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Sample records for based mathematical model

  1. Mathematical modeling of acid-base physiology

    PubMed Central

    Occhipinti, Rossana; Boron, Walter F.

    2015-01-01

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

  2. An agent-based mathematical model about carp aggregation

    NASA Astrophysics Data System (ADS)

    Liang, Yu; Wu, Chao

    2005-05-01

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

  3. Validation and upgrading of physically based mathematical models

    NASA Technical Reports Server (NTRS)

    Duval, Ronald

    1992-01-01

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

  4. PREFACE: Physics-Based Mathematical Models for Nanotechnology

    NASA Astrophysics Data System (ADS)

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

    2008-03-01

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

  5. Retrospective Study on Mathematical Modeling Based on Computer Graphic Processing

    NASA Astrophysics Data System (ADS)

    Zhang, Kai Li

    Graphics & image making is an important field in computer application, in which visualization software has been widely used with the characteristics of convenience and quick. However, it was thought by modeling designers that the software had been limited in it's function and flexibility because mathematics modeling platform was not built. A non-visualization graphics software appearing at this moment enabled the graphics & image design has a very good mathematics modeling platform. In the paper, a polished pyramid is established by multivariate spline function algorithm, and validate the non-visualization software is good in mathematical modeling.

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

    PubMed

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

    2016-08-01

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

  7. Mathematical Modeling and Pure Mathematics

    ERIC Educational Resources Information Center

    Usiskin, Zalman

    2015-01-01

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

  8. Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model

    PubMed Central

    Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V.

    2016-01-01

    Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods. PMID:27387139

  9. Mathematical Modelling Approach in Mathematics Education

    ERIC Educational Resources Information Center

    Arseven, Ayla

    2015-01-01

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

  10. Teaching Mathematical Modeling in Mathematics Education

    ERIC Educational Resources Information Center

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

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

  11. Summer Teacher Enhancement Institute for Science, Mathematics, and Technology Using the Problem-Based Learning Model

    NASA Technical Reports Server (NTRS)

    Petersen, Richard H.

    1997-01-01

    The objectives of the Institute were: (a) increase participants' content knowledge about aeronautics, science, mathematics, and technology, (b) model and promote the use of scientific inquiry through problem-based learning, (c) investigate the use of instructional technologies and their applications to curricula, and (d) encourage the dissemination of TEI experiences to colleagues, students, and parents.

  12. Frequencies as proportions: Using a teaching model based on Pirie and Kieren's model of mathematical understanding

    NASA Astrophysics Data System (ADS)

    Wright, Vince

    2014-03-01

    Pirie and Kieren (1989 For the learning of mathematics, 9(3)7-11, 1992 Journal of Mathematical Behavior, 11, 243-257, 1994a Educational Studies in Mathematics, 26, 61-86, 1994b For the Learning of Mathematics, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which learners develop their mathematical understanding. The model was adapted to create the teaching model used in the New Zealand Numeracy Development Projects (Ministry of Education, 2007). A case study of a 3-week sequence of instruction with a group of eight 12- and 13-year-old students provided the data. The teacher/researcher used folding back to materials and images and progressing from materials to imaging to number properties to assist students to develop their understanding of frequencies as proportions. The data show that successful implementation of the model is dependent on the teacher noticing and responding to the layers of understanding demonstrated by the students and the careful selection of materials, problems and situations. It supports the use of the model as a useful part of teachers' instructional strategies and the importance of pedagogical content knowledge to the quality of the way the model is used.

  13. Development of a Diffusion-Based Mathematical Model for Predicting Chemotherapy Effects

    PubMed Central

    Wang, Zhihui; Kerketta, Romica; Chuang, Yao-Li; Cristini, Vittorio

    2016-01-01

    Mathematical modeling of drug transport can complement current experimental and clinical investigations to understand drug resistance mechanisms, which eventually will help to develop patient-specific chemotherapy treatments. In this paper, we present a general time- and space-dependent mathematical model based on diffusion theory for predicting chemotherapy outcome. This model has two important parameters: the blood volume fraction and radius of blood vessels divided by drug diffusion penetration length. Model analysis finds that a larger ratio of the radius of blood vessel to diffusion penetration length resulted in to a larger fraction of tumor killed, thereby leading to a better treatment outcome. Clinical translation of the model can help quantify and predict the optimal dosage size and frequency of chemotherapy for individual patients. PMID:25570493

  14. Mathematical modeling of cross-linking monomer elution from resin-based dental composites.

    PubMed

    Manojlovic, Dragica; Radisic, Marina; Lausevic, Mila; Zivkovic, Slavoljub; Miletic, Vesna

    2013-01-01

    Elution of potentially toxic substances, including monomers, from resin-based dental composites may affect the biocompatibility of these materials in clinical conditions. In addition to the amounts of eluted monomers, mathematical modeling of elution kinetics reveals composite restorations as potential chronic sources of leachable monomers. The aim of this work was to experimentally quantify elution of main cross-linking monomers from four commercial composites and offer a mathematical model of elution kinetics. Composite samples (n = 7 per group) of Filtek Supreme XT (3M ESPE), Tetric EvoCeram (Ivoclar Vivadent), Admira (Voco), and Filtek Z250 (3M ESPE) were prepared in 2-mm thick Teflon moulds and cured with halogen or light-emitting diode light. Monomer elution in ethanol and water was analyzed using high-performance liquid chromatography up to 28 days postimmersion. The mathematical model was expressed as a sum of two exponential regression functions representing the first-order kinetics law. Elution kinetics in all cases followed the same mathematical model though differences in rate constants as well as the extent of monomer elution were material-, LCU-, medium-dependent. The proposed mechanisms of elution indicate fast elution from surface and subsurface layers and up to 100 times slower monomer extraction from the bulk polymer. PMID:22997145

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

    ERIC Educational Resources Information Center

    Yilmaz, Suha; Tekin-Dede, Ayse

    2016-01-01

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

  16. Mathematical model of a galvanometer-based scanner: simulations and experiments

    NASA Astrophysics Data System (ADS)

    Mnerie, Corina; Preitl, Stefan; Duma, Virgil-Florin

    2013-05-01

    The paper presents an insight into our current researches on galvanometer-based scanners (GSs). A brief overview is first performed on the state-of-the-art, as well as on some of our contributions to optimize the scanning and the command functions of this most used scanning device. Considerations on the use of GSs in high-end biomedical imaging applications such as Optical Coherence Tomography (OCT) are made, with a focus towards obtaining the best possible duty cycles and artifact-free OCT images when using GSs for lateral scanning, as studied in our previous works. The scope of our present study is to obtain the mathematical model of a GS system (motor and controller included) in order to optimize the command functions of the device and to support the development of some more advanced control structures. The study is centered on the mathematical and experimental modeling of GSs. Thus, the results of an experimental identification made on a classical multi-parameter mathematical model proposed for such a system are presented. The experiments are carried out in different operating regimes, and the specific characteristic parameters of the GS are determined. Using these parameters obtained experimentally, we carry out simulations in Mathlab Simulink to validate the theoretical model. With the indentified model, an extended control solution is proposed. We point out the match between the theory and the results of the simulations and of the testing for different types of input signals, such as triangular, sinusoidal, and sawtooth with different duty cycles.

  17. Phase errors elimination in compact digital holoscope (CDH) based on a reasonable mathematical model

    NASA Astrophysics Data System (ADS)

    Wen, Yongfu; Qu, Weijuan; Cheng, Cheeyuen; Wang, Zhaomin; Asundi, Anand

    2015-03-01

    In the compact digital holoscope (CDH) measurement process, theoretically, we need to ensure the distances between the reference wave and object wave to the hologram plane exactly match. However, it is not easy to realize in practice due to the human factors. This can lead to a phase error in the reconstruction result. In this paper, the strict theoretical analysis of the wavefront interference is performed to demonstrate the mathematical model of the phase error and then a phase errors elimination method is proposed based on the advanced mathematical model, which has a more explicit physical meaning. Experiments are carried out to verify the performance of the presented method and the results indicate that it is effective and allows the operator can make operation more flexible.

  18. Mathematical model accurately predicts protein release from an affinity-based delivery system.

    PubMed

    Vulic, Katarina; Pakulska, Malgosia M; Sonthalia, Rohit; Ramachandran, Arun; Shoichet, Molly S

    2015-01-10

    Affinity-based controlled release modulates the delivery of protein or small molecule therapeutics through transient dissociation/association. To understand which parameters can be used to tune release, we used a mathematical model based on simple binding kinetics. A comprehensive asymptotic analysis revealed three characteristic regimes for therapeutic release from affinity-based systems. These regimes can be controlled by diffusion or unbinding kinetics, and can exhibit release over either a single stage or two stages. This analysis fundamentally changes the way we think of controlling release from affinity-based systems and thereby explains some of the discrepancies in the literature on which parameters influence affinity-based release. The rate of protein release from affinity-based systems is determined by the balance of diffusion of the therapeutic agent through the hydrogel and the dissociation kinetics of the affinity pair. Equations for tuning protein release rate by altering the strength (KD) of the affinity interaction, the concentration of binding ligand in the system, the rate of dissociation (koff) of the complex, and the hydrogel size and geometry, are provided. We validated our model by collapsing the model simulations and the experimental data from a recently described affinity release system, to a single master curve. Importantly, this mathematical analysis can be applied to any single species affinity-based system to determine the parameters required for a desired release profile. PMID:25449806

  19. A MULTISTAGE BIOLOGICALLY BASED MATHEMATICAL MODEL FOR MOUSE LIVER TUMORS INDUCED BY DICHLOROACETIC ACID (DCA) - EXPLORATION OF THE MODEL

    EPA Science Inventory

    A biologically based mathematical model for the induction of liver tumors in mice by dichloroacetic acid (DCA) has been developed from histopathologic analysis of the livers of exposed mice. This analysis suggests that following chronic exposure to DCA, carcinomas can arise dire...

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

    ERIC Educational Resources Information Center

    Wright, Vince

    2014-01-01

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

  1. Mathematical Modeling of Biosensors Based on an Array of Enzyme Microreactors

    PubMed Central

    Baronas, Romas; Ivanauskas, Feliksas; Kulys, Juozas

    2006-01-01

    This paper presents a two-dimensional-in-space mathematical model of biosensors based on an array of enzyme microreactors immobilised on a single electrode. The modeling system acts under amperometric conditions. The microreactors were modeled by particles and by strips. The model is based on the diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of the enzymatic reaction. The model involves three regions: an array of enzyme microreactors where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region, where the analyte concentration is maintained constant. Using computer simulation, the influence of the geometry of the microreactors and of the diffusion region on the biosensor response was investigated. The digital simulation was carried out using the finite difference technique.

  2. Quasi-Three-Dimensional Mathematical Modeling of Morphological Processes Based on Equilibrium Sediment Transport

    NASA Astrophysics Data System (ADS)

    Charafi, My. M.; Sadok, A.; Kamal, A.; Menai, A.

    A quasi-three-dimensional mathematical model has been developed to study the morphological processes based on equilibrium sediment transport method. The flow velocities are computed by a two-dimensional horizontal depth-averaged flow model (H2D) in combination with logarithmic velocity profiles. The transport of sediment particles by a flow water has been considered in the form of bed load and suspended load. The bed load transport rate is defined as the transport of particles by rolling and saltating along the bed surface and is given by the Van Rijn relationship (1987). The equilibrium suspended load transport is described in terms of an equilibrium sediment concentration profile (ce) and a logarithmic velocity (u). Based on the equilibrium transport, the bed change rate is given by integration of the sediment mass-balance equation. The model results have been compared with a Van Rijn results (equilibrium approach) and good agreement has been found.

  3. Differential properties of Van der Pol — Duffing mathematical model of cerebrovascular haemodynamics based on clinical measurements

    NASA Astrophysics Data System (ADS)

    Parshin, D. V.; Ufimtseva, I. V.; Cherevko, A. A.; Khe, A. K.; Orlov, K. Yu; Krivoshapkin, A. L.; Chupakhin, A. P.

    2016-06-01

    The present paper discusses the method of identification (diseased/healthy) human cerebral vessels by using of mathematical model. Human cerebral circulation as a single tuned circuit, which consists of blood flow, elastic vessels and elastic brain gel tissue is under consideration. Non linear Van der Pol-Duffing equation is assumed as mathematical model of cerebrovascular circulation. Hypothesis of vascular pathology existence in some position of blood vessel, based on mathematical model properties for this position is formulated. Good reliability of hypothesis is proved statistically for 7 patients with arterial aneurysms.

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

    ERIC Educational Resources Information Center

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

    1979-01-01

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

  5. Mathematical model for adaptive evolution of populations based on a complex domain

    PubMed Central

    Ibrahim, Rabha W.; Ahmad, M.Z.; Al-Janaby, Hiba F.

    2015-01-01

    A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function. PMID:26858564

  6. A biophysically based mathematical model for the catalytic mechanism of glutathione reductase.

    PubMed

    Pannala, Venkat R; Bazil, Jason N; Camara, Amadou K S; Dash, Ranjan K

    2013-12-01

    Glutathione reductase (GR) catalyzes the reduction of oxidized glutathione (GSSG) to reduced glutathione (GSH) using NADPH as the reducing cofactor, and thereby maintains a constant GSH level in the system. GSH scavenges superoxide (O2(*-)) and hydroxyl radicals (OH) nonenzymatically or by serving as an electron donor to several enzymes involved in reactive oxygen species (ROS) detoxification. In either case, GSH oxidizes to GSSG and is subsequently regenerated by the catalytic action of GR. Although the GR kinetic mechanism has been extensively studied under various experimental conditions with variable substrates and products, the catalytic mechanism has not been studied in terms of a mechanistic model that accounts for the effects of the substrates and products on the reaction kinetics. The aim of this study is therefore to develop a comprehensive mathematical model for the catalytic mechanism of GR. We use available experimental data on GR kinetics from various species/sources to develop the mathematical model and estimate the associated model parameters. The model simulations are consistent with the experimental observation that GR operates via both ping-pong and sequential branching mechanisms based on relevant concentrations of its reaction substrate GSSG. Furthermore, we show the observed pH-dependent substrate inhibition of GR activity by GSSG and bimodal behavior of GR activity with pH. The model presents a unique opportunity to understand the effects of products on the kinetics of GR. The model simulations show that under physiological conditions, where both substrates and products are present, the flux distribution depends on the concentrations of both GSSG and NADP(+), with ping-pong flux operating at low levels and sequential flux dominating at higher levels. The kinetic model of GR may serve as a key module for the development of integrated models for ROS-scavenging systems to understand protection of cells under normal and oxidative stress

  7. Empirical and physics based mathematical models of uranium hydride decomposition kinetics with quantified uncertainties.

    SciTech Connect

    Salloum, Maher N.; Gharagozloo, Patricia E.

    2013-10-01

    Metal particle beds have recently become a major technique for hydrogen storage. In order to extract hydrogen from such beds, it is crucial to understand the decomposition kinetics of the metal hydride. We are interested in obtaining a a better understanding of the uranium hydride (UH3) decomposition kinetics. We first developed an empirical model by fitting data compiled from different experimental studies in the literature and quantified the uncertainty resulting from the scattered data. We found that the decomposition time range predicted by the obtained kinetics was in a good agreement with published experimental results. Secondly, we developed a physics based mathematical model to simulate the rate of hydrogen diffusion in a hydride particle during the decomposition. We used this model to simulate the decomposition of the particles for temperatures ranging from 300K to 1000K while propagating parametric uncertainty and evaluated the kinetics from the results. We compared the kinetics parameters derived from the empirical and physics based models and found that the uncertainty in the kinetics predicted by the physics based model covers the scattered experimental data. Finally, we used the physics-based kinetics parameters to simulate the effects of boundary resistances and powder morphological changes during decomposition in a continuum level model. We found that the species change within the bed occurring during the decomposition accelerates the hydrogen flow by increasing the bed permeability, while the pressure buildup and the thermal barrier forming at the wall significantly impede the hydrogen extraction.

  8. Physically based mathematical models in soil science: History, current state, problems, and outlook (Analytical Review)

    NASA Astrophysics Data System (ADS)

    Shein, E. V.

    2015-07-01

    The formation, development, and some problems of the current physically based models of water and solute transfer are considered in this review. These models appeared about a half century ago. They were based on the basic laws of soil physics and other branches of soil science (laws of balance, transfer, diffusion, hydrodynamic dispersion, etc.) described by the corresponding equations and programs and supported by the experimental data in the form of physically based parameters. At present, one of the main problems in the development, adaptation, and application of these models is that the current and future mathematical models should rest upon the experimental support with a clear physical basis characterizing the nature of the phenomenon described. This experimental support enables creating research models, drawing conceptual conclusions, and, hence, understanding, analyzing, and managing soil processes. This is apparently possible only if the set of methods for the experimental support of models is substantiated, preferably in direct physical experiments and under field conditions close to the future model prognoses.

  9. Mathematical Modeling: A Structured Process

    ERIC Educational Resources Information Center

    Anhalt, Cynthia Oropesa; Cortez, Ricardo

    2015-01-01

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

  10. Mathematical models of hysteresis

    SciTech Connect

    1998-08-01

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

  11. Coupled inductors-based chaotic Colpitts oscillators: Mathematical modeling and synchronization issues

    NASA Astrophysics Data System (ADS)

    Kamdoum Tamba, V.; Fotsin, H. B.; Kengne, J.; Kapche Tagne, F.; Talla, P. K.

    2015-07-01

    This paper deals with the mathematical modelling and synchronization of a new controlled Colpitts oscillator. The new electronic oscillator is constructed by considering standard/classical Colpitts oscillator with two further elements (coupled inductors and variable resistor). An accurate mathematical model is provided. The dynamics of the new controlled Colpitts oscillator is investigated theoretically and experimentally by examining dissipativity, equilibrium point, stability, bifurcation and Lyapunov exponent. It is found that the oscillator moves from the limit cycle motion to chaos via the usual paths of period-doubling, intermittency and interior crisis routes as the control resistor R L is monitored. The electronic circuit of the oscillator is implemented, and a very good qualitative agreement is obtained between the theoretical and experimental results. Furthermore, the problem of synchronization is investigated, in order to promote chaos-based synchronization designs of this type of oscillators. Firstly, we design a coupling function for unidirectional coupling in identical and mismatched controlled Colpitts oscillators to realize a modified function projective synchronization through the open-plus-closed-loop (OPCL) method. Secondly, two different coupling configurations, namely, coupled collector nodes (C-C) and coupled emitter nodes (E-E) of controlled Colpitts oscillators, are studied. Numerical simulations and experimental results are performed to show the effectiveness and robustness of the proposed control schemes.

  12. Design of greenbelt for an industrial complex based on mathematical modelling.

    PubMed

    Khan, F I; Abbasi, S A

    2002-07-01

    Greenbelt is a strip of vegetation for which species of trees and shrubs are scientifically chosen and planted to serve a designated purpose such as control of wind erosion, of dust, of noise etc. In the context of air pollution attenuation, greenbelts must be developed around a source of air pollutant in a manner so as to effectively reduce the pollution caused by that source. Design of effective greenbelts involves consideration of meteorological, physico-chemical, biological, and horticultural aspects relevant to pollutant source and the area where greenbelt has to be established. These authors have recently developed mathematical models for effective design of greenbelts. This paper presents an overview of the methodology based on the models, and describes a case study in which the methodology has been applied to design a greenbelt for a real-life situation. PMID:12164640

  13. [Mathematical models of hysteresis

    SciTech Connect

    Mayergoyz, I.D.

    1991-01-01

    The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories''. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.

  14. Authenticity of Mathematical Modeling

    ERIC Educational Resources Information Center

    Tran, Dung; Dougherty, Barbara J.

    2014-01-01

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

  15. Analysis of laser remote fusion cutting based on a mathematical model

    SciTech Connect

    Matti, R. S.; Ilar, T.; Kaplan, A. F. H.

    2013-12-21

    Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, laser remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.

  16. Whole body acid-base and fluid-electrolyte balance: a mathematical model.

    PubMed

    Wolf, Matthew B

    2013-10-15

    A cellular compartment was added to our previous mathematical model of steady-state acid-base and fluid-electrolyte chemistry to gain further understanding and aid diagnosis of complex disorders involving cellular involvement in critically ill patients. An important hypothesis to be validated was that the thermodynamic, standard free-energy of cellular H(+) and Na(+) pumps remained constant under all conditions. In addition, a hydrostatic-osmotic pressure balance was assumed to describe fluid exchange between plasma and interstitial fluid, including incorporation of compliance curves of vascular and interstitial spaces. The description of the cellular compartment was validated by close comparison of measured and model-predicted cellular pH and electrolyte changes in vitro and in vivo. The new description of plasma-interstitial fluid exchange was validated using measured changes in fluid volumes after isoosmotic and hyperosmotic fluid infusions of NaCl and NaHCO3. The validated model was used to explain the role of cells in the mechanism of saline or dilutional acidosis and acid-base effects of acidic or basic fluid infusions and the acid-base disorder due to potassium depletion. A module was created that would allow users, who do not possess the software, to determine, for free, the results of fluid infusions and urinary losses of water and solutes to the whole body. PMID:23884137

  17. Validation of 2DH hydrodynamic and morphological mathematical models. A methodology based on SAR imaging

    NASA Astrophysics Data System (ADS)

    Canelas, Ricardo; Heleno, Sandra; Pestana, Rita; Ferreira, Rui M. L.

    2014-05-01

    The objective of the present work is to devise a methodology to validate 2DH shallow-water models suitable to simulate flow hydrodynamics and channel morphology. For this purpose, a 2DH mathematical model, assembled at CEHIDRO, IST, is employed to model Tagus river floods over a 70 km reach and Synthetic Aperture Radar (SAR) images are collected to retrieve planar inundation extents. The model is suited for highly unsteady discontinuous flows over complex, time-evolving geometries, employing a finite-volume discretization scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver. Novel closure terms for the non-equilibrium sediment transport model are included. New boundary conditions are employed, based on the Riemann variables associated the outgoing characteristic fields, coping with the provided hydrographs in a mathematically coherent manner. A high resolution Digital Elevation Model (DEM) is used and levee structures are considered as fully erodible elements. Spatially heterogeneous roughness characteristics are derived from land-use databases such as CORINE LandCover 2006. SAR satellite imagery of the floods is available and is used to validate the simulation results, with particular emphasis on the 2000/2001 flood. The delimited areas from the satellite and simulations are superimposed. The quality of the adjustment depends on the calibration of roughness coefficients and the spatial discretization of with small structures, with lengths at the order of the spatial discretization. Flow depths and registered discharges are recovered from the simulation and compared with data from a measuring station in the domain, with the comparison revealing remarkably high accuracy, both in terms of amplitudes and phase. Further inclusion of topographical detail should improve the comparison of flood extents regarding satellite data. The validated model was then employed to simulate 100-year floods in the same reach. The

  18. Problem-Based Learning--Buginese Cultural Knowledge Model--Case Study: Teaching Mathematics at Junior High School

    ERIC Educational Resources Information Center

    Cheriani, Cheriani; Mahmud, Alimuddin; Tahmir, Suradi; Manda, Darman; Dirawan, Gufran Darma

    2015-01-01

    This study aims to determine the differences in learning output by using Problem Based Model combines with the "Buginese" Local Cultural Knowledge (PBL-Culture). It is also explores the students activities in learning mathematics subject by using PBL-Culture Models. This research is using Mixed Methods approach that combined quantitative…

  19. Identifying potential misfit items in cognitive process of learning engineering mathematics based on Rasch model

    NASA Astrophysics Data System (ADS)

    Ataei, Sh; Mahmud, Z.; Khalid, M. N.

    2014-04-01

    The students learning outcomes clarify what students should know and be able to demonstrate after completing their course. So, one of the issues on the process of teaching and learning is how to assess students' learning. This paper describes an application of the dichotomous Rasch measurement model in measuring the cognitive process of engineering students' learning of mathematics. This study provides insights into the perspective of 54 engineering students' cognitive ability in learning Calculus III based on Bloom's Taxonomy on 31 items. The results denote that some of the examination questions are either too difficult or too easy for the majority of the students. This analysis yields FIT statistics which are able to identify if there is data departure from the Rasch theoretical model. The study has identified some potential misfit items based on the measurement of ZSTD where the removal misfit item was accomplished based on the MNSQ outfit of above 1.3 or less than 0.7 logit. Therefore, it is recommended that these items be reviewed or revised to better match the range of students' ability in the respective course.

  20. Mathematical Modeling: Convoying Merchant Ships

    ERIC Educational Resources Information Center

    Mathews, Susann M.

    2004-01-01

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

  1. A Primer for Mathematical Modeling

    ERIC Educational Resources Information Center

    Sole, Marla

    2013-01-01

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

  2. Mathematical modeling of high-rate Anammox UASB reactor based on granular packing patterns.

    PubMed

    Tang, Chong-Jian; He, Rui; Zheng, Ping; Chai, Li-Yuan; Min, Xiao-Bo

    2013-04-15

    A novel mathematical model was developed to estimate the volumetric nitrogen conversion rates of a high-rate Anammox UASB reactor based on the packing patterns of granular sludge. A series of relationships among granular packing density, sludge concentration, hydraulic retention time and volumetric conversion rate were constructed to correlate Anammox reactor performance with granular packing patterns. It was suggested that the Anammox granules packed as the equivalent simple cubic pattern in high-rate UASB reactor with packing density of 50-55%, which not only accommodated a high concentration of sludge inside the reactor, but also provided large pore volume, thus prolonging the actual substrate conversion time. Results also indicated that it was necessary to improve Anammox reactor performance by enhancing substrate loading when sludge concentration was higher than 37.8 gVSS/L. The established model was carefully calibrated and verified, and it well simulated the performance of granule-based high-rate Anammox UASB reactor. PMID:23434474

  3. Analysis of Physiological Systems via Mathematical Models.

    ERIC Educational Resources Information Center

    Hazelrig, Jane B.

    1983-01-01

    Discusses steps to be executed when studying physiological systems with theoretical mathematical models. Steps considered include: (1) definition of goals; (2) model formulation; (3) mathematical description; (4) qualitative evaluation; (5) parameter estimation; (6) model fitting; (7) evaluation; and (8) design of new experiments based on the…

  4. A mathematical model for crop spectral-temporal trajectories based on a plant growth model

    NASA Technical Reports Server (NTRS)

    Woolford, T. L.

    1983-01-01

    The Kubelka-Munk radiative transfer model is combined with an approximation of Kauth-Thomas greeness and brightness transforms to derive approximate closed form expressions for crop greeness and brightness surrogates in terms of canopy biomass. The greeness relation derived resembles an existing empirical relation between leaf area index and greeness. A simple growth model based on interception and utilization of photosynthetically active radiation is developed and used to describe the time evolution of greeness and brightness. The model developed does not yet yield definitive profile calculations but suggests a conceptual framework which may be found useful for further profile analysis.

  5. Modeling Zombie Outbreaks: A Problem-Based Approach to Improving Mathematics One Brain at a Time

    ERIC Educational Resources Information Center

    Lewis, Matthew; Powell, James A.

    2016-01-01

    A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans versus Zombies moderated tag game played on the Utah State University campus. We discuss…

  6. Monitoring and forecast of hydro meteorological hazards basing on data of distant assay and mathematical modeling

    NASA Astrophysics Data System (ADS)

    Sapunov, Valentin; Dikinis, Alexandr; Voronov, Nikolai

    2014-05-01

    Russian Federation having giant area has low concentration of land meteorological check points. Net of monitoring is not enough for effective forecast and prediction of weather dynamics and extremely situations. Under increase of extremely situations and incidents - hurricanes et al (two times from begin of XXI century) reconstruction and "perestroika" of monitoring net is needful and necessary. The basis of such a progress is distant monitoring using planes and satellites adding land contact monitoring base on efforts of existed points and stations. Interaction of contact and distant views may make hydro meteorological data and prediction more fine and significant. Tradition physical methods must be added by new biological methods of modern study. According to gotten researches animal are able to predict extremely hazards of natural and anthropogenic nature basing of interaction between biological matter and probable physical field that is under primary study. For example it was animals which forecasted dropping of Chelyabinsk meteorite of 2013. Adding of biological indication with complex of meteorological data may increase significance of hazard prediction. The uniting of all data and approaches may become basis of proposed mathematical hydro meteorological weather models. Introduction to practice reported complex methods may decrease of loss from hydro meteorological risks and hazards and increase stability of country economics.

