposure levels to individual chemicals, most cases of environmental contamination can result in concurrent or sequential exposure to more than one chemical. Toxicological predictions of such combinations must be based on an understanding of the mechanisms of action and interaction of the components of the mixtures. Statistical and experimental methods test the existence of toxicological interactions in a mixture. However, these methods are limited to experimental data ranges for which they are derived, in addition to limitations caused by response differences from experimental animals to humans. Empirical methods such as isobolograms, median-effect principle and response surface methodology (RSM) are based on statistical experimental design and regression of data. For that reason, the predicted response surfaces can be used for extrapolation across dose regions where interaction mechanisms are not anticipated to change. In general, using these methods for predictions can be problematic without including biologically based mechanistic descriptions that can account for dose and species differences. Mechanistically based models, such as physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) models, include explicit descriptions of interaction mechanisms which are related to target tissues levels. These models include dose-dependent mechanistic hypotheses of toxicological interactions which can be tested by model-directed experimental design and used to identify dose regions where interactions are not significant

  15. Mathematical modelling of flooding at Magela Creek

    International Nuclear Information System (INIS)

    Vardavas, I.

    1989-01-01

    The extent and frequency of the flooding at Magela Creek can be predicted from a mathematical/computer model describing the hydrological phases of surface runoff. Surface runoff involves complex water transfer processes over very inhomogeneous terrain. A simple mathematical model of these has been developed which includes the interception of rainfall by the plant canopy, evapotranspiration, infiltration of surface water into the soil, the storage of water in surface depressions, and overland and subsurface water flow. The rainfall-runoff model has then been incorporated into a more complex computer model to predict the amount of water that enters and leaves the Magela Creek flood plain, downstream of the mine. 2 figs., ills

  16. Mechanistic modeling of insecticide risks to breeding birds in ...

    Science.gov (United States)

    Insecticide usage in the United States is ubiquitous in urban, suburban, and rural environments. In evaluating data for an insecticide registration application and for registration review, scientists at the United States Environmental Protection Agency (USEPA) assess the fate of the insecticide and the risk the insecticide poses to the environment and non-target wildlife. At the present time, current USEPA risk assessments do not include population-level endpoints. In this paper, we present a new mechanistic model, which allows risk assessors to estimate the effects of insecticide exposure on the survival and seasonal productivity of birds known to use agricultural fields during their breeding season. The new model was created from two existing USEPA avian risk assessment models, the Terrestrial Investigation Model (TIM v.3.0) and the Markov Chain Nest Productivity model (MCnest). The integrated TIM/MCnest model has been applied to assess the relative risk of 12 insecticides used to control corn pests on a suite of 31 avian species known to use cornfields in midwestern agroecosystems. The 12 insecticides that were assessed in this study are all used to treat major pests of corn (corn root worm borer, cutworm, and armyworm). After running the integrated TIM/MCnest model, we found extensive differences in risk to birds among insecticides, with chlorpyrifos and malathion (organophosphates) generally posing the greatest risk, and bifenthrin and ë-cyhalothrin (

  17. Innovative mathematical modeling in environmental remediation

    Energy Technology Data Exchange (ETDEWEB)

    Yeh, Gour T. [Taiwan Typhoon and Flood Research Institute (Taiwan); National Central Univ. (Taiwan); Univ. of Central Florida (United States); Gwo, Jin Ping [Nuclear Regulatory Commission (NRC), Rockville, MD (United States); Siegel, Malcolm D. [Sandia National Laboratories, Albuquerque, NM (United States); Li, Ming-Hsu [National Central Univ. (Taiwan); ; Fang, Yilin [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States); Zhang, Fan [Inst. of Tibetan Plateau Research, Chinese Academy of Sciences (China); Luo, Wensui [Inst. of Tibetan Plateau Research, Chinese Academy of Sciences (China); Yabusaki, Steven B. [Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

    2013-05-01

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

  18. Innovative mathematical modeling in environmental remediation

    International Nuclear Information System (INIS)

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

    2013-01-01

    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

  19. Mathematical Modelling for Micropiles Embedded in Salt Rock

    Directory of Open Access Journals (Sweden)

    Rădan (Toader Georgiana

    2016-03-01

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

  20. A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

    Science.gov (United States)

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

    2018-04-01

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

  1. Methods of mathematical modelling continuous systems and differential equations

    CERN Document Server

    Witelski, Thomas

    2015-01-01

    This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

  2. Mutual Dependence Between Sedimentary Organic Carbon and Infaunal Macrobenthos Resolved by Mechanistic Modeling

    Science.gov (United States)

    Zhang, Wenyan; Wirtz, Kai

    2017-10-01

    The mutual dependence between sedimentary total organic carbon (TOC) and infaunal macrobenthos is here quantified by a mechanistic model. The model describes (i) the vertical distribution of infaunal macrobenthic biomass resulting from a trade-off between nutritional benefit (quantity and quality of TOC) and the costs of burial (respiration) and mortality, and (ii) the variable vertical distribution of TOC being in turn shaped by bioturbation of local macrobenthos. In contrast to conventional approaches, our model emphasizes variations of bioturbation both spatially and temporally depending on local food resources and macrobenthic biomass. Our implementation of the dynamic interaction between TOC and infaunal macrobenthos is able to capture a temporal benthic response to both depositional and erosional environments and provides improved estimates of the material exchange flux at the sediment-water interface. Applications to literature data for the North Sea demonstrate the robustness and accuracy of the model and its potential as an analysis tool for the status of TOC and macrobenthos in marine sediments. Results indicate that the vertical distribution of infaunal biomass is shaped by both the quantity and the quality of OC, while the community structure is determined only by the quality of OC. Bioturbation intensity may differ by 1 order of magnitude over different seasons owing to variations in the OC input, resulting in a significant modulation on the distribution of OC. Our relatively simple implementation may further improve models of early diagenesis and marine food web dynamics by mechanistically connecting the vertical distribution of both TOC and macrobenthic biomass.

  3. Proceedings of the international workshop on mechanistic understanding of radionuclide migration in compacted/intact systems

    International Nuclear Information System (INIS)

    Tachi, Yukio; Yui, Mikazu

    2010-03-01

    The international workshop on mechanistic understanding of radionuclide migration in compacted / intact systems was held at ENTRY, JAEA, Tokai on 21st - 23rd January, 2009. This workshop was hosted by Japan Atomic Energy Agency (JAEA) as part of the project on the mechanistic model/database development for radionuclide sorption and diffusion behavior in compacted / intact systems. The overall goal of the project is to develop the mechanistic model / database for a consistent understanding and prediction of migration parameters and its uncertainties for performance assessment of geological disposal of radioactive waste. The objective of the workshop is to integrate the state-of-the-art of mechanistic sorption and diffusion model in compacted / intact systems, especially in bentonite / clay systems, and discuss the JAEA's mechanistic approaches and future challenges, especially the following discussions points; 1) What's the status and difficulties for mechanistic model/database development? 2) What's the status and difficulties for applicability of mechanistic model to the compacted/intact system? 3) What's the status and difficulties for obtaining evidences for mechanistic model? 4) What's the status and difficulties for standardization of experimental methodology for batch sorption and diffusion? 5) What's the uncertainties of transport parameters in radionuclides migration analysis due to a lack of understanding/experimental methodologies, and how do we derive them? This report includes workshop program, overview and materials of each presentation, summary of discussions. (author)

  4. Phenomenological and mechanistic modeling of melt-structure-water interactions in a light water reactor severe accident

    Energy Technology Data Exchange (ETDEWEB)

    Bui, V.A

    1998-10-01

    The objective of this work is to address the modeling of the thermal hydrodynamic phenomena and interactions occurring during the progression of reactor severe accidents. Integrated phenomenological models are developed to describe the accident scenarios, which consist of many processes, while mechanistic modeling, including direct numerical simulation, is carried out to describe separate effects and selected physical phenomena of particular importance 88 refs, 54 figs, 7 tabs

  5. Linking spring phenology with mechanistic models of host movement to predict disease transmission risk

    Science.gov (United States)

    Merkle, Jerod A.; Cross, Paul C.; Scurlock, Brandon M.; Cole, Eric K.; Courtemanch, Alyson B.; Dewey, Sarah R.; Kauffman, Matthew J.

    2018-01-01

    Disease models typically focus on temporal dynamics of infection, while often neglecting environmental processes that determine host movement. In many systems, however, temporal disease dynamics may be slow compared to the scale at which environmental conditions alter host space-use and accelerate disease transmission.Using a mechanistic movement modelling approach, we made space-use predictions of a mobile host (elk [Cervus Canadensis] carrying the bacterial disease brucellosis) under environmental conditions that change daily and annually (e.g., plant phenology, snow depth), and we used these predictions to infer how spring phenology influences the risk of brucellosis transmission from elk (through aborted foetuses) to livestock in the Greater Yellowstone Ecosystem.Using data from 288 female elk monitored with GPS collars, we fit step selection functions (SSFs) during the spring abortion season and then implemented a master equation approach to translate SSFs into predictions of daily elk distribution for five plausible winter weather scenarios (from a heavy snow, to an extreme winter drought year). We predicted abortion events by combining elk distributions with empirical estimates of daily abortion rates, spatially varying elk seroprevelance and elk population counts.Our results reveal strong spatial variation in disease transmission risk at daily and annual scales that is strongly governed by variation in host movement in response to spring phenology. For example, in comparison with an average snow year, years with early snowmelt are predicted to have 64% of the abortions occurring on feedgrounds shift to occurring on mainly public lands, and to a lesser extent on private lands.Synthesis and applications. Linking mechanistic models of host movement with disease dynamics leads to a novel bridge between movement and disease ecology. Our analysis framework offers new avenues for predicting disease spread, while providing managers tools to proactively mitigate

  6. Perspectives on instructor modeling in mathematics teacher education

    OpenAIRE

    Brown, Cassondra

    2009-01-01

    Teachers' instructional practices are greatly shaped by their own learning experiences as students in K-12 and college classrooms, which for most teachers was traditional, teacher-centered instruction. One of the challenges facing mathematics education reform is that, traditional teaching is in contrast to reform student- centered instruction. If teachers learn from their experiences as mathematics students, mathematics teacher educators are encouraged to model practices they would like teach...

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

    Directory of Open Access Journals (Sweden)

    Hafizh Nizham

    2017-12-01

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

  8. An Integrated Approach to Mathematical Modeling: A Classroom Study.

    Science.gov (United States)

    Doerr, Helen M.

    Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…

  9. Mathematical models of information and stochastic systems

    CERN Document Server

    Kornreich, Philipp

    2008-01-01

    From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t

  10. Mathematical modelling with case studies using Maple and Matlab

    CERN Document Server

    Barnes, B

    2014-01-01

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

  11. A practical course in differential equations and mathematical modeling

    CERN Document Server

    Ibragimov , Nail H

    2009-01-01

    A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

  12. Technological geological and mathematical models of petroleum stratum

    International Nuclear Information System (INIS)

    Zhumagulov, B.T.; Monakhov, V.N.

    1997-01-01

    The comparative analysis of different mathematical methods of petroleum stratum, the limit of their applicability and hydrodynamical analysis of numerical calculation's results is carried out. The problem of adaptation of the mathematical models and the identification of petroleum stratum parameters are considered. (author)

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

    Science.gov (United States)

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

    2011-07-01

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

  14. PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE

    Directory of Open Access Journals (Sweden)

    N. V. Andrianov

    2006-01-01

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

  15. Mathematics in Nature Modeling Patterns in the Natural World

    CERN Document Server

    Adam, John A

    2011-01-01

    From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathem

  16. Mathematical modeling of white adipocyte exocytosis predicts adiponectin secretion and quantifies the rates of vesicle exo- and endocytosis.

    Science.gov (United States)

    Brännmark, Cecilia; Lövfors, William; Komai, Ali M; Axelsson, Tom; El Hachmane, Mickaël F; Musovic, Saliha; Paul, Alexandra; Nyman, Elin; Olofsson, Charlotta S

    2017-12-08

    Adiponectin is a hormone secreted from white adipocytes and takes part in the regulation of several metabolic processes. Although the pathophysiological importance of adiponectin has been thoroughly investigated, the mechanisms controlling its release are only partly understood. We have recently shown that adiponectin is secreted via regulated exocytosis of adiponectin-containing vesicles, that adiponectin exocytosis is stimulated by cAMP-dependent mechanisms, and that Ca 2+ and ATP augment the cAMP-triggered secretion. However, much remains to be discovered regarding the molecular and cellular regulation of adiponectin release. Here, we have used mathematical modeling to extract detailed information contained within our previously obtained high-resolution patch-clamp time-resolved capacitance recordings to produce the first model of adiponectin exocytosis/secretion that combines all mechanistic knowledge deduced from electrophysiological experimental series. This model demonstrates that our previous understanding of the role of intracellular ATP in the control of adiponectin exocytosis needs to be revised to include an additional ATP-dependent step. Validation of the model by introduction of data of secreted adiponectin yielded a very close resemblance between the simulations and experimental results. Moreover, we could show that Ca 2+ -dependent adiponectin endocytosis contributes to the measured capacitance signal, and we were able to predict the contribution of endocytosis to the measured exocytotic rate under different experimental conditions. In conclusion, using mathematical modeling of published and newly generated data, we have obtained estimates of adiponectin exo- and endocytosis rates, and we have predicted adiponectin secretion. We believe that our model should have multiple applications in the study of metabolic processes and hormonal control thereof. © 2017 by The American Society for Biochemistry and Molecular Biology, Inc.

  17. Analysis of a Farquhar-von Caemmerer-Berry leaf-level photosynthetic rate model for Populus tremuloides in the context of modeling and measurement limitations

    Science.gov (United States)

    K.E. Lenz; G.E. Host; K. Roskoski; A. Noormets; A. Sober; D.F. Karnosky

    2010-01-01

    The balance of mechanistic detail with mathematical simplicity contributes to the broad use of the Farquhar, von Caemmerer and Berry (FvCB) photosynthetic rate model. Here the FvCB model was coupled with a stomatal conductance model to form an [A,gs] model, and parameterized for mature Populus tremuloides leaves under varying CO2...

  18. Unification and mechanistic detail as drivers of model construction: models of networks in economics and sociology.

    Science.gov (United States)

    Kuorikoski, Jaakko; Marchionni, Caterina

    2014-12-01

    We examine the diversity of strategies of modelling networks in (micro) economics and (analytical) sociology. Field-specific conceptions of what explaining (with) networks amounts to or systematic preference for certain kinds of explanatory factors are not sufficient to account for differences in modelling methodologies. We argue that network models in both sociology and economics are abstract models of network mechanisms and that differences in their modelling strategies derive to a large extent from field-specific conceptions of the way in which a good model should be a general one. Whereas the economics models aim at unification, the sociological models aim at a set of mechanism schemas that are extrapolatable to the extent that the underlying psychological mechanisms are general. These conceptions of generality induce specific biases in mechanistic explanation and are related to different views of when knowledge from different fields should be seen as relevant.

  19. Mathematical models to predict rheological parameters of lateritic hydromixtures

    Directory of Open Access Journals (Sweden)

    Gabriel Hernández-Ramírez

    2017-10-01

    Full Text Available The present work had as objective to establish mathematical models that allow the prognosis of the rheological parameters of the lateritic pulp at concentrations of solids from 35% to 48%, temperature of the preheated hydromixture superior to 82 ° C and number of mineral between 3 and 16. Four samples of lateritic pulp were used in the study at different process locations. The results allowed defining that the plastic properties of the lateritic pulp in the conditions of this study conform to the Herschel-Bulkley model for real plastics. In addition, they show that for current operating conditions, even for new situations, UPD mathematical models have a greater ability to predict rheological parameters than least squares mathematical models.

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

    Directory of Open Access Journals (Sweden)

    Himmatul Afthina

    2017-12-01

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

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

    Science.gov (United States)

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

    2014-08-28

    Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

  2. Mathematical Models of Breast and Ovarian Cancers

    Science.gov (United States)

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

    2016-01-01

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

  3. Parallel Boltzmann machines : a mathematical model

    NARCIS (Netherlands)

    Zwietering, P.J.; Aarts, E.H.L.

    1991-01-01

    A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a

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

    CERN Document Server

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

    2016-01-01

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

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

    Science.gov (United States)

    Çelik, H. Coskun

    2017-01-01

    The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

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

    Science.gov (United States)

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

    2016-11-01

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

  7. Constraint theory multidimensional mathematical model management

    CERN Document Server

    Friedman, George J

    2017-01-01

    Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...

  8. 2nd Tbilisi-Salerno Workshop on Modeling in Mathematics

    CERN Document Server

    Ricci, Paolo; Tavkhelidze, Ilia

    2017-01-01

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

  9. A Mathematical Approach to Establishing Constitutive Models for Geomaterials

    Directory of Open Access Journals (Sweden)

    Guang-hua Yang

    2013-01-01

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

  10. Methods and models in mathematical biology deterministic and stochastic approaches

    CERN Document Server

    Müller, Johannes

    2015-01-01

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

  11. A mechanistic nitrogen limitation model for CLM(ED)

    Science.gov (United States)

    Ali, A. A.; Xu, C.; McDowell, N. G.; Rogers, A.; Wullschleger, S. D.; Fisher, R.; Vrugt, J. A.

    2014-12-01

    Photosynthetic capacity is a key plant trait that determines the rate of photosynthesis; however, in Earth System Models it is either a fixed value or derived from a linear function of leaf nitrogen content. A mechanistic leaf nitrogen allocation model have been developed for a DOE-sponsored Community Land Model coupled to the Ecosystem Demography model (CLM-ED) to predict the photosynthetic capacity [Vc,max25 (μmol CO2 m-2 s-1)] under different environmental conditions at the global scale. We collected more than 800 data points of photosynthetic capacity (Vc,max25) for 124 species from 57 studies with the corresponding leaf nitrogen content and environmental conditions (temperature, radiation, humidity and day length) from literature and the NGEE arctic site (Barrow). Based on the data, we found that environmental control of Vc,max25 is about 4 times stronger than the leaf nitrogen content. Using the Markov-Chain Monte Carlo simulation approach, we fitted the collected data to our newly developed nitrogen allocation model, which predict the leaf nitrogen investment in different components including structure, storage, respiration, light capture, carboxylation and electron transport at different environmental conditions. Our results showed that our nitrogen allocation model explained 52% of variance in observed Vc,max25 and 65% variance in observed Jmax25 using a single set of fitted model parameters for all species. Across the growing season, we found that the modeled Vc,max25 explained 49% of the variability in measured Vc,max25. In the context of future global warming, our model predicts that a temperature increase by 5oC and the doubling of atmospheric carbon dioxide reduced the Vc,max25 by 5%, 11%, respectively.

  12. Mathematical modelling in economic processes.

    Directory of Open Access Journals (Sweden)

    L.V. Kravtsova

    2008-06-01

    Full Text Available In article are considered a number of methods of mathematical modelling of economic processes and opportunities of use of spreadsheets Excel for reception of the optimum decision of tasks or calculation of financial operations with the help of the built-in functions.

  13. mathematical modelling of atmospheric dispersion of pollutants

    International Nuclear Information System (INIS)

    Mohamed, M.E.

    2002-01-01

    the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established

  14. Mathematical models and methods for planet Earth

    CERN Document Server

    Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta

    2014-01-01

    In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.

  15. Turbofan engine mathematic model for its static and dynamic characteristics research

    Directory of Open Access Journals (Sweden)

    О.Є. Карпов

    2004-01-01

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

  16. Mathematical modeling of the flash converting process

    Energy Technology Data Exchange (ETDEWEB)

    Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)

    1996-12-31

    An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)

  17. Mathematical modeling of the flash converting process

    Energy Technology Data Exchange (ETDEWEB)

    Sohn, H Y; Perez-Tello, M; Riihilahti, K M [Utah Univ., Salt Lake City, UT (United States)

    1997-12-31

    An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)

  18. A dynamic, mechanistic model of metabolism in adipose tissue of lactating dairy cattle.

    Science.gov (United States)

    McNamara, J P; Huber, K; Kenéz, A

    2016-07-01

    Research in dairy cattle biology has resulted in a large body of knowledge on nutrition and metabolism in support of milk production and efficiency. This quantitative knowledge has been compiled in several model systems to balance and evaluate rations and predict requirements. There are also systems models for metabolism and reproduction in the cow that can be used to support research programs. Adipose tissue plays a significant role in the success and efficiency of lactation, and recent research has resulted in several data sets on genomic differences and changes in gene transcription of adipose tissue in dairy cattle. To fully use this knowledge, we need to build and expand mechanistic, dynamic models that integrate control of metabolism and production. Therefore, we constructed a second-generation dynamic, mechanistic model of adipose tissue metabolism of dairy cattle. The model describes the biochemical interconversions of glucose, acetate, β-hydroxybutyrate (BHB), glycerol, C16 fatty acids, and triacylglycerols. Data gathered from our own research and published references were used to set equation forms and parameter values. Acetate, glucose, BHB, and fatty acids are taken up from blood. The fatty acids are activated to the acyl coenzyme A moieties. Enzymatically catalyzed reactions are explicitly described with parameters including maximal velocity and substrate sensitivity. The control of enzyme activity is partially carried out by insulin and norepinephrine, portraying control in the cow. Model behavior was adequate, with sensitive responses to changing substrates and hormones. Increased nutrient uptake and increased insulin stimulate triacylglycerol synthesis, whereas a reduction in nutrient availability or increase in norepinephrine increases triacylglycerol hydrolysis and free fatty acid release to blood. This model can form a basis for more sophisticated integration of existing knowledge and future studies on metabolic efficiency of dairy cattle

  19. Mathematical Modeling of Circadian/Performance Countermeasures

    Data.gov (United States)

    National Aeronautics and Space Administration — We developed and refined our current mathematical model of circadian rhythms to incorporate melatonin as a marker rhythm. We used an existing physiologically based...

  20. A mathematical model of embodied consciousness

    NARCIS (Netherlands)

    Rudrauf, D.; Bennequin, D.; Granic, I.; Landini, G.; Friston, K.; Williford, K.

    2017-01-01

    We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM

  1. MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM

    Directory of Open Access Journals (Sweden)

    Olha Sushchenko

    2017-07-01

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

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

    CERN Document Server

    Hosking, Roger J

    2008-01-01

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

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

    Science.gov (United States)

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

    2014-09-01

    In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. Copyright © 2014 Elsevier Inc. All rights reserved.