  7. Physical and mathematical cochlear models

    NASA Astrophysics Data System (ADS)

    Lim, Kian-Meng

    2000-10-01

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

  8. Modelling and Optimizing Mathematics Learning in Children

    ERIC Educational Resources Information Center

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

    2013-01-01

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

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

    ERIC Educational Resources Information Center

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

    2014-01-01

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

  10. Mathematical modeling and analysis of EDM process parameters based on Taguchi design of experiments

    NASA Astrophysics Data System (ADS)

    Laxman, J.; Raj, K. Guru

    2015-12-01

    Electro Discharge Machining is a process used for machining very hard metals, deep and complex shapes by metal erosion in all types of electro conductive materials. The metal is removed through the action of an electric discharge of short duration and high current density between the tool and the work piece. The eroded metal on the surface of both work piece and the tool is flushed away by the dielectric fluid. The objective of this work is to develop a mathematical model for an Electro Discharge Machining process which provides the necessary equations to predict the metal removal rate, electrode wear rate and surface roughness. Regression analysis is used to investigate the relationship between various process parameters. The input parameters are taken as peak current, pulse on time, pulse off time, tool lift time. and the Metal removal rate, electrode wear rate and surface roughness are as responses. Experiments are conducted on Titanium super alloy based on the Taguchi design of experiments i.e. L27 orthogonal experiments.

  11. Calculation procedures for oil free scroll compressors based on mathematical modelling of working process

    NASA Astrophysics Data System (ADS)

    Paranin, Y.; Burmistrov, A.; Salikeev, S.; Fomina, M.

    2015-08-01

    Basic propositions of calculation procedures for oil free scroll compressors characteristics are presented. It is shown that mathematical modelling of working process in a scroll compressor makes it possible to take into account such factors influencing the working process as heat and mass exchange, mechanical interaction in working chambers, leakage through slots, etc. The basic mathematical model may be supplemented by taking into account external heat exchange, elastic deformation of scrolls, inlet and outlet losses, etc. To evaluate the influence of procedure on scroll compressor characteristics calculations accuracy different calculations were carried out. Internal adiabatic efficiency was chosen as a comparative parameter which evaluates the perfection of internal thermodynamic and gas-dynamic compressor processes. Calculated characteristics are compared with experimental values obtained for the compressor pilot sample.

  12. Explorations in Elementary Mathematical Modeling

    ERIC Educational Resources Information Center

    Shahin, Mazen

    2010-01-01

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

  13. Growth of Microbial Populations. Mathematical Modeling, Laboratory Exercises, and Model-Based Data Analysis

    ERIC Educational Resources Information Center

    Juska, Alfonsas; Gedminiene, Genovaite; Ivanec, Ruta

    2006-01-01

    This paper has arisen as a result of teaching Models in Biology to undergraduates of Bioengineering at the Gediminas Technical University of Vilnius. The aim is to teach the students to use a fresh approach to the problems they are familiar with, to come up with an articulate verbal model after a mental effort, to express it in rigorous…

  14. Students' Mathematical Modeling of Motion

    ERIC Educational Resources Information Center

    Marshall, Jill A.; Carrejo, David J.

    2008-01-01

    We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…

  15. Mathematical modeling of glycerol biotransformation

    NASA Astrophysics Data System (ADS)

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

    2013-12-01

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

  16. Mathematical model for gyroscope effects

    NASA Astrophysics Data System (ADS)

    Usubamatov, Ryspek

    2015-05-01

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

  17. Mathematical Modeling of Diverse Phenomena

    NASA Technical Reports Server (NTRS)

    Howard, J. C.

    1979-01-01

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

  18. Social and Motivational Bases for Mathematical Understanding.

    ERIC Educational Resources Information Center

    Hatano, Giyoo

    1988-01-01

    Describes a model of cognitive and motivational processes in mathematics learning and relates the model to Brazilian street mathematics and abacus operation. Proposes instructional strategies for motivating conceptual understanding in school mathematics learning. (RJC)

  19. A Biophysically Based Mathematical Model of Unitary Potential Activity in Interstitial Cells of Cajal

    PubMed Central

    Faville, R. A.; Pullan, A. J.; Sanders, K. M; Smith, N. P.

    2008-01-01

    Unitary potential (UP) depolarizations are the basic intracellular events responsible for pacemaker activity in interstitial cells of Cajal (ICCs), and are generated at intracellular sites termed “pacemaker units”. In this study, we present a mathematical model of the transmembrane ion flows and intracellular Ca2+ dynamics from a single ICC pacemaker unit acting at near-resting membrane potential. This model quantitatively formalizes the framework of a novel ICC pacemaking mechanism that has recently been proposed. Model simulations produce spontaneously rhythmic UP depolarizations with an amplitude of ∼3 mV at a frequency of 0.05 Hz. The model predicts that the main inward currents, carried by a Ca2+-inhibited nonselective cation conductance, are activated by depletion of sub-plasma-membrane [Ca2+] caused by sarcoendoplasmic reticulum calcium ATPase Ca2+ sequestration. Furthermore, pacemaker activity predicted by our model persists under simulated voltage clamp and is independent of [IP3] oscillations. The model presented here provides a basis to quantitatively analyze UP depolarizations and the biophysical mechanisms underlying their production. PMID:18339738

  20. Mathematical modelling of cucumber (cucumis sativus) drying

    NASA Astrophysics Data System (ADS)

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

    2014-07-01

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

  1. Preliminary work for SiC-based piezoelectric energy harvester with mathematical modelling and simulation study

    NASA Astrophysics Data System (ADS)

    M. N. Fakhzan M., K.; Nasrul F. M., N.; Raman, S.; Muthalif, Asan G. A.

    2015-05-01

    This paper is a preliminary work to explore the feasibility of cubic silicon carbide on silicon wafers with integrated proof mass as horizontal cantilever with vertical displacement. The reason of harvesting ambient vibration energy is to convert mechanical energy produces by piezoelectric into useful electrical energy. The collectable energy is useful for powering the low-power devices. Theoretically, the resonant phenomena are a special characteristic in order to optimize the generated output power. The natural frequency of the cantilever can to be tuned with difference proof masses. Another parameter considered in this paper is the damping ratio. Throughout analytical study, small damping ratio will enhance the output power of the piezoelectric energy harvester (PEH). This paper will present a mathematical modelling approach and the simulation validation.

  2. Mathematical Modeling of Human Glioma Growth Based on Brain Topological Structures: Study of Two Clinical Cases

    PubMed Central

    Suarez, Cecilia; Maglietti, Felipe; Colonna, Mario; Breitburd, Karina; Marshall, Guillermo

    2012-01-01

    Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from brain slices covering the whole human brain. The Talairach atlas included in the model describes brain structures at different levels. Also, the inclusion of the Brodmann areas allows prediction of the brain functions affected during tumor evolution and the estimation of correlated symptoms. The model is solved numerically using patient-specific parametrization and finite differences. Simulations consider an initial state with cellular proliferation alone (benign tumor), and an advanced state when infiltration starts (malign tumor). Survival time is estimated on the basis of tumor size and location. The model is used to predict tumor evolution in two clinical cases. In the first case, predictions show that real infiltrative areas are underestimated by current diagnostic imaging. In the second case, tumor spreading predictions were shown to be more accurate than those derived from previous models in the literature. Our results suggest that the inclusion of differential migration in glioma growth models constitutes another step towards a better prediction of tumor infiltration at the moment of surgical or radiosurgical target definition. Also, the addition of physiological/psychological considerations to classical anatomical models will provide a better and integral understanding of the patient disease at the moment of deciding therapeutic options, taking into account not only survival but also life quality. PMID:22761843

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

    ERIC Educational Resources Information Center

    Suppes, Patrick

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

  4. Mathematical Models for Doppler Measurements

    NASA Technical Reports Server (NTRS)

    Lear, William M.

    1987-01-01

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

  5. FINAL PROJECT REPORT DOE Early Career Principal Investigator Program Project Title: Developing New Mathematical Models for Multiphase Flows Based on a Fundamental Probability Density Function Approach

    SciTech Connect

    Shankar Subramaniam

    2009-04-01

    This final project report summarizes progress made towards the objectives described in the proposal entitled “Developing New Mathematical Models for Multiphase Flows Based on a Fundamental Probability Density Function Approach”. Substantial progress has been made in theory, modeling and numerical simulation of turbulent multiphase flows. The consistent mathematical framework based on probability density functions is described. New models are proposed for turbulent particle-laden flows and sprays.

  6. Automatic mathematical modeling for space application

    NASA Technical Reports Server (NTRS)

    Wang, Caroline K.

    1987-01-01

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

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  8. The Development of Learning Devices Based Guided Discovery Model to Improve Understanding Concept and Critical Thinking Mathematically Ability of Students at Islamic Junior High School of Medan

    ERIC Educational Resources Information Center

    Yuliani, Kiki; Saragih, Sahat

    2015-01-01

    The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…

  9. Mathematical Models Based on Transfer Functions to Estimate Tissue Temperature During RF Cardiac Ablation in Real Time

    PubMed Central

    Alba-Martínez, Jose; Trujillo, Macarena; Blasco-Gimenez, Ramon; Berjano, Enrique

    2012-01-01

    Radiofrequency cardiac ablation (RFCA) has been used to treat certain types of cardiac arrhythmias by producing a thermal lesion. Even though a tissue temperature higher than 50ºC is required to destroy the target, thermal mapping is not currently used during RFCA. Our aim was thus to develop mathematical models capable of estimating tissue temperature from tissue characteristics acquired or estimated at the beginning of the procedure (electrical conductivity, thermal conductivity, specific heat and density) and the applied voltage at any time. Biological tissue was considered as a system with an input (applied voltage) and output (tissue temperature), and so the mathematical models were based on transfer functions relating these variables. We used theoretical models based on finite element method to verify the mathematical models. Firstly, we solved finite element models to identify the transfer functions between the temperature at a depth of 4 mm and a constant applied voltage using a 7Fr and 4 mm electrode. The results showed that the relationships can be expressed as first-order transfer functions. Changes in electrical conductivity only affected the static gain of the system, while specific heat variations produced a change in the dynamic system response. In contrast, variations in thermal conductivity modified both the static gain and the dynamic system response. Finally, to assess the performance of the transfer functions obtained, we conducted a new set of computer simulations using a controlled temperature protocol and considering the temperature dependence of the thermal and electrical conductivities, i.e. conditions closer to those found in clinical use. The results showed that the difference between the values estimated from transfer functions and the temperatures obtained from finite element models was less than 4ºC, which suggests that the proposed method could be used to estimate tissue temperature in real time. PMID:22715345

  10. And So It Grows: Using a Computer-Based Simulation of a Population Growth Model to Integrate Biology & Mathematics

    ERIC Educational Resources Information Center

    Street, Garrett M.; Laubach, Timothy A.

    2013-01-01

    We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

  11. A method of ecological and economic risk assessment during the development of the shelf based on mathematical modelling

    NASA Astrophysics Data System (ADS)

    Solovyova, N. V.; Lobkovsky, L. I.

    2015-09-01

    This paper proposes a method of mathematical modelling of ecological risk based on a synthesis of dynamic and probabilistic risk assessment techniques. The probability of assessment of an acceptable probability of an anthropogenic impact to minimize economic costs is proposed. The dependence of an acceptable probability of an anthropogenic impact on the ecological risk is demonstrated with an example calculation. The results of the modelling of the state of a shelf ecosystem based on the dynamic model are used for the calculation as source information. Based on this synthesis, the calculation results bring about the opportunity to balance ecological-economic goals of achieving safe development of the shelf and to satisfy the involuntary necessity to reduce the costs on environmental protection measures, while maintaining the priority of environmental requirements.

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

    ERIC Educational Resources Information Center

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

    2014-01-01

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

  13. Qualitative mathematical models to support ecosystem-based management of Australia's Northern Prawn Fishery.

    PubMed

    Dambacher, Jeffrey M; Rothlisberg, Peter C; Loneragan, Neil R

    2015-01-01

    A major decline in the catch of the banana prawn [shrimp], Penaeus (Fenneropenaeus) merguiensis, occurred over a six-year period in the Weipa region of the northeastern Gulf of Carpentaria, Australia. Three main hypotheses have been developed to explain this decline: (1) prawn recruitment collapsed due to overfishing; (2) recruitment collapsed due to a change in the prawn's environment; and (3) adult banana prawns were still present, but fishers could no longer effectively find or catch them. Qualitative mathematical models were used to link population biology, environmental factors, and fishery dynamics to evaluate the alternative hypotheses. This modeling approach provides the means to rapidly integrate knowledge across disciplines and consider alternative hypotheses about how the structure and function of an ecosystem affects its dynamics. Alternative models were constructed to address the different hypotheses and also to encompass a diversity of opinion about the underlying dynamics of the system. Key findings from these analyses are that: instability in the system can arise when discarded fishery bycatch supports relatively high predation pressure; system stability can be enhanced by management of fishing effort or stock catchability; catch per unit effort is not necessarily a reliable indicator of stock abundance; a change in early-season rainfall should affect all stages in the banana prawn's life cycle; and a reduced catch in the Weipa region can create and reinforce a shift in fishing effort away from Weipa. Results from the models informed an approach to test the hypotheses (i.e., an experimental fishing program), and promoted understanding of the system among researchers, management agencies, and industry. The analytical tools developed in this work to address stages of a prawn life cycle and fishery dynamics are generally applicable to any exploited natural. resource. PMID:26255373

  14. Mathematical modeling in soil science

    NASA Astrophysics Data System (ADS)

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

    2015-04-01

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

  15. Mathematical modeling based evaluation and simulation of boron removal in bioelectrochemical systems.

    PubMed

    Ping, Qingyun; Abu-Reesh, Ibrahim M; He, Zhen

    2016-11-01

    Boron removal is an arising issue in desalination plants due to boron's toxicity. As an emerging treatment concept, bioelectrochemical systems (BES) can achieve potentially cost-effective boron removal by taking advantage of cathodic-produced alkali. Prior studies have demonstrated successful removal of boron in microbial desalination cells (MDCs) and microbial fuel cells (MFCs), both of which are representative BES. Herein, mathematical models were developed to further evaluate boron removal by different BES and understand the key operating factors. The models delivered very good prediction of the boron concentration in the MDC integrated with Donnan Dialysis (DD) system with the lowest relative root-mean-square error (RMSE) of 0.00%; the predication of the MFC performance generated the highest RMSE of 18.55%. The model results of salt concentration, solution pH, and current generation were well fitted with experimental data for RMSE values mostly below 10%. The long term simulation of the MDC-DD system suggests that the accumulation of salt in the catholyte/stripping solution could have a positive impact on the removal of boron due to osmosis-driven convection. The current generation in the MDC may have little influence on the boron removal, while in the MFC the current-driven electromigration can contribute up to 40% of boron removal. Osmosis-induced convection transport of boron could be the major driving force for boron removal to a low level <2mgL(-1). The ratio between the anolyte and the catholyte flow rates should be kept >22.2 in order to avoid boron accumulation in the anolyte effluent. PMID:27387806

  16. Mathematical Models of Gene Regulation

    NASA Astrophysics Data System (ADS)

    Mackey, Michael C.

    2004-03-01

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

  17. Mathematical model for bone mineralization

    PubMed Central

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

    2015-01-01

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

  18. Using Covariation Reasoning to Support Mathematical Modeling

    ERIC Educational Resources Information Center

    Jacobson, Erik

    2014-01-01

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

  19. Mathematical models for exotic wakes

    NASA Astrophysics Data System (ADS)

    Basu, Saikat; Stremler, Mark

    2014-11-01

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

  20. Development of 4D mathematical observer models for the task-based evaluation of gated myocardial perfusion SPECT

    NASA Astrophysics Data System (ADS)

    Lee, Taek-Soo; Frey, Eric C.; Tsui, Benjamin M. W.

    2015-04-01

    This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of 99mTc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman’s rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the

  1. Development of 4D mathematical observer models for the task-based evaluation of gated myocardial perfusion SPECT.

    PubMed

    Lee, Taek-Soo; Frey, Eric C; Tsui, Benjamin M W

    2015-04-01

    This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of (99m)Tc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman's rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the

  2. Mathematical circulatory system model

    NASA Technical Reports Server (NTRS)

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

    2010-01-01

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

  3. Mathematical Modeling: A Bridge to STEM Education

    ERIC Educational Resources Information Center

    Kertil, Mahmut; Gurel, Cem

    2016-01-01

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

  4. The 24-Hour Mathematical Modeling Challenge

    ERIC Educational Resources Information Center

    Galluzzo, Benjamin J.; Wendt, Theodore J.

    2015-01-01

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

  5. Comprehensive Mathematical Model Of Real Fluids

    NASA Technical Reports Server (NTRS)

    Anderson, Peter G.

    1996-01-01

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

  6. Mathematical Model-Based Accelerated Development of Extended-release Metformin Hydrochloride Tablet Formulation.

    PubMed

    Chen, W; Desai, D; Good, D; Crison, J; Timmins, P; Paruchuri, S; Wang, J; Ha, K

    2016-08-01

    A computational fluid dynamic (CFD) model was developed to predict metformin release from a hydroxypropylmethylcellulose (HPMC) matrix-based extended-release formulation that took into consideration the physical and chemical properties of the drug substance, composition, as well as size and shape of the tablet. New high dose strength (1000 mg) tablet geometry was selected based on the surface area/volume (SA/V) approach advocated by Lapidus/Lordi/Reynold to obtain the desired equivalent metformin release kinetics. Maintaining a similar SA/V ratio across all extended-release metformin hydrochloride (Met XR) tablet strengths that had different geometries provided similar simulations of dissolution behavior. Experimental dissolution profiles of three lots of high-strength tablets agreed with the simulated release kinetics. Additionally, a pharmacokinetic absorption model was developed using GastroPlus™ software and known physicochemical, pharmacokinetic, and in vitro dissolution properties of metformin to predict the clinical exposure of the new high strength (1000 mg) tablet prior to conducting a human clinical bioequivalence study. In vitro metformin release kinetics were utilized in the absorption model to predict exposures in humans for new 1000-mg Met XR tablets, and the absorption model correctly projected equivalent in vivo exposure across all dose strengths. A clinical bioequivalence study was pursued based on the combined modeling results and demonstrated equivalent exposure as predicted by the simulations. PMID:26729531

  7. Mathematical modelling in nuclear medicine

    PubMed Central

    Kuikka, Jyrki T.; Bassingthwaighte, James B.; Henrich, Michael M.; Feinendegen, Ludwig E.

    2010-01-01

    Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space. Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging. One formulates a model first by defining what it should represent: this is the hypothesis. When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. This is what one would like to test against data. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations. The former are known as distributed models and the latter as lumped compartmental or mixing chamber models. Since both are derived from the same ideas, the parameters are usually the same; their differences are in their ability to represent the hypothesis correctly, quantitatively, and sometimes in their computability. In this essay we review the philosophical and practical aspects of such modelling analysis for translating image sequences into physiological terms. PMID:1936044

  8. The Child's Introduction to Mathematics: A Transfer Model Based in Measurement.

    ERIC Educational Resources Information Center

    Van Wagenen, R. Keith; Zellner, Ronald D.

    Tested was a method of learning numeration, addition, and subtraction using measuring operations in place of the more usual counting operations. It is claimed that an approach through "units of measurement" to continuous variables is mathematically more powerful than counting, which leads only to nominal and ordinal variables. Twelve children…

  9. Mathematical modeling of piezoresistive elements

    NASA Astrophysics Data System (ADS)

    Geremias, M.; Moreira, R. C.; Rasia, L. A.; Moi, A.

    2015-10-01

    This article presents the longitudinal piezoresistive coefficients for thin film amorphous semiconductor type a-C:H. Experimental data and mathematical models have been used in computer simulations. The results show that a reduction of the longitudinal piezoresistive coefficient occurs due to the increased concentration of impurities in the films analyzed.

  10. Landslide Susceptibility Evaluation on agricultural terraces of DOURO VALLEY (PORTUGAL), using physically based mathematical models.

    NASA Astrophysics Data System (ADS)

    Faria, Ana; Bateira, Carlos; Laura, Soares; Fernandes, Joana; Gonçalves, José; Marques, Fernando

    2016-04-01

    The work focuses the evaluation of landslide susceptibility in Douro Region agricultural terraces, supported by dry stone walls and earth embankments, using two physically based models. The applied models, SHALSTAB (Montgomery et al.,1994; Dietrich et al., 1995) and SINMAP (PACK et al., 2005), combine an infinite slope stability model with a steady state hydrological model, and both use the following geophysical parameters: cohesion, friction angle, specific weight and soil thickness. The definition of the contributing areas is different in both models. The D∞ methodology used by SINMAP model suggests a great influence of the terraces morphology, providing a much more diffuse flow on the internal flow modelling. The MD8 used in SHALSTAB promotes an important degree of flow concentration, representing an internal flow based on preferential paths of the runoff as the areas more susceptible to saturation processes. The model validation is made through the contingency matrix method (Fawcett, 2006; Raia et al., 2014) and implies the confrontation with the inventory of past landslides. The True Positive Rate shows that SHALSTAB classifies 77% of the landslides on the high susceptibility areas, while SINMAP reaches 90%. The SINMAP has a False Positive Rate (represents the percentage of the slipped area that is classified as unstable but without landslides) of 83% and the SHALSTAB has 67%. The reliability (analyzes the areas that were correctly classified on the total area) of SHALSTAB is better (33% against 18% of SINMAP). Relative to Precision (refers to the ratio of the slipped area correctly classified over the whole area classified as unstable) SHALSTAB has better results (0.00298 against 0.00283 of SINMAP). It was elaborate the index TPR/FPR and better results obtained by SHALSTAB (1.14 against 1.09 of SINMAP). SHALSTAB shows a better performance in the definition of susceptibility most prone areas to instability processes. One of the reasons for the difference of

  11. Teachers' Conceptions of Mathematical Modeling

    ERIC Educational Resources Information Center

    Gould, Heather

    2013-01-01

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

  12. A Mathematical Study to Select Fractionation Regimen Based on Physical Dose Distribution and the Linear-Quadratic Model

    SciTech Connect

    Mizuta, Masahiro; Takao, Seishin; Date, Hiroyuki; Kishimoto, Naoki; Sutherland, Kenneth L.; Onimaru, Rikiya; Shirato, Hiroki

    2012-11-01

    Purpose: Hypofractionated irradiation is often used in precise radiotherapy instead of conventional multifractionated irradiation. We propose a novel mathematical method for selecting a hypofractionated or multifractionated irradiation regimen based on physical dose distribution adding to biologic consideration. Methods and Materials: The linear-quadratic model was used for the radiation effects on tumor and normal tissues, especially organs at risk (OARs). On the basis of the assumption that the OAR receives a fraction of the dose intended for the tumor, the minimization problem for the damage effect on the OAR was treated under the constraint that the radiation effect on the tumor is fixed. Results: For an N-time fractionated irradiation regimen, the constraint of tumor lethality was described by an N-dimensional hypersphere. The total dose of the fractionated irradiations was considered for minimizing the damage effect on the OAR under the hypersphere condition. It was found that the advantage of hypofractionated or multifractionated irradiation therapies depends on the magnitude of the ratio of {alpha}/{beta} parameters for the OAR and tumor in the linear-quadratic model and the ratio of the dose for the OAR and tumor. Conclusions: Our mathematical method shows that multifractionated irradiation with a constant dose is better if the ratio of {alpha}/{beta} for the OAR and tumor is less than the ratio of the dose for the OAR and tumor, whereas hypofractionated irradiation is better otherwise.

  13. Mathematical modeling riparian vegetation zonation in semiarid conditions based on a transpiration index.

    NASA Astrophysics Data System (ADS)

    Real, Joaquin; Morales, Marco; Garcia, Alicia; Garofano, Virginia; Martinez-Capel, Francisco; Frances, Felix

    2010-05-01

    Initially riparian vegetation modeling was focused on the study of ecological patches without taking into account the interactive effects of structures and processes in between them (Tabacchi et al., 1998). One of the greatest challenges, when carrying out a riparian ecosystem restoration, is to understand the physical and ecological processes of a system and the interaction and feedback within these processes. Jorde (2002) pointed out the importance of addressing complex linkages between processes and biotic interactions in research and in the development of restoration projects over larger spatial and temporal scales in the future. According to Tabacchi et al. (2000), the water cycle in riparian zones depends on three important relations: the water absorption by the plants, water storage and atmospherical return by evaporation. During recent years a variety of ecological models have taken into account the changes in the plant species as consequence of changes in the environmental variables and hydrological alterations (Baptist, 2005; Braatne et al., 2002; Glenz, 2005; Hooke et al., 2005; Murphy et al., 2006). Most of these models are based on functional relationships between river hydrology and vegetation species or communities. In semiarid regions we make the hypothesis transpiration will be one of the key factors determining the riparian vegetation presence and therefore, we will not consider in our model other factors as recruitment, flood damages, etc. The objectives of this work are: firstly to develop a model capable of simulating several riparian vegetation types which can be applied in a wide range of conditions across Mediterranean environments; and secondly to calibrate and to validate the model in several Mediterranean river stretches of the Iberian Peninsula, both in undisturbed and disturbed flow regimes. To achieve these objectives the following methodology has been applied. The model has been conceptualized as a static tank flow model based on the

  14. Application of a high throughput bioluminescence-based method and mathematical model for the quantitative comparison of polymer microbicide efficiency.

    PubMed

    Stratton, Thomas R; García, R Edwin; Applegate, Bruce M; Youngblood, Jeffrey P

    2009-05-11

    Quaternized poly(4-vinyl pyridine)-based copolymers are known to be effective against a wide range of bacteria and possess biocompatible properties. Extensive testing of a wide range of copolymers is necessary to further explore and enhance the biocidal properties. However, testing is hampered by labor-intensive bacteria testing techniques. The present paper presents a new testing method, based on bioluminescent reporter strains to enable fast evaluation of bactericidal properties. The reported method enables us to create real-time characterization of bacteria behavior with far less labor than required through traditional testing methods. A mathematical model was also developed to characterize the change in bacteria populations exposed to biocides and to enable the quantitative comparison of minimum bactericidal concentrations. PMID:19338347

  15. Mathematical Modeling of Cellular Metabolism.

    PubMed

    Berndt, Nikolaus; Holzhütter, Hermann-Georg

    2016-01-01

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

  16. Mathematical Models for Somite Formation

    PubMed Central

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

    2009-01-01

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

  17. Mathematical modeling of molecular diffusion through mucus

    PubMed Central

    Cu, Yen; Saltzman, W. Mark

    2008-01-01

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

  18. Establishing an Explanatory Model for Mathematics Identity

    ERIC Educational Resources Information Center

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

    2015-01-01

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

  19. Strategies to Support Students' Mathematical Modeling

    ERIC Educational Resources Information Center

    Jung, Hyunyi

    2015-01-01

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

  20. Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

    ERIC Educational Resources Information Center

    Tutak, Tayfun; Güder, Yunus

    2013-01-01

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

  1. Mathematical modeling of genome replication

    NASA Astrophysics Data System (ADS)

    Retkute, Renata; Nieduszynski, Conrad A.; de Moura, Alessandro

    2012-09-01

    Eukaryotic DNA replication is initiated from multiple sites on the chromosome, but little is known about the global and local regulation of replication. We present a mathematical model for the spatial dynamics of DNA replication, which offers insight into the kinetics of replication in different types of organisms. Most biological experiments involve average quantities over large cell populations (typically >107 cells) and therefore can mask the cell-to-cell variability present in the system. Although the model is formulated in terms of a population of cells, using mathematical analysis we show that one can obtain signatures of stochasticity in individual cells from averaged quantities. This work generalizes the result by Retkute [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.068103 107, 068103 (2011)] to a broader set of parameter regimes.