  4. Ordinary Mathematical Models in Calculating the Aviation GTE Parameters

    Directory of Open Access Journals (Sweden)

    E. A. Khoreva

    2017-01-01

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

  5. Potential of mathematical modeling in fruit quality

    African Journals Online (AJOL)

    ONOS

    2010-01-18

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

  6. Mathematical modeling of cancer metabolism.

    Science.gov (United States)

    Medina, Miguel Ángel

    2018-04-01

    Systemic approaches are needed and useful for the study of the very complex issue of cancer. Modeling has a central position in these systemic approaches. Metabolic reprogramming is nowadays acknowledged as an essential hallmark of cancer. Mathematical modeling could contribute to a better understanding of cancer metabolic reprogramming and to identify new potential ways of therapeutic intervention. Herein, I review several alternative approaches to metabolic modeling and their current and future impact in oncology. Copyright © 2018 Elsevier B.V. All rights reserved.

  7. Mathematical models in biological discovery

    CERN Document Server

    Walter, Charles

    1977-01-01

    When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con­ tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog­ ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...

  8. Comparative ecophysiology of two sympatric lizards. Laying the groundwork for mechanistic distribution models

    Directory of Open Access Journals (Sweden)

    Enrique García-Muñoz

    2013-12-01

    Full Text Available Distribution modelling usually makes inferences correlating species presence and environmental variables but does not take biotic relations into account. Alternative approaches based on a mechanistic understanding of biological processes are now being applied. Regarding lacertid lizards, physiological traits such as preferred body temperature (Tp are well known to correlate with several physiological optima. Much less is known about their water ecology although body temperature and evaporative water loss (Wl may trade-off. Two saxicolous lacertids, Algyroides marchi and Podarcis hispanica ss are sympatric in the Subbetic Mountains (SE Spain were they can be found in syntopy. Previous distribution modelling indicates the first species is associated with mountains, low temperatures; high precipitation and forest cover whereas the second one is more generalistic. Here, we perform two ecophysiological tests with both species: a Tp experiment in thermal gradient and a Wl experiment in sealed chambers. Although both species attained similar body temperatures, A. marchi lost more water and more uniformly in time than P. hispanica ss that displayed an apparent response to dehydration. These results suggest that water loss rather temperature is crucial to explain the distribution patterns of A. marchi in relation to P. hispanica ss, the former risking dehydration in dry areas no matter what temperature is. Ecophysiological traits represent a promising tool to build future mechanistic models for (lacertid lizards. Additionally, the implications for their biogeography and conservation are discussed.

  9. Electrorheological fluids modeling and mathematical theory

    CERN Document Server

    Růžička, Michael

    2000-01-01

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

  10. Mathematical model of polyethylene pipe bending stress state

    Science.gov (United States)

    Serebrennikov, Anatoly; Serebrennikov, Daniil

    2018-03-01

    Introduction of new machines and new technologies of polyethylene pipeline installation is usually based on the polyethylene pipe flexibility. It is necessary that existing bending stresses do not lead to an irreversible polyethylene pipe deformation and to violation of its strength characteristics. Derivation of the mathematical model which allows calculating analytically the bending stress level of polyethylene pipes with consideration of nonlinear characteristics is presented below. All analytical calculations made with the mathematical model are experimentally proved and confirmed.

  11. Modelling as a foundation for academic forming in mathematics education

    NARCIS (Netherlands)

    Perrenet, J.C.; Morsche, ter H.G.

    2004-01-01

    The Bachelor curriculum of Applied Mathematics in Eindhoven includes a series of modelling projects where pairs of students solve mathematical problems posed in non-mathematical language. Communication skills training is integrated with this track. Recently a new course has been added. The students

  12. Mathematical Modeling of Biofilm Structures Using COMSTAT Data

    Directory of Open Access Journals (Sweden)

    Davide Verotta

    2017-01-01

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

  13. Mathematical model comparing of the multi-level economics systems

    Science.gov (United States)

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

    2017-12-01

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

  14. A mathematical model

    International Nuclear Information System (INIS)

    Castillo M, J.A.; Pimentel P, A.E.

    2000-01-01

    This work presents the results to define the adult egg viability behavior (VHA) of two species, Drosophila melanogaster and D. simulans obtained with the mathematical model proposed, as well as the respective curves. The data are the VHA result of both species coming from the vicinity of the Laguna Verde Nuclear Power plant (CNLV) comprise a 10 years collect period starting from 1987 until 1997. Each collect includes four series of data which are the VHA result obtained after treatment with 0, 4, 6 and 8 Gy of gamma rays. (Author)

  15. Mathematical Modeling of Biofilm Structures Using COMSTAT Data

    DEFF Research Database (Denmark)

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

    2017-01-01

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

  16. A mathematical look at a physical power prediction model

    DEFF Research Database (Denmark)

    Landberg, L.

    1998-01-01

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

  17. Mathematical model for solid fuel combustion in fluidized bed

    International Nuclear Information System (INIS)

    Kostikj, Zvonimir; Noshpal, Aleksandar

    1994-01-01

    A mathematical model for computation of the combustion process of solid fuel in fluidized bed is presented in this work. Only the combustor part of the plant (the fluidized bed and the free board) is treated with this model. In that manner, all principal, physical presumption and improvements (upon which this model is based) are given. Finally, the results of the numerical realisation of the mathematical model for combustion of minced straw as well as the results of the experimental investigation of a concrete physical model are presented. (author)

  18. Mathematical Modeling: Are Prior Experiences Important?

    Science.gov (United States)

    Czocher, Jennifer A.; Moss, Diana L.

    2017-01-01

    Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

  19. The role of mathematical models in the optimization of radiopharmaceutical therapy

    International Nuclear Information System (INIS)

    Divgi, C.

    2001-01-01

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

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

    Science.gov (United States)

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

    2013-01-01

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

  1. Mathematical model of two-phase flow in accelerator channel

    Directory of Open Access Journals (Sweden)

    О.Ф. Нікулін

    2010-01-01

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

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

    Science.gov (United States)

    Widayanto, Arif; Pratiwi, Hasih; Mardiyana

    2018-04-01

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

  3. Mechanistic kinetic models of enzymatic cellulose hydrolysis-A review.

    Science.gov (United States)

    Jeoh, Tina; Cardona, Maria J; Karuna, Nardrapee; Mudinoor, Akshata R; Nill, Jennifer

    2017-07-01

    Bioconversion of lignocellulose forms the basis for renewable, advanced biofuels, and bioproducts. Mechanisms of hydrolysis of cellulose by cellulases have been actively studied for nearly 70 years with significant gains in understanding of the cellulolytic enzymes. Yet, a full mechanistic understanding of the hydrolysis reaction has been elusive. We present a review to highlight new insights gained since the most recent comprehensive review of cellulose hydrolysis kinetic models by Bansal et al. (2009) Biotechnol Adv 27:833-848. Recent models have taken a two-pronged approach to tackle the challenge of modeling the complex heterogeneous reaction-an enzyme-centric modeling approach centered on the molecularity of the cellulase-cellulose interactions to examine rate limiting elementary steps and a substrate-centric modeling approach aimed at capturing the limiting property of the insoluble cellulose substrate. Collectively, modeling results suggest that at the molecular-scale, how rapidly cellulases can bind productively (complexation) and release from cellulose (decomplexation) is limiting, while the overall hydrolysis rate is largely insensitive to the catalytic rate constant. The surface area of the insoluble substrate and the degrees of polymerization of the cellulose molecules in the reaction both limit initial hydrolysis rates only. Neither enzyme-centric models nor substrate-centric models can consistently capture hydrolysis time course at extended reaction times. Thus, questions of the true reaction limiting factors at extended reaction times and the role of complexation and decomplexation in rate limitation remain unresolved. Biotechnol. Bioeng. 2017;114: 1369-1385. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

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

    Directory of Open Access Journals (Sweden)

    Dinh An Nguyen

    2012-07-01

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

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

    CERN Document Server

    Rappaz, Jacques

    2013-01-01

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

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

    African Journals Online (AJOL)

    kofimereku

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

  7. Mathematical model of gluconic acid fermentation by Aspergillus niger

    Energy Technology Data Exchange (ETDEWEB)

    Takamatsu, T.; Shioya, S.; Furuya, T.

    1981-11-01

    A mathematical model for the study of gluconic acid fermentation by Aspergillus niger has been developed. The model has been deduced from the basic biological concept of multicellular filamentous microorganisms, i.e. cell population balance. It can be used to explain the behaviour of both batch and continuous cultures, even when in a lag phase. A new characteristic, involving the existence of dual equilibrium stages during fermentation, has been predicted using this mathematical model. (Refs. 6).

  8. A mathematical model for camera calibration based on straight lines

    Directory of Open Access Journals (Sweden)

    Antonio M. G. Tommaselli

    2005-12-01

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

  9. Mathematical modeling of infectious disease dynamics

    Science.gov (United States)

    Siettos, Constantinos I.; Russo, Lucia

    2013-01-01

    Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814

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

    Directory of Open Access Journals (Sweden)

    Melike TURAL SÖNMEZ

    2017-12-01

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

  11. Mathematical modeling of the mixing zone for getting bimetallic compound

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Stanislav L. [Institute of Applied Mechanics, Ural Branch, Izhevsk (Russian Federation)

    2011-07-01

    A mathematical model of the formation of atomic bonds in metals and alloys, based on the electrostatic interaction between the outer electron shells of atoms of chemical elements. Key words: mathematical model, the interatomic bonds, the electron shell of atoms, the potential, the electron density, bimetallic compound.

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

    Science.gov (United States)

    Lombarte, Mercedes; Lupo, Maela; Campetelli, German; Basualdo, Marta; Rigalli, Alfredo

    2013-10-01

    According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat. Copyright © 2013 Elsevier Inc. All rights reserved.

  13. Modeling eBook acceptance: A study on mathematics teachers

    Science.gov (United States)

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

    2014-12-01

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

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

    International Nuclear Information System (INIS)

    Easters, D J

    2014-01-01

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

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

    Science.gov (United States)

    Easters, D. J.

    2014-03-01

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

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

    International Nuclear Information System (INIS)

    Begum, N.N.; Ahmed, J.

    2006-01-01

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

  17. short communication mathematical modelling for magnetite

    African Journals Online (AJOL)

    Preferred Customer

    The present research focuses to develop mathematical model for the ..... Staler, M.J. The Principle of Ion Exchange Technology, Butterworth-Heinemann: Boston; ... Don, W.G. Perry's Chemical Engineering Hand Book, 7th ed., McGraw-Hill:.

  18. Outlooks for mathematical modelling of the glass melting process

    Energy Technology Data Exchange (ETDEWEB)

    Waal, H. de [TNO Institute of Applied Physics, Delft (Netherlands)

    1997-12-31

    Mathematical modelling is nowadays a standard tool for major producers of float glass, T.V. glass and fiberglass. Also for container glass furnaces, glass tank modelling proves to be a valuable method to optimize process conditions. Mathematical modelling is no longer just a way to visualize the flow patterns and to provide data on heat transfer. It can also predict glass quality in relation to process parameters, because all chemical and physical phenomena are included in the latest generation of models, based on experimental and theoretical research on these phenomena.

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

    Science.gov (United States)

    Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

    2015-07-22

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

  20. The prediction of epidemics through mathematical modeling.

    Science.gov (United States)

    Schaus, Catherine

    2014-01-01

    Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.

  1. IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS

    Directory of Open Access Journals (Sweden)

    L. V. Ursulyak

    2017-12-01

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

  2. Productivity of "Collisions Generate Heat" for Reconciling an Energy Model with Mechanistic Reasoning: A Case Study

    Science.gov (United States)

    Scherr, Rachel E.; Robertson, Amy D.

    2015-01-01

    We observe teachers in professional development courses about energy constructing mechanistic accounts of energy transformations. We analyze a case in which teachers investigating adiabatic compression develop a model of the transformation of kinetic energy to thermal energy. Among their ideas is the idea that thermal energy is generated as a…

  3. Mechanistic Basis of Cocrystal Dissolution Advantage.

    Science.gov (United States)

    Cao, Fengjuan; Amidon, Gordon L; Rodríguez-Hornedo, Naír; Amidon, Gregory E

    2018-01-01

    Current interest in cocrystal development resides in the advantages that the cocrystal may have in solubility and dissolution compared with the parent drug. This work provides a mechanistic analysis and comparison of the dissolution behavior of carbamazepine (CBZ) and its 2 cocrystals, carbamazepine-saccharin (CBZ-SAC) and carbamazepine-salicylic acid (CBZ-SLC) under the influence of pH and micellar solubilization. A simple mathematical equation is derived based on the mass transport analyses to describe the dissolution advantage of cocrystals. The dissolution advantage is the ratio of the cocrystal flux to drug flux and is defined as the solubility advantage (cocrystal to drug solubility ratio) times the diffusivity advantage (cocrystal to drug diffusivity ratio). In this work, the effective diffusivity of CBZ in the presence of surfactant was determined to be different and less than those of the cocrystals. The higher effective diffusivity of drug from the dissolved cocrystals, the diffusivity advantage, can impart a dissolution advantage to cocrystals with lower solubility than the parent drug while still maintaining thermodynamic stability. Dissolution conditions where cocrystals can display both thermodynamic stability and a dissolution advantage can be obtained from the mass transport models, and this information is useful for both cocrystal selection and formulation development. Copyright © 2018 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

  4. Effectiveness of discovery learning model on mathematical problem solving

    Science.gov (United States)

    Herdiana, Yunita; Wahyudin, Sispiyati, Ririn

    2017-08-01

    This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.

  5. Mathematical model of three winding auto transformer

    International Nuclear Information System (INIS)

    Volcko, V.; Eleschova, Z.; Belan, A.; Janiga, P.

    2012-01-01

    This article deals with the design of mathematical model of three-winding auto transformer for steady state analyses. The article is focused on model simplicity for the purposes of the use in complex transmission systems and authenticity of the model taking into account different types of step-voltage regulator. (Authors)

  6. Mathematical Modelling of Intraretinal Oxygen Partial Pressure ...

    African Journals Online (AJOL)

    Purpose: The aim of our present work is to develop a simple steady state model for intraretinal oxygen partial pressure distribution and to investigate the effect of various model parameters on the partial pressure distribution under adapted conditions of light and darkness.. Method: A simple eight-layered mathematical model ...

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

    Science.gov (United States)

    Bartley, Sarah R.; Ingram, Naomi

    2017-12-01

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

  8. Mathematical human body modelling for impact loading

    NARCIS (Netherlands)

    Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.

    1999-01-01

    Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models

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

    Science.gov (United States)

    Gould, Heather; Wasserman, Nicholas H.

    2014-01-01

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

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

    Science.gov (United States)

    Jacobs, Gerrie J.; Durandt, Rina

    2017-01-01

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

  11. Mathematical modeling of CANDU-PHWR

    Energy Technology Data Exchange (ETDEWEB)

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

    2003-07-01

    The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR). This study involved mathematical modeling of CANDU-PHWR to study its thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique. The reactor model includes the neutronic, reactivity, and fuel channel heat transfer. The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and the reactivity feed back due to the changes in the fuel temperature and coolant temperature. The CANDU-PHWR model was coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)

  12. Mathematical models of viscous friction

    CERN Document Server

    Buttà, Paolo; Marchioro, Carlo

    2015-01-01

    In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...

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

    African Journals Online (AJOL)

    Timothy

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

  14. Description and evaluation of a mechanistically based conceptual model for spall

    Energy Technology Data Exchange (ETDEWEB)

    Hansen, F.D.; Knowles, M.K.; Thompson, T.W. [and others

    1997-08-01

    A mechanistically based model for a possible spall event at the WIPP site is developed and evaluated in this report. Release of waste material to the surface during an inadvertent borehole intrusion is possible if future states of the repository include high gas pressure and waste material consisting of fine particulates having low mechanical strength. The conceptual model incorporates the physics of wellbore hydraulics coupled to transient gas flow to the intrusion borehole, and mechanical response of the waste. Degraded waste properties using of the model. The evaluations include both numerical and analytical implementations of the conceptual model. A tensile failure criterion is assumed appropriate for calculation of volumes of waste experiencing fragmentation. Calculations show that for repository gas pressures less than 12 MPa, no tensile failure occurs. Minimal volumes of material experience failure below gas pressure of 14 MPa. Repository conditions dictate that the probability of gas pressures exceeding 14 MPa is approximately 1%. For these conditions, a maximum failed volume of 0.25 m{sup 3} is calculated.

  15. Description and evaluation of a mechanistically based conceptual model for spall

    International Nuclear Information System (INIS)

    Hansen, F.D.; Knowles, M.K.; Thompson, T.W.

    1997-08-01

    A mechanistically based model for a possible spall event at the WIPP site is developed and evaluated in this report. Release of waste material to the surface during an inadvertent borehole intrusion is possible if future states of the repository include high gas pressure and waste material consisting of fine particulates having low mechanical strength. The conceptual model incorporates the physics of wellbore hydraulics coupled to transient gas flow to the intrusion borehole, and mechanical response of the waste. Degraded waste properties using of the model. The evaluations include both numerical and analytical implementations of the conceptual model. A tensile failure criterion is assumed appropriate for calculation of volumes of waste experiencing fragmentation. Calculations show that for repository gas pressures less than 12 MPa, no tensile failure occurs. Minimal volumes of material experience failure below gas pressure of 14 MPa. Repository conditions dictate that the probability of gas pressures exceeding 14 MPa is approximately 1%. For these conditions, a maximum failed volume of 0.25 m 3 is calculated

  16. Cooking Potatoes: Experimentation and Mathematical Modeling.

    Science.gov (United States)

    Chen, Xiao Dong

    2002-01-01

    Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)

  17. A Mathematical Model, Implementation and Study of a Swarm System

    OpenAIRE

    Varghese, Blesson; McKee, Gerard

    2013-01-01

    The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to conf...

  18. Fetal programming of CVD and renal disease: animal models and mechanistic considerations.

    Science.gov (United States)

    Langley-Evans, Simon C

    2013-08-01

    The developmental origins of health and disease hypothesis postulates that exposure to a less than optimal maternal environment during fetal development programmes physiological function, and determines risk of disease in adult life. Much evidence of such programming comes from retrospective epidemiological cohorts, which demonstrate associations between birth anthropometry and non-communicable diseases of adulthood. The assertion that variation in maternal nutrition drives these associations is supported by studies using animal models, which demonstrate that maternal under- or over-nutrition during pregnancy can programme offspring development. Typically, the offspring of animals that are undernourished in pregnancy exhibit a relatively narrow range of physiological phenotypes that includes higher blood pressure, glucose intolerance, renal insufficiency and increased adiposity. The observation that common phenotypes arise from very diverse maternal nutritional insults has led to the proposal that programming is driven by a small number of mechanistic processes. The remodelling of tissues during development as a consequence of maternal nutritional status being signalled by endocrine imbalance or key nutrients limiting processes in the fetus may lead to organs having irreversibly altered structures that may limit their function with ageing. It has been proposed that the maternal diet may impact upon epigenetic marks that determine gene expression in fetal tissues, and this may be an important mechanism connecting maternal nutrient intakes to long-term programming of offspring phenotype. The objective for this review is to provide an overview of the mechanistic basis of fetal programming, demonstrating the critical role of animal models as tools for the investigation of programming phenomena.

  19. Mechanistic modelling of a cathode-supported tubular solid oxide fuel cell

    Science.gov (United States)

    Suwanwarangkul, R.; Croiset, E.; Pritzker, M. D.; Fowler, M. W.; Douglas, P. L.; Entchev, E.

    A two-dimensional mechanistic model of a tubular solid oxide fuel cell (SOFC) considering momentum, energy, mass and charge transport is developed. The model geometry of a single cell comprises an air-preheating tube, air channel, fuel channel, anode, cathode and electrolyte layers. The heat radiation between cell and air-preheating tube is also incorporated into the model. This allows the model to predict heat transfer between the cell and air-preheating tube accurately. The model is validated and shows good agreement with literature data. It is anticipated that this model can be used to help develop efficient fuel cell designs and set operating variables under practical conditions. The transport phenomena inside the cell, including gas flow behaviour, temperature, overpotential, current density and species concentration, are analysed and discussed in detail. Fuel and air velocities are found to vary along flow passages depending on the local temperature and species concentrations. This model demonstrates the importance of incorporating heat radiation into a tubular SOFC model. Furthermore, the model shows that the overall cell performance is limited by O 2 diffusion through the thick porous cathode and points to the development of new cathode materials and designs being important avenues to enhance cell performance.

  20. Thermoregulation in premature infants: A mathematical model.

    Science.gov (United States)

    Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen

    2016-12-01

    In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright © 2016 Elsevier Ltd. All rights reserved.

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

    OpenAIRE

    Edwin Musdi

    2016-01-01

    This research aims to develop a mathematics instructional model based realistic mathematics education (RME) to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase.  At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characterist...

  2. Uncertainty and Complexity in Mathematical Modeling

    Science.gov (United States)

    Cannon, Susan O.; Sanders, Mark

    2017-01-01

    Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…

  3. Mathematical Modeling of Column-Base Connections under Monotonic Loading

    Directory of Open Access Journals (Sweden)

    Gholamreza Abdollahzadeh

    2014-12-01

    Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.

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

    Science.gov (United States)

    Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

    2011-04-01

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

  5. Mathematical Model for the Control of measles 1*PETER, OJ ...

    African Journals Online (AJOL)

    PROF HORSFALL

    2018-04-16

    Apr 16, 2018 ... 5Department of Mathematics/Statistics, Federal University of Technology, Minna, Nigeria ... ABSTRACT: We proposed a mathematical model of measles disease dynamics with vaccination by ...... Equation with application.

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

    OpenAIRE

    Klein, Cornel; Rumpe, Bernhard; Broy, Manfred

    2014-01-01

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

  7. Improving the prediction of methane production and representation of rumen fermentation for finishing beef cattle within a mechanistic model

    NARCIS (Netherlands)

    Ellis, J.L.; Dijkstra, J.; Bannink, A.; Kebreab, E.; Archibeque, S.; Benchaar, C.; Beauchemin, K.; Nkrumah, D.J.; France, J.