  2. A Novel Physiology-Based Mathematical Model to Estimate Red Blood Cell Lifespan in Different Human Age Groups.

    PubMed

    An, Guohua; Widness, John A; Mock, Donald M; Veng-Pedersen, Peter

    2016-09-01

    Direct measurement of red blood cell (RBC) survival in humans has improved from the original accurate but limited differential agglutination technique to the current reliable, safe, and accurate biotin method. Despite this, all of these methods are time consuming and require blood sampling over several months to determine the RBC lifespan. For situations in which RBC survival information must be obtained quickly, these methods are not suitable. With the exception of adults and infants, RBC survival has not been extensively investigated in other age groups. To address this need, we developed a novel, physiology-based mathematical model that quickly estimates RBC lifespan in healthy individuals at any age. The model is based on the assumption that the total number of RBC recirculations during the lifespan of each RBC (denoted by N max) is relatively constant for all age groups. The model was initially validated using the data from our prior infant and adult biotin-labeled red blood cell studies and then extended to the other age groups. The model generated the following estimated RBC lifespans in 2-year-old, 5-year-old, 8-year-old, and 10-year-old children: 62, 74, 82, and 86 days, respectively. We speculate that this model has useful clinical applications. For example, HbA1c testing is not reliable in identifying children with diabetes because HbA1c is directly affected by RBC lifespan. Because our model can estimate RBC lifespan in children at any age, corrections to HbA1c values based on the model-generated RBC lifespan could improve diabetes diagnosis as well as therapy in children. PMID:27215601

  3. Mathematical models of diabetes progression.

    PubMed

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

    2008-12-01

    Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page. PMID:18780774

  4. Mathematical modelling in MHD technology

    SciTech Connect

    Scheindlin, A.E.; Medin, S.A. )

    1990-01-01

    The technological scheme and the general parameters of the commercial scale pilot MHD power plant are described. The characteristics of the flow train components and the electrical equipment are discussed. The basic ideas of the mathematical modelling of the processes and the devices operation in MHD systems are considered. The application of different description levels in computer simulation is analyzed and the examples of typical solutions are presented.

  5. Trends and techniques for space base electronics. [mathematical models, ion implantation, and semiconductors

    NASA Technical Reports Server (NTRS)

    Gassaway, J. D.; Mahmood, Q.; Trotter, J. D.

    1978-01-01

    A system was developed for depositing aluminum and aluminum alloys by the D.C. sputtering technique. This system which was designed for a high level of cleanliness and ion monitoring the deposition parameters during film preparation is ready for studying the deposition and annealing parameters upon double level metal preparation. The finite element method was studied for use in the computer modeling of two dimensional MOS transistor structures. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions typical of those used at MSFC. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients. Data are given showing both two dimensional effects and the evolution of the junction depth, sheet resistance and integrated dose with redistribution time.

  6. In Silico Neuro-Oncology: Brownian Motion-Based Mathematical Treatment as a Potential Platform for Modeling the Infiltration of Glioma Cells into Normal Brain Tissue

    PubMed Central

    Antonopoulos, Markos; Stamatakos, Georgios

    2015-01-01

    Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided. PMID:26309390

  7. Summer Camp of Mathematical Modeling in China

    ERIC Educational Resources Information Center

    Tian, Xiaoxi; Xie, Jinxing

    2013-01-01

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

  8. [Mathematical model of mental time].

    PubMed

    Glasko, A V; Sadykhova, L G

    2014-01-01

    On the basis of Ernst Mach's ideas and developed before the mathematical theory of mental processes, mathematical definition of duration of an interval of mental time, all over again for perception (experience) of separate event, and then--generally, i.e. for perception (experience) of sequence of events is entered. Its dependence on duration of an appropriating interval of physical time is investigated. Communication of mental time with perception of time (for two cases: "greater" and "small" intervals) is investigated. Comparison of theoretical formulas with results of experimental measurements is spent. Is defined process time which can be used, in particular, as a measure of work. The effect of the inverse of the psychological time, described in works of the Mach is analyzed and modelled. PMID:25723024

  9. Mathematical Modeling of Loop Heat Pipes

    NASA Technical Reports Server (NTRS)

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

    1998-01-01

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

  10. Mathematical models of bipolar disorder

    NASA Astrophysics Data System (ADS)

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

    2009-07-01

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

  11. Inquiry-Based Mathematics Curriculum Design for Young Children-Teaching Experiment and Reflection

    ERIC Educational Resources Information Center

    Wu, Su-Chiao; Lin, Fou-Lai

    2016-01-01

    A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In…

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

    NASA Technical Reports Server (NTRS)

    Solomon, A. D.

    1980-01-01

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

  13. Mathematical models in medicine: Diseases and epidemics

    SciTech Connect

    Witten, M.

    1987-01-01

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

  14. Revisions to the PARCC Model Content Frameworks for Mathematics and ELA/Literacy Based on Public Feedback

    ERIC Educational Resources Information Center

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

    2011-01-01

    The PARCC Model Content Frameworks for Mathematics and ELA/Literacy have been developed through a state-led process in collaboration with members of the Common Core State Standards (CCSS) writing teams. The frameworks were reviewed by the public between August 3-31, 2011. Nearly 1,000 responses were collected, and respondents included K-12…

  15. Identification of the noise using mathematical modelling

    NASA Astrophysics Data System (ADS)

    Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav

    2016-03-01

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

  16. Conversations about Curriculum Change: Mathematical Thinking and Team-Based Learning in a Discrete Mathematics Course

    ERIC Educational Resources Information Center

    Paterson, Judy; Sneddon, Jamie

    2011-01-01

    This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…

  17. Lensless ghost imaging based on mathematical simulation and experimental simulation

    NASA Astrophysics Data System (ADS)

    Liu, Yanyan; Wang, Biyi; Zhao, Yingchao; Dong, Junzhang

    2014-02-01

    The differences of conventional imaging and correlated imaging are discussed in this paper. The mathematical model of lensless ghost imaging system is set up and the image of double slits is computed by mathematical simulation. The results are also testified by the experimental verification. Both the theory simulation and experimental verifications results shows that the mathematical model based on statistical optical principle are keeping consistent with real experimental results.

  18. Mathematical models of malaria - a review

    PubMed Central

    2011-01-01

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

  19. Mathematical modeling of cold cap

    SciTech Connect

    Pokorny, Richard; Hrma, Pavel R.

    2012-10-13

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

  20. Mathematical modeling of drying of potato slices in a forced convective dryer based on important parameters.

    PubMed

    Naderinezhad, Samira; Etesami, Nasrin; Poormalek Najafabady, Arefe; Ghasemi Falavarjani, Majid

    2016-01-01

    The effect of air temperature, air velocity, and sample shapes (circle and square with the same cross-sectional area) on kinetic drying of potato slices in a tunnel dryer was investigated experimentally and a suitable drying model was developed. The experiments of drying of potato slices were conducted at an air temperature of 45-70°C with an air velocity 1.60 and 1.81 m sec(-1). Results showed that drying temperature was the most effective parameter in the drying rate. The influence of air velocity was more profound in low temperature. The time for drying square slices was lower compared to the circle ones. Furthermore, drying data were fitted to different empirical models. Among the models, Midilli-Kucuk was the best to explain the single layer drying of potato slices. The parameters of this model were determined as functions of air velocity and temperature by multiple regression analysis for circle and square slices. Various statistical parameters were examined for evaluating the model. PMID:26788317

  1. Examining the Implementation of a Problem-Based Learning and Traditional Hybrid Model of Instruction in Remedial Mathematics Classes Designed for State Testing Preparation of Eleventh Grade Students

    ERIC Educational Resources Information Center

    Rodgers, Lindsay D.

    2011-01-01

    The following paper examined the effects of a new method of teaching for remedial mathematics, named the hybrid model of instruction. Due to increasing importance of high stakes testing, the study sought to determine if this method of instruction, that blends traditional teaching and problem-based learning, had different learning effects on…

  2. A mathematical model of a computational problem solving system

    NASA Astrophysics Data System (ADS)

    Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan

    2015-05-01

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

  3. Teaching Mathematical Modelling for Earth Sciences via Case Studies

    NASA Astrophysics Data System (ADS)

    Yang, Xin-She

    2010-05-01

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

  4. A Generative Model of Mathematics Learning

    ERIC Educational Resources Information Center

    Wittrock, M. C.

    1974-01-01

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

  5. On Fences, Forms and Mathematical Modeling

    ERIC Educational Resources Information Center

    Lege, Jerry

    2009-01-01

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

  6. Regulation of amniotic fluid volume: mathematical model based on intramembranous transport mechanisms

    PubMed Central

    Anderson, Debra F.; Cheung, Cecilia Y.

    2014-01-01

    Experimentation in late-gestation fetal sheep has suggested that regulation of amniotic fluid (AF) volume occurs primarily by modulating the rate of intramembranous transport of water and solutes across the amnion into underlying fetal blood vessels. In order to gain insight into intramembranous transport mechanisms, we developed a computer model that allows simulation of experimentally measured changes in AF volume and composition over time. The model included fetal urine excretion and lung liquid secretion as inflows into the amniotic compartment plus fetal swallowing and intramembranous absorption as outflows. By using experimental flows and solute concentrations for urine, lung liquid, and swallowed fluid in combination with the passive and active transport mechanisms of the intramembranous pathway, we simulated AF responses to basal conditions, intra-amniotic fluid infusions, fetal intravascular infusions, urine replacement, and tracheoesophageal occlusion. The experimental data are consistent with four intramembranous transport mechanisms acting in concert: 1) an active unidirectional bulk transport of AF with all dissolved solutes out of AF into fetal blood presumably by vesicles; 2) passive bidirectional diffusion of solutes, such as sodium and chloride, between fetal blood and AF; 3) passive bidirectional water movement between AF and fetal blood; and 4) unidirectional transport of lactate into the AF. Further, only unidirectional bulk transport is dynamically regulated. The simulations also identified areas for future study: 1) identifying intramembranous stimulators and inhibitors, 2) determining the semipermeability characteristics of the intramembranous pathway, and 3) characterizing the vesicles that are the primary mediators of intramembranous transport. PMID:25186112

  7. Regulation of amniotic fluid volume: mathematical model based on intramembranous transport mechanisms.

    PubMed

    Brace, Robert A; Anderson, Debra F; Cheung, Cecilia Y

    2014-11-15

    Experimentation in late-gestation fetal sheep has suggested that regulation of amniotic fluid (AF) volume occurs primarily by modulating the rate of intramembranous transport of water and solutes across the amnion into underlying fetal blood vessels. In order to gain insight into intramembranous transport mechanisms, we developed a computer model that allows simulation of experimentally measured changes in AF volume and composition over time. The model included fetal urine excretion and lung liquid secretion as inflows into the amniotic compartment plus fetal swallowing and intramembranous absorption as outflows. By using experimental flows and solute concentrations for urine, lung liquid, and swallowed fluid in combination with the passive and active transport mechanisms of the intramembranous pathway, we simulated AF responses to basal conditions, intra-amniotic fluid infusions, fetal intravascular infusions, urine replacement, and tracheoesophageal occlusion. The experimental data are consistent with four intramembranous transport mechanisms acting in concert: 1) an active unidirectional bulk transport of AF with all dissolved solutes out of AF into fetal blood presumably by vesicles; 2) passive bidirectional diffusion of solutes, such as sodium and chloride, between fetal blood and AF; 3) passive bidirectional water movement between AF and fetal blood; and 4) unidirectional transport of lactate into the AF. Further, only unidirectional bulk transport is dynamically regulated. The simulations also identified areas for future study: 1) identifying intramembranous stimulators and inhibitors, 2) determining the semipermeability characteristics of the intramembranous pathway, and 3) characterizing the vesicles that are the primary mediators of intramembranous transport. PMID:25186112

  8. On mathematical modelling of flameless combustion

    SciTech Connect

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

    2007-07-15

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

  9. Mathematical modeling of bone marrow - peripheral blood dynamics in the disease state based on current emerging paradigms, part I.

    PubMed

    Afenya, Evans K; Ouifki, Rachid; Camara, Baba I; Mundle, Suneel D

    2016-04-01

    Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow - peripheral blood architecture. PMID:26877072

  10. Mathematical model for classification of EEG signals

    NASA Astrophysics Data System (ADS)

    Ortiz, Victor H.; Tapia, Juan J.

    2015-09-01

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

  11. Mathematical model for alopecia areata.

    PubMed

    Dobreva, Atanaska; Paus, Ralf; Cogan, N G

    2015-09-01

    Alopecia areata (AA) is an autoimmune disease, and its clinical phenotype is characterized by the formation of distinct hairless patterns on the scalp or other parts of the body. In most cases hair falls out in round patches. A well-established hypothesis for the pathogenesis of AA states that collapse of hair follicle immune privilege is one of the essential elements in disease development. To investigate the dynamics of alopecia areata, we develop a mathematical model that incorporates immune system components and hair follicle immune privilege agents whose involvement in AA has been confirmed in clinical studies and experimentally. We perform parameter sensitivity analysis in order to determine which inputs have the greatest effect on outcome variables. Our findings suggest that, among all processes reflected in the model, immune privilege guardians and the pro-inflammatory cytokine interferon-γ govern disease dynamics. These results agree with the immune privilege collapse hypothesis for the development of AA. PMID:26047853

  12. How parrots talk: insights based on CT scans, image processing, and mathematical models

    NASA Astrophysics Data System (ADS)

    Patterson, Dianne K.; Pepperberg, Irene M.; Story, Brad H.; Hoffman, Eric A.

    1997-05-01

    Little is known about mechanisms of speech production in parrots. Recently, however, techniques for correlating vocal tract shape with vowel production in humans have become more sophisticated and we have adapted these techniques for use with parrots. We scanned two grey parrot heads with intact vocal tracts. One specimen, 'Oldbird' was fixed with its beak propped open; the second 'Youngbird' was fixed with its beak closed. Using VIDA software, we (1) established that differences in tongue and larynx positioning resulted from opening or closing the beak; and (2) obtained lengths and area functions for the trachea, glottis, pharynx, mouth, and choana for both specimens and esophageal length and area functions for the first specimen. We entered lengths and area functions into a 1D wave propagation model to determine the natural formant frequencies associated with an open versus closed beak. We also determined how manipulating lengths and area functions could affect formant frequency and relative intensity. Finally, by comparing observed grey parrot vowel formant, we predict how the parrot uses its vocal tract to produce speech.

  13. A universal optimization strategy for ant colony optimization algorithms based on the Physarum-inspired mathematical model.

    PubMed

    Zhang, Zili; Gao, Chao; Liu, Yuxin; Qian, Tao

    2014-09-01

    Ant colony optimization (ACO) algorithms often fall into the local optimal solution and have lower search efficiency for solving the travelling salesman problem (TSP). According to these shortcomings, this paper proposes a universal optimization strategy for updating the pheromone matrix in the ACO algorithms. The new optimization strategy takes advantages of the unique feature of critical paths reserved in the process of evolving adaptive networks of the Physarum-inspired mathematical model (PMM). The optimized algorithms, denoted as PMACO algorithms, can enhance the amount of pheromone in the critical paths and promote the exploitation of the optimal solution. Experimental results in synthetic and real networks show that the PMACO algorithms are more efficient and robust than the traditional ACO algorithms, which are adaptable to solve the TSP with single or multiple objectives. Meanwhile, we further analyse the influence of parameters on the performance of the PMACO algorithms. Based on these analyses, the best values of these parameters are worked out for the TSP. PMID:24613939

  14. Students' Approaches to Learning a New Mathematical Model

    ERIC Educational Resources Information Center

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

    2013-01-01

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

  15. Tracing the molecular basis of transcriptional dynamics in noisy data by using an experiment-based mathematical model

    PubMed Central

    Rybakova, Katja N.; Tomaszewska, Aleksandra; van Mourik, Simon; Blom, Joke; Westerhoff, Hans V.; Carlberg, Carsten; Bruggeman, Frank J.

    2015-01-01

    Changes in transcription factor levels, epigenetic status, splicing kinetics and mRNA degradation can each contribute to changes in the mRNA dynamics of a gene. We present a novel method to identify which of these processes is changed in cells in response to external signals or as a result of a diseased state. The method employs a mathematical model, for which the kinetics of gene regulation, splicing, elongation and mRNA degradation were estimated from experimental data of transcriptional dynamics. The time-dependent dynamics of several species of adipose differentiation-related protein (ADRP) mRNA were measured in response to ligand activation of the transcription factor peroxisome proliferator-activated receptor δ (PPARδ). We validated the method by monitoring the mRNA dynamics upon gene activation in the presence of a splicing inhibitor. Our mathematical model correctly identifies splicing as the inhibitor target, despite the noise in the data. PMID:25477385

  16. Tracing the molecular basis of transcriptional dynamics in noisy data by using an experiment-based mathematical model.

    PubMed

    Rybakova, Katja N; Tomaszewska, Aleksandra; van Mourik, Simon; Blom, Joke; Westerhoff, Hans V; Carlberg, Carsten; Bruggeman, Frank J

    2015-01-01

    Changes in transcription factor levels, epigenetic status, splicing kinetics and mRNA degradation can each contribute to changes in the mRNA dynamics of a gene. We present a novel method to identify which of these processes is changed in cells in response to external signals or as a result of a diseased state. The method employs a mathematical model, for which the kinetics of gene regulation, splicing, elongation and mRNA degradation were estimated from experimental data of transcriptional dynamics. The time-dependent dynamics of several species of adipose differentiation-related protein (ADRP) mRNA were measured in response to ligand activation of the transcription factor peroxisome proliferator-activated receptor δ (PPARδ). We validated the method by monitoring the mRNA dynamics upon gene activation in the presence of a splicing inhibitor. Our mathematical model correctly identifies splicing as the inhibitor target, despite the noise in the data. PMID:25477385

  17. Mathematical modelling of leprosy and its control.

    PubMed

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

    2015-03-01

    Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital. PMID:25765193

  18. A mathematical model of collagen lattice contraction

    PubMed Central

    Dallon, J. C.; Evans, E. J.; Ehrlich, H. Paul

    2014-01-01

    Two mathematical models for fibroblast–collagen interaction are proposed which reproduce qualitative features of fibroblast-populated collagen lattice contraction. Both models are force based and model the cells as individual entities with discrete attachment sites; however, the collagen lattice is modelled differently in each model. In the collagen lattice model, the lattice is more interconnected and formed by triangulating nodes to form the fibrous structure. In the collagen fibre model, the nodes are not triangulated, are less interconnected, and the collagen fibres are modelled as a string of nodes. Both models suggest that the overall increase in stress of the lattice as it contracts is not the cause of the reduced rate of contraction, but that the reduced rate of contraction is due to inactivation of the fibroblasts. PMID:25142520

  19. Basic Perforator Flap Hemodynamic Mathematical Model

    PubMed Central

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

    2016-01-01

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

  20. Mathematical Modelling: Transitions between the Real World and the Mathematical Model

    ERIC Educational Resources Information Center

    Crouch, Rosalind; Haines, Christopher

    2004-01-01

    Applications in engineering, science and technology within undergraduate programmes can be difficult for students to understand. In this paper, new results are presented which go some way to demonstrate and explain the problems faced by students in linking mathematical models to real-world applications. The study is based on student responses to…

  1. Mathematical modeling of deformation during hot rolling

    SciTech Connect

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

    1994-12-31

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

  2. Comprehensive diagnosis of whole-body acid-base and fluid-electrolyte disorders using a mathematical model and whole-body base excess.

    PubMed

    Wolf, Matthew B

    2015-08-01

    A mathematical model of whole-body acid-base and fluid-electrolyte balance was used to provide information leading to the diagnosis and fluid-therapy treatment in patients with complex acid-base disorders. Given a set of measured laboratory-chemistry values for a patient, a model of their unique, whole-body chemistry was created. This model predicted deficits or excesses in the masses of Na(+), K(+), Cl(-) and H2O as well as the plasma concentration of unknown or unmeasured species, such as ketoacids, in diabetes mellitus. The model further characterized the acid-base disorder by determining the patient's whole-body base excess and quantitatively partitioning it into ten components, each contributing to the overall disorder. The results of this study showed the importance of a complete set of laboratory measurements to obtain sufficient accuracy of the quantitative diagnosis; having only a minimal set, just pH and PCO2, led to a large scatter in the predicted results. A computer module was created that would allow a clinician to achieve this diagnosis at the bedside. This new diagnostic approach should prove to be valuable in the treatment of the critically ill. PMID:25281215

  3. Predicting electroporation of cells in an inhomogeneous electric field based on mathematical modeling and experimental CHO-cell permeabilization to propidium iodide determination.

    PubMed

    Dermol, Janja; Miklavčič, Damijan

    2014-12-01

    High voltage electric pulses cause electroporation of the cell membrane. Consequently, flow of the molecules across the membrane increases. In our study we investigated possibility to predict the percentage of the electroporated cells in an inhomogeneous electric field on the basis of the experimental results obtained when cells were exposed to a homogeneous electric field. We compared and evaluated different mathematical models previously suggested by other authors for interpolation of the results (symmetric sigmoid, asymmetric sigmoid, hyperbolic tangent and Gompertz curve). We investigated the density of the cells and observed that it has the most significant effect on the electroporation of the cells while all four of the mathematical models yielded similar results. We were able to predict electroporation of cells exposed to an inhomogeneous electric field based on mathematical modeling and using mathematical formulations of electroporation probability obtained experimentally using exposure to the homogeneous field of the same density of cells. Models describing cell electroporation probability can be useful for development and presentation of treatment planning for electrochemotherapy and non-thermal irreversible electroporation. PMID:24731594

  4. Analysis of observed and model mt fields based on three-dimensional mathematical modeling: Case study of the Verkhnee Penzhino-Korf profile

    NASA Astrophysics Data System (ADS)

    Belyavskii, V. V.; Nikolayev, Yu. I.

    2011-01-01

    We propose a system for the analysis of magnetotelluric (MT) data, which makes use of the invariant characteristics of the impedance tensor such as the maximum and minimum induction curves and the phase tensor. We examine the coefficients of the appearance and normalization of principal values of the impedance tensor. By the case study for Koryakiya, it is shown that the three-dimensional (3D) mathematical modeling and the Wiese-Parkinson vectors allow one to correct the results of one-dimensional (1D) and two-dimensional (2D) inversion of MT curves. Comparison between model and observed data based on the 1D inversion of MTS curves provides a pictorial view of the distortions of MT curves and their sensitivity to the parameters of a geological cross section.

  5. Aircraft engine mathematical model - linear system approach

    NASA Astrophysics Data System (ADS)

    Rotaru, Constantin; Roateşi, Simona; Cîrciu, Ionicǎ

    2016-06-01

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

  6. Mathematical and computational models of plasma flows

    NASA Astrophysics Data System (ADS)

    Brushlinsky, K. V.

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

  7. Mathematical Models and the Experimental Analysis of Behavior

    PubMed Central

    Mazur, James E

    2006-01-01

    The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make equally accurate predictions for a large body of data. In such cases, it is important to find and investigate situations for which the competing models make different predictions because, unless two models are actually mathematically equivalent, they are based on different assumptions about the psychological processes that underlie an observed behavior. Mathematical models developed in basic behavioral research have been used to predict and control behavior in applied settings, and they have guided research in other areas of psychology. A good mathematical model can provide a common framework for understanding what might otherwise appear to be diverse and unrelated behavioral phenomena. Because psychologists vary in their quantitative skills and in their tolerance for mathematical equations, it is important for those who develop mathematical models of behavior to find ways (such as verbal analogies, pictorial representations, or concrete examples) to communicate the key premises of their models to nonspecialists. PMID:16673829

  8. Constructing a Model of Mathematical Literacy.

    ERIC Educational Resources Information Center

    Pugalee, David K.

    1999-01-01

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

  9. Scaffolding Mathematical Modelling with a Solution Plan

    ERIC Educational Resources Information Center

    Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

    2015-01-01

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

  10. Mathematical Modelling and New Theories of Learning.

    ERIC Educational Resources Information Center

    Boaler, Jo

    2001-01-01

    Demonstrates the importance of expanding notions of learning beyond knowledge to the practices in mathematics classrooms. Considers a three-year study of students who learned through mathematical modeling. Shows that a modeling approach encouraged the development of a range of important practices in addition to knowledge that were useful in real…

  11. Mathematical Modelling as a Professional Task

    ERIC Educational Resources Information Center

    Frejd, Peter; Bergsten, Christer

    2016-01-01

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

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

    ERIC Educational Resources Information Center

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

    2005-01-01

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

  13. Rival approaches to mathematical modelling in immunology

    NASA Astrophysics Data System (ADS)

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

    2007-08-01

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

  14. Computer-Game-Based Tutoring of Mathematics

    ERIC Educational Resources Information Center

    Ke, Fengfeng

    2013-01-01

    This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…

  15. The mathematical bases for qualitative reasoning

    NASA Technical Reports Server (NTRS)

    Kalagnanam, Jayant; Simon, Herbert A.; Iwasaki, Yumi

    1991-01-01

    The practices of researchers in many fields who use qualitative reasoning are summarized and explained. The goal is to gain an understanding of the formal assumptions and mechanisms that underlie this kind of analysis. The explanations given are based on standard mathematical formalisms, particularly on ordinal properties, continuous differentiable functions, and the mathematics of nonlinear dynamic systems.

  16. Women in mathematics, science, and engineering college majors: A model predicting career aspirations based on ability, self-efficacy, role model influence, and role conflict

    NASA Astrophysics Data System (ADS)

    Nauta, Margaret Mary

    1997-09-01

    This study investigated a model of predictors of career aspirations among two groups of women: students in mathematics, physical science, and engineering majors and students in biological science majors. Based on theories of women's career development and social-cognitive theories, it was hypothesized that ability, self-efficacy, positivity of role model influence, and role conflict would influence the career aspirations of these women. It was further hypothesized that the students' year in school would contribute to this model as a predictor variable. Five hundred forty-six students (representing a 71% response rate) from Iowa State University were surveyed by mail to evaluate the fit of this model. The structural equation modeling procedure revealed that the career aspirations of the two groups of women were directly predicted by self-efficacy and role conflict and indirectly predicted by year in school, academic ability, and positivity of role model influence. The model for this combined group of students represented a good overall fit, explaining 94% of the covariation among the measured variables. When the two groups of students were compared, identical models for women in the two groups revealed different relationships among the variables. In contrast to the women in math, physical science, and engineering majors, the relationships between ability and self-efficacy and between positivity of role model influence and self-efficacy were significantly lower in magnitude for women in the biological sciences group. In addition to providing a parsimonious model for conceptualizing the experiences of women in traditionally male fields, this study's findings have implications for increasing the number of women who aspire to advanced careers in these occupations. Primarily, this study suggests that interventions designed to increase the degree to which students are influenced positively by role models may increase their self-efficacy expectations and may decrease the

  17. MATHEMATICAL MODEL FOR THE SELECTIVE DEPOSITION OF INHALED PHARMACEUTICALS

    EPA Science Inventory

    To accurately assess the potential therapeutic effects of airborne drugs, the deposition sites of inhaled particles must be known. erein, an original theory is presented for physiologically based pharmacokinetic modeling and related prophylaxis of airway diseases. he mathematical...

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

    ERIC Educational Resources Information Center

    Horton, Robert M.; Leonard, William H.

    2005-01-01

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

  19. A Seminar in Mathematical Model-Building.

    ERIC Educational Resources Information Center

    Smith, David A.

    1979-01-01

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

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

    ERIC Educational Resources Information Center

    Mischo, Christoph; Maaß, Katja

    2013-01-01

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

  1. The mathematics of cancer: integrating quantitative models.

    PubMed

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

    2015-12-01

    Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology. PMID:26597528

  2. A mathematical model of adult subventricular neurogenesis

    PubMed Central

    Ashbourn, J. M. A.; Miller, J. J.; Reumers, V.; Baekelandt, V.; Geris, L.

    2012-01-01

    Neurogenesis has been the subject of active research in recent years and many authors have explored the phenomenology of the process, its regulation and its purported purpose. Recent developments in bioluminescent imaging (BLI) allow direct in vivo imaging of neurogenesis, and in order to interpret the experimental results, mathematical models are necessary. This study proposes such a mathematical model that describes adult mammalian neurogenesis occurring in the subventricular zone and the subsequent migration of cells through the rostral migratory stream to the olfactory bulb (OB). This model assumes that a single chemoattractant is responsible for cell migration, secreted both by the OB and in an endocrine fashion by the cells involved in neurogenesis. The solutions to the system of partial differential equations are compared with the physiological rodent process, as previously documented in the literature and quantified through the use of BLI, and a parameter space is described, the corresponding solution to which matches that of the rodent model. A sensitivity analysis shows that this parameter space is stable to perturbation and furthermore that the system as a whole is sloppy. A large number of parameter sets are stochastically generated, and it is found that parameter spaces corresponding to physiologically plausible solutions generally obey constraints similar to the conditions reported in vivo. This further corroborates the model and its underlying assumptions based on the current understanding of the investigated phenomenon. Concomitantly, this leaves room for further quantitative predictions pertinent to the design of future proposed experiments. PMID:22572029

  3. Mathematical Models for Library Systems Analysis.

    ERIC Educational Resources Information Center

    Leimkuhler, F. F.

    1967-01-01

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

  4. Mathematical Modelling in the Early School Years

    ERIC Educational Resources Information Center

    English, Lyn D.; Watters, James J.

    2005-01-01

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

  5. A mathematical model for Vertical Attitude Takeoff and Landing (VATOL) aircraft simulation. Volume 2: Model equations and base aircraft data

    NASA Technical Reports Server (NTRS)

    Fortenbaugh, R. L.

    1980-01-01

    Equations incorporated in a VATOL six degree of freedom off-line digital simulation program and data for the Vought SF-121 VATOL aircraft concept which served as the baseline for the development of this program are presented. The equations and data are intended to facilitate the development of a piloted VATOL simulation. The equation presentation format is to state the equations which define a particular model segment. Listings of constants required to quantify the model segment, input variables required to exercise the model segment, and output variables required by other model segments are included. In several instances a series of input or output variables are followed by a section number in parentheses which identifies the model segment of origination or termination of those variables.

  6. Mathematical modeling of ligaments and tendons.

    PubMed

    Woo, S L; Johnson, G A; Smith, B A

    1993-11-01

    Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model. PMID:8302027

  7. Modelling Mathematical Argumentation: The Importance of Qualification

    ERIC Educational Resources Information Center

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

    2007-01-01

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

  8. a Discrete Mathematical Model to Simulate Malware Spreading

    NASA Astrophysics Data System (ADS)

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

    2012-10-01

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

  9. Inverse Mathematical Model: Yet Another Aspect of Applications and Modeling in Undergraduate Mathematics for Prospective Teachers

    ERIC Educational Resources Information Center

    Peretz, Dvora

    2005-01-01

    This article conceptualises a real-like model of a mathematical model as an inverse model. The inverse model draws on the un-complexity of concrete real life operations in order to help students to add concrete meaning to mathematical algorithms. The inverse model is described in the context of a pedagogical perception, which grants students in…

  10. Mathematical Modeling of Chemical Stoichiometry

    ERIC Educational Resources Information Center

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

    2007-01-01

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

  11. A Mathematical Model of Idiopathic Pulmonary Fibrosis

    PubMed Central

    Hao, Wenrui; Marsh, Clay; Friedman, Avner

    2015-01-01

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

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

    PubMed Central

    Gaff, Holly; Weisstein, Anton E.

    2010-01-01

    Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. PMID:20810952

  13. Mathematical Modeling and the Presidential Election.

    ERIC Educational Resources Information Center

    Witkowski, Joseph C.

    1992-01-01

    Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)

  14. Mathematical Model Development and Simulation Support

    NASA Technical Reports Server (NTRS)

    Francis, Ronald C.; Tobbe, Patrick A.

    2000-01-01

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

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

    ERIC Educational Resources Information Center

    Eric, Chan Chun Ming

    2009-01-01

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

  16. Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

    PubMed Central

    Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

  17. Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

    PubMed

    Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

  18. The Mathematical Models of the Periodical Literature Publishing Process.

    ERIC Educational Resources Information Center

    Guang, Yu; Daren, Yu; Yihong, Rong

    2000-01-01

    Describes two mathematical models of the periodical publishing process based on a theoretical analysis. Discusses the publishing process for periodical literature, explains the continuous model and the discrete model, presents partial differential equations, and demonstrates the adaptability and the validity of the models. (LRW)

  19. Mathematical modeling of a rotary hearth calciner

    SciTech Connect

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

    1996-10-01

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

  20. Assessing the Effectiveness of STAD Model and Problem Based Learning in Mathematics Learning Achievement and Problem Solving Ability

    ERIC Educational Resources Information Center

    Rattanatumma, Tawachai; Puncreobutr, Vichian

    2016-01-01

    The objective of this study was to compare the effectiveness of teaching methods in improving Mathematics Learning Achievement and Problem solving ability of students at an international college. This is a Quasi-Experimental Research which was done the study with the first year students who have registered to study Mathematics subject at St.…

  1. Identifying Subtypes among Children with Developmental Coordination Disorder and Mathematical Learning Disabilities, Using Model-Based Clustering

    ERIC Educational Resources Information Center

    Pieters, Stefanie; Roeyers, Herbert; Rosseel, Yves; Van Waelvelde, Hilde; Desoete, Annemie

    2015-01-01

    A relationship between motor and mathematical skills has been shown by previous research. However, the question of whether subtypes can be differentiated within developmental coordination disorder (DCD) and/or mathematical learning disability (MLD) remains unresolved. In a sample of children with and without DCD and/or MLD, a data-driven…

  2. Mathematical model of tumor-immune surveillance.

    PubMed

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

    2016-09-01

    We present a novel mathematical model involving various immune cell populations and tumor cell populations. The model describes how tumor cells evolve and survive the brief encounter with the immune system mediated by natural killer (NK) cells and the activated CD8(+) cytotoxic T lymphocytes (CTLs). The model is composed of ordinary differential equations describing the interactions between these important immune lymphocytes and various tumor cell populations. Based on up-to-date knowledge of immune evasion and rational considerations, the model is designed to illustrate how tumors evade both arms of host immunity (i.e. innate and adaptive immunity). The model predicts that (a) an influx of an external source of NK cells might play a crucial role in enhancing NK-cell immune surveillance; (b) the host immune system alone is not fully effective against progression of tumor cells; (c) the development of immunoresistance by tumor cells is inevitable in tumor immune surveillance. Our model also supports the importance of infiltrating NK cells in tumor immune surveillance, which can be enhanced by NK cell-based immunotherapeutic approaches. PMID:27317864

  3. Mathematical modeling of electrocardiograms: a numerical study.

    PubMed

    Boulakia, Muriel; Cazeau, Serge; Fernández, Miguel A; Gerbeau, Jean-Frédéric; Zemzemi, Nejib

    2010-03-01

    This paper deals with the numerical simulation of electrocardiograms (ECG). Our aim is to devise a mathematical model, based on partial differential equations, which is able to provide realistic 12-lead ECGs. The main ingredients of this model are classical: the bidomain equations coupled to a phenomenological ionic model in the heart, and a generalized Laplace equation in the torso. The obtention of realistic ECGs relies on other important features--including heart-torso transmission conditions, anisotropy, cell heterogeneity and His bundle modeling--that are discussed in detail. The numerical implementation is based on state-of-the-art numerical methods: domain decomposition techniques and second order semi-implicit time marching schemes, offering a good compromise between accuracy, stability and efficiency. The numerical ECGs obtained with this approach show correct amplitudes, shapes and polarities, in all the 12 standard leads. The relevance of every modeling choice is carefully discussed and the numerical ECG sensitivity to the model parameters investigated. PMID:20033779

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

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

    ERIC Educational Resources Information Center

    Czocher, Jennifer A.

    2016-01-01

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

  6. Mathematical biodynamic feedthrough model applied to rotorcraft.

    PubMed

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

    2014-07-01

    Biodynamic feedthrough (BDFT) occurs when vehicle accelerations feed through the human body and cause involuntary control inputs. This paper proposes a model to quantitatively predict this effect in rotorcraft. This mathematical BDFT model aims to fill the gap between the currently existing black box BDFT models and physical BDFT models. The model structure was systematically constructed using asymptote modeling, a procedure described in detail in this paper. The resulting model can easily be implemented in many typical rotorcraft BDFT studies, using the provided model parameters. The model's performance was validated in both the frequency and time domain. Furthermore, it was compared with several recent BDFT models. The results show that the proposed mathematical model performs better than typical black box models and is easier to parameterize and implement than a recent physical model. PMID:24013832

  7. Mathematical model for contemplative amoeboid locomotion

    NASA Astrophysics Data System (ADS)

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

    2011-02-01

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

  8. Learning and Teaching Mathematics through Real Life Models

    ERIC Educational Resources Information Center

    Takaci, Djurdjica; Budinski, Natalija

    2011-01-01

    This paper proposes modelling based learning as a tool for learning and teaching mathematics in high school. We report on an example of modelling real world problems in two high schools in Serbia where students were introduced for the first time to the basic concepts of modelling. Student use of computers and educational software, GeoGebra, was…

  9. Incorporating neurophysiological concepts in mathematical thermoregulation models

    NASA Astrophysics Data System (ADS)

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

    2014-01-01

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

  10. Mathematical Model of Evolution of Brain Parcellation.

    PubMed

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

    2016-01-01

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

  11. Mathematical Model of Evolution of Brain Parcellation

    PubMed Central

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

    2016-01-01

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

  12. Mathematical Models of Tuberculosis Reactivation and Relapse

    PubMed Central

    Wallis, Robert S.

    2016-01-01

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

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

    ERIC Educational Resources Information Center

    Ciltas, Alper; Isik, Ahmet

    2013-01-01

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

  14. Mathematical Modeling of Viral Zoonoses in Wildlife

    PubMed Central

    Allen, L. J. S.; Brown, V. L.; Jonsson, C. B.; Klein, S. L.; Laverty, S. M.; Magwedere, K.; Owen, J. C.; van den Driessche, P.

    2011-01-01

    Zoonoses are a worldwide public health concern, accounting for approximately 75% of human infectious diseases. In addition, zoonoses adversely affect agricultural production and wildlife. We review some mathematical models developed for the study of viral zoonoses in wildlife and identify areas where further modeling efforts are needed. PMID:22639490

  15. Mathematical Model For Scattering From Mirrors

    NASA Technical Reports Server (NTRS)

    Wang, Yaujen

    1988-01-01

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

  16. Mathematical model for predicting human vertebral fracture

    NASA Technical Reports Server (NTRS)

    Benedict, J. V.

    1973-01-01

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

  17. Voters' Fickleness:. a Mathematical Model

    NASA Astrophysics Data System (ADS)

    Boccara, Nino

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

  18. Mathematical Modeling of Electrochemical Flow Capacitors

    SciTech Connect

    Hoyt, NC; Wainright, JS; Savinell, RF

    2015-01-13

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

  19. Mathematical modeling relevant to closed artificial ecosystems

    USGS Publications Warehouse

    DeAngelis, D.L.

    2003-01-01

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

  20. Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

    NASA Astrophysics Data System (ADS)

    Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.

    2016-02-01

    This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

  1. Mathematical modelling of animate and intentional motion.

    PubMed Central

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

    2003-01-01

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

  2. Cocaine addiction and personality: a mathematical model.

    PubMed

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

    2010-05-01

    The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse. PMID:20030966

  3. Mathematical modeling of endovenous laser treatment (ELT)

    PubMed Central

    Mordon, Serge R; Wassmer, Benjamin; Zemmouri, Jaouad

    2006-01-01

    Background and objectives Endovenous laser treatment (ELT) has been recently proposed as an alternative in the treatment of reflux of the Great Saphenous Vein (GSV) and Small Saphenous Vein (SSV). Successful ELT depends on the selection of optimal parameters required to achieve an optimal vein damage while avoiding side effects. Mathematical modeling of ELT could provide a better understanding of the ELT process and could determine the optimal dosage as a function of vein diameter. Study design/materials and methods The model is based on calculations describing the light distribution using the diffusion approximation of the transport theory, the temperature rise using the bioheat equation and the laser-induced injury using the Arrhenius damage model. The geometry to simulate ELT was based on a 2D model consisting of a cylindrically symmetric blood vessel including a vessel wall and surrounded by an infinite homogenous tissue. The mathematical model was implemented using the Macsyma-Pdease2D software (Macsyma Inc., Arlington, MA, USA). Damage to the vein wall for CW and single shot energy was calculated for 3 and 5 mm vein diameters. In pulsed mode, the pullback distance (3, 5 and 7 mm) was considered. For CW mode simulation, the pullback speed (1, 2, 3 mm/s) was the variable. The total dose was expressed as joules per centimeter in order to perform comparison to results already reported in clinical studies. Results In pulsed mode, for a 3 mm vein diameter, irrespective of the pullback distance (2, 5 or 7 mm), a minimum fluence of 15 J/cm is required to obtain a permanent damage of the intima. For a 5 mm vein diameter, 50 J/cm (15W-2s) is required. In continuous mode, for a 3 mm and 5 mm vein diameter, respectively 65 J/cm and 100 J/cm are required to obtain a permanent damage of the vessel wall. Finally, the use of different wavelengths (810 nm or 980 nm) played only a minor influence on these results. Discussion and conclusion The parameters determined by

  4. Mathematical modeling plasma transport in tokamaks

    SciTech Connect

    Quiang, Ji

    1995-12-31

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

  5. Wheels, Cranks, and Cams: An Animated Spreadsheet-Based Mathematical Model of a Four-Stroke Engine.

    ERIC Educational Resources Information Center

    Callender, J. T.; Jackson, R.

    1998-01-01

    Analyzes the mathematics of rotational and translational motion and how one can influence the other in the context of cams and cranks. Describes how the individual components can be brought together to simulate a four-stroke engine and how the engine animates again using the same simple macro. (Author/ASK)

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

    ERIC Educational Resources Information Center

    Karali, Diren; Durmus, Soner

    2015-01-01

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

  7. The (Mathematical) Modeling Process in Biosciences

    PubMed Central

    Torres, Nestor V.; Santos, Guido

    2015-01-01

    In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology. PMID:26734063

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

    ERIC Educational Resources Information Center

    Carrejo, David J.; Marshall, Jill

    2007-01-01

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

  9. Turbulent motion of mass flows. Mathematical modeling

    NASA Astrophysics Data System (ADS)

    Eglit, Margarita; Yakubenko, Alexander; Yakubenko, Tatiana

    2016-04-01

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

  10. On Mathematical Modeling Of Quantum Systems

    SciTech Connect

    Achuthan, P.; Narayanankutty, Karuppath

    2009-07-02

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

  11. Mathematical Models of Cardiac Pacemaking Function

    NASA Astrophysics Data System (ADS)

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

    2013-10-01

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

  12. Mathematical model of self-cycling fermentation

    SciTech Connect

    Wincure, B.M.; Cooper, D.G.; Rey, A.

    1995-04-20

    This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation.

  13. Two Mathematical Models of Nonlinear Vibrations

    NASA Technical Reports Server (NTRS)

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

    2007-01-01

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

  14. A mathematical model of the CH-53 helicopter

    NASA Technical Reports Server (NTRS)

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

    1980-01-01

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

  15. Mathematical Model Of Nerve/Muscle Interaction

    NASA Technical Reports Server (NTRS)

    Hannaford, Blake

    1990-01-01

    Phasic Excitation/Activation (PEA) mathematical model simulates short-term nonlinear dynamics of activation and control of muscle by nerve. Includes electronic and mechanical elements. Is homeomorphic at level of its three major building blocks, which represent motoneuron, dynamics of activation of muscle, and mechanics of muscle.

  16. Mathematical and physical modelling of materials processing

    NASA Technical Reports Server (NTRS)

    1982-01-01

    Mathematical and physical modeling of turbulence phenomena in metals processing, electromagnetically driven flows in materials processing, gas-solid reactions, rapid solidification processes, the electroslag casting process, the role of cathodic depolarizers in the corrosion of aluminum in sea water, and predicting viscoelastic flows are described.

  17. Introduction to mathematical models and methods

    SciTech Connect

    Siddiqi, A. H.; Manchanda, P.

    2012-07-17

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

  18. Some mathematical tools for a modeller's workbench

    NASA Technical Reports Server (NTRS)

    Cohen, E.

    1984-01-01

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

  19. Mathematical model of the SH-3G helicopter

    NASA Technical Reports Server (NTRS)

    Phillips, J. D.

    1982-01-01

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

  20. Mathematical challenges in glacier modeling (Invited)

    NASA Astrophysics Data System (ADS)

    jouvet, G.

    2013-12-01

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

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

    ERIC Educational Resources Information Center

    Bukova-Guzel, Esra

    2011-01-01

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

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

    ERIC Educational Resources Information Center

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

    2012-01-01

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

  3. Analysis of Mathematical Modelling on Potentiometric Biosensors

    PubMed Central

    Mehala, N.; Rajendran, L.

    2014-01-01

    A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

  4. Analysis of mathematical modelling on potentiometric biosensors.

    PubMed

    Mehala, N; Rajendran, L

    2014-01-01

    A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

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

    NASA Astrophysics Data System (ADS)

    Smith, Erick; Haarer, Shawn; Confrey, Jere

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

  6. A physics-based two-dimensional comprehensive mathematical model to predict non-uniform regression rate in solid fuels for hybrid rocket motors

    NASA Astrophysics Data System (ADS)

    Antoniou, Antonis

    A numerical study using a comprehensive physics based mathematical model is conducted to predict the fuel regression rate in hybrid rocket fuels. The physical model adopted for the study is based on an unsteady, two-domain (solid fuel and gaseous oxidizer coupled through a moving interface) concept where both domains are assumed to be two-dimensional. The oxidizer gas flow is assumed to be compressible and turbulent with Navier-Stokes Assumptions. The radiative heat transfer is incorporated to the energy equation for the gas domain using the Rosseland diffusion approximation. Fuel is assumed to be a nontransparent isotropic solid. The two domains are coupled through an energy balance at the interface that includes heat transfer due to radiation, conduction, and ablation. The regression rate of the fuel surface due to ablation is modeled using the first-order Arrhenius Equation. The combustion of the ablated fuel is modeled by single step, three species chemical reaction equation of second order Arrhenius type. The solution to the governing differential equations of the present model is obtained by first transform the solution domain using a time and space dependent transformation. In the gas domain the transformed set of differential equations is discretized by a fully implicit finite-difference technique then linearized by using Newton linearization method. The resulting set of algebraic equations are transformed by the Coupled Modified Strongly Implicit Procedure (CMSIP) for the primitive variables of the problem. Validation of the solution algorithm and the CMSIP that is developed for this study is validated through the study of two bench mark cases: driven cavity and flow through channel. Furthermore, the results of the comprehensive model are compared to those of the parabolic incompressible model. Finally the proposed comprehensive mathematical model is used to predict the unsteady temperature and pressure distributions, and the velocity field in the gas

  7. Mathematical modeling as a tool for planning anticancer therapy

    PubMed Central

    Swierniak, Andrzej; Kimmel, Marek; Smieja, Jaroslaw

    2009-01-01

    We review a large volume of literature concerning mathematical models of cancer therapy, oriented towards optimization of treatment protocols. The review, although partly idiosyncratic, covers such major areas of therapy optimization as phase-specific chemotherapy, antiangiogenic therapy and therapy under drug resistance. We start from early cell-cycle progression models, very simple but admitting explicit mathematical solutions, based on methods of control theory. We continue with more complex models involving evolution of drug resistance and pharmacokinetic and pharmacodynamic effects. Then, we consider two more recent areas: angiogenesis of tumors and molecular signaling within and among cells. We discuss biological background and mathematical techniques of this field, which has a large although only partly realized potential for contributing to cancer treatment. PMID:19825370

  8. Mathematical modeling of biomass fuels formation process

    SciTech Connect

    Gaska, Krzysztof Wandrasz, Andrzej J.

    2008-07-01

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

  9. The stability of colorectal cancer mathematical models

    NASA Astrophysics Data System (ADS)

    Khairudin, Nur Izzati; Abdullah, Farah Aini

    2013-04-01

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

  10. Multi-Objective Ant Colony Optimization Based on the Physarum-Inspired Mathematical Model for Bi-Objective Traveling Salesman Problems.

    PubMed

    Zhang, Zili; Gao, Chao; Lu, Yuxiao; Liu, Yuxin; Liang, Mingxin

    2016-01-01

    Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs. PMID:26751562

  11. Multi-Objective Ant Colony Optimization Based on the Physarum-Inspired Mathematical Model for Bi-Objective Traveling Salesman Problems

    PubMed Central

    Zhang, Zili; Gao, Chao; Lu, Yuxiao; Liu, Yuxin; Liang, Mingxin

    2016-01-01

    Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs. PMID:26751562

  12. Aspects Of Multicriterial Mathematical Modeling And Of The Fuzzy Formalism For The Hierarchization Of Study Programs Based On Several Quality Characteristics

    NASA Astrophysics Data System (ADS)

    Bucur, Amelia

    2015-09-01

    The aim of this paper is to present aspects of mathematical modeling for the hierarchization of study programs from universities, based on several quality characteristics. The tools used pertain to multicriterial optimization, to the different methods of assessing importance coefficients, to the utility theory, the fuzzy formalism, and to the fuzzy simple additive weighting method. The conclusion is that multicriterial decision-making methods can be efficiently used in assessing the quality of study programs, noting that, just like other methods from the decision theory, the multicriterial decision-making methods highlight aspects of problems differently, therefore, there can be no comparison or competitiveness between them, and choosing one over the other is up to the decision-maker.

  13. Mathematical modeling of the aerodynamic characteristics in flight dynamics

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

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

  14. Computing Linear Mathematical Models Of Aircraft

    NASA Technical Reports Server (NTRS)

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

    1991-01-01

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

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

    ERIC Educational Resources Information Center

    Swetz, Frank

    1991-01-01

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

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

    ERIC Educational Resources Information Center

    Lingefjard, Thomas

    2002-01-01

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

  17. An Experimental Approach to Mathematical Modeling in Biology

    ERIC Educational Resources Information Center

    Ledder, Glenn

    2008-01-01

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

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

    PubMed

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

    2013-12-01

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

  19. Use of mathematical modeling in nuclear measurements projects

    SciTech Connect

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

    2011-07-01

    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)

  20. Agent-based mathematical modeling as a tool for estimating Trypanosoma cruzi vector-host contact rates.

    PubMed

    Yong, Kamuela E; Mubayi, Anuj; Kribs, Christopher M

    2015-11-01

    The parasite Trypanosoma cruzi, spread by triatomine vectors, affects over 100 mammalian species throughout the Americas, including humans, in whom it causes Chagas' disease. In the U.S., only a few autochthonous cases have been documented in humans, but prevalence is high in sylvatic hosts (primarily raccoons in the southeast and woodrats in Texas). The sylvatic transmission of T. cruzi is spread by the vector species Triatoma sanguisuga and Triatoma gerstaeckeri biting their preferred hosts and thus creating multiple interacting vector-host cycles. The goal of this study is to quantify the rate of contacts between different host and vector species native to Texas using an agent-based model framework. The contact rates, which represent bites, are required to estimate transmission coefficients, which can be applied to models of infection dynamics. In addition to quantitative estimates, results confirm host irritability (in conjunction with host density) and vector starvation thresholds and dispersal as determining factors for vector density as well as host-vector contact rates. PMID:26215127

  1. Mathematical model of electrical contact bouncing

    NASA Astrophysics Data System (ADS)

    Kharin, Stanislav

    2015-09-01

    Mathematical model of a contact bouncing takes into account elastic-plastic and electrodynamic forces, phase transformations during interaction of electrical arc with the contact surface as a result of increasing temperature. It is based on the integro-differential equations for the contact motion and Stefan problem for the temperature field. These equations describe four consecutive stages of the contact vibration from the impact at contact closing up to opening after bouncing including effects of penetration and restitution. The new method for the solution of the Stefan problem is elaborated, which enables us to get the information about dynamics of zones of elasticity, plasticity and phase transformations during contact vibration. It is shown that the decrement of damping depends on the coefficient of plasticity and the moment of inertia only, while the frequency of vibration depends also on the hardness of contact, its temperature, properties of contact spring, and geometry of rotational mechanism. It is found also from the solution of Stefan problem that the relationship between dynamical zones of plasticity and melting explains the decrease of current density and contact welding. The results of calculations are compared with the experimental data.

  2. Gifted Learners and Mathematical Achievement: An Analysis of Gifted Instructional Models

    ERIC Educational Resources Information Center

    Anderson, Lezley Barker

    2013-01-01

    The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…

  3. Mathematical Modeling of Photochemical Air Pollution.

    NASA Astrophysics Data System (ADS)

    McRae, Gregory John

    Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations. The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms. Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF(,6)) tracer experiments. Conventional models are employed for neutral and stable conditions. A new formulation for gaseous deposition fluxes

  4. Mathematical modeling of vertebrate limb development.

    PubMed

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

    2013-05-01

    In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton. PMID:23219575

  5. Editorial: Mathematical modelling of infectious diseases.

    PubMed

    Fenton, Andy

    2016-06-01

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

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

    ERIC Educational Resources Information Center

    Edwards, Thomas

    1995-01-01

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

  7. Mathematical Models for HIV Transmission Dynamics

    PubMed Central

    Cassels, Susan; Clark, Samuel J.; Morris, Martina

    2012-01-01

    Summary HIV researchers have long appreciated the need to understand the social and behavioral determinants of HIV-related risk behavior, but the cumulative impact of individual behaviors on population-level HIV outcomes can be subtle and counterintuitive, and the methods for studying this are rarely part of a traditional social science or epidemiology training program. Mathematical models provide a way to examine the potential effects of the proximate biologic and behavioral determinants of HIV transmission dynamics, alone and in combination. The purpose of this article is to show how mathematical modeling studies have contributed to our understanding of the dynamics and disparities in the global spread of HIV. Our aims are to demonstrate the value that these analytic tools have for social and behavioral sciences in HIV prevention research, to identify gaps in the current literature, and to suggest directions for future research. PMID:18301132

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

    ERIC Educational Resources Information Center

    Jurow, A. Susan

    2004-01-01

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

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

    ERIC Educational Resources Information Center

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

    2008-01-01

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

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

    ERIC Educational Resources Information Center

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

    2009-01-01

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

  11. Mathematical Model For Deposition Of Soot

    NASA Technical Reports Server (NTRS)

    Makel, Darby B.

    1991-01-01

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

  12. Modeling eBook acceptance: A study on mathematics teachers

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

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

  13. Mathematical models for quantifying eruption velocity in degassing pipes based on exsolution of a single gas and simultaneous exsolution of multiple gases

    NASA Astrophysics Data System (ADS)

    Leon, Arturo S.

    2016-09-01

    After the limnic eruptions at Nyos and Monoun in the 1980s, degassing pipes were installed to reduce the continuous increase of CO2 at the bottom of these lakes. The degassing system consists of a vertical pipe from the lake bottom to the surface and a small pump located near the top of the pipe, which raises water in the pipe up to a level where it becomes saturated with gas, which in turn leads to volume expansion and eruption. This paper describes two new mathematical models for predicting eruption velocity in degassing pipes based on exsolution of a single gas and the simultaneous exsolution of multiple gases. The models were applied to the degassing system of lakes Nyos and Monoun, which contain two main gases, namely CO2 and CH4. Because the volume proportion of CH4 is significant only in Lake Monoun, the Lake Nyos test case considered the CO2 gas only, while as the Lake Monoun test case considered the simultaneous exsolution of CO2 and CH4. Good agreement between the results of the models and observed data is found for both test cases. The results for the eruption in Lake Monoun considering the two main gases measured in this lake (CO2 and CH4) were found to have a better agreement with the measurements compared to the model results obtained considering the main gas only (CO2).

  14. Automatic mathematical modeling for real time simulation system

    NASA Technical Reports Server (NTRS)

    Wang, Caroline; Purinton, Steve

    1988-01-01

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

  15. Mathematical Models and the Experimental Analysis of Behavior

    ERIC Educational Resources Information Center

    Mazur, James E.