    2014-01-01

    The purpose of this study was to evaluate prediction of methane emissions from finishing beef cattle using an extant mechanistic model with pH-independent or pH-dependent VFA stoichiometries, a recent stoichiometry adjustment for the use of monensin, and adaptation of the underlying model structure,

  8. SOME TRENDS IN MATHEMATICAL MODELING FOR BIOTECHNOLOGY

    Directory of Open Access Journals (Sweden)

    O. M. Klyuchko

    2018-02-01

    Full Text Available The purpose of present research is to demonstrate some trends of development of modeling methods for biotechnology according to contemporary achievements in science and technique. At the beginning the general approaches are outlined, some types of classifications of modeling methods are observed. The role of mathematic methods modeling for biotechnology in present époque of information computer technologies intensive development is studied and appropriate scheme of interrelation of all these spheres is proposed. Further case studies are suggested: some mathematic models in three different spaces (1D, 2D, 3D models are described for processes in living objects of different levels of hierarchic organization. In course of this the main attention was paid to some processes modeling in neurons as well as in their aggregates of different forms, including glioma cell masses (1D, 2D, 3D brain processes models. Starting from the models that have only theoretical importance for today, we describe at the end a model which application may be important for the practice. The work was done after the analysis of approximately 250 current publications in fields of biotechnology, including the authors’ original works.

  9. Development of a mechanistic model for prediction of CO2 capture from gas mixtures by amine solutions in porous membranes.

    Science.gov (United States)

    Ghadiri, Mehdi; Marjani, Azam; Shirazian, Saeed

    2017-06-01

    A mechanistic model was developed in order to predict capture and removal of CO 2 from air using membrane technology. The considered membrane was a hollow-fiber contactor module in which gas mixture containing CO 2 was assumed as feed while 2-amino-2-metyl-1-propanol (AMP) was used as an absorbent. The mechanistic model was developed according to transport phenomena taking into account mass transfer and chemical reaction between CO 2 and amine in the contactor module. The main aim of modeling was to track the composition and flux of CO 2 and AMP in the membrane module for process optimization. For modeling of the process, the governing equations were computed using finite element approach in which the whole model domain was discretized into small cells. To confirm the simulation findings, model outcomes were compared with experimental data and good consistency was revealed. The results showed that increasing temperature of AMP solution increases CO 2 removal in the hollow-fiber membrane contactor.

  10. Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification

    Directory of Open Access Journals (Sweden)

    Grzegorz Mikułowski

    2016-01-01

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

  11. Mathematical Modelling of Intraretinal Oxygen Partial Pressure

    African Journals Online (AJOL)

    Erah

    The system of non-linear differential equations was solved numerically using Runge-kutta. Nystroms method. ... artery occlusion. Keywords: Mathematical modeling, Intraretinal oxygen pressure, Retinal capillaries, Oxygen ..... Mass transfer,.

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

    DEFF Research Database (Denmark)

    Jurlewicz, Agnieszka; Nunes, Claudia; Russo, Giovanni

    2018-01-01

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

  13. Solutions manual to accompany finite mathematics models and applications

    CERN Document Server

    Morris, Carla C

    2015-01-01

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

  14. Development of mechanistic sorption model and treatment of uncertainties for Ni sorption on montmorillonite/bentonite

    International Nuclear Information System (INIS)

    Ochs, Michael; Ganter, Charlotte; Tachi, Yukio; Suyama, Tadahiro; Yui, Mikazu

    2011-02-01

    Sorption and diffusion of radionuclides in buffer materials (bentonite) are the key processes in the safe geological disposal of radioactive waste, because migration of radionuclides in this barrier is expected to be diffusion-controlled and retarded by sorption processes. It is therefore necessary to understand the detailed/coupled processes of sorption and diffusion in compacted bentonite and develop mechanistic /predictive models, so that reliable parameters can be set under a variety of geochemical conditions relevant to performance assessment (PA). For this purpose, JAEA has developed the integrated sorption and diffusion (ISD) model/database in montmorillonite/bentonite systems. The main goal of the mechanistic model/database development is to provide a tool for a consistent explanation, prediction, and uncertainty assessment of K d as well as diffusion parameters needed for the quantification of radionuclide transport. The present report focuses on developing the thermodynamic sorption model (TSM) and on the quantification and handling of model uncertainties in applications, based on illustrating by example of Ni sorption on montmorillonite/bentonite. This includes 1) a summary of the present state of the art of thermodynamic sorption modeling, 2) a discussion of the selection of surface species and model design appropriate for the present purpose, 3) possible sources and representations of TSM uncertainties, and 4) details of modeling, testing and uncertainty evaluation for Ni sorption. Two fundamentally different approaches are presented and compared for representing TSM uncertainties: 1) TSM parameter uncertainties calculated by FITEQL optimization routines and some statistical procedure, 2) overall error estimated by direct comparison of modeled and experimental K d values. The overall error in K d is viewed as the best representation of model uncertainty in ISD model/database development. (author)

  15. Mathematical modeling of optical glazing performance

    NARCIS (Netherlands)

    Nijnatten, van P.A.; Wittwer, V.; Granqvist, C.G.; Lampert, C.M.

    1994-01-01

    Mathematical modelling can be a powerful tool in the design and optimalization of glazing. By calculation, the specifications of a glazing design and the optimal design parameters can be predicted without building costly prototypes first. Furthermore, properties which are difficult to measure, like

  16. Introduction to mathematical models and methods

    Energy Technology Data Exchange (ETDEWEB)

    Siddiqi, A. H.; Manchanda, P. [Gautam Budha University, Gautam Budh Nagar-201310 (India); Department of Mathematics, Guru Nanak Dev University, Amritsar (India)

    2012-07-17

    Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.

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

    CERN Document Server

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

    2014-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Y. A. Perminov

    2014-01-01

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

  19. Mathematical modelling and numerical simulation of forces in milling process

    Science.gov (United States)

    Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.

    2018-04-01

    Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.

  20. Applicability of one-dimensional mechanistic post-dryout prediction model

    International Nuclear Information System (INIS)

    Jeong, Hae Yong; No Hee Cheon

    1996-01-01

    Through the analysis of many experimental post-dryout data, it is shown that the most probable flow regime near dryout or quench front is not annular flow but churn-turbulent flow when the mass flux is low. A correlation describing the initial droplet size just after the CHF position at low mass flux is low. A correlation describing the initial droplet size just after the CHF position at low mass flux is suggested through regression analysis. In the post-dryout region at low pressure and low flow, it is found that the suggested one-dimensional mechanistic model is not applicable when the vapor superficial velocity is very low, i. e., when the flow is bubbly or slug flow regime. This is explained by the change of main entrainment mechanism with the change of flow regime. Therefore, the suggested correlation is valid only in the churn-turbulent flow regime (j * g = 0.5 ∼ 4.5)

  1. Identification of Chemical Reactor Plant’s Mathematical Model

    OpenAIRE

    Pyakullya, Boris Ivanovich; Kladiev, Sergey Nikolaevich

    2015-01-01

    This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.

  2. A mathematical model of forgetting and amnesia

    NARCIS (Netherlands)

    Murre, J.M.J.; Chessa, A.G.; Meeter, M.

    2013-01-01

    We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in

  3. A mechanistic model for electricity consumption on dairy farms: definition, validation, and demonstration.

    Science.gov (United States)

    Upton, J; Murphy, M; Shalloo, L; Groot Koerkamp, P W G; De Boer, I J M

    2014-01-01

    Our objective was to define and demonstrate a mechanistic model that enables dairy farmers to explore the impact of a technical or managerial innovation on electricity consumption, associated CO2 emissions, and electricity costs. We, therefore, (1) defined a model for electricity consumption on dairy farms (MECD) capable of simulating total electricity consumption along with related CO2 emissions and electricity costs on dairy farms on a monthly basis; (2) validated the MECD using empirical data of 1yr on commercial spring calving, grass-based dairy farms with 45, 88, and 195 milking cows; and (3) demonstrated the functionality of the model by applying 2 electricity tariffs to the electricity consumption data and examining the effect on total dairy farm electricity costs. The MECD was developed using a mechanistic modeling approach and required the key inputs of milk production, cow number, and details relating to the milk-cooling system, milking machine system, water-heating system, lighting systems, water pump systems, and the winter housing facilities as well as details relating to the management of the farm (e.g., season of calving). Model validation showed an overall relative prediction error (RPE) of less than 10% for total electricity consumption. More than 87% of the mean square prediction error of total electricity consumption was accounted for by random variation. The RPE values of the milk-cooling systems, water-heating systems, and milking machine systems were less than 20%. The RPE values for automatic scraper systems, lighting systems, and water pump systems varied from 18 to 113%, indicating a poor prediction for these metrics. However, automatic scrapers, lighting, and water pumps made up only 14% of total electricity consumption across all farms, reducing the overall impact of these poor predictions. Demonstration of the model showed that total farm electricity costs increased by between 29 and 38% by moving from a day and night tariff to a flat

  4. Optimization and mathematical modeling in computer architecture

    CERN Document Server

    Sankaralingam, Karu; Nowatzki, Tony

    2013-01-01

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

  5. Mathematical modeling of a V-stack piezoelectric aileron actuation

    Directory of Open Access Journals (Sweden)

    Ioan URSU

    2016-12-01

    Full Text Available The article presents a mathematical modeling of aileron actuation that uses piezo V-shaped stacks. The aim of the actuation is the increasing of flutter speed in the context of a control law, in order to widen the flight envelope. In this way the main advantage of such a piezo actuator, the bandwidth is exploited. The mathematical model is obtained based on free body diagrams, and the numerical simulations allow a preliminary sizing of the actuator.

  6. Description of a comprehensive mathematical model

    DEFF Research Database (Denmark)

    Li, Xiyan; Yin, Chungen

    2017-01-01

    Biomass gasification is still a promising technology after over 30 years’ research and development and has success only in a few niche markets. In this paper, a comprehensive mathematical model for biomass particle gasification is developed within a generic particle framework, assuming the feed...

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

    Science.gov (United States)

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

    2014-01-01

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

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

    International Nuclear Information System (INIS)

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

    2014-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

    Ru, Changhai, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [College of Automation, Harbin Engineering University, Harbin 150001 (China); Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Chen, Jie; Shao, Zhushuai [Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Pang, Ming [College of Automation, Harbin Engineering University, Harbin 150001 (China); Luo, Jun, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072 (China)

    2014-01-15

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

  10. Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

    Science.gov (United States)

    Winda, A.; Sufyani, P.; Elah, N.

    2018-05-01

    Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

  11. Mechanistic modelling of gaseous fission product behaviour in UO2 fuel by Rtop code

    International Nuclear Information System (INIS)

    Kanukova, V.D.; Khoruzhii, O.V.; Kourtchatov, S.Y.; Likhanskii, V.V.; Matveew, L.V.

    2002-01-01

    The current status of a mechanistic modelling by the RTOP code of the fission product behaviour in polycrystalline UO 2 fuel is described. An outline of the code and implemented physical models is presented. The general approach to code validation is discussed. It is exemplified by the results of validation of the models of fuel oxidation and grain growth. The different models of intragranular and intergranular gas bubble behaviour have been tested and the sensitivity of the code in the framework of these models has been analysed. An analysis of available models of the resolution of grain face bubbles is also presented. The possibilities of the RTOP code are presented through the example of modelling behaviour of WWER fuel over the course of a comparative WWER-PWR experiment performed at Halden and by comparison with Yanagisawa experiments. (author)

  12. Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

    Science.gov (United States)

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

    2016-01-01

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

  13. Mathematical modelling of tissue formation in chondrocyte filter cultures.

    Science.gov (United States)

    Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J

    2011-12-17

    In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

  14. Teaching Writing and Communication in a Mathematical Modeling Course

    Science.gov (United States)

    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…

  15. Reduced modeling of signal transduction – a modular approach

    Directory of Open Access Journals (Sweden)

    Ederer Michael

    2007-09-01

    Full Text Available Abstract Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good

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

    Science.gov (United States)

    Mischo, Christoph; Maaß, Katja

    2013-01-01

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

  17. Influence of mathematical models in design of PV-Diesel systems

    International Nuclear Information System (INIS)

    Dufo-Lopez, Rodolfo; Bernal-Agustin, Jose L.