    2006-01-01

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

  16. Mathematical models of breast and ovarian cancers.

    PubMed

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

    2016-07-01

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

  17. Discipline-Based Remediation: Bridging the Mathematics Gap

    NASA Astrophysics Data System (ADS)

    Wenner, Jennifer M.; Baer, Eric M.; Burn, Helen E.

    2013-10-01

    Geoscience relies on numbers, data, equations, graphical representations, and other quantitative skills; therefore, introductory geoscience courses need to accurately portray the science as quantitative [e.g., Wenner et al., 2009]. However, up to 57% of students arrive at college underprepared to perform mathematics at the level necessary to succeed in introductory courses [ACT, 2011]. Although some institutions have turned to prerequisites as a way to ensure appropriate preparation, these extra courses can place undue financial, temporal, and academic burdens on interested students, keeping them from enrolling in science courses that may interest them. As an alternative to mathematics prerequisites, geoscience faculty at the University of Wisconsin Oshkosh and Highline Community College in Des Moines, Wash., funded by the National Science Foundation, developed a model of successful integration of discipline-based mathematics remediation into an introductory geoscience course: The Math You Need, When You Need It (TMYN; http://serc.carleton.edu/mathyouneed/).

  18. Computational oncology - mathematical modelling of drug regimens for precision medicine.

    PubMed

    Barbolosi, Dominique; Ciccolini, Joseph; Lacarelle, Bruno; Barlési, Fabrice; André, Nicolas

    2016-04-01

    Computational oncology is a generic term that encompasses any form of computer-based modelling relating to tumour biology and cancer therapy. Mathematical modelling can be used to probe the pharmacokinetics and pharmacodynamics relationships of the available anticancer agents in order to improve treatment. As a result of the ever-growing numbers of druggable molecular targets and possible drug combinations, obtaining an optimal toxicity-efficacy balance is an increasingly complex task. Consequently, standard empirical approaches to optimizing drug dosing and scheduling in patients are now of limited utility; mathematical modelling can substantially advance this practice through improved rationalization of therapeutic strategies. The implementation of mathematical modelling tools is an emerging trend, but remains largely insufficient to meet clinical needs; at the bedside, anticancer drugs continue to be prescribed and administered according to standard schedules. To shift the therapeutic paradigm towards personalized care, precision medicine in oncology requires powerful new resources for both researchers and clinicians. Mathematical modelling is an attractive approach that could help to refine treatment modalities at all phases of research and development, and in routine patient care. Reviewing preclinical and clinical examples, we highlight the current achievements and limitations with regard to computational modelling of drug regimens, and discuss the potential future implementation of this strategy to achieve precision medicine in oncology. PMID:26598946

  19. A Computational and Mathematical Model for Device Induced Thrombosis

    NASA Astrophysics Data System (ADS)

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

    2015-11-01

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

  20. Mathematical Modeling of Ultraporous Nonmetallic Reticulated Materials

    NASA Astrophysics Data System (ADS)

    Alifanov, O. M.; Cherepanov, V. V.; Morzhukhina, A. V.

    2015-01-01

    We have developed an imitation statistical mathematical model reflecting the structure and the thermal, electrophysical, and optical properties of nonmetallic ultraporous reticulated materials. This model, in combination with a nonstationary thermal experiment and methods of the theory of inverse heat transfer problems, permits determining the little-studied characteristics of the above materials such as the radiative and conductive heat conductivities, the spectral scattering and absorption coefficients, the scattering indicatrix, and the dielectric constants, which are of great practical interest but are difficult to investigate.

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

    PubMed

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

    2014-04-01

    A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations. PMID:24560011

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  3. Development of a Multidisciplinary Middle School Mathematics Infusion Model

    ERIC Educational Resources Information Center

    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…

  4. Assessment of Primary 5 Students' Mathematical Modelling Competencies

    ERIC Educational Resources Information Center

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

    2012-01-01

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

  5. Exploring the Relationship between Mathematical Modelling and Classroom Discourse

    ERIC Educational Resources Information Center

    Redmond, Trevor; Sheehy, Joanne; Brown, Raymond

    2010-01-01

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

  6. Mathematical modeling of COD removal via the combined treatment of domestic wastewater and landfill leachate based on the PACT process.

    PubMed

    Fernández Bou, Ángel S; Nascentes, Alexandre Lioi; Costa Pereira, Barbara; Da Silva, Leonardo Duarte Batista; Alberto Ferreira, João; Campos, Juacyara Carbonelli

    2015-01-01

    The experiments performed in this study consisted of 16 batch reactors fed different mixtures of landfill leachate combined with synthetic wastewater treated using the Powdered Activated Carbon Treatment (PACT) process. The objective was to measure the COD mass removal per liter each day for each reactor using two models: the first model combined the variables PAC concentration (0 g·L(-1), 2 g·L(-1), 4 g·L(-1), and 6 g·L(-1)) and leachate rate in the wastewater (0%, 2%, 5%, and 10%), and the second model combined the PAC concentration and the influent COD. The Response Surface Methodology with Central Composite Design was used to describe the response surface of both models considered in this study. Domestic wastewater was produced under controlled conditions in the laboratory where the experiments were performed. The results indicated that the PAC effect was null when the influent did not contain leachate; however, as the concentration of leachate applied to the mixture was increased, the addition of a higher PAC concentration resulted in a better COD mass removal in the reactors. The adjusted R(2) values of the two models were greater than 0.95, and the predicted R(2) values were greater than 0.93. The models may be useful for wastewater treatment companies to calculate PAC requirements in order to meet COD mass removal objectives in combined treatment. PMID:25723064

  7. Modelling of and Conjecturing on a Soccer Ball in a Korean Eighth Grade Mathematics Classroom

    ERIC Educational Resources Information Center

    Lee, Kyeong-Hwa

    2011-01-01

    The purpose of this article was to describe the task design and implementation of cultural artefacts in a mathematics lesson based on the integration of modelling and conjecturing perspectives. The conceived process of integrating a soccer ball into mathematics lessons via modelling- and conjecturing-based instruction was first detailed. Next, the…

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

    PubMed

    Li, Xuefang; Xu, Jian-Xin

    2016-10-01

    Pancreatic cancer is one of the most deadly types of cancer since it typically spreads rapidly and can seldom be detected in its early stage. Pancreatic cancer therapy is thus a challenging task, and appropriate prognosis or assessment for pancreatic cancer therapy is of critical importance. In this work, based on available clinical data in Niu et al. (2013) we develop a mathematical prognosis model that can predict the overall survival of pancreatic cancer patients who receive immunotherapy. The mathematical model incorporates pancreatic cancer cells, pancreatic stellate cells, three major classes of immune effector cells CD8+ T cells, natural killer cells, helper T cells, and two major classes of cytokines interleukin-2 (IL-2) and interferon-γ (IFN-γ). The proposed model describes the dynamic interaction between tumor and immune cells. In order for the model to be able to generate appropriate prognostic results for disease progression, the distribution and stability properties of equilibria in the mathematical model are computed and analysed in absence of treatments. In addition, numerical simulations for disease progression with or without treatments are performed. It turns out that the median overall survival associated with CIK immunotherapy is prolonged from 7 to 13months compared with the survival without treatment, this is consistent with the clinical data observed in Niu et al. (2013). The validity of the proposed mathematical prognosis model is thus verified. Our study confirms that immunotherapy offers a better prognosis for pancreatic cancer patients. As a direct extension of this work, various new therapy methods that are under exploration and clinical trials could be assessed or evaluated using the newly developed mathematical prognosis model. PMID:27338302

  9. A community effort towards a knowledge-base and mathematical model of the human pathogen Salmonella Typhimurium LT2

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Metabolic reconstructions (MRs) are common denominators in systems biology and represent biochemical, genetic, and genomic (BiGG) knowledge-bases for target organisms by capturing currently available information in a consistent, structured manner. Salmonella enterica subspecies I serovar Typhimurium...

  10. Mathematical model to predict drivers' reaction speeds.

    PubMed

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

    2012-02-01

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

  11. Mathematical modelling of submarine landslide motion

    NASA Astrophysics Data System (ADS)

    Burminskij, A.

    2012-04-01

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

  12. Lipid Raft Size and Lipid Mobility in Non-raft Domains Increase during Aging and Are Exacerbated in APP/PS1 Mice Model of Alzheimer's Disease. Predictions from an Agent-Based Mathematical Model

    PubMed Central

    Santos, Guido; Díaz, Mario; Torres, Néstor V.

    2016-01-01

    A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease. PMID:27014089

  13. Lipid Raft Size and Lipid Mobility in Non-raft Domains Increase during Aging and Are Exacerbated in APP/PS1 Mice Model of Alzheimer's Disease. Predictions from an Agent-Based Mathematical Model.

    PubMed

    Santos, Guido; Díaz, Mario; Torres, Néstor V

    2016-01-01

    A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease. PMID:27014089

  14. Mathematical modeling of the West Africa Ebola epidemic.

    PubMed

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

    2015-01-01

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

  15. Mathematical Modeling of Extinction of Inhomogeneous Populations.

    PubMed

    Karev, G P; Kareva, I

    2016-04-01

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

  16. Mathematical Modeling of Extinction of Inhomogeneous Populations

    PubMed Central

    Karev, G.P.; Kareva, I.

    2016-01-01

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

  17. Mathematical Models of Continuous Flow Electrophoresis

    NASA Technical Reports Server (NTRS)

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

    1985-01-01

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

  18. Mathematics of tsunami: modelling and identification

    NASA Astrophysics Data System (ADS)

    Krivorotko, Olga; Kabanikhin, Sergey

    2015-04-01

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

  19. Mathematical modeling of diesel fuel hydrotreating

    NASA Astrophysics Data System (ADS)

    Tataurshikov, A.; Ivanchina, E.; Krivtcova, N.; Krivtsov, E.; Syskina, A.

    2015-11-01

    Hydrotreating of the diesel fraction with the high initial sulfur content of 1,4 mass% is carried out in the flow-through laboratory setup with the industrial GKD-202 catalyst at various process temperature. On the basis of the experimental data the regularities of the hydrogenation reactions are revealed, and the formalized scheme of sulfur-containing components (sulfides, benzothiophenes, and dibenzothiophenes) transformations is made. The mathematical model of hydrotreating process is developed, the constant values for the reaction rate of hydrodesulfurization of the specified components are calculated.

  20. Mathematical model of laser PUVA psoriasis treatment

    NASA Astrophysics Data System (ADS)

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

    1991-05-01

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

  1. Place-Based Mathematics Education: A Conflated Pedagogy?

    ERIC Educational Resources Information Center

    Showalter, Daniel A.

    2013-01-01

    Place-based mathematics education (PBME) has the potential to engage students with the mathematics inherent in the local land, culture, and community. However, research has identified daunting barriers to this pedagogy, especially in abstract mathematics courses such as algebra and beyond. In this study, 15 graduates of a doctoral program in rural…

  2. Mathematical modeling to predict residential solid waste generation

    SciTech Connect

    Ojeda Benitez, Sara; Vega, Carolina Armijo de

    2008-07-01

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

  3. Mathematical modeling of infectious disease dynamics

    PubMed Central

    Siettos, Constantinos I.; Russo, Lucia

    2013-01-01

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

  4. Development of a new version of the Liverpool Malaria Model. I. Refining the parameter settings and mathematical formulation of basic processes based on a literature review

    PubMed Central

    2011-01-01

    Background A warm and humid climate triggers several water-associated diseases such as malaria. Climate- or weather-driven malaria models, therefore, allow for a better understanding of malaria transmission dynamics. The Liverpool Malaria Model (LMM) is a mathematical-biological model of malaria parasite dynamics using daily temperature and precipitation data. In this study, the parameter settings of the LMM are refined and a new mathematical formulation of key processes related to the growth and size of the vector population are developed. Methods One of the most comprehensive studies to date in terms of gathering entomological and parasitological information from the literature was undertaken for the development of a new version of an existing malaria model. The knowledge was needed to allow the justification of new settings of various model parameters and motivated changes of the mathematical formulation of the LMM. Results The first part of the present study developed an improved set of parameter settings and mathematical formulation of the LMM. Important modules of the original LMM version were enhanced in order to achieve a higher biological and physical accuracy. The oviposition as well as the survival of immature mosquitoes were adjusted to field conditions via the application of a fuzzy distribution model. Key model parameters, including the mature age of mosquitoes, the survival probability of adult mosquitoes, the human blood index, the mosquito-to-human (human-to-mosquito) transmission efficiency, the human infectious age, the recovery rate, as well as the gametocyte prevalence, were reassessed by means of entomological and parasitological observations. This paper also revealed that various malaria variables lack information from field studies to be set properly in a malaria modelling approach. Conclusions Due to the multitude of model parameters and the uncertainty involved in the setting of parameters, an extensive literature survey was carried out

  5. A community effort towards a knowledge-base and mathematical model of the human pathogen Salmonella Typhimurium LT2

    SciTech Connect

    Thiele, Ines; Hyduke, Daniel R.; Steeb, Benjamin; Fankam, Guy; Allen, Douglas K.; Bazzani, Susanna; Charusanti, Pep; Chen, Feng-Chi; Fleming, Ronan MT; Hsiung, Chao A.; De Keersmaecker, Sigrid CJ; Liao, Yu-Chieh; Marchal, Kathleen; Mo, Monica L.; Özdemir, Emre; Raghunathan, Anu; Reed, Jennifer L.; Shin, Sook-Il; Sigurbjörnsdóttir, Sara; Steinmann, Jonas; Sudarsan, Suresh; Swainston, Neil; Thijs, Inge M.; Zengler, Karsten; Palsson, Bernhard O.; Adkins, Joshua N.; Bumann, Dirk

    2011-01-01

    Metabolic reconstructions (MRs) are common denominators in systems biology and represent biochemical, genetic, and genomic (BiGG) knowledge-bases for target organisms by capturing currently available information in a consistent, structured manner. Salmonella enterica subspecies I serovar Typhimurium is a human pathogen, causes various diseases and its increasing antibiotic resistance poses a public health problem. Here, we describe a community-driven effort, in which more than 20 experts in S. Typhimurium biology and systems biology collaborated to reconcile and expand the S. Typhimurium BiGG knowledge-base. The consensus MR was obtained starting from two independently developed MRs for S. Typhimurium. Key results of this reconstruction jamboree include i) development and implementation of a community-based workflow for MR annotation and reconciliation; ii) incorporation of thermodynamic information; and iii) use of the consensus MR to identify potential multi-target drug therapy approaches. Finally, taken together, with the growing number of parallel MRs a structured, community-driven approach will be necessary to maximize quality while increasing adoption of MRs in experimental design and interpretation.

  6. Exploration of the R code-based mathematical model for PMI estimation using profiling of RNA degradation in rat brain tissue at different temperatures.

    PubMed

    Ma, Jianlong; Pan, Hui; Zeng, Yan; Lv, Yehui; Zhang, Heng; Xue, Aimin; Jiang, Jieqing; Ma, Kaijun; Chen, Long

    2015-12-01

    Precise estimation of postmortem interval (PMI) is crucial in some criminal cases. This study aims to find some optimal markers for PMI estimation and build a mathematical model that could be used in various temperature conditions. Different mRNA and microRNA markers in rat brain samples were detected using real-time fluorescent quantitative PCR at 12 time points within 144 h postmortem and at temperatures of 4, 15, 25, and 35 °C. Samples from 36 other rats were used to verify the animal mathematical model. Brain-specific mir-9 and mir-125b are effective endogenous control markers that are not affected by PMI up to 144 h postmortem under these temperatures, whereas the commonly used U6 is not a suitable endogenous control in this study. Among all the candidate markers, ΔCt (β-actin) has the best correlation coefficient with PMI and was used to build a new model using R software which can simultaneously manage both PMI and temperature parameters. This animal mathematical model is verified using samples from 36 other rats and shows increased accuracy for higher temperatures and longer PMI. In this study, β-actin was found to be an optimal marker to estimate PMI and some other markers were found to be suitable to act as endogenous controls. Additionally, we have used R code software to build a model of PMI estimation that could be used in various temperature conditions. PMID:26363634

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

    PubMed

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

    2010-05-01

    We present a biologically-based mathematical model that accounts for several features of the human sleep/wake cycle. These features include the timing of sleep and wakefulness under normal and sleep-deprived conditions, ultradian rhythms, more frequent switching between sleep and wakefulness due to the loss of orexin and the circadian dependence of several sleep measures. The model demonstrates how these features depend on interactions between a circadian pacemaker and a sleep homeostat and provides a biological basis for the two-process model for sleep regulation. The model is based on previous "flip-flop" conceptual models for sleep/wake and REM/NREM and we explore whether the neuronal components in these flip-flop models, with the inclusion of a sleep-homeostatic process and the circadian pacemaker, are sufficient to account for the features of the sleep/wake cycle listed above. The model is minimal in the sense that, besides the sleep homeostat and constant cortical drives, the model includes only those nuclei described in the flip-flop models. Each of the cell groups is modeled by at most two differential equations for the evolution of the total population activity, and the synaptic connections are consistent with those described in the flip-flop models. A detailed analysis of the model leads to an understanding of the mathematical mechanisms, as well as insights into the biological mechanisms, underlying sleep/wake dynamics. PMID:19557415

  8. Mathematical modelling of eukaryotic DNA replication.

    PubMed

    Hyrien, Olivier; Goldar, Arach

    2010-01-01

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

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

    ERIC Educational Resources Information Center

    Jung, Hyunyi; Mintos, Alexia; Newton, Jill

    2015-01-01

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

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

    ERIC Educational Resources Information Center

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

    2012-01-01

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

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

    SciTech Connect

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

    2014-10-17

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

  12. Mathematical Model of the Jet Engine Fuel System

    NASA Astrophysics Data System (ADS)

    Klimko, Marek

    2015-05-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-02-01

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

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

    SciTech Connect

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

    2014-01-15

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

  15. Mathematics Teacher Education: A Model from Crimea.

    ERIC Educational Resources Information Center

    Ferrucci, Beverly J.; Evans, Richard C.

    1993-01-01

    Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)

  16. Missing the Promise of Mathematical Modeling

    ERIC Educational Resources Information Center

    Meyer, Dan

    2015-01-01

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

  17. Mathematical modeling of a thermovoltaic cell

    NASA Technical Reports Server (NTRS)

    White, Ralph E.; Kawanami, Makoto

    1992-01-01

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

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

    PubMed

    Clément, Frédérique

    2016-07-01

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

  19. Kinetic models - mathematical models of everything?. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

    NASA Astrophysics Data System (ADS)

    Banasiak, J.

    2016-03-01

    Since the emergence of systematic science it has been recognized that a natural phenomenon can be described by different models that vary in their complexity and their ability to capture the details of the features relevant at the required level of the resolution. It has been tacitly assumed that whenever two such models are applicable at the same level, they must provide equivalent descriptions of the phenomenon. One of the earliest and most celebrated examples of this type is offered by gas flow which can be described either by the Boltzmann equation at a suitably understood molecular level or by the Euler or Navier-Stokes equations at the level of continuum. More precisely, the flow of a gas as a continuous medium, or, in other words, at the macro level, can be explained in more detail by analysing elementary collisions between pairs of molecules. Thus, the Boltzmann equation is often recognized as a more detailed equation of gas at the so-called mesoscopic, or kinetic, level from which macroscopic properties of gas, such as density, momentum or temperature, can be derived. It should be noted that one can model gas at an even more fundamental, or micro, level by tracing the motion of individual molecules by solving the system of the Newton equations that describe their interactions, [11].

  20. Balancing Classroom Management with Mathematical Learning: Using Practice-Based Task Design in Mathematics Teacher Education

    ERIC Educational Resources Information Center

    Biza, Irene; Nardi, Elena; Joel, Gareth

    2015-01-01

    In this paper we present the results from a study in which 21 mathematics trainee teachers engage with two practice-based tasks in which classroom management interferes with mathematical learning. We investigate the trainees' considerations when they make decisions in classroom situations and how these tasks can trigger their reflections on the…

  1. Mechanical-mathematical modeling for landslide process

    NASA Astrophysics Data System (ADS)

    Svalova, V.

    2009-04-01

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

  2. Attitude determination of a high altitude balloon system. Part 1: Development of the mathematical model

    NASA Technical Reports Server (NTRS)

    Nigro, N. J.; Elkouh, A. F.; Shen, K. S.; Nimityongskul, P.; Jhaveri, V. N.; Sethi, A.

    1975-01-01

    A mathematical model for predicting the three dimensional motion of the balloon system is developed, which includes the effects of bounce, pendulation and spin of each subsystem. Boundary layer effects are also examined, along with the aerodynamic forces acting on the balloon. Various simplified forms of the system mathematical model were developed, based on an order of magnitude analysis.

  3. Generalized Mathematical Model Predicting the Mechanical Processing Topography

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  4. Using mathematical models to understand metabolism, genes, and disease.

    PubMed

    Nijhout, H Frederik; Best, Janet A; Reed, Michael C

    2015-01-01

    Mathematical models are a useful tool for investigating a large number of questions in metabolism, genetics, and gene-environment interactions. A model based on the underlying biology and biochemistry is a platform for in silico biological experimentation that can reveal the causal chain of events that connect variation in one quantity to variation in another. We discuss how we construct such models, how we have used them to investigate homeostatic mechanisms, gene-environment interactions, and genotype-phenotype mapping, and how they can be used in precision and personalized medicine. PMID:26400419

  5. Student Perspectives of Web-Based Mathematics

    ERIC Educational Resources Information Center

    Loong, Esther Yook-Kin; Herbert, Sandra

    2012-01-01

    This paper presents the results of a survey conducted with students (N = 97) whose teachers have used the Web in their mathematics classes. Their responses to the use of the Internet for learning mathematics are reported here. Factor analyses were used to determine the constructs that underlie the survey. These constructs were found to be…

  6. Mathematical modelling of the anaerobic hybrid reactor.

    PubMed

    Soroa, S; Gomez, J; Ayesa, E; Garcia-Heras, J L

    2006-01-01

    This paper presents a new mathematical model for the anaerobic hybrid reactor (AHR) (a UASB reactor and an anaerobic filter in series) and its experimental calibration and verification. The model includes a biochemical part and a mass transport one, which considers the AHR as two contact reactors in series. The anaerobic process transformations are described by the model developed by Siegrist et al. The fraction (F) of solids in the clarification zone of the UASB reactor that leaves this first reactor is the key physical parameter to be estimated. The main parameters of the model were calibrated using experimental results from a bench-scale AHR fed with real slaughterhouse wastewater. The fraction of inert particulate COD in the influent and the factor F were estimated by a trial and error procedure comparing experimental and simulated results of the mass of solids in the lower tank and the VSS concentration in the AHR effluent. A good fit was obtained. The final verification was carried out by comparing a set of experiments with simulated data. The model's capability to predict the process performance was thus proved. PMID:16939085

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

    ERIC Educational Resources Information Center

    Akgün, Levent

    2015-01-01

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

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

    ERIC Educational Resources Information Center

    Rash, Agnes M.; Zurbach, E. Peter

    2004-01-01

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

  9. Mathematical Modeling of the Origins of Life

    NASA Technical Reports Server (NTRS)

    Pohorille, Andrew

    2006-01-01

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

  10. Mathematical analysis of epidemiological models with heterogeneity

    SciTech Connect

    Van Ark, J.W.

    1992-01-01

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

  11. Filler segmentation of SEM paper images based on mathematical morphology.

    PubMed

    Ait Kbir, M; Benslimane, Rachid; Princi, Elisabetta; Vicini, Silvia; Pedemonte, Enrico

    2007-07-01

    Recent developments in microscopy and image processing have made digital measurements on high-resolution images of fibrous materials possible. This helps to gain a better understanding of the structure and other properties of the material at micro level. In this paper SEM image segmentation based on mathematical morphology is proposed. In fact, paper models images (Whatman, Murillo, Watercolor, Newsprint paper) selected in the context of the Euro Mediterranean PaperTech Project have different distributions of fibers and fillers, caused by the presence of SiAl and CaCO3 particles. It is a microscopy challenge to make filler particles in the sheet distinguishable from the other components of the paper surface. This objectif is reached here by using switable strutural elements and mathematical morphology operators. PMID:17867540

  12. Mathematical modeling of stormwater pollution in a tidal embayment

    SciTech Connect

    Najjar, K.F.

    1989-01-01

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

  13. Mathematical and computer modeling of component surface shaping

    NASA Astrophysics Data System (ADS)

    Lyashkov, A.

    2016-04-01

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

  14. Mathematical modeling of human secondary osteons.

    PubMed

    Ascenzi, Maria-Grazia; Andreuzzi, Marta; Kabo, J Michael

    2004-01-01

    This investigation explores the structural dimensions and patterns within single secondary osteons, with consideration of their biological variation. New data from images obtained previously of osteons observed through linearly polarized light, electron microscopy, and micro-x-ray, combined with recent findings on lamellae by circularly polarized light, confocal microscopy, synchrotron x-ray diffraction, and micro-x-ray, provide the basis for novel computerized models of single osteons and single lamellae. The novelty of such models is the concurrent representation of (1) collagen-hydroxyapatite orientation, (2) relative hydroxyapatite percentage, (3) distributions of osteocytes' lacunae and canaliculae, and (4) biological variations in dimensions of the relevant structures. The mathematical software Maple realizes the computerized models. While the parts of the models are constructed on a personal computer, the voluminous data associated with the representation of lacunar and canalicular distributions require a supercomputer for assembly of the models and final analysis. The programming used to define the models affords the option to randomize the dimensional specifications of osteons, lamellae, lacunae, and canaliculae within the experimentally observed numeric ranges and distributions. Through this option, the program can operate so that each run of the file produces a unique random model within the observed biological variations. The program can also be run to implement specific dimensional requirements. The modeling has applications in the microstructural study of fracture propagation and remodeling, as well as in the simulation of mechanical testing. The approach taken here is of wide application and could be of value in other areas of microscopy such as scanning electron microscopy, microcomputerized tomography scan, and magnetic resonance imaging on cancellous bone structures. PMID:15000289

  15. Mathematical Model for the Mineralization of Bone

    NASA Technical Reports Server (NTRS)

    Martin, Bruce

    1994-01-01

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

  16. Mathematical Model for the Mineralization of Bone

    NASA Technical Reports Server (NTRS)

    Martin, Bruce

    1994-01-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

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

  18. Learning Achievement in Solving Word-Based Mathematical Questions through a Computer-Assisted Learning System

    ERIC Educational Resources Information Center

    Huang, Tzu-Hua; Liu, Yuan-Chen; Chang, Hsiu-Chen

    2012-01-01

    This study developed a computer-assisted mathematical problem-solving system in the form of a network instruction website to help low-achieving second- and third-graders in mathematics with word-based addition and subtraction questions in Taiwan. According to Polya's problem-solving model, the system is designed to guide these low-achievers…

  19. Prediction Assessments: Using Video-Based Predictions to Assess Prospective Teachers' Knowledge of Students' Mathematical Thinking

    ERIC Educational Resources Information Center

    Norton, Anderson; McCloskey, Andrea; Hudson, Rick A.

    2011-01-01

    In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child's mathematics…

  20. Learning Mathematics by Designing, Programming, and Investigating with Interactive, Dynamic Computer-Based Objects

    ERIC Educational Resources Information Center

    Marshall, Neil; Buteau, Chantal

    2014-01-01

    As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…

  1. Development of a mechanism and an accurate and simple mathematical model for the description of drug release: Application to a relevant example of acetazolamide-controlled release from a bio-inspired elastin-based hydrogel.

    PubMed

    Fernández-Colino, A; Bermudez, J M; Arias, F J; Quinteros, D; Gonzo, E

    2016-04-01

    Transversality between mathematical modeling, pharmacology, and materials science is essential in order to achieve controlled-release systems with advanced properties. In this regard, the area of biomaterials provides a platform for the development of depots that are able to achieve controlled release of a drug, whereas pharmacology strives to find new therapeutic molecules and mathematical models have a connecting function, providing a rational understanding by modeling the parameters that influence the release observed. Herein we present a mechanism which, based on reasonable assumptions, explains the experimental data obtained very well. In addition, we have developed a simple and accurate “lumped” kinetics model to correctly fit the experimentally observed drug-release behavior. This lumped model allows us to have simple analytic solutions for the mass and rate of drug release as a function of time without limitations of time or mass of drug released, which represents an important step-forward in the area of in vitro drug delivery when compared to the current state of the art in mathematical modeling. As an example, we applied the mechanism and model to the release data for acetazolamide from a recombinant polymer. Both materials were selected because of a need to develop a suitable ophthalmic formulation for the treatment of glaucoma. The in vitro release model proposed herein provides a valuable predictive tool for ensuring product performance and batch-to-batch reproducibility, thus paving the way for the development of further pharmaceutical devices. PMID:26838852

  2. Mathematical models of Ebola-Consequences of underlying assumptions.

    PubMed

    Feng, Zhilan; Zheng, Yiqiang; Hernandez-Ceron, Nancy; Zhao, Henry; Glasser, John W; Hill, Andrew N

    2016-07-01

    Mathematical models have been used to study Ebola disease transmission dynamics and control for the recent epidemics in West Africa. Many of the models used in these studies are based on the model of Legrand et al. (2007), and most failed to accurately project the outbreak's course (Butler, 2014). Although there could be many reasons for this, including incomplete and unreliable data on Ebola epidemiology and lack of empirical data on how disease-control measures quantitatively affect Ebola transmission, we examine the underlying assumptions of the Legrand model, and provide alternate formulations that are simpler and provide additional information regarding the epidemiology of Ebola during an outbreak. We developed three models with different assumptions about disease stage durations, one of which simplifies to the Legrand model while the others have more realistic distributions. Control and basic reproduction numbers for all three models are derived and shown to provide threshold conditions for outbreak control and prevention. PMID:27130854

  3. Mathematical model of one-man air revitalization system

    NASA Technical Reports Server (NTRS)

    1976-01-01

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

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

    PubMed

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

    2016-03-01

    In this work, we develop an impulsive mathematical model of Vitamin C (ascorbic acid) metabolism in healthy subjects for daily intake over a long period of time. The model includes the dynamics of ascorbic acid plasma concentration, the ascorbic acid absorption in the intestines and a novel approach to quantify the glomerular excretion of ascorbic acid. We investigate qualitative and quantitative dynamics. We show the existence and uniqueness of the global asymptotic stability of the periodic solution. We also perform a numerical simulation for the entire time period based on published data reporting parameters reflecting ascorbic acid metabolism at different oral doses of ascorbic acid. PMID:26724712

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

    NASA Astrophysics Data System (ADS)

    Shen, Ganghui; Xia, Yuanqing; Sun, Haoran

    2015-04-01

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

  6. TriBITS lifecycle model. Version 1.0, a lean/agile software lifecycle model for research-based computational science and engineering and applied mathematical software.

    SciTech Connect

    Willenbring, James M.; Bartlett, Roscoe Ainsworth; Heroux, Michael Allen

    2012-01-01

    Software lifecycles are becoming an increasingly important issue for computational science and engineering (CSE) software. The process by which a piece of CSE software begins life as a set of research requirements and then matures into a trusted high-quality capability is both commonplace and extremely challenging. Although an implicit lifecycle is obviously being used in any effort, the challenges of this process - respecting the competing needs of research vs. production - cannot be overstated. Here we describe a proposal for a well-defined software lifecycle process based on modern Lean/Agile software engineering principles. What we propose is appropriate for many CSE software projects that are initially heavily focused on research but also are expected to eventually produce usable high-quality capabilities. The model is related to TriBITS, a build, integration and testing system, which serves as a strong foundation for this lifecycle model, and aspects of this lifecycle model are ingrained in the TriBITS system. Here, we advocate three to four phases or maturity levels that address the appropriate handling of many issues associated with the transition from research to production software. The goals of this lifecycle model are to better communicate maturity levels with customers and to help to identify and promote Software Engineering (SE) practices that will help to improve productivity and produce better software. An important collection of software in this domain is Trilinos, which is used as the motivation and the initial target for this lifecycle model. However, many other related and similar CSE (and non-CSE) software projects can also make good use of this lifecycle model, especially those that use the TriBITS system. Indeed this lifecycle process, if followed, will enable large-scale sustainable integration of many complex CSE software efforts across several institutions.

  7. Modelling Mathematical Reasoning in Physics Education

    ERIC Educational Resources Information Center

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

    2012-01-01

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

  8. Model Learner Outcomes for Mathematics Education.

    ERIC Educational Resources Information Center

    Halvorson, Judith K.; Stenglein, Sharon M.

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

  9. Mathematics Teacher TPACK Standards and Development Model

    ERIC Educational Resources Information Center

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

    2009-01-01

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

  10. A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor

    NASA Technical Reports Server (NTRS)

    Sayyah, Rana; Hunt, Mitchell; MacLeod, Todd C.; Ho, Fat D.

    2009-01-01

    This paper presents a mathematical model characterizing the behavior of a simple amplifier using a FeFET. The model is based on empirical data and incorporates several variables that affect the output, including frequency, load resistance, and gate-to-source voltage. Since the amplifier is the basis of many circuit configurations, a mathematical model that describes the behavior of a FeFET-based amplifier will help in the integration of FeFETs into many other circuits.

  11. Mathematical modeling of Chikungunya fever control

    NASA Astrophysics Data System (ADS)

    Hincapié-Palacio, Doracelly; Ospina, Juan

    2015-05-01

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

  12. Teaching Modelling as an Alternative Approach to School Mathematics

    ERIC Educational Resources Information Center

    Yanagimoto, Tomoko

    2005-01-01

    Nowadays, mathematics has come to be increasingly put into practical use in various fields in society. However, Japanese students dislike mathematics. The purpose of this study is to consider the significance of teaching modelling. In this paper, I take up "Fuzzy modelling" as teaching material for senior high school students. As a result, it was…

  13. Mathematical Models of the Value of Achievement Testing.

    ERIC Educational Resources Information Center

    Pinsky, Paul D.

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

  14. iSTEM: Promoting Fifth Graders' Mathematical Modeling

    ERIC Educational Resources Information Center

    Yanik, H. Bahadir; Karabas, Celil

    2014-01-01

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

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

    ERIC Educational Resources Information Center

    Sendova, Evgenia; Grkovska, Slavica

    2005-01-01

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

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

    ERIC Educational Resources Information Center

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

    2010-01-01

    Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process--1) use of physical manipulatives, 2) interactive exploration of computer…

  17. Influence of viscosity on myocardium mechanical activity: a mathematical model.

    PubMed

    Katsnelson, Leonid B; Nikitina, Larissa V; Chemla, Denis; Solovyova, Olga; Coirault, Catherine; Lecarpentier, Yves; Markhasin, Vladimir S

    2004-10-01

    We have previously proposed and validated a mathematical model of myocardium contraction-relaxation cycle based on current knowledge of regulatory role of Ca2+ and cross-bridge kinetics in cardiac cell. That model did not include viscous elements. Here we propose a modification of the model, in which two viscous elements are added, one in parallel to the contractile element, and one more in parallel to the series elastic element. The modified model allowed us to simulate and explain some subtle experimental data on relaxation velocity in isotonic twitches and on a mismatch between the time course of sarcomere shortening/lengthening and the time course of active force generation in isometric twitches. Model results were compared with experimental data obtained from 28 rat LV papillary muscles contracting and relaxing against various loads. Additional model analysis suggested contribution of viscosity to main inotropic and lusitropic characteristics of myocardium performance. PMID:15302547

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

    NASA Astrophysics Data System (ADS)

    Forjan, Matej

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

  19. A mathematical model of biological evolution.

    PubMed

    Ishii, K; Matsuda, H; Ogita, N

    1982-01-01

    In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dNn(t)/dt = (mn(t) - mu)Nn(t) + muNn-1(t) (n = 0,1,2,3,...), where Nn(t) and mn(t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and mean is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by v infinity identical to lim t leads to infinity sigma infinity n = o nNn(t)/t sigma infinity n = o Nn(t) is rigorously obtained for the case (i) mn(t) = mn is independent of t (constant fitness model), where mn is essentially periodic with respect to n, and for the case (ii) mn(t) = s(-1) n+[t/tau] (periodic fitness model), together with the long time average -m infinity of the average Malthusian parameter -m identical to sigma infinity n = o mn(t)Nn(t)/sigma infinity n = o Nn(t). The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations. PMID:7119589

  20. Is there Life after Modelling? Student conceptions of mathematics

    NASA Astrophysics Data System (ADS)

    Houston, Ken; Mather, Glyn; Wood, Leigh N.; Petocz, Peter; Reid, Anna; Harding, Ansie; Engelbrecht, Johann; Smith, Geoff H.

    2010-09-01

    We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This questionnaire was completed by 1,200 undergraduate students of mathematics in Australia, the UK, Canada, South Africa, and Brunei. The sample included students ranging from those majoring in mathematics to those taking only one or two modules in mathematics. Responses were analysed starting from a previously-developed phenomenographic framework that required only minor modification, leading to an outcome space of four levels of conceptions about mathematics. We found that for many students modelling is fundamental to their conception of "What is mathematics?". In a small number of students, we identified a broader conception of mathematics, that we have labelled Life. This describes a view of mathematics as a way of thinking about reality and as an integral part of life, and represents an ideal aim for university mathematics education.

  1. Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability

    ERIC Educational Resources Information Center

    Saragih, Sahat; Napitupulu, Elvis

    2015-01-01

    The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…

  2. Mathematical modeling and the neuroscience of metaphor

    NASA Astrophysics Data System (ADS)

    Rising, Hawley K., III

    2008-02-01

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

  3. Mathematical modeling as a tool for investigating cell cycle control networks.

    PubMed

    Sible, Jill C; Tyson, John J

    2007-02-01

    Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems. PMID:17189866

  4. Mathematical modeling of the human knee joint

    SciTech Connect

    Ricafort, Juliet

    1996-05-01

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

  5. Mathematical models in biology: from molecules to life

    PubMed Central

    Kaznessis, Yiannis N.

    2011-01-01

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

  6. The development and evaluation of a mathematical nutrition model to predict digestible energy intake of broodmares based on body condition changes.

    PubMed

    Cordero, V V; Cavinder, C A; Tedeschi, L O; Sigler, D H; Vogelsang, M M; Arnold, C E

    2013-05-01

    Mathematical nutrition models have been developed for beef and dairy cattle to estimate dietary energy intake needed to change BCS. Similar technology has not been used to improve nutrition and feeding strategies for horses. An accurate equine nutrition model may enhance feeding management and reduce the costs of unnecessary overfeeding and promote an optimal level of fatness to achieve reproductive efficiency. The objectives of this study were to develop and evaluate a mathematical nutrition model capable of accurately predicting dietary energy changes to alter BW, rump fat (RF) thickness, and overall body fat (BF), which is needed to maximize profitability and productivity of mares. Model structure was similar to a previously developed model for cattle, and literature data for Quarter Horse mares were used to parameterize the horse model in predicting DE requirement associated with BCS changes. Evaluation of the horse model was performed using an independent dataset comprising 20 nonlactating Quarter Horse mares. Pretrial BCS was used to assign mares to 1 of 4 treatment groups and fed to alter BCS by 1 unit as follows: from 4 to 5 (Group 1), 5 to 4 (Group 2), 6 to 7 (Group 3), and 7 to 6 (Group 4). The BCS, RF thickness, and BW were measured for each mare before the commencement of the feeding trial and once per week thereafter for the duration of a 30-d feeding trial. Initial and target BCS, percent BF, and BW data were collected from each mare and inputted into the model. Mares were individually fed according to the DE suggestions proposed by the model to achieve the targeted BCS change within 30 d. The coefficient of determination of observed and model-predicted values (model precision) was 0.907 (P < 0.001) for BCS, 0.607 (P < 0.001) for percent BF, and 0.94 (P < 0.001) for BW. The BCS was highly correlated to percent BF (r = 0.808; P = 0.01). We concluded the reparameterized model was reliable to predict changes in BW and BCS, but more work is needed to

  7. The Consequences of a Problem-Based Mathematics Curriculum

    ERIC Educational Resources Information Center

    Clarke, David; Breed, Margarita; Fraser, Sherry

    2004-01-01

    Implementation of a problem-based mathematics curriculum, the "Interactive Mathematics Program" (IMP), at three high schools in California has been associated with more than just differences in student achievement. The outcomes that distinguished students who participated in the IMP program from students who followed a conventional…

  8. Web-Based Mathematics: Some "Dos" and "Don'ts"

    ERIC Educational Resources Information Center

    Loong, Esther Yook-Kin

    2011-01-01

    This case study describes an "out of field" teacher's use of the Internet to teach a range of mathematical topics in a modified Year 8 mathematics class. It highlights the importance of three factors for implementing a discernible web-based teaching strategy: appropriate choice of web objects, effective "virtual" pedagogy, and technical support…

  9. College Students Attitude and Mathematics Achievement Using Web Based Homework

    ERIC Educational Resources Information Center

    Leong, Kwan Eu; Alexander, Nathan

    2014-01-01

    The goal of this study was to understand how students' attitudes were connected to their mathematics learning and achievement. This investigation of students (n = 78) and their attitudes was specific to web-based homework in developmental mathematics courses in a two-year community college located in a large urban city in the United States. A…

  10. Inquiry-Based Learning and the Art of Mathematical Discourse

    ERIC Educational Resources Information Center

    von Renesse, Christine; Ecke, Volker

    2015-01-01

    Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…

  11. Mathematical modeling of the West Africa Ebola epidemic

    PubMed Central

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

    2015-01-01

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

  12. Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

    PubMed Central

    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

  13. Computer-Based Mathematics Instructions for Engineering Students

    NASA Technical Reports Server (NTRS)

    Khan, Mustaq A.; Wall, Curtiss E.

    1996-01-01

    Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

  14. Mathematical-Artificial Neural Network Hybrid Model to Predict Roll Force during Hot Rolling of Steel

    NASA Astrophysics Data System (ADS)

    Rath, S.; Sengupta, P. P.; Singh, A. P.; Marik, A. K.; Talukdar, P.

    2013-03-01

    Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

  15. Mathematical modeling of heat transfer problems in the permafrost

    NASA Astrophysics Data System (ADS)

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

    2014-11-01

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

  16. Mathematical models for predicting G-duration tolerances.

    PubMed

    Burton, R R

    2000-10-01

    Mathematical models that predict fatigue-based G-duration tolerances for relaxed and straining subjects are developed and validated using published data. These models are based on regression analysis calculations using published G-duration tolerance data of relaxed subjects exposed to 3-5 G and subjects exposed to 6-9 G using an anti-G suit and performing the anti-G straining maneuver. These G-duration models are derived from published G-level tolerance models based on intravascular hydrostatic pressures and physiologic responses to maximum voluntary contractions (MVC%). Included in the validation of these models are the baroreceptor and muscle contraction cardiovascular reflexes that support arterial BP. A basic energy pool that supports a G-duration of 140 s for G exposures > 5 G is theorized. Because of the long duration of sustained G exposures in these models, the physiologic dynamics involved in predicting straining G-duration tolerances, are identified and validated using different time periods, i.e., Phases I and II. These models, based on sustained G exposures to a constant G level are also applicable to exposures of variable G levels known as simulated aerial combat maneuver (SACM) G-profile tolerances. G-duration tolerances > 9 G are predicted using these models for subjects using reclined-seat backs and positive pressure breathing. PMID:11051304

  17. Physical vs. Mathematical Models in Rock Mechanics

    NASA Astrophysics Data System (ADS)

    Morozov, I. B.; Deng, W.

    2013-12-01

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

  18. Explorations in the Modeling of the Learning of Mathematics.

    ERIC Educational Resources Information Center

    Fuson, Karen C., Ed.; And Others

    Eleven research reports in the area of models of learning mathematics are presented in this publication of the Mathematics Education Reports series. The papers represent a mixture of theories, viewpoints, and references to other areas. Content areas addressed range from preschool to college levels. All the papers are concerned with the learning of…

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

    ERIC Educational Resources Information Center

    Greer, Brian

    1997-01-01

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

  20. Teaching Writing and Communication in a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Linhart, Jean Marie

    2014-01-01

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

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

    ERIC Educational Resources Information Center

    Carlton, Kevin; Nicholls, Mike; Ponsonby, David

    2004-01-01

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

  2. An Assessment Model for Proof Comprehension in Undergraduate Mathematics

    ERIC Educational Resources Information Center

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

    2012-01-01

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

  3. Description of a tilt wing mathematical model for piloted simulation

    NASA Technical Reports Server (NTRS)

    Totah, Joseph J.

    1991-01-01

    A tilt-wing mathematical model that was used in a piloted six-deg-of-freedom flight simulation application is presented. Two types of control systems developed for the model - a conventional programmed-flap wing-tilt control system and a geared-flap wing-tilt control system - are discussed. The objective of this effort was to develop the capability to study tilt-wing aircraft. Experienced tilt-wing pilots subjectively evaluated the model using programmed-flap control to assess the quality of the simulation. The objective was met and the model was then applied to study geared-flap control to investigate the possibility of eliminating the need for auxiliary pitch control devices. This was performed in the moving-base simulation environment, and the vehicle responses with programmed-flap and geared-flap control were compared.

  4. Pattern formation in stromatolites: insights from mathematical modelling

    PubMed Central

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

    2012-01-01

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

  5. Mathematical Model of a Lithium/Thionyl Chloride Battery

    SciTech Connect

    Jain, M.; Jungst, R.G.; Nagasubramanian, G.; Weidner, J.W.

    1998-11-24

    A mathematical model of a spirally wound lithium/thionyl chloride primary battery has been developed ~d used for parameter estimation and design studies. The model formulation is based on the fimdarnental Consemation laws using porous electrode theory and concentrated solution theory. The model is used to estimate the difision coefficient and the kinetic parameters for the reactions at the anode and the cathode as a function of temperature. These parameters are obtained by fitting the simulated capacity and average cell voltage to experimental data over a wide range of temperatures (-55 to 49"C) and discharge loads (10 to 250 ohms). The experiments were performed on D-sized, cathode-limited, spirally wound lithium/thionyl chloride cells. The model is also used to study the effkct of cathode thickness on the cell capacity as a finction of temperature, and it was found that the optimum thickness for the cathode- limited design is temperature and load dependent.

  6. Mathematical model of a telomerase transcriptional regulatory network developed by cell-based screening: analysis of inhibitor effects and telomerase expression mechanisms.

    PubMed

    Bilsland, Alan E; Stevenson, Katrina; Liu, Yu; Hoare, Stacey; Cairney, Claire J; Roffey, Jon; Keith, W Nicol

    2014-02-01

    Cancer cells depend on transcription of telomerase reverse transcriptase (TERT). Many transcription factors affect TERT, though regulation occurs in context of a broader network. Network effects on telomerase regulation have not been investigated, though deeper understanding of TERT transcription requires a systems view. However, control over individual interactions in complex networks is not easily achievable. Mathematical modelling provides an attractive approach for analysis of complex systems and some models may prove useful in systems pharmacology approaches to drug discovery. In this report, we used transfection screening to test interactions among 14 TERT regulatory transcription factors and their respective promoters in ovarian cancer cells. The results were used to generate a network model of TERT transcription and to implement a dynamic Boolean model whose steady states were analysed. Modelled effects of signal transduction inhibitors successfully predicted TERT repression by Src-family inhibitor SU6656 and lack of repression by ERK inhibitor FR180204, results confirmed by RT-QPCR analysis of endogenous TERT expression in treated cells. Modelled effects of GSK3 inhibitor 6-bromoindirubin-3'-oxime (BIO) predicted unstable TERT repression dependent on noise and expression of JUN, corresponding with observations from a previous study. MYC expression is critical in TERT activation in the model, consistent with its well known function in endogenous TERT regulation. Loss of MYC caused complete TERT suppression in our model, substantially rescued only by co-suppression of AR. Interestingly expression was easily rescued under modelled Ets-factor gain of function, as occurs in TERT promoter mutation. RNAi targeting AR, JUN, MXD1, SP3, or TP53, showed that AR suppression does rescue endogenous TERT expression following MYC knockdown in these cells and SP3 or TP53 siRNA also cause partial recovery. The model therefore successfully predicted several aspects of TERT

  7. Mathematical models of tumor heterogeneity and drug resistance

    NASA Astrophysics Data System (ADS)

    Greene, James

    In this dissertation we develop mathematical models of tumor heterogeneity and drug resistance in cancer chemotherapy. Resistance to chemotherapy is one of the major causes of the failure of cancer treatment. Furthermore, recent experimental evidence suggests that drug resistance is a complex biological phenomena, with many influences that interact nonlinearly. Here we study the influence of such heterogeneity on treatment outcomes, both in general frameworks and under specific mechanisms. We begin by developing a mathematical framework for describing multi-drug resistance to cancer. Heterogeneity is reflected by a continuous parameter, which can either describe a single resistance mechanism (such as the expression of P-gp in the cellular membrane) or can account for the cumulative effect of several mechanisms and factors. The model is written as a system of integro-differential equations, structured by the continuous "trait," and includes density effects as well as mutations. We study the limiting behavior of the model, both analytically and numerically, and apply it to study treatment protocols. We next study a specific mechanism of tumor heterogeneity and its influence on cell growth: the cell-cycle. We derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations, when the number of cells is large. The model is closely tied to experimental data of cell growth, and includes a novel implementation of

  8. Evolvable mathematical models: A new artificial Intelligence paradigm

    NASA Astrophysics Data System (ADS)

    Grouchy, Paul

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

  9. Standards-Based Mathematics Reforms and Mathematics Achievement of American Indian/Alaska Native Eighth Graders

    ERIC Educational Resources Information Center

    Akiba, Motoko; Chiu, Ya-Fang; Zhuang, Yue-Lin; Mueller, Heather E.

    2008-01-01

    Using the NAEP nationally-representative data collected from eighth-graders, we investigated the relative exposure of American Indian/Alaska Native (AIAN) students to mathematics teachers who are knowledgeable about standards, participate in standards-based professional development, and practice standards-based instruction; American Indian/Alaska…

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

    NASA Astrophysics Data System (ADS)

    Tuckwell, Henry C.

    2008-07-01

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

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

    PubMed

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

    2014-09-01

    In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. PMID:25057777

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

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

    NASA Astrophysics Data System (ADS)

    Jovanović, Ivana; Miljanović, Igor

    2015-12-01

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

  14. Innovative mathematical modeling in environmental remediation.

    PubMed

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

    2013-05-01

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

  15. Discrete Mathematical Approaches to Graph-Based Traffic Analysis

    SciTech Connect

    Joslyn, Cliff A.; Cowley, Wendy E.; Hogan, Emilie A.; Olsen, Bryan K.

    2014-04-01

    Modern cyber defense and anlaytics requires general, formal models of cyber systems. Multi-scale network models are prime candidates for such formalisms, using discrete mathematical methods based in hierarchically-structured directed multigraphs which also include rich sets of labels. An exemplar of an application of such an approach is traffic analysis, that is, observing and analyzing connections between clients, servers, hosts, and actors within IP networks, over time, to identify characteristic or suspicious patterns. Towards that end, NetFlow (or more generically, IPFLOW) data are available from routers and servers which summarize coherent groups of IP packets flowing through the network. In this paper, we consider traffic analysis of Netflow using both basic graph statistics and two new mathematical measures involving labeled degree distributions and time interval overlap measures. We do all of this over the VAST test data set of 96M synthetic Netflow graph edges, against which we can identify characteristic patterns of simulated ground-truth network attacks.

  16. Modeling Students' Interest in Mathematics Homework

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  17. Mathematics and Science Integration: Models and Characterizations

    ERIC Educational Resources Information Center

    Stinson, Kevin; Harkness, Shelly Sheats; Meyer, Helen; Stallworth, James

    2009-01-01

    The squeeze on instructional time and other factors increasingly leads educators to consider mathematics and science integration in an effort to be more efficient and effective. Unfortunately, the need for common understandings for what it means to integrate these disciplines, as well as the need for improving disciplinary knowledge, appears to…

  18. The Mathematical Modeling of Chaotic Social Structures.

    ERIC Educational Resources Information Center

    Marion, Russ; Richardson, Michael D.

    Chaos theory describes the way systems change over time. It proposes that systems governed by physical laws can undergo transitions to a highly irregular form of behavior and that although chaotic behavior appears random, it is governed by strict mathematical conditions. This paper applies chaos theory to administrative and organizational issues.…

  19. Making Insulation Decisions through Mathematical Modeling

    ERIC Educational Resources Information Center

    Yanik, H. Bahadir; Memis, Yasin

    2014-01-01

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

  20. Computational and mathematical models of microstructural evolution

    SciTech Connect

    Bullard, J.W.; Chen, L.Q.; Kalia, R.K.; Stoneham, A.M.

    1998-12-31

    This symposium was designed to bring together the foremost materials theorists and applied mathematicians from around the world to share and discuss some of the newest and most promising mathematical and computational tools for simulating, understanding, and predicting the various complex processes that occur during the evolution of microstructures. Separate abstracts were prepared for 25 papers.

  1. System and mathematical modeling of quadrotor dynamics

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

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

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

    SciTech Connect

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

    1992-01-01

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

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

    SciTech Connect

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

    1992-12-31

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

  4. Mathematical Model of Oxygen Transport in Tuberculosis Granulomas

    PubMed Central

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

    2016-01-01

    Pulmonary granulomas—the hallmark of Mycobacterium tuberculosis (MTB) infection—are dense cellular lesions that often feature regions of hypoxia and necrosis, partially due to limited transport of oxygen. Low oxygen in granulomas can impair the host immune response, while MTB are able to adapt and persist in hypoxic environments. Here, we used a physiologically based mathematical model of oxygen diffusion and consumption to calculate oxygen profiles within the granuloma, assuming Michaelis–Menten kinetics. An approximate analytical solution—using a priori and newly estimated parameters from experimental data in a rabbit model of tuberculosis—was able to predict the size of hypoxic and necrotic regions in agreement with experimental results from the animal model. Such quantitative understanding of transport limitations can inform future tuberculosis therapeutic strategies that may include adjunct host-directed therapies that facilitate oxygen and drug delivery for more effective treatment. PMID:26253038

  5. Mathematical Model of Oxygen Transport in Tuberculosis Granulomas.

    PubMed

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

    2016-04-01

    Pulmonary granulomas-the hallmark of Mycobacterium tuberculosis (MTB) infection-are dense cellular lesions that often feature regions of hypoxia and necrosis, partially due to limited transport of oxygen. Low oxygen in granulomas can impair the host immune response, while MTB are able to adapt and persist in hypoxic environments. Here, we used a physiologically based mathematical model of oxygen diffusion and consumption to calculate oxygen profiles within the granuloma, assuming Michaelis-Menten kinetics. An approximate analytical solution-using a priori and newly estimated parameters from experimental data in a rabbit model of tuberculosis-was able to predict the size of hypoxic and necrotic regions in agreement with experimental results from the animal model. Such quantitative understanding of transport limitations can inform future tuberculosis therapeutic strategies that may include adjunct host-directed therapies that facilitate oxygen and drug delivery for more effective treatment. PMID:26253038

  6. A mathematical model of pH, based on the total stoichiometric concentration of acids, bases and ampholytes dissolved in water.

    PubMed

    Mioni, Roberto; Mioni, Giuseppe

    2015-10-01

    In chemistry and in acid-base physiology, the Henderson-Hasselbalch equation plays a pivotal role in studying the behaviour of the buffer solutions. However, it seems that the general function to calculate the valence of acids, bases and ampholytes, N = f(pH), at any pH, has only been provided by Kildeberg. This equation can be applied to strong acids and bases, pluriprotic weak acids, bases and ampholytes, with an arbitrary number of acid strength constants, pKA, including water. By differentiating this function with respect to pH, we obtain the general equation for the buffer value. In addition, by integrating the titration curve, TA, proposed by Kildeberg, and calculating its Legendre transform, we obtain the Gibbs free energy of pH (or pOH)-dependent titratable acid. Starting from the law of electroneutrality and applying suitable simplifications, it is possible to calculate the pH of the buffer solutions by numerical methods, available in software packages such as Excel. The concept of buffer capacity has also been clarified by Urbansky, but, at variance with our approach, not in an organic manner. In fact, for each set of monobasic, dibasic, tribasic acids, etc., various equations are presented which independently fit each individual acid-base category. Consequently, with the increase in acid groups (pKA), the equations become more and more difficult, both in practice and in theory. Some examples are proposed to highlight the boundary that exists between acid-base physiology and the thermodynamic concepts of energy, chemical potential, amount of substance and acid resistance. PMID:26059505

  7. A MATHEMATICAL MODEL OF ELECTROSTATIC PRECIPITATION: REVISION 1

    EPA Science Inventory

    The computer program performs the calculations in the mathematical model of electrostatic precipitation and is documented in other publications. The program predicts collection efficiency in an electrostatic precipitator as a function of particle diameter, electrical operating co...