    2008-01-01

    This paper presents a study of the influence of mathematical models in the optimal design of PV-Diesel systems. For this purpose, a design tool developed by the authors, which allows obtaining the most cost effective design of a PV-Diesel system through the genetic algorithm technique, has been used. The mathematical models of some elements of the hybrid system have been improved in comparison to those usually employed in hybrid systems design programs. Furthermore, a more complete general control strategy has been developed, one that also takes into account more characteristics than those usually considered in this kind of design. Several designs have been made, evaluating the effect on the results of the different mathematical models and the novel strategy that can be considered

  18. Tracer kinetic modelling of receptor data with mathematical metabolite correction

    International Nuclear Information System (INIS)

    Burger, C.; Buck, A.

    1996-01-01

    Quantitation of metabolic processes with dynamic positron emission tomography (PET) and tracer kinetic modelling relies on the time course of authentic ligand in plasma, i.e. the input curve. The determination of the latter often requires the measurement of labelled metabilites, a laborious procedure. In this study we examined the possibility of mathematical metabolite correction, which might obviate the need for actual metabolite measurements. Mathematical metabilite correction was implemented by estimating the input curve together with kinetic tissue parameters. The general feasibility of the approach was evaluated in a Monte Carlo simulation using a two tissue compartment model. The method was then applied to a series of five human carbon-11 iomazenil PET studies. The measured cerebral tissue time-activity curves were fitted with a single tissue compartment model. For mathematical metabolite correction the input curve following the peak was approximated by a sum of three decaying exponentials, the amplitudes and characteristic half-times of which were then estimated by the fitting routine. In the simulation study the parameters used to generate synthetic tissue time-activity curves (K 1 -k 4 ) were refitted with reasonable identifiability when using mathematical metabolite correciton. Absolute quantitation of distribution volumes was found to be possible provided that the metabolite and the kinetic models are adequate. If the kinetic model is oversimplified, the linearity of the correlation between true and estimated distribution volumes is still maintained, although the linear regression becomes dependent on the input curve. These simulation results were confirmed when applying mathematical metabolite correction to the 11 C iomazenil study. Estimates of the distribution volume calculated with a measured input curve were linearly related to the estimates calculated using mathematical metabolite correction with correlation coefficients >0.990. (orig./MG)

  19. Mathematical model and simulations of radiation fluxes from buried radionuclides

    International Nuclear Information System (INIS)

    Ahmad Saat

    1999-01-01

    A mathematical model and a simple Monte Carlo simulations were developed to predict radiation fluxes from buried radionuclides. The model and simulations were applied to measured (experimental) data. The results of the mathematical model showed good acceptable order of magnitude agreement. A good agreement was also obtained between the simple simulations and the experimental results. Thus, knowing the radionuclide distribution profiles in soil from a core sample, it can be applied to the model or simulations to estimate the radiation fluxes emerging from the soil surface. (author)

  20. The mathematical model of thread unrolling from a bobbin

    Directory of Open Access Journals (Sweden)

    S. M. Tenenbaum

    2014-01-01

    Full Text Available I. Introduction The subject of research in this work is a process of thread unrolling from a bobbin. The mathematical model of this process considering motion of thread peace on a bobbin and unrolled peace is proposed. The dimension of system of differential equations for this model is constant during deploying.The relevance to simulate this process for design of Heliogyro-like solar sails (Heliogyro [1], BMSTU-Sail [2] is proved. The paper briefly characterizes a blade for such solar sail as a simulation object. It proves the possibility for using a flexible thread model for a long blade because of very small blade thickness (less than 10 μm [3] relative to blade width and the phenomena of Koriolis forces [4] that lead to buckling failure of blade flatness.The major features of the proposed model are:-- simulated as a motion of the thread piece both being on a bobbin and its unrolled peace;-- splitting a thread length into nodes does not depend on the demand to ensure a sufficient number of nodes on a single thread turn on the coil;-- because of avoiding a problem of contact between the thread and bobbin a stable integration of motion equations is provided by the conventional Runge-Kutta method of fourth order with a constant step [5];-- in the course of solution the number of freedom degrees (number of motion equation is constant, thereby simplifying a calculation algorithm.The closest mathematical model is proposed in [6].The scientific novelty of this research is the approach to solving the problem of unrolling thread from a bobbin using a constant number of motion equations while preserving real kinematics coiling process.II. Problem formulationIn this section the problem of unrolling thread with length L from a bobbin of radius r is posed while any kind of forces are acting on the unrolled peace of thread. Moreover, the law of bobbin rotation φ(t assumed to be known with the proviso that the model can be modified if φ(t is the result of

  1. Mathematical Modeling in Combustion Science

    CERN Document Server

    Takeno, Tadao

    1988-01-01

    An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.

  2. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

    Science.gov (United States)

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

  3. ECONOMIC AND MATHEMATICAL MODELING INNOVATION SYSTEMS

    Directory of Open Access Journals (Sweden)

    D.V. Makarov

    2014-06-01

    Full Text Available The paper presents one of the mathematical tools for modeling innovation processes. With the help of Kondratieff long waves can define innovation cycles. However, complexity of the innovation system implies a qualitative description. The article describes the problems of this area of research.

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

    Science.gov (United States)

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

    2018-01-01

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

  5. Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

    Science.gov (United States)

    Ludwig, Patrice; Tongen, Anthony; Walton, Brian

    2018-01-01

    James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

  6. Identification of Chemical Reactor Plant’s Mathematical Model

    Directory of Open Access Journals (Sweden)

    Pyakillya Boris

    2015-01-01

    Full Text Available This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.

  7. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

    OpenAIRE

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

  8. Mathematical models of granular matter

    CERN Document Server

    Mariano, Paolo; Giovine, Pasquale

    2008-01-01

    Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

  9. Aspects of Mathematical Modelling of Pressure Retarded Osmosis

    Science.gov (United States)

    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

  10. Mathematical modeling of a convective textile drying process

    Directory of Open Access Journals (Sweden)

    G. Johann

    2014-12-01

    Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.

  11. Proposal of a pedagogical model for mathematics teacher education

    Directory of Open Access Journals (Sweden)

    Alfonso Jiménez Espinosa

    2011-01-01

    Full Text Available This research-based article reflects on mathematics teacher education, and proposes a pedagogical model for this purpose, called Gradual Research Pedagogical Model (MPGI. This model considers the central curricular elements of any academic education process: student, teacher and contents, with evaluation as transversal element for analysis and feedback. The training of future teachers is constituted by three moments, each with its specific emphasis: the first is “contextualization”, which aims at having the student understand his or her new academic role, and identify and overcome his or her academic weak points, the second is “knowledge foundation”, which offers basic education in the fields of mathematics and pedagogy, as well as sensibilization towards social issues, opening up the student’s possibilities as leader and agent of change, and lastly, “knowledge immersion”, which is centered on research and the identification and study of topics and problems of the mathematical discipline as well as the pedagogical field.

  12. Mathematical Modelling of Surfactant Self-assembly at Interfaces

    KAUST Repository

    Morgan, C. E.

    2015-01-01

    © 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary differential equations that couple the rearrangement of surfactant within the multilayer to the surface adsorption kinetics is first derived. This model is then extended to the macroscopic scale by taking the continuum limit that exploits the typically large number of surfactant layers, which results in a novel third-order partial differential equation. The model is generalized to allow for the presence of two adsorbing boundaries, which results in an implicit free-boundary problem. The system predicts physically observed features in multilayer systems such as the initial formation of smaller lamellar structures and the typical number of layers that form in equilibrium.

  13. Soil pH controls the environmental availability of phosphorus: Experimental and mechanistic modelling approaches

    International Nuclear Information System (INIS)

    Devau, Nicolas; Cadre, Edith Le; Hinsinger, Philippe; Jaillard, Benoit; Gerard, Frederic

    2009-01-01

    Inorganic P is the least mobile major nutrient in most soils and is frequently the prime limiting factor for plant growth in terrestrial ecosystems. In this study, the extraction of soil inorganic P with CaCl 2 (P-CaCl 2 ) and geochemical modelling were combined in order to unravel the processes controlling the environmentally available P (EAP) of a soil over a range of pH values (pH ∼ 4-10). Mechanistic descriptions of the adsorption of cations and anions by the soil constituents were used (1-pK Triple Plane, ion-exchange and NICA-Donnan models). These models are implemented into the geochemical code Visual MINTEQ. An additive approach was used for their application to the surface horizon of a Cambisol. The geochemical code accurately reproduced the concentration of extracted P at the different soil pH values (R 2 = 0.9, RMSE = 0.03 mg kg -1 ). Model parameters were either directly found in the literature or estimated by fitting published experimental results in single mineral systems. The strong agreement between measurements and modelling results demonstrated that adsorption processes exerted a major control on the EAP of the soil over a large range of pH values. An influence of the precipitation of P-containing mineral is discounted based on thermodynamic calculations. Modelling results indicated that the variations in P-CaCl 2 with soil pH were controlled by the deprotonation/protonation of the surface hydroxyl groups, the distribution of P surface complexes, and the adsorption of Ca and Cl from the electrolyte background. Iron-oxides and gibbsite were found to be the major P-adsorbing soil constituents at acidic and alkaline pHs, whereas P was mainly adsorbed by clay minerals at intermediate pH values. This study demonstrates the efficacy of geochemical modelling to understand soil processes, and the applicability of mechanistic adsorption models to a 'real' soil, with its mineralogical complexity and the additional contribution of soil organic matter.