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

    ERIC Educational Resources Information Center

    Arabie, Phipps

    1980-01-01

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

  9. Mathematical modeling of non-equilibrium sorption

    NASA Astrophysics Data System (ADS)

    Kaliev, Ibragim A.; Mukhambetzhanov, Saltanbek T.; Sabitova, Gulnara S.; Sakhit, Anghyz E.

    2016-08-01

    We consider the system of equations modeling the process of non-equilibrium sorption. Difference approximation of differential problem by the implicit scheme is formulated. The solution of the difference problem is constructed using the sweep method. Based on the numerical results we can conclude the following: when the relaxation time decreases to 0, then the solution of non-equilibrium problem tends with increasing time to solution of the equilibrium problem.

  10. A new mathematical programming model for scheduling flexible manufacturing systems

    SciTech Connect

    MacCarthy, B.; Liu, J.

    1994-12-31

    Flexibility is now a major consideration in the design of many manufacturing systems. Flexible manufacturing systems (FMS) have been developed in the last two decades. The principal elements of an FMS are (1) computer controlled machine tools, (2) a transport system and (3) a host computer system. Such systems may combine high flexibility with high productivity and may allow unsupervised production. However, in order to achieve these benefits, the control system must be capable of exercising intelligent supervisory management. Scheduling is at the heart of the control system and is still a major problem area. This paper describes a new mathematical programming model for a wide class of FMS scheduling problems based on a new classification scheme. A global optimization approach is adopted based on a mixed-integer linear programming model. Many important aspects of operational FMS, omitted form earlier models, are included. Key elements of model structure are highlighted. Computational experience with a comprehensive set of designed experiments is described. The applications of the model are noted and the development of effective heuristic procedures based on the model is highlighted.

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

    NASA Astrophysics Data System (ADS)

    Gyulov, Tihomir B.; Valkov, Radoslav L.

    2011-12-01

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

  12. The Answering Process for Multiple-Choice Questions in Collaborative Learning: A Mathematical Learning Model Analysis

    ERIC Educational Resources Information Center

    Nakamura, Yasuyuki; Nishi, Shinnosuke; Muramatsu, Yuta; Yasutake, Koichi; Yamakawa, Osamu; Tagawa, Takahiro

    2014-01-01

    In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…

  13. Development of mathematical models and numerical methods for aerodynamic design on multiprocessor computers

    NASA Astrophysics Data System (ADS)

    Maksimov, F. A.; Churakov, D. A.; Shevelev, Yu. D.

    2011-02-01

    Complex-geometry design and grid generation are addressed. The gasdynamic equations are solved, and the numerical results are compared with experimental data. For aerodynamic problems, a suite of mathematical and information technology tools is proposed for the support and management of geometric models of actual objects. Based on the mathematical modeling methods developed, numerical experiments can be performed for a wide class of geometric forms and the aerodynamic properties of aircraft can be predicted with allowance for the viscosity effects.

  14. Mathematical modeling of the growth and development of the mussel Mytilus galloprovincialis on artificial substrates

    NASA Astrophysics Data System (ADS)

    Vasechkina, E. F.; Kazankova, I. I.

    2014-11-01

    A mathematical model simulating the growth and development of the mussel Mytilus galloprovincialis Lam. on artificial substrates has been constructed. The model is based on experimental data and contains mathematical descriptions of the filtration, respiration, excretion, spawning, and growth of an individual during its ontogenesis from the moment it attaches to a solid substrate to the attainment of a marketable size. The test computations have been compared to the available observation data for mussel farms.

  15. Innovative mathematical modeling in environmental remediation

    SciTech Connect

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

    2013-05-01

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

  16. A Mathematical Model of the Mouse Ventricular Myocyte Contraction

    PubMed Central

    Mullins, Paula D.; Bondarenko, Vladimir E.

    2013-01-01

    Mathematical models of cardiac function at the cellular level include three major components, such as electrical activity, Ca2+ dynamics, and cellular shortening. We developed a model for mouse ventricular myocyte contraction which is based on our previously published comprehensive models of action potential and Ca2+ handling mechanisms. The model was verified with extensive experimental data on mouse myocyte contraction at room temperature. In the model, we implemented variable sarcomere length and indirect modulation of the tropomyosin transition rates by Ca2+ and troponin. The resulting model described well steady-state force-calcium relationships, dependence of the contraction force on the sarcomere length, time course of the contraction force and myocyte shortening, frequency dependence of the contraction force and cellular contraction, and experimentally measured derivatives of the myocyte length variation. We emphasized the importance of the inclusion of variable sarcomere length into a model for ventricular myocyte contraction. Differences in contraction force and cell shortening for epicardial and endocardial ventricular myocytes were investigated. Model applicability for the experimental studies and model limitations were discussed. PMID:23671664

  17. Comprehensive Mathematical Model for Simulating Electroslag Remelting

    NASA Astrophysics Data System (ADS)

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

    2016-04-01

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

  18. Radiation induced base excision repair (BER): a mechanistic mathematical approach.

    PubMed

    Rahmanian, Shirin; Taleei, Reza; Nikjoo, Hooshang

    2014-10-01

    This paper presents a mechanistic model of base excision repair (BER) pathway for the repair of single-stand breaks (SSBs) and oxidized base lesions produced by ionizing radiation (IR). The model is based on law of mass action kinetics to translate the biochemical processes involved, step-by-step, in the BER pathway to translate into mathematical equations. The BER is divided into two subpathways, short-patch repair (SPR) and long-patch repair (LPR). SPR involves in replacement of single nucleotide via Pol β and ligation of the ends via XRCC1 and Ligase III, while LPR involves in replacement of multiple nucleotides via PCNA, Pol δ/ɛ and FEN 1, and ligation via Ligase I. A hallmark of IR is the production of closely spaced lesions within a turn of DNA helix (named complex lesions), which have been attributed to a slower repair process. The model presented considers fast and slow component of BER kinetics by assigning SPR for simple lesions and LPR for complex lesions. In the absence of in vivo reaction rate constants for the BER proteins, we have deduced a set of rate constants based on different published experimental measurements including accumulation kinetics obtained from UVA irradiation, overall SSB repair kinetic experiments, and overall BER kinetics from live-cell imaging experiments. The model was further used to calculate the repair kinetics of complex base lesions via the LPR subpathway and compared to foci kinetic experiments for cells irradiated with γ rays, Si, and Fe ions. The model calculation show good agreement with experimental measurements for both overall repair and repair of complex lesions. Furthermore, using the model we explored different mechanisms responsible for inhibition of repair when higher LET and HZE particles are used and concluded that increasing the damage complexity can inhibit initiation of LPR after the AP site removal step in BER. PMID:25117268

  19. Some Aspects of Mathematical Model of Collaborative Learning

    ERIC Educational Resources Information Center

    Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu

    2012-01-01

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

  20. Academic Libraries as a Context for Teaching Mathematical Modeling

    ERIC Educational Resources Information Center

    Warwick, Jon

    2008-01-01

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

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

    PubMed

    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. PMID:21802501

  2. A mathematical model for the iron/chromium redox battery

    NASA Technical Reports Server (NTRS)

    Fedkiw, P. S.; Watts, R. W.

    1984-01-01

    A mathematical model has been developed to describe the isothermal operation of a single anode-separator-cathode unit cell in a redox-flow battery and has been applied to the NASA iron/chromium system. The model, based on porous electrode theory, incorporates redox kinetics, mass transfer, and ohmic effects as well as the parasitic hydrogen reaction which occurs in the chromium electrode. A numerical parameter study was carried out to predict cell performance to aid in the rational design, scale-up, and operation of the flow battery. The calculations demonstrate: (1) an optimum electrode thickness and electrolyte flow rate exist; (2) the amount of hydrogen evolved and, hence, cycle faradaic efficiency, can be affected by cell geometry, flow rate, and charging procedure; (3) countercurrent flow results in enhanced cell performance over cocurrent flow; and (4) elevated temperature operation enhances cell performance.

  3. Mathematical modeling of synthetic unit hydrograph case study: Citarum watershed

    NASA Astrophysics Data System (ADS)

    Islahuddin, Muhammad; Sukrainingtyas, Adiska L. A.; Kusuma, M. Syahril B.; Soewono, Edy

    2015-09-01

    Deriving unit hydrograph is very important in analyzing watershed's hydrologic response of a rainfall event. In most cases, hourly measures of stream flow data needed in deriving unit hydrograph are not always available. Hence, one needs to develop methods for deriving unit hydrograph for ungagged watershed. Methods that have evolved are based on theoretical or empirical formulas relating hydrograph peak discharge and timing to watershed characteristics. These are usually referred to Synthetic Unit Hydrograph. In this paper, a gamma probability density function and its variant are used as mathematical approximations of a unit hydrograph for Citarum Watershed. The model is adjusted with real field condition by translation and scaling. Optimal parameters are determined by using Particle Swarm Optimization method with weighted objective function. With these models, a synthetic unit hydrograph can be developed and hydrologic parameters can be well predicted.

  4. The dynamic mathematical model of heavy-medium cyclone

    SciTech Connect

    Xu Jianping

    1997-12-31

    For ascertaining the effect of the various variables during the coal separation process of heavy medium (HM) cyclone, a dynamic mathematical model for simulating the separating process of the HM cyclone has been developed based on data obtained through both laboratory and industrial experiments. As evidenced by the result of study, increase to a certain extent of inlet pressure and media-coal ratio may result in higher separating precision. The effect of rheological property of the suspension is particularly important, and often plays a decisive role in this respect. The research-derived model can either be used for predicting the separating process and performance or for effecting process control of a HM cyclone through simulating its operation.

  5. Mathematical Model of the Biosensors Acting in a Trigger Mode

    PubMed Central

    Baronas, Romas; Kulys, Juozas; Ivanauskas, Feliksas

    2004-01-01

    A mathematical model of biosensors acting in a trigger mode has been developed. One type of the biosensors utilized a trigger enzymatic reaction followed by the cyclic enzymatic and electrochemical conversion of the product (CCE scheme). Other biosensors used the enzymatic trigger reaction followed by the electrochemical and enzymatic product cyclic conversion (CEC scheme). The models were based on diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. The digital simulation was carried out using the finite difference technique. The influence of the substrate concentration, the maximal enzymatic rate as well as the membrane thickness on the biosensor response was investigated. The numerical experiments demonstrated a significant gain (up to dozens of times) in biosensor sensitivity when the biosensor response was under diffusion control. In the case of significant signal amplification, the response time with triggering was up to several times longer than that of the biosensor without triggering.

  6. Mathematical modelling of flow distribution in the human cardiovascular system

    NASA Technical Reports Server (NTRS)

    Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.

    1992-01-01

    The paper presents a detailed model of the entire human cardiovascular system which aims to study the changes in flow distribution caused by external stimuli, changes in internal parameters, or other factors. The arterial-venous network is represented by 325 interconnected elastic segments. The mathematical description of each segment is based on equations of hydrodynamics and those of stress/strain relationships in elastic materials. Appropriate input functions provide for the pumping of blood by the heart through the system. The analysis employs the finite-element technique which can accommodate any prescribed boundary conditions. Values of model parameters are from available data on physical and rheological properties of blood and blood vessels. As a representative example, simulation results on changes in flow distribution with changes in the elastic properties of blood vessels are discussed. They indicate that the errors in the calculated overall flow rates are not significant even in the extreme case of arteries and veins behaving as rigid tubes.

  7. Mathematical models for nonparametric inferences from line transect data

    USGS Publications Warehouse

    Burnham, K.P.; Anderson, D.R.

    1976-01-01

    A general mathematical theory of line transects is develoepd which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(O) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y/r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(O/r).

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

    ERIC Educational Resources Information Center

    Michelsen, Claus

    2015-01-01

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

  9. Mathematical framework for activity-based cancer biomarkers

    PubMed Central

    Kwong, Gabriel A.; Dudani, Jaideep S.; Carrodeguas, Emmanuel; Mazumdar, Eric V.; Zekavat, Seyedeh M.; Bhatia, Sangeeta N.

    2015-01-01

    Advances in nanomedicine are providing sophisticated functions to precisely control the behavior of nanoscale drugs and diagnostics. Strategies that coopt protease activity as molecular triggers are increasingly important in nanoparticle design, yet the pharmacokinetics of these systems are challenging to understand without a quantitative framework to reveal nonintuitive associations. We describe a multicompartment mathematical model to predict strategies for ultrasensitive detection of cancer using synthetic biomarkers, a class of activity-based probes that amplify cancer-derived signals into urine as a noninvasive diagnostic. Using a model formulation made of a PEG core conjugated with protease-cleavable peptides, we explore a vast design space and identify guidelines for increasing sensitivity that depend on critical parameters such as enzyme kinetics, dosage, and probe stability. According to this model, synthetic biomarkers that circulate in stealth but then activate at sites of disease have the theoretical capacity to discriminate tumors as small as 5 mm in diameter—a threshold sensitivity that is otherwise challenging for medical imaging and blood biomarkers to achieve. This model may be adapted to describe the behavior of additional activity-based approaches to allow cross-platform comparisons, and to predict allometric scaling across species. PMID:26417077

  10. Mathematical framework for activity-based cancer biomarkers.

    PubMed

    Kwong, Gabriel A; Dudani, Jaideep S; Carrodeguas, Emmanuel; Mazumdar, Eric V; Zekavat, Seyedeh M; Bhatia, Sangeeta N

    2015-10-13

    Advances in nanomedicine are providing sophisticated functions to precisely control the behavior of nanoscale drugs and diagnostics. Strategies that coopt protease activity as molecular triggers are increasingly important in nanoparticle design, yet the pharmacokinetics of these systems are challenging to understand without a quantitative framework to reveal nonintuitive associations. We describe a multicompartment mathematical model to predict strategies for ultrasensitive detection of cancer using synthetic biomarkers, a class of activity-based probes that amplify cancer-derived signals into urine as a noninvasive diagnostic. Using a model formulation made of a PEG core conjugated with protease-cleavable peptides, we explore a vast design space and identify guidelines for increasing sensitivity that depend on critical parameters such as enzyme kinetics, dosage, and probe stability. According to this model, synthetic biomarkers that circulate in stealth but then activate at sites of disease have the theoretical capacity to discriminate tumors as small as 5 mm in diameter-a threshold sensitivity that is otherwise challenging for medical imaging and blood biomarkers to achieve. This model may be adapted to describe the behavior of additional activity-based approaches to allow cross-platform comparisons, and to predict allometric scaling across species. PMID:26417077

  11. Use of artificial intelligence and simple mathematics to analyze a physiological model

    SciTech Connect

    Kunz, J.C.

    1984-01-01

    The objective of this research is to demonstrate a methodology for design and use of a physiological model in a computer program that suggests medical decisions. This methodology uses a physiological model based on first principles and facts of physiology and anatomy. The model includes inference rules for analysis of causal relations between physiological events. The model is used to analyze physiological behavior, identify the effects of abnormalities, identify appropriate therapies, and predict the results of therapy. This methodology integrates heuristic knowledge traditionally used in artificial intelligence programs with mathematical knowledge traditionally used in mathematical modeling programs. A vocabulary for representing a physiological model is proposed.

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

    PubMed Central

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

    2015-01-01

    Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns. PMID:25716372

  13. A Mathematical Model of Immune-System-Melanoma Competition

    PubMed Central

    Pennisi, Marzio

    2012-01-01

    We present a mathematical model developed to reproduce the immune response entitled with the combined administration of activated OT1 cytotoxic T lymphocytes (CTLs) and Anti-CD137 monoclonal antibodies. The treatment is directed against melanoma in B16 OVA mouse models exposed to a specific immunotherapy strategy. We model two compartments: the injection point compartment where the treatment is administered and the skin compartment where melanoma tumor cells proliferate. To model the migration of OT1 CTLs and antibodies from the injection to the skin compartment, we use delay differential equations (DDEs). The outcomes of the mathematical model are in good agreement with the in vivo results. Moreover, sensitivity analysis of the mathematical model underlines the key role of OT1 CTLs and suggests that a possible reduction of the number of injected antibodies should not affect substantially the treatment efficacy. PMID:22701144

  14. A Mathematical Model for Evolution and SETI

    NASA Astrophysics Data System (ADS)

    Maccone, Claudio

    2011-12-01

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

  15. A mathematical model for evolution and SETI.

    PubMed

    Maccone, Claudio

    2011-12-01

    Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation. PMID:22139521

  16. The role of mathematical models in understanding pattern formation in developmental biology.

    PubMed

    Umulis, David M; Othmer, Hans G

    2015-05-01

    In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

  17. The Mathematical Analysis of Style: A Correlation-Based Approach.

    ERIC Educational Resources Information Center

    Oppenheim, Rosa

    1988-01-01

    Examines mathematical models of style analysis, focusing on the pattern in which literary characteristics occur. Describes an autoregressive integrated moving average model (ARIMA) for predicting sentence length in different works by the same author and comparable works by different authors. This technique is valuable in characterizing stylistic…

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

    ERIC Educational Resources Information Center

    Baker, Duke H.; Mamlin, Joseph

    1976-01-01

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

  19. A Review on Mathematical Modeling for Textile Processes

    NASA Astrophysics Data System (ADS)

    Chattopadhyay, R.

    2015-10-01

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

  20. Mathematical modeling of plasma deposition and hardening of coatings-switched electrical parameters

    NASA Astrophysics Data System (ADS)

    Kadyrmetov, A. M.; Sharifullin, S. N.; Pustovalov, AS

    2016-01-01

    This paper presents the results of simulation of plasma deposition and hardening of coatings in modulating the electrical parameters. Mathematical models are based on physical models of gas-dynamic mechanisms more dynamic and thermal processes of the plasma jet. As an example the modeling of dynamic processes of heterogeneous plasma jet, modulated current pulses indirect arc plasma torch.

  1. Teachers' Temporary Support and Worked-Out Examples as Elements of Scaffolding in Mathematical Modeling

    ERIC Educational Resources Information Center

    Tropper, Natalie; Leiss, Dominik; Hänze, Martin

    2015-01-01

    Empirical findings show that students have manifold difficulties when dealing with mathematical modeling problems. Accordingly, approaches for supporting students in modeling-based learning environments have to be investigated. In the research presented here, we adopted a scaffolding perspective on teaching modeling with the aim of both providing…

  2. Web-Based Progress Monitoring in First Grade Mathematics

    ERIC Educational Resources Information Center

    Salaschek, Martin; Souvignier, Elmar

    2013-01-01

    The purpose of our research was to examine a web-based tool for mathematics progress monitoring in first grade. The newly developed assessment tool uses several robust indicators and curriculum-based measures forming three competences (Basic Precursors, Advanced Precursors, and Computation) to determine comprehensive early numeracy skills in…

  3. Assessment of toxicity using dehydrogenases activity and mathematical modeling.

    PubMed

    Matyja, Konrad; Małachowska-Jutsz, Anna; Mazur, Anna K; Grabas, Kazimierz

    2016-07-01

    Dehydrogenase activity is frequently used to assess the general condition of microorganisms in soil and activated sludge. Many studies have investigated the inhibition of dehydrogenase activity by various compounds, including heavy metal ions. However, the time after which the measurements are carried out is often chosen arbitrarily. Thus, it can be difficult to estimate how the toxic effects of compounds vary during the reaction and when the maximum of the effect would be reached. Hence, the aim of this study was to create simple and useful mathematical model describing changes in dehydrogenase activity during exposure to substances that inactivate enzymes. Our model is based on the Lagergrens pseudo-first-order equation, the rate of chemical reactions, enzyme activity, and inactivation and was created to describe short-term changes in dehydrogenase activity. The main assumption of our model is that toxic substances cause irreversible inactivation of enzyme units. The model is able to predict the maximum direct toxic effect (MDTE) and the time to reach this maximum (TMDTE). In order to validate our model, we present two examples: inactivation of dehydrogenase in microorganisms in soil and activated sludge. The model was applied successfully for cadmium and copper ions. Our results indicate that the predicted MDTE and TMDTE are more appropriate than EC50 and IC50 for toxicity assessments, except for long exposure times. PMID:27021434

  4. A mathematical model of peritoneal fluid absorption in tissue.

    PubMed

    Stachowska-Pietka, Joanna; Waniewski, Jacek; Flessner, Michael F; Lindholm, Bengt

    2005-01-01

    To investigate how water flow and interstitial pressure change in tissue during a peritoneal dwell with isotonic fluid, we developed a mathematical model of water transport in the tissue. Transport through muscle alone (M) and through muscle with intact skin (MS) were considered for the rat abdominal wall, using various parameters for muscle and skin. Based on the concept of distributed capillary and lymphatic systems, two main transport barriers were taken into account. capillary membrane and interstitium. We calculated the tissue hydrostatic pressure profiles and compared them with experimental data. The theoretic steady-state pressure distribution for model M is in good agreement with the experimental data. In model MS, the theoretic distribution diverges from the data in the subcutaneous layer. The transient times for fluid flow in the tissue for both model simulations are rather long (40 minutes in model M and 95 minutes in model MS) and depend on intraperitoneal pressure. The fraction of fluid absorbed from the tissue by the lymphatics increases with time from 10% to 97% of fluid flow from the peritoneal cavity. PMID:16686276

  5. On a Mathematical Model of Brain Activities

    SciTech Connect

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

    2007-12-03

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

  6. Mathematical Modeling of Primary Wood Processing

    NASA Astrophysics Data System (ADS)

    Szyszka, Barbara; Rozmiarek, Klaudyna

    2008-09-01

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

  7. Investigating and developing engineering students' mathematical modelling and problem-solving skills

    NASA Astrophysics Data System (ADS)

    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.

  8. Modal test and analysis: Multiple tests concept for improved validation of large space structure mathematical models

    NASA Technical Reports Server (NTRS)

    Wada, B. K.; Kuo, C-P.; Glaser, R. J.

    1986-01-01

    For the structural dynamic analysis of large space structures, the technology in structural synthesis and the development of structural analysis software have increased the capability to predict the dynamic characteristics of the structural system. The various subsystems which comprise the system are represented by various displacement functions; the displacement functions are then combined to represent the total structure. Experience has indicated that even when subsystem mathematical models are verified by test, the mathematical representations of the total system are often in error because the mathematical model of the structural elements which are significant when loads are applied at the interconnection points are not adequately verified by test. A multiple test concept, based upon the Multiple Boundary Condition Test (MBCT), is presented which will increase the accuracy of the system mathematical model by improving the subsystem test and test/analysis correlation procedure.

  9. A mathematical model for flight guidance in honeybee swarms.

    PubMed

    Fetecau, R C; Guo, A

    2012-11-01

    When a colony of honeybees relocates to a new nest site, less than 5 % of the bees (the scout bees) know the location of the new nest. Nevertheless, the small minority of informed bees manages to provide guidance to the rest and the entire swarm is able to fly to the new nest intact. The streaker bee hypothesis, one of the several theories proposed to explain the guidance mechanism in bee swarms, seems to be supported by recent experimental observations. The theory suggests that the informed bees make high-speed flights through the swarm in the direction of the new nest, hence conspicuously pointing to the desired direction of travel. This work presents a mathematical model of flight guidance in bee swarms based on the streaker bee hypothesis. Numerical experiments, parameter studies, and comparison with experimental data are presented. PMID:22890574

  10. Predictions of cardiovascular responses during STS reentry using mathematical models

    NASA Technical Reports Server (NTRS)

    Leonard, J. I.; Srinivasan, R.

    1985-01-01

    The physiological adaptation to weightless exposure includes cardiovascular deconditioning arising in part from a loss of total circulating blood volume and resulting in a reduction of orthostatic tolerance. The crew of the Shuttle orbiter are less tolerant to acceleration forces in the head-to-foot direction during the reentry phase of the flight at a time they must function at a high level of performance. The factors that contribute to orthostatic intolerance during and following reentry and to predict the likelihood of impaired crew performance are evaluated. A computer simulation approach employing a mathematical model of the cardiovascular system is employed. It is shown that depending on the severity of blood volume loss, the reentry acceleration stress may be detrimental to physiologic function and may place the physiologic status of the crew near the borderline of some type of impairment. They are in agreement with conclusions from early ground-based experiments and from observations of early Shuttle flights.

  11. Mathematical modeling of fluid-electrolyte alterations during weightlessness

    NASA Technical Reports Server (NTRS)

    Leonard, J. I.

    1984-01-01

    Fluid electrolyte metabolism and renal endocrine control as it pertains to adaptation to weightlessness were studied. The mathematical models that have been particularly useful are discussed. However, the focus of the report is on the physiological meaning of the computer studies. A discussion of the major ground based analogs of weightlessness are included; for example, head down tilt, water immersion, and bed rest, and a comparison of findings. Several important zero g phenomena are described, including acute fluid volume regulation, blood volume regulation, circulatory changes, longer term fluid electrolyte adaptations, hormonal regulation, and body composition changes. Hypotheses are offered to explain the major findings in each area and these are integrated into a larger hypothesis of space flight adaptation. A conceptual foundation for fluid electrolyte metabolism, blood volume regulation, and cardiovascular regulation is reported.

  12. Computer Support for Learning Mathematics: A Learning Environment Based on Recreational Learning Objects

    ERIC Educational Resources Information Center

    Lopez-Morteo, Gabriel; Lopez, Gilberto

    2007-01-01

    In this paper, we introduce an electronic collaborative learning environment based on Interactive Instructors of Recreational Mathematics (IIRM), establishing an alternative approach for motivating students towards mathematics. The IIRM are educational software components, specializing in mathematical concepts, presented through recreational…

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

    NASA Astrophysics Data System (ADS)

    Bezruchko, Boris P.; Smirnov, Dmitry A.

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

  14. A mathematical model for mesenchymal and chemosensitive cell dynamics.

    PubMed

    Häcker, Anita

    2012-01-01

    The structure of an underlying tissue network has a strong impact on cell dynamics. If, in addition, cells alter the network by mechanical and chemical interactions, their movement is called mesenchymal. Important examples for mesenchymal movement include fibroblasts in wound healing and metastatic tumour cells. This paper is focused on the latter. Based on the anisotropic biphasic theory of Barocas and Tranquillo, which models a fibre network and interstitial solution as two-component fluid, a mathematical model for the interactions of cells with a fibre network is developed. A new description for fibre reorientation is given and orientation-dependent proteolysis is added to the model. With respect to cell dynamics, the equation, based on anisotropic diffusion, is extended by haptotaxis and chemotaxis. The chemoattractants are the solute network fragments, emerging from proteolysis, and the epidermal growth factor which may guide the cells to a blood vessel. Moreover the cell migration is impeded at either high or low network density. This new model enables us to study chemotactic cell migration in a complex fibre network and the consequential network deformation. Numerical simulations for the cell migration and network deformation are carried out in two space dimensions. Simulations of cell migration in underlying tissue networks visualise the impact of the network structure on cell dynamics. In a scenario for fibre reorientation between cell clusters good qualitative agreement with experimental results is achieved. The invasion speeds of cells in an aligned and an isotropic fibre network are compared. PMID:21437671

  15. Mathematical Modeling of Environmental Dynamics in Fukushima Prefecture

    NASA Astrophysics Data System (ADS)

    Kitamura, Akihiro; Kurikami, Hiroshi; Oda, Yoshihiro; Nakama, Shigeo; Malins, Alex; Yamada, Susumu; Okumura, Masahiko; Machida, Masahiko

    2015-04-01

    Radioactive cesium, which strongly adheres to soils, is one of the major concerns regarding health physics in Fukushima today. It migrates mainly by soil erosion and subsequent sediment transport within surface water during times of widespread flooding. In order to predict the future distribution and resulting air dose rate at any location in Fukushima, we have prepared a number of mathematical models for radioactive cesium transport with different space and time scales. In this presentation we cover our prediction methodology, ranging from sediment and radioactive cesium movement to resulting long term air dose rate changes. Specifically, we present simulation results of sediment movement and radioactive cesium migration using semi-empirical and physics based watershed models, and that of sediment and radioactive cesium behavior in dam reservoirs using one and two dimensional water system simulation models. The results are compared with monitoring based estimates to demonstrate the validity of the models. We also present some simulation results on air dose rate at a particular location and compared with direct measurement value.

  16. Redundancy management of electrohydraulic servoactuators by mathematical model referencing

    NASA Technical Reports Server (NTRS)

    Campbell, R. A.

    1971-01-01

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

  17. Inquiry Based-Computational Experiment, Acquisition of Threshold Concepts and Argumentation in Science and Mathematics Education

    ERIC Educational Resources Information Center

    Psycharis, Sarantos

    2016-01-01

    Computational experiment approach considers models as the fundamental instructional units of Inquiry Based Science and Mathematics Education (IBSE) and STEM Education, where the model take the place of the "classical" experimental set-up and simulation replaces the experiment. Argumentation in IBSE and STEM education is related to the…

  18. Mathematical and computational models of drug transport in tumours

    PubMed Central

    Groh, C. M.; Hubbard, M. E.; Jones, P. F.; Loadman, P. M.; Periasamy, N.; Sleeman, B. D.; Smye, S. W.; Twelves, C. J.; Phillips, R. M.

    2014-01-01

    The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a ‘tumour cord’ geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are ‘pharmacokinetically resistant’ to chemotherapeutic strategies. PMID:24621814

  19. Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration

    ERIC Educational Resources Information Center

    Warwick, Jon

    2015-01-01

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

  20. MATHEMATICAL MODEL OF ELECTROSTATIC PRECIPITATION (REVISION 3): SOURCE CODE

    EPA Science Inventory

    This tape contains the source code (FORTRAN) for Revision 3 of the Mathematical Model of Electrostatic Precipitation. Improvements found in Revision 3 of the model include a new method of calculating the solutions to the electric field equations, a dynamic method for calculating ...

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

    ERIC Educational Resources Information Center

    Williams, Julian; Wake, Geoff

    2007-01-01

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

  2. The mathematical modeling of grouping the dipole water clusters

    NASA Astrophysics Data System (ADS)

    Shaidurov, Vladimir; Kornienko, Viktoria; Vyatkin, Alexander

    2016-08-01

    In the present paper, a physical-mathematical model and a computational algorithm implementing the model are proposed to study the behavior of particles having an electric dipole moment in an external electric field. Computational experiments demonstrate the orientation dynamics of water clusters with the increase of the generated field. The dipole properties of some water clusters were previously determined using Hyperchem program.

  3. Mathematical model of bisubject qualimetric arbitrary objects evaluation

    NASA Astrophysics Data System (ADS)

    Morozova, A.

    2016-04-01

    An analytical basis and the process of formalization of arbitrary objects bisubject qualimetric evaluation mathematical model information spaces are developed. The model is applicable in solving problems of control over both technical and socio-economic systems for objects evaluation using systems of parameters generated by different subjects taking into account their performance and priorities of decision-making.

  4. [Mathematical model of baroreflex regulation of hemodynamics in the dog].

    PubMed

    Palets, B L

    1983-11-01

    A non-linear mathematical model of dog hemodynamics regulation was developed including descriptions of the cardiovascular system, the arterial baroreflex and the Beinbridge reflex. Model calculated arterial and venous pressure, blood flow, and heart rate are in good agreement with experimental data. PMID:6653829

  5. MATHEMATICAL MODELING OF OZONE ABSORPTION IN THE LOWER RESPIRATORY TRACT

    EPA Science Inventory

    A mathematical O3 dosimetry model has been developed for simulating the local absorption of O3 in the lower respiratory tract (LRT) of animals and man. The model takes into account LRT anatomy, transport in the lumen and air spaces, transport and chemical reactions in the liquid ...

  6. The Singing Wineglass: An Exercise in Mathematical Modelling

    ERIC Educational Resources Information Center

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

    2008-01-01

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

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

    PubMed

    Beregovskaya, N; Maiboroda, R

    1995-01-21

    The role of mitochondrial DNA (mtDNA) damage in ageing processes and in malignant transformation of a cell is discussed. A mathematical model of the mtDNA population in a cell and in tissue is constructed. The model describes the effects of mtDNA damages accumulated during ageing and some features of malignant transformation and regeneration. PMID:7891454

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

    ERIC Educational Resources Information Center

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

    2011-01-01

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

  9. RECEIVING WATER QUALITY DATABASE FOR TESTING OF MATHEMATICAL MODELS

    EPA Science Inventory

    Many mathematical models exist for simulation of quantity and quality parameters of receiving waters. Such models are frequently used in the evaluation of effects on receiving waters of pollution control alternatives such as advanced waste treatment and nonpoint source runoff aba...

  10. Mathematical Modeling Of A Nuclear/Thermionic Power Source

    NASA Technical Reports Server (NTRS)

    Vandersande, Jan W.; Ewell, Richard C.

    1992-01-01

    Report discusses mathematical modeling to predict performance and lifetime of spacecraft power source that is integrated combination of nuclear-fission reactor and thermionic converters. Details of nuclear reaction, thermal conditions in core, and thermionic performance combined with model of swelling of fuel.

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

    NASA Astrophysics Data System (ADS)

    McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

    2013-10-01

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

  12. Light driven microactuators: Design, fabrication, and mathematical modeling

    NASA Astrophysics Data System (ADS)

    Han, Li-Hsin

    This dissertation is concerned with design, fabrication, and mathematical modeling of three different microactuators driven by light. Compared to electricity, electromagnetic wave is a wireless source of power. A distant light source can be delivered, absorbed, and converted to generate a driving force for a microactuator. The study of light-driven microsystems, still at its early stage, is already expanding the horizon for the research of microsystems. The microactuators of this dissertation include micro-cantilevers driven by pulsed laser, photo-deformable microshells coated with gold nanospheres, and a nano-particles coated micro-turbine driven by visible light. Experimental investigation and theoretical analysis of these microactuators showed interesting results. These microactuators were functioned based on cross-linked, multiple physics phenomenon, such as photo-heating, thermal expansion, photo-chemistry effect, plasomonics enhancement, and thermal convection in rarefied gas. These multiple physics effects dominate the function of a mechanical system, when the system size becomes small. The modeling results of the microactuators suggest that, to simulate a microscale mechanical system accurately, one has to take account the minimum dimension of the system and to consider the validity of a theoretical model. Examples of the building of different microstructures were shown to demonstrate the capacity of a digital-micromirror-device (DMD) based apparatus for three-dimensional, heterogeneous fabrication of polymeric microstructures.

  13. Mathematical model of galactose regulation and metabolic consumption in yeast.

    PubMed

    Mitre, Tina M; Mackey, Michael C; Khadra, Anmar

    2016-10-21

    The galactose network has been extensively studied at the unicellular level to broaden our understanding of the regulatory mechanisms governing galactose metabolism in multicellular organisms. Although the key molecular players involved in the metabolic and regulatory processes of this system have been known for decades, their interactions and chemical kinetics remain incompletely understood. Mathematical models can provide an alternative method to study the dynamics of this network from a quantitative and a qualitative perspective. Here, we employ this approach to unravel the main properties of the galactose network, including equilibrium binary and temporal responses, as a way to decipher its adaptation to actively-changing inputs. We combine its two main components: the genetic branch, which allows for bistable responses, and a metabolic branch, encompassing the relevant metabolic processes that can be repressed by glucose. We use both computational tools to estimate model parameters based on published experimental data, as well as bifurcation analysis to decipher the properties of the system in various parameter regimes. Our model analysis reveals that the interplay between the inducer (galactose) and the repressor (glucose) creates a bistable regime which dictates the temporal responses of the system. Based on the same bifurcation techniques, we explain why the system is robust to genetic mutations and molecular instabilities. These findings may provide experimentalists with a theoretical framework with which they can determine how the galactose network functions under various conditions. PMID:27395401

  14. An Examination of the Effects of Collaborative Scientific Visualization via Model-Based Reasoning on Science, Technology, Engineering, and Mathematics (STEM) Learning within an Immersive 3D World

    ERIC Educational Resources Information Center

    Soleimani, Ali

    2013-01-01

    Immersive 3D worlds can be designed to effectively engage students in peer-to-peer collaborative learning activities, supported by scientific visualization, to help with understanding complex concepts associated with learning science, technology, engineering, and mathematics (STEM). Previous research studies have shown STEM learning benefits…

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

    NASA Astrophysics Data System (ADS)

    Neves, Rui Gomes; Teodoro, Vítor Duarte

    2012-09-01

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

  16. Novel Mathematical Models for Investigating Topics in Obesity123

    PubMed Central

    Dawson, John A.; Hall, Kevin D.; Thomas, Diana M.; Hardin, James W.; Allison, David B.; Heymsfield, Steven B.

    2014-01-01

    There is limited insight into the mechanisms, progression, and related comorbidities of obesity through simple modeling tools such as linear regression. Keeping in mind the words of the late George E. P. Box that “all models are wrong, some are useful,” this symposium presented 4 useful mathematical models or methodologic refinements. Presenters placed specific emphasis on how these novel models and methodologies can be applied to further our knowledge of the etiology of obesity. PMID:25469395

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2015-09-01

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

  19. Mathematical modelling in the computer-aided process planning

    NASA Astrophysics Data System (ADS)

    Mitin, S.; Bochkarev, P.

    2016-04-01

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

  20. A mathematical look at a physical power prediction model

    SciTech Connect

    Landberg, L.

    1997-12-31

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

  1. Dynamic mathematical model of high rate algal ponds (HRAP).

    PubMed

    Jupsin, H; Praet, E; Vasel, J L

    2003-01-01

    This article presents a mathematical model to describe High-Rate Algal Ponds (HRAPs). The hydrodynamic behavior of the reactor is described as completely mixed tanks in series with recirculation. The hydrodynamic pattern is combined with a subset of River Water Quality Model 1 (RWQM1), including the main processes in liquid phase. Our aim is to develop models for WSPs and aerated lagoons, too, but we focused on HRAPs first for several reasons: Sediments are usually less abundant in HRAP and can be neglected, Stratification is not observed and state variables are constant in a reactor cross section, Due to the system's geometry, the reactor is quite similar to a plugflow type reactor with recirculation, with a simple advection term. The model is based on mass balances and includes the following processes: *Phytoplankton growth with NO3-, NO2- and death, *Aerobic growth of heterotrophs with NO3-, NH4+ and respiration, *Anoxic growth of heterotrophs with NO3-, NO2- and anoxic respiration, *Growth of nitrifiers (two stages) and respiration. The differences with regard to RWQM1 are that we included a limiting term associated with inorganic carbon on the growth rate of algae and nitrifiers, gas transfers are taken into account by the familiar Adeney equation, and a subroutine calculates light intensity at the water surface. This article presents our first simulations. PMID:14510211

  2. Using mathematical models to understand the AIDS spidemic. [None

    SciTech Connect

    Hyman, J.M.; Stanley, E.A.

    1987-01-01

    The most urgent public health problem today is to devise effective strategies to minimize the destruction caused by the AIDS epidemic. This complex problem will involve medical advances and new public health and education initiatives. Mathematical models based on the underlying transmission mechanisms of the AIDS virus can help the medical/scientific community understand and anticipate its spread in different populations and evaluate the potential effectiveness of different approaches for bringing the epidemic under control. Before we can use models to predict the future, we must carefully test them against the past spread of the infection and for sensitivity to parameter changes. The long and extremely variable incubation period and the low probability of transmitting the AIDS virus in a single contact imply that population structure and variations in infectivity both play an important role in its spread. This structure occurs because of differences between people in numbers of sexual partners and the use of intravenous drugs and because of the way in which people mix among age, ethnic, and social groups. We use a simplified approach to investigate the effects of variation in incubation periods and infectivity specific to the AIDS virus and we compare a model of random partner choices with a model in which partners both come from similar behavior groups. 60 refs., 15 figs.

  3. Mathematical models of polymer solutions motion and their symmetries

    NASA Astrophysics Data System (ADS)

    Bozhkov, Yu. D.; Pukhnachev, V. V.; Pukhnacheva, T. P.

    2015-10-01

    We consider three mathematical models describing motion of aqueous polymer solutions. All of them are derived from equations of Maxwell type viscoelastic medium at small relaxation time. Distinction consists in the choice of time derivative in the rheological constitutive law. Namely, we can choose (a) connective, (b) partial or (c) objective derivative of the strain tensor in time. We found widest symmetry groups admitted by each of these models. Systems (a) and (c) admit the extended Galilei group containing four arbitrary functions of time while the group admitted by system (b) is rather poor. Wide classes of exact solutions are obtained and their behaviors are analyzed if the relaxation viscosity tends to zero. Asymptotic expansion in this solution's parameter describing the flow near a critical point in planar and axially symmetric cases is derived. Analogs of the classical Hagen-Poiseuille and Nusselt solutions are studied too. We found difference in the pressure distribution between solutions calculated on the base of model (c) and two other models.

  4. Soloworks: Computer-Based Laboratories for High School Mathematics.

    ERIC Educational Resources Information Center

    Dwyer, Thomas A.

    1975-01-01

    The Soloworks project is based on the belief that student-controlled computing is a promising innovation in secondary mathematics instruction. The Soloworks project is following up three years of experience in the Pittsburgh public school system with a new program encorporating both student-controlled computing and modern math curricula. The work…

  5. Mathematics. Nevada Competency-Based Adult High School Diploma Project.

    ERIC Educational Resources Information Center

    Nevada Univ., Las Vegas. Coll. of Education.

    This document is one of ten curriculum guides developed by the Nevada Competency-Based Adult High School Diploma (CBAHSD) Project. This curriculum guide on mathematics is divided into three topics. The topics included are Problem Solving, Computation, and Geometry and Measurement. Competency statements and performance indicators are provided for…

  6. Web-Based Mathematics Progress Monitoring in Second Grade

    ERIC Educational Resources Information Center

    Salaschek, Martin; Souvignier, Elmar

    2014-01-01

    We examined a web-based mathematics progress monitoring tool for second graders. The tool monitors the learning progress of two competences, number sense and computation. A total of 414 students from 19 classrooms in Germany were checked every 3 weeks from fall to spring. Correlational analyses indicate that alternate-form reliability was adequate…

  7. Using Curriculum-Based Measurement To Monitor Kindergarteners' Mathematics Development

    ERIC Educational Resources Information Center

    Seethaler, Pamela M.; Fuchs, Lynn S.

    2011-01-01

    The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

  8. Opportunities for Learning-Based Conversations in High School Mathematics

    ERIC Educational Resources Information Center

    McFeetors, Janelle

    2015-01-01

    Conversations as moments for interpersonal and intimate turning round of ideas for the purpose of growth are well-defined within curriculum inquiry. Interactions among grade 12 students in this study demonstrate the possibility of learning to learn mathematics through conversation. Attending to opportunities for learning-based conversations,…

  9. Using Curriculum-Based Measurement to Monitor Kindergarteners' Mathematics Development

    ERIC Educational Resources Information Center

    Seethaler, Pamela M.; Fuchs, Lynn S.

    2011-01-01

    The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

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

    PubMed

    Campitelli, Guillermo; Gerrans, Paul

    2014-04-01

    We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research. PMID:24132723

  11. A Mathematical Programming Model for the Efficient Allocation of Vocational Technical Education Funds.

    ERIC Educational Resources Information Center

    McNamara, James F.

    This mathematical programing model was developed to provide the State Board of Education with complete information for evaluating decisions about the efficient allocation of vocational education funds to local school districts. The model, based on a supply-demand criterion, was tested on a set of occupational training programs within a given Labor…

  12. Mathematical Learning Models that Depend on Prior Knowledge and Instructional Strategies

    ERIC Educational Resources Information Center

    Pritchard, David E.; Lee, Young-Jin; Bao, Lei

    2008-01-01

    We present mathematical learning models--predictions of student's knowledge vs amount of instruction--that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also…

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

    PubMed

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

    2008-07-28

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

  14. A complex mathematical model of the human menstrual cycle.

    PubMed

    Reinecke, Isabel; Deuflhard, Peter

    2007-07-21

    Despite the fact that more than 100 million women worldwide use birth control pills and that half of the world's population is concerned, the menstrual cycle has so far received comparatively little attention in the field of mathematical modeling. The term menstrual cycle comprises the processes of the control system in the female body that, under healthy circumstances, lead to ovulation at regular intervals, thus making reproduction possible. If this is not the case or ovulation is not desired, the question arises how this control system can be influenced, for example, by hormonal treatments. In order to be able to cover a vast range of external manipulations, the mathematical model must comprise the main components where the processes belonging to the menstrual cycle occur, as well as their interrelations. A system of differential equations serves as the mathematical model, describing the dynamics of hormones, enzymes, receptors, and follicular phases. Since the processes take place in different parts of the body and influence each other with a certain delay, passing over to delay differential equations is deemed a reasonable step. The pulsatile release of the gonadotropin-releasing hormone (GnRH) is controlled by a complex neural network. We choose to model the pulse time points of this GnRH pulse generator by a stochastic process. Focus in this paper is on the model development. This rather elaborate mathematical model is the basis for a detailed analysis and could be helpful for possible drug design. PMID:17448501

  15. Mathematical modeling of damage in unidirectional composites

    NASA Technical Reports Server (NTRS)

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

    1981-01-01

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

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  17. A Mathematical Model for Segmenting ECG Signals

    NASA Astrophysics Data System (ADS)

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

    2010-09-01

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

  18. Undergraduate Research: Mathematical Modeling of Mortgages

    ERIC Educational Resources Information Center

    Choi, Youngna; Spero, Steven

    2010-01-01

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

  19. Rotor systems research aircraft simulation mathematical model

    NASA Technical Reports Server (NTRS)

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

    1977-01-01

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

  20. Mathematical Modeling Of Life-Support Systems

    NASA Technical Reports Server (NTRS)

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

    1994-01-01

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

  1. Cancer Evolution: Mathematical Models and Computational Inference

    PubMed Central

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

    2015-01-01

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

  2. A mathematical model for spatial orientation from pictorial perspective displays

    NASA Technical Reports Server (NTRS)

    Grunwald, Arthur J.; Ellis, Stephen R.; Smith, Stephen

    1988-01-01

    A previously formulated mathematical model, describing how observers reconstruct three-dimensional spatial layouts from perspective projections, has been extended to more complex situations. The model assumes that the observer has a priori knowledge of certain characteristics of the viewed objects, like size, shape, or parallelism or perpendicularity of lines or planes. These assumptions are used in a three-dimensional process to reconstruct a spatial layout that `best matches' the perceived lines of sight to the object coordinates. Sources of errors and biases in this process are specified and their effects on model outputs are discussed. An experiment, in which eight subjects judged the relative direction of one object with respect to another, has been conducted to validate the model. The model has been found to generally reproduce the systematic trends of the experimental results and also has provided an analytical explanation for them. The mathematical model is expected to be a useful tool in analyzing and developing pictorial perspective flight displays.

  3. A Mathematical Model for Railway Control Systems

    NASA Technical Reports Server (NTRS)

    Hoover, D. N.

    1996-01-01

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

  4. Mathematical model for methane production from landfill bioreactor

    SciTech Connect

    Lay, J.J.; Noike, Tatsuya; Li, Y.Y.

    1998-08-01

    A mathematical model for the development of methane production from a landfill bioreactor (LFBR) treating the organic fraction of municipal solid wastes was developed from the Gompertz equation. The model incorporates three biokinetic parameters: methane production lag phase time, rate, and potential. The methane converting capacity test experiment was conducted to monitor the specific methane production rate consuming anaerobic fermentative intermediates, including carbohydrates, proteins, and lipids. The model developed in this study can be used to predict methane production based on the chemical nature and the decomposition characteristics of the organic fraction of municipal solid wastes. The simulative results indicate that the leachate recycle for the LFBR resulted in a more rapid methane production from the consumption of the carbohydrate but in less rapid production from that of the protein and lipid. Moreover, the same specific methane production rate of 2.6 mL/g volatile solid (VS) per day occurred at the LFBR with/without leachate recycle; however, a sharp drop in methane production lag phase time, from 125 to 25 days, was obtained at the LFBR incubated with leachate recycle.

  5. Mathematical modeling of a single stage ultrasonically assisted distillation process.

    PubMed

    Mahdi, Taha; Ahmad, Arshad; Ripin, Adnan; Abdullah, Tuan Amran Tuan; Nasef, Mohamed M; Ali, Mohamad W

    2015-05-01

    The ability of sonication phenomena in facilitating separation of azeotropic mixtures presents a promising approach for the development of more intensified and efficient distillation systems than conventional ones. To expedite the much-needed development, a mathematical model of the system based on conservation principles, vapor-liquid equilibrium and sonochemistry was developed in this study. The model that was founded on a single stage vapor-liquid equilibrium system and enhanced with ultrasonic waves was coded using MATLAB simulator and validated with experimental data for ethanol-ethyl acetate mixture. The effects of both ultrasonic frequency and intensity on the relative volatility and azeotropic point were examined, and the optimal conditions were obtained using genetic algorithm. The experimental data validated the model with a reasonable accuracy. The results of this study revealed that the azeotropic point of the mixture can be totally eliminated with the right combination of sonication parameters and this can be utilized in facilitating design efforts towards establishing a workable ultrasonically intensified distillation system. PMID:25432400

  6. Grip Forces During Object Manipulation: Experiment, Mathematical Model & Validation

    PubMed Central

    Slota, Gregory P.; Latash, Mark L.; Zatsiorsky, Vladimir M.

    2011-01-01

    When people transport handheld objects, they change the grip force with the object movement. Circular movement patterns were tested within three planes at two different rates (1.0, 1.5 Hz), and two diameters (20, 40 cm). Subjects performed the task reasonably well, matching frequencies and dynamic ranges of accelerations within expectations. A mathematical model was designed to predict the applied normal forces from kinematic data. The model is based on two hypotheses: (a) the grip force changes during movements along complex trajectories can be represented as the sum of effects of two basic commands associated with the parallel and orthogonal manipulation, respectively; (b) different central commands are sent to the thumb and virtual finger (Vf- four fingers combined). The model predicted the actual normal forces with a total variance accounted for of better than 98%. The effects of the two components of acceleration—along the normal axis and the resultant acceleration within the shear plane—on the digit normal forces are additive. PMID:21735245

  7. Mathematical modeling of a Fermilab helium liquefier coldbox

    SciTech Connect

    Geynisman, M.G.; Walker, R.J.

    1995-12-01

    Fermilab Central Helium Liquefier (CHL) facility is operated 24 hours-a-day to supply 4.6{degrees}K for the Fermilab Tevatron superconducting proton-antiproton collider Ring and to recover warm return gases. The centerpieces of the CHL are two independent cold boxes rated at 4000 and 5400 liters/hour with LN{sub 2} precool. These coldboxes are Claude cycle and have identical heat exchangers trains, but different turbo-expanders. The Tevatron cryogenics demand for higher helium supply from CHL was the driving force to investigate an installation of an expansion engine in place of the Joule-Thompson valve. A mathematical model was developed to describe the thermo- and gas-dynamic processes for the equipment included in the helium coldbox. The model is based on a finite element approach, opposite to a global variables approach, thus providing for higher accuracy and conversion stability. Though the coefficients used in thermo- and gas-dynamic equations are unique for a given coldbox, the general approach, the equations, the methods of computations, and most of the subroutines written in FORTRAN can be readily applied to different coldboxes. The simulation results are compared against actual operating data to demonstrate applicability of the model.

  8. Mathematical Modelling of Metabolic Regulation in Aging

    PubMed Central

    Mc Auley, Mark T.; Mooney, Kathleen M.; Angell, Peter J.; Wilkinson, Stephen J.

    2015-01-01

    The underlying cellular mechanisms that characterize aging are complex and multifaceted. However, it is emerging that aging could be regulated by two distinct metabolic hubs. These hubs are the pathway defined by the mammalian target of rapamycin (mTOR) and that defined by the NAD+-dependent deacetylase enzyme, SIRT1. Recent experimental evidence suggests that there is crosstalk between these two important pathways; however, the mechanisms underpinning their interaction(s) remains poorly understood. In this review, we propose using computational modelling in tandem with experimentation to delineate the mechanism(s). We briefly discuss the main modelling frameworks that could be used to disentangle this relationship and present a reduced reaction pathway that could be modelled. We conclude by outlining the limitations of computational modelling and by discussing opportunities for future progress in this area. PMID:25923415

  9. Mathematical modelling of metabolic regulation in aging.

    PubMed

    Auley, Mark T Mc; Mooney, Kathleen M; Angell, Peter J; Wilkinson, Stephen J

    2015-01-01

    The underlying cellular mechanisms that characterize aging are complex and multifaceted. However, it is emerging that aging could be regulated by two distinct metabolic hubs. These hubs are the pathway defined by the mammalian target of rapamycin (mTOR) and that defined by the NAD+-dependent deacetylase enzyme, SIRT1. Recent experimental evidence suggests that there is crosstalk between these two important pathways; however, the mechanisms underpinning their interaction(s) remains poorly understood. In this review, we propose using computational modelling in tandem with experimentation to delineate the mechanism(s). We briefly discuss the main modelling frameworks that could be used to disentangle this relationship and present a reduced reaction pathway that could be modelled. We conclude by outlining the limitations of computational modelling and by discussing opportunities for future progress in this area. PMID:25923415

  10. Integrating Mathematical Modeling for Undergraduate Pre-Service Science Education Learning and Instruction in Middle School Classrooms

    ERIC Educational Resources Information Center

    Carrejo, David; Robertson, William H.

    2011-01-01

    Computer-based mathematical modeling in physics is a process of constructing models of concepts and the relationships between them in the scientific characteristics of work. In this manner, computer-based modeling integrates the interactions of natural phenomenon through the use of models, which provide structure for theories and a base for…

  11. Mathematical Model For Engineering Analysis And Optimization

    NASA Technical Reports Server (NTRS)

    Sobieski, Jaroslaw

    1992-01-01

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

  12. Program Helps Generate Boundary-Element Mathematical Models

    NASA Technical Reports Server (NTRS)

    Goldberg, R. K.

    1995-01-01

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

  13. Mathematical modeling of polymer electrolyte fuel cells

    NASA Astrophysics Data System (ADS)

    Sousa, Ruy; Gonzalez, Ernesto R.

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

  14. The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process

    NASA Astrophysics Data System (ADS)

    Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko

    2012-06-01

    A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.

  15. Prospective Teachers' Perspectives on Mathematics Teaching and Learning: Lens for Interpreting Experiences in a Standards-Based Mathematics Course

    ERIC Educational Resources Information Center

    Chamberlin, Michelle T.

    2013-01-01

    In a mathematics course for prospective elementary teachers, we strove to model standards-based pedagogy. However, an end-of-class reflection revealed the prospective teachers were considering incorporating standards-based strategies in their future classrooms in ways different from our intent. Thus, we drew upon the framework presented by Simon,…

  16. Mathematical Model Of Variable-Polarity Plasma Arc Welding

    NASA Technical Reports Server (NTRS)

    Hung, R. J.

    1996-01-01

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

  17. A mathematical model of a large open fire

    NASA Technical Reports Server (NTRS)

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

    1981-01-01

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

  18. Engaging Students in Mathematical Modeling through Service-Learning

    ERIC Educational Resources Information Center

    Carducci, Olivia M.

    2014-01-01

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

  19. Schoolwide Mathematics Achievement within the Gifted Cluster Grouping Model

    ERIC Educational Resources Information Center

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

    2012-01-01

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

  20. A mathematical model concerning reflectance from a row crop

    NASA Technical Reports Server (NTRS)

    Jaggi, R. K.

    1972-01-01

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