  14. Soil pH controls the environmental availability of phosphorus: Experimental and mechanistic modelling approaches

    Energy Technology Data Exchange (ETDEWEB)

    Devau, Nicolas [INRA, UMR 1222 Eco and Sols - Ecologie Fonctionnelle et Biogeochimie des Sols (INRA-IRD-SupAgro), Place Viala, F-34060 Montpellier (France); Cadre, Edith Le [Supagro, UMR 1222 Eco and Sols - Ecologie Fonctionnelle et Biogeochimie des Sols (INRA-IRD-SupAgro), Place Viala, F-34060 Montpellier (France); Hinsinger, Philippe; Jaillard, Benoit [INRA, UMR 1222 Eco and Sols - Ecologie Fonctionnelle et Biogeochimie des Sols (INRA-IRD-SupAgro), Place Viala, F-34060 Montpellier (France); Gerard, Frederic, E-mail: gerard@supagro.inra.fr [INRA, UMR 1222 Eco and Sols - Ecologie Fonctionnelle et Biogeochimie des Sols (INRA-IRD-SupAgro), Place Viala, F-34060 Montpellier (France)

    2009-11-15

    Inorganic P is the least mobile major nutrient in most soils and is frequently the prime limiting factor for plant growth in terrestrial ecosystems. In this study, the extraction of soil inorganic P with CaCl{sub 2} (P-CaCl{sub 2}) and geochemical modelling were combined in order to unravel the processes controlling the environmentally available P (EAP) of a soil over a range of pH values (pH {approx} 4-10). Mechanistic descriptions of the adsorption of cations and anions by the soil constituents were used (1-pK Triple Plane, ion-exchange and NICA-Donnan models). These models are implemented into the geochemical code Visual MINTEQ. An additive approach was used for their application to the surface horizon of a Cambisol. The geochemical code accurately reproduced the concentration of extracted P at the different soil pH values (R{sup 2} = 0.9, RMSE = 0.03 mg kg{sup -1}). Model parameters were either directly found in the literature or estimated by fitting published experimental results in single mineral systems. The strong agreement between measurements and modelling results demonstrated that adsorption processes exerted a major control on the EAP of the soil over a large range of pH values. An influence of the precipitation of P-containing mineral is discounted based on thermodynamic calculations. Modelling results indicated that the variations in P-CaCl{sub 2} with soil pH were controlled by the deprotonation/protonation of the surface hydroxyl groups, the distribution of P surface complexes, and the adsorption of Ca and Cl from the electrolyte background. Iron-oxides and gibbsite were found to be the major P-adsorbing soil constituents at acidic and alkaline pHs, whereas P was mainly adsorbed by clay minerals at intermediate pH values. This study demonstrates the efficacy of geochemical modelling to understand soil processes, and the applicability of mechanistic adsorption models to a 'real' soil, with its mineralogical complexity and the additional

  15. How to Build a Course in Mathematical-Biological Modeling: Content and Processes for Knowledge and Skill

    Science.gov (United States)

    Hoskinson, Anne-Marie

    2010-01-01

    Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity…

  16. On the mathematical modeling of aeolian saltation

    DEFF Research Database (Denmark)

    Jensen, Jens Ledet; Sørensen, Michael

    1983-01-01

    The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...... on aeolian saltation. This comparison points out the necessity of discriminating between pure and real saltation. -Authors...

  17. Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration.

    Science.gov (United States)

    Agur, Zvia; Elishmereni, Moran; Kheifetz, Yuri

    2014-01-01

    Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug-patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence-based tools for simulating pharmacokinetics, Bayesian-estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P-trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology. © 2014 Wiley Periodicals, Inc.

  18. Taking the mystery out of mathematical model applications to karst aquifers—A primer

    Science.gov (United States)

    Kuniansky, Eve L.

    2014-01-01

    Advances in mathematical model applications toward the understanding of the complex flow, characterization, and water-supply management issues for karst aquifers have occurred in recent years. Different types of mathematical models can be applied successfully if appropriate information is available and the problems are adequately identified. The mathematical approaches discussed in this paper are divided into three major categories: 1) distributed parameter models, 2) lumped parameter models, and 3) fitting models. The modeling approaches are described conceptually with examples (but without equations) to help non-mathematicians understand the applications.

  19. Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

    Science.gov (United States)

    Ganusov, Vitaly V

    2016-01-01

    While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

  20. Strong inference in mathematical modeling: a method for robust science in the 21st century

    Directory of Open Access Journals (Sweden)

    Vitaly V. Ganusov

    2016-07-01

    Full Text Available While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers [1], the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions and data. Following the principle of strong inference for experimental sciences proposed by Platt [2], I suggest ``strong inference in mathematical modeling'' as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are 1 to develop multiple alternative models for the phenomenon in question; 2 to compare the models with available experimental data and to determine which of the models are not consistent with the data; 3 to determine reasons why rejected models failed to explain the data, and 4 to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the 21st century.

  1. Mathematical models of human cerebellar development in the fetal period.

    Science.gov (United States)

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

    2018-04-01

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

  2. Radiation fields, dosimetry, biokinetics and biophysical models for cancer induction by ionising radiation 1996-1999. Biophysical models for the induction of cancer by radiation. Final report

    International Nuclear Information System (INIS)

    Paretzke, H.G.; Ballarini, F.; Brugmans, M.

    2000-01-01

    The overall project is organised into seven work packages. WP1 concentrates on the development of mechanistic, quantitative models for radiation oncogenesis using selected data sets from radiation epidemiology and from experimental animal studies. WP2 concentrates on the development of mechanistic, mathematical models for the induction of chromosome aberrations. WP3 develops mechanistic models for radiation mutagenesis, particularly using the HPRT-mutation as a paradigm. WP4 will develop mechanistic models for damage and repair of DNA, and compare these with experimentally derived data. WP5 concentrates on the improvement of our knowledge on the chemical reaction pathways of initial radiation chemical species in particular those that migrate to react with the DNA and on their simulation in track structure codes. WP6 models by track structure simulation codes the production of initial physical and chemical species, within DNA, water and other components of mammalian cells, in the tracks of charged particles following the physical processes of energy transfer, migration, absorption, and decay of excited states. WP7 concentrates on the determination of the start spectra of those tracks considered in WP6 for different impinging radiation fields and different irradiated biological objects. (orig.)

  3. A Mathematical Model of Cardiovascular Response to Dynamic Exercise

    National Research Council Canada - National Science Library

    Magosso, E

    2001-01-01

    A mathematical model of cardiovascular response to dynamic exercise is presented, The model includes the pulsating heart, the systemic and pulmonary, circulation, a functional description of muscle...

  4. Mechanistic Links Between PARP, NAD, and Brain Inflammation After TBI

    Science.gov (United States)

    2015-10-01

    1 AWARD NUMBER: W81XWH-13-2-0091 TITLE: Mechanistic Links Between PARP, NAD , and Brain Inflammation After TBI PRINCIPAL INVESTIGATOR...COVERED 25 Sep 2014 - 24 Sep 2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Mechanistic Links Between PARP, NAD , and Brain Inflammation After TBI 5b. GRANT...efficacy of veliparib and NAD as agents for suppressing inflammation and improving outcomes after traumatic brain injury. The animal models include

  5. Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

    Science.gov (United States)

    Ganusov, Vitaly V.

    2016-01-01

    While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

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

    Science.gov (United States)

    Nasser-Abu Alhija, Fadia; Amasha, Marcel

    2012-01-01

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

  7. Mathematical models in Slowpoke reactor internal irradiation site

    International Nuclear Information System (INIS)

    Raza, J.

    2007-01-01

    The main objective is to build representative mathematical models of neutron activation analysis in a Slowpoke internal irradiation site. Another significant objective is to correct various elements neutron activation analysis measured mass using these models. The neutron flux perturbation is responsible for the measured under-estimation of real masses. We supposed that neutron flux perturbation measurements taken during the Ecole Polytechnique de Montreal Slowpoke reactor first fuel loading were still valid after the second fuelling. .We also supposed that the thermal neutrons spatial and kinetic energies distributions as well as the absorption microscopic cross section dependence on the neutrons kinetic energies were important factors to satisfactorily represent neutron activation analysis results. In addition, we assumed that the neutron flux is isotropic in the laboratory system. We used experimental results from the Slowpoke reactor internal irradiation sites, in order to validate our mathematical models. Our models results are in close agreement with these experimental results..We established an accurate global mathematical correlation of the neutron flux perturbation in function of samples volumes and macroscopic neutron absorption cross sections. It is applicable to sample volumes ranging from 0,1 to 1,3 ml and macroscopic neutron absorption cross section up to 5 moles-b for seven (7) elements with atomic numbers (Z) ranging from 5 to 79. We first came up with a heuristic neutron transport mathematical semi-analytical model, in order to better understand neutrons behaviour in presence of one of several different nuclei samples volumes and mass. In order to well represent the neutron flux perturbation, we combined a neutron transport solution obtained from the spherical harmonics method of a finite cylinder and a mathematical expression combining two cylindrical harmonic functions..With the help of this model and the least squares method, we made extensive

  8. Mathematical models of bipolar disorder

    Science.gov (United States)

    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.

  9. А mathematical model study of suspended monorail

    OpenAIRE

    Viktor GUTAREVYCH

    2012-01-01

    The mathematical model of suspended monorail track with allowance for elastic strain which occurs during movement of the monorail carriage was developed. Standard forms for single span and double span of suspended monorail sections were established.

  10. Investigating and developing engineering students' mathematical modelling and problem-solving skills

    Science.gov (United States)

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

    2015-09-01

    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 problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.

  11. The Conceptualization of the Mathematical Modelling Process in Technology-Aided Environment

    Science.gov (United States)

    Hidiroglu, Çaglar Naci; Güzel, Esra Bukova

    2017-01-01

    The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…

  12. Mathematical modelling and numerical simulation of oil pollution problems

    CERN Document Server

    2015-01-01

    Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics,  together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems.   The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...

  13. A mechanistic modeling and data assimilation framework for Mojave Desert ecohydrology

    Science.gov (United States)

    Ng, Gene-Hua Crystal; Bedford, David R.; Miller, David M.

    2014-06-01

    This study demonstrates and addresses challenges in coupled ecohydrological modeling in deserts, which arise due to unique plant adaptations, marginal growing conditions, slow net primary production rates, and highly variable rainfall. We consider model uncertainty from both structural and parameter errors and present a mechanistic model for the shrub Larrea tridentata (creosote bush) under conditions found in the Mojave National Preserve in southeastern California (USA). Desert-specific plant and soil features are incorporated into the CLM-CN model by Oleson et al. (2010). We then develop a data assimilation framework using the ensemble Kalman filter (EnKF) to estimate model parameters based on soil moisture and leaf-area index observations. A new implementation procedure, the "multisite loop EnKF," tackles parameter estimation difficulties found to affect desert ecohydrological applications. Specifically, the procedure iterates through data from various observation sites to alleviate adverse filter impacts from non-Gaussianity in small desert vegetation state values. It also readjusts inconsistent parameters and states through a model spin-up step that accounts for longer dynamical time scales due to infrequent rainfall in deserts. Observation error variance inflation may also be needed to help prevent divergence of estimates from true values. Synthetic test results highlight the importance of adequate observations for reducing model uncertainty, which can be achieved through data quality or quantity.

  14. A mechanistic modeling and data assimilation framework for Mojave Desert ecohydrology

    Science.gov (United States)

    Ng, Gene-Hua Crystal.; Bedford, David; Miller, David

    2014-01-01

    This study demonstrates and addresses challenges in coupled ecohydrological modeling in deserts, which arise due to unique plant adaptations, marginal growing conditions, slow net primary production rates, and highly variable rainfall. We consider model uncertainty from both structural and parameter errors and present a mechanistic model for the shrub Larrea tridentata (creosote bush) under conditions found in the Mojave National Preserve in southeastern California (USA). Desert-specific plant and soil features are incorporated into the CLM-CN model by Oleson et al. (2010). We then develop a data assimilation framework using the ensemble Kalman filter (EnKF) to estimate model parameters based on soil moisture and leaf-area index observations. A new implementation procedure, the “multisite loop EnKF,” tackles parameter estimation difficulties found to affect desert ecohydrological applications. Specifically, the procedure iterates through data from various observation sites to alleviate adverse filter impacts from non-Gaussianity in small desert vegetation state values. It also readjusts inconsistent parameters and states through a model spin-up step that accounts for longer dynamical time scales due to infrequent rainfall in deserts. Observation error variance inflation may also be needed to help prevent divergence of estimates from true values. Synthetic test results highlight the importance of adequate observations for reducing model uncertainty, which can be achieved through data quality or quantity.

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

    Science.gov (United States)

    Sgouralis, Ioannis; Layton, Anita T

    2015-06-01

    In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.

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

    CERN Document Server

    Papapantoleon, Antonis

    2016-01-01

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

  17. Mathematical modelling of zirconium salicylate solvent extraction process

    International Nuclear Information System (INIS)

    Smirnova, N.S.; Evseev, A.M.; Fadeeva, V.I.; Kochetkova, S.K.

    1979-01-01

    Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built

  18. Mathematical modelling of zirconium salicylate solvent extraction process

    Energy Technology Data Exchange (ETDEWEB)

    Smirnova, N S; Evseev, A M; Fadeeva, V I; Kochetkova, S K [Moskovskij Gosudarstvennyj Univ. (USSR)

    1979-11-01

    Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built.

  19. Modeling life the mathematics of biological systems

    CERN Document Server

    Garfinkel, Alan; Guo, Yina

    2017-01-01

    From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...

  20. Mathematical Modeling in the People's Republic of China--Indicators of Participation and Performance on COMAP's Modeling Contest

    Science.gov (United States)

    Tian, Xiaoxi

    2014-01-01

    In recent years, Mainland Chinese teams have been the dominant participants in the two COMAP-sponsored mathematical modeling competitions: the Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM). This study examines five factors that lead to the Chinese teams' dramatic increase in participation rate and…

  1. A rigorous mechanistic model for predicting gas hydrate formation kinetics: The case of CO2 recovery and sequestration

    International Nuclear Information System (INIS)

    ZareNezhad, Bahman; Mottahedin, Mona

    2012-01-01

    Highlights: ► A mechanistic model for predicting gas hydrate formation kinetics is presented. ► A secondary nucleation rate model is proposed for the first time. ► Crystal–crystal collisions and crystal–impeller collisions are distinguished. ► Simultaneous determination of nucleation and growth kinetics are established. ► Important for design of gas hydrate based energy storage and CO 2 recovery systems. - Abstract: A rigorous mechanistic model for predicting gas hydrate formation crystallization kinetics is presented and the special case of CO 2 gas hydrate formation regarding CO 2 recovery and sequestration processes has been investigated by using the proposed model. A physical model for prediction of secondary nucleation rate is proposed for the first time and the formation rates of secondary nuclei by crystal–crystal collisions and crystal–impeller collisions are formulated. The objective functions for simultaneous determination of nucleation and growth kinetics are presented and a theoretical framework for predicting the dynamic behavior of gas hydrate formation is presented. Predicted time variations of CO 2 content, total number and surface area of produced hydrate crystals are in good agreement with the available experimental data. The proposed approach can have considerable application for design of gas hydrate converters regarding energy storage and CO 2 recovery processes.

  2. Mathematical models for correction of images, obtained at radioisotope scan

    International Nuclear Information System (INIS)

    Glaz, A.; Lubans, A.

    2002-01-01

    The images, which obtained at radioisotope scintigraphy, contain distortions. Distortions appear as a result of absorption of radiation by patient's body's tissues. Two mathematical models for reducing of such distortions are proposed. Image obtained by only one gamma camera is used in the first mathematical model. Unfortunately, this model allows processing of the images only in case, when it can be assumed, that the investigated organ has a symmetric form. The images obtained by two gamma cameras are used in the second model. It gives possibility to assume that the investigated organ has non-symmetric form and to acquire more precise results. (authors)

  3. A Mathematical Model of Marine Diesel Engine Speed Control System

    Science.gov (United States)

    Sinha, Rajendra Prasad; Balaji, Rajoo

    2018-02-01

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

  4. Mathematical modelling in engineering: A proposal to introduce linear algebra concepts

    Directory of Open Access Journals (Sweden)

    Andrea Dorila Cárcamo

    2016-03-01

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

  5. Mathematical Models for Immunology: Current State of the Art and Future Research Directions.

    Science.gov (United States)

    Eftimie, Raluca; Gillard, Joseph J; Cantrell, Doreen A

    2016-10-01

    The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

  6. Structured Mathematical Modeling of Industrial Boiler

    OpenAIRE

    Aziz, Abdullah Nur; Nazaruddin, Yul Yunazwin; Siregar, Parsaulian; Bindar, Yazid

    2014-01-01

    As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. T...

  7. Predicting the impact of long-term temperature changes on the epidemiology and control of schistosomiasis: a mechanistic model.

    Directory of Open Access Journals (Sweden)

    Tara D Mangal

    2008-01-01

    Full Text Available Many parasites of medical and veterinary importance are transmitted by cold-blooded intermediate hosts or vectors, the abundance of which will vary with ambient temperatures, potentially altering disease prevalence. In particular, if global climate change will increase mean ambient temperature in a region endemic with a human pathogen then it is possible that the incidence of disease will similarly increase. Here we examine this possibility by using a mathematical model to explore the effects of increasing long-term mean ambient temperature on the prevalence and abundance of the parasite Schistosoma mansoni, the causative agent of schistosomiasis in humans.The model showed that the impact of temperature on disease prevalence and abundance is not straightforward; the mean infection burden in humans increases up to 30 degrees C, but then crashes at 35 degrees C, primarily due to increased mortalities of the snail intermediate host. In addition, increased temperatures changed the dynamics of disease from stable, endemic infection to unstable, epidemic cycles at 35 degrees C. However, the prevalence of infection was largely unchanged by increasing temperatures. Temperature increases also affected the response of the model to changes in each parameter, indicating certain control strategies may become less effective with local temperature changes. At lower temperatures, the most effective single control strategy is to target the adult parasites through chemotherapy. However, as temperatures increase, targeting the snail intermediate hosts, for example through molluscicide use, becomes more effective.These results show that S. mansoni will not respond to increased temperatures in a linear fashion, and the optimal control strategy is likely to change as temperatures change. It is only through a mechanistic approach, incorporating the combined effects of temperature on all stages of the life-cycle, that we can begin to predict the consequences of climate

  8. From inverse problems in mathematical physiology to quantitative differential diagnoses.

    Directory of Open Access Journals (Sweden)

    Sven Zenker

    2007-11-01

    Full Text Available The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting, using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge. We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of

  9. From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses

    Science.gov (United States)

    Zenker, Sven; Rubin, Jonathan; Clermont, Gilles

    2007-01-01

    The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses

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

    Science.gov (United States)

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

    2014-12-11

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

  11. А mathematical model study of suspended monorail

    Directory of Open Access Journals (Sweden)

    Viktor GUTAREVYCH

    2012-01-01

    Full Text Available The mathematical model of suspended monorail track with allowance for elastic strain which occurs during movement of the monorail carriage was developed. Standard forms for single span and double span of suspended monorail sections were established.

  12. A mechanistic compartmental model for total antibody uptake in tumors.

    Science.gov (United States)

    Thurber, Greg M; Dane Wittrup, K

    2012-12-07

    Antibodies are under development to treat a variety of cancers, such as lymphomas, colon, and breast cancer. A major limitation to greater efficacy for this class of drugs is poor distribution in vivo. Localization of antibodies occurs slowly, often in insufficient therapeutic amounts, and distributes heterogeneously throughout the tumor. While the microdistribution around individual vessels is important for many therapies, the total amount of antibody localized in the tumor is paramount for many applications such as imaging, determining the therapeutic index with antibody drug conjugates, and dosing in radioimmunotherapy. With imaging and pretargeted therapeutic strategies, the time course of uptake is critical in determining when to take an image or deliver a secondary reagent. We present here a simple mechanistic model of antibody uptake and retention that captures the major rates that determine the time course of antibody concentration within a tumor including dose, affinity, plasma clearance, target expression, internalization, permeability, and vascularization. Since many of the parameters are known or can be estimated in vitro, this model can approximate the time course of antibody concentration in tumors to aid in experimental design, data interpretation, and strategies to improve localization. Copyright © 2012 Elsevier Ltd. All rights reserved.

  13. Development of syntax of intuition-based learning model in solving mathematics problems

    Science.gov (United States)

    Yeni Heryaningsih, Nok; Khusna, Hikmatul

    2018-01-01

    The aim of the research was to produce syntax of Intuition Based Learning (IBL) model in solving mathematics problem for improving mathematics students’ achievement that valid, practical and effective. The subject of the research were 2 classes in grade XI students of SMAN 2 Sragen, Central Java. The type of the research was a Research and Development (R&D). Development process adopted Plomp and Borg & Gall development model, they were preliminary investigation step, design step, realization step, evaluation and revision step. Development steps were as follow: (1) Collected the information and studied of theories in Preliminary Investigation step, studied about intuition, learning model development, students condition, and topic analysis, (2) Designed syntax that could bring up intuition in solving mathematics problem and then designed research instruments. They were several phases that could bring up intuition, Preparation phase, Incubation phase, Illumination phase and Verification phase, (3) Realized syntax of Intuition Based Learning model that has been designed to be the first draft, (4) Did validation of the first draft to the validator, (5) Tested the syntax of Intuition Based Learning model in the classrooms to know the effectiveness of the syntax, (6) Conducted Focus Group Discussion (FGD) to evaluate the result of syntax model testing in the classrooms, and then did the revision on syntax IBL model. The results of the research were produced syntax of IBL model in solving mathematics problems that valid, practical and effective. The syntax of IBL model in the classroom were, (1) Opening with apperception, motivations and build students’ positive perceptions, (2) Teacher explains the material generally, (3) Group discussion about the material, (4) Teacher gives students mathematics problems, (5) Doing exercises individually to solve mathematics problems with steps that could bring up students’ intuition: Preparations, Incubation, Illumination, and

  14. Developing Predictive Approaches to Characterize Adaptive Responses of the Reproductive Endocrine Axis to Aromatase Inhibition II: Computational Modeling

    Science.gov (United States)

    ABSTRACT Exposure to endocrine disrupting chemicals can affect reproduction and development in both humans and wildlife. We developed a mechanistic mathematical model of the hypothalamic­ pituitary-gonadal (HPG) axis in female fathead minnows to predic...

  15. Mathematical Model of Age Aggression

    OpenAIRE

    Golovinski, P. A.

    2013-01-01

    We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...

  16. Mathematical model of the reactor coolant pump

    International Nuclear Information System (INIS)

    Kozuh, M.

    1989-01-01

    The mathematical model of reactor coolant pump is described in this paper. It is based on correlations for centrifugal reactor coolant pumps. This code is one of the elements needed for the simulation of the whole NPP primary system. In subroutine developed according to this model we tried in every possible detail to incorporate plant specific data for Krsko NPP. (author)

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

    NARCIS (Netherlands)

    Perrenet, J.; Adan, I.

    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

  18. The academic merits of modelling in higher mathematics education : a case study

    NARCIS (Netherlands)

    Perrenet, J.C.; Adan, I.J.B.F.

    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

  19. A theory of drug tolerance and dependence II: the mathematical model.

    Science.gov (United States)

    Peper, Abraham

    2004-08-21

    The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.

  20. 78 FR 20148 - Reporting Procedure for Mathematical Models Selected To Predict Heated Effluent Dispersion in...

    Science.gov (United States)

    2013-04-03

    ... procedure acceptable to the NRC staff for providing summary details of mathematical modeling methods used in... NUCLEAR REGULATORY COMMISSION [NRC-2013-0062] Reporting Procedure for Mathematical Models Selected... Regulatory Guide (RG) 4.4, ``Reporting Procedure for Mathematical Models Selected to Predict Heated Effluent...