#### Sample records for accurate mathematical model

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

PubMed Central

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

2015-01-01

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

2. Accurate state estimation from uncertain data and models: an application of data assimilation to mathematical models of human brain tumors

PubMed Central

2011-01-01

Background Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor. Results We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise. Conclusions The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling. Reviewers This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck). PMID:22185645

3. 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…

4. A mathematical recursive model for accurate description of the phase behavior in the near-critical region by Generalized van der Waals Equation

Kim, Jibeom; Jeon, Joonhyeon

2015-01-01

Recently, related studies on Equation Of State (EOS) have reported that generalized van der Waals (GvdW) shows poor representations in the near critical region for non-polar and non-sphere molecules. Hence, there are still remains a problem of GvdW parameters to minimize loss in describing saturated vapor densities and vice versa. This paper describes a recursive model GvdW (rGvdW) for an accurate representation of pure fluid materials in the near critical region. For the performance evaluation of rGvdW in the near critical region, other EOS models are also applied together with two pure molecule group: alkane and amine. The comparison results show rGvdW provides much more accurate and reliable predictions of pressure than the others. The calculating model of EOS through this approach gives an additional insight into the physical significance of accurate prediction of pressure in the nearcritical region.

5. New model accurately predicts reformate composition

SciTech Connect

Ancheyta-Juarez, J.; Aguilar-Rodriguez, E. )

1994-01-31

Although naphtha reforming is a well-known process, the evolution of catalyst formulation, as well as new trends in gasoline specifications, have led to rapid evolution of the process, including: reactor design, regeneration mode, and operating conditions. Mathematical modeling of the reforming process is an increasingly important tool. It is fundamental to the proper design of new reactors and revamp of existing ones. Modeling can be used to optimize operating conditions, analyze the effects of process variables, and enhance unit performance. Instituto Mexicano del Petroleo has developed a model of the catalytic reforming process that accurately predicts reformate composition at the higher-severity conditions at which new reformers are being designed. The new AA model is more accurate than previous proposals because it takes into account the effects of temperature and pressure on the rate constants of each chemical reaction.

6. 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…

7. 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…

8. Mathematical Models of Gene Regulation

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.

9. Teaching Mathematical Modelling.

ERIC Educational Resources Information Center

Jones, Mark S.

1997-01-01

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

10. Mathematical modeling in neuroendocrinology.

PubMed

Bertram, Richard

2015-04-01

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

11. 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…

12. [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.

13. 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…

14. Richardson, mathematical modeller

Vreugdenhil, C. B.

1994-03-01

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

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

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

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

16. Mathematical Modelling in European Education

ERIC Educational Resources Information Center

Ferri, Rita Borromeo

2013-01-01

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

17. 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…

18. 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…

19. Mathematical models of vaccination.

PubMed

Scherer, Almut; McLean, Angela

2002-01-01

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

20. Mathematical model for gyroscope effects

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).

1. 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…

2. Teaching and Assessing Mathematical Modelling.

ERIC Educational Resources Information Center

Lingefjard, T.

2002-01-01

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

3. Pre-Modeling Ensures Accurate Solid Models

ERIC Educational Resources Information Center

Gow, George

2010-01-01

Successful solid modeling requires a well-organized design tree. The design tree is a list of all the object's features and the sequential order in which they are modeled. The solid-modeling process is faster and less prone to modeling errors when the design tree is a simple and geometrically logical definition of the modeled object. Few high…

4. 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…

5. Mathematical modelling in developmental biology.

PubMed

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

2013-06-01

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

6. An Accurate, Simplified Model Intrabeam Scattering

SciTech Connect

Bane, Karl LF

2002-05-23

Beginning with the general Bjorken-Mtingwa solution for intrabeam scattering (IBS) we derive an accurate, greatly simplified model of IBS, valid for high energy beams in normal storage ring lattices. In addition, we show that, under the same conditions, a modified version of Piwinski's IBS formulation (where {eta}{sub x,y}{sup 2}/{beta}{sub x,y} has been replaced by {Eta}{sub x,y}) asymptotically approaches the result of Bjorken-Mtingwa.

7. 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.

8. 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.

9. 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…

10. 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…

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

ERIC Educational Resources Information Center

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

2014-01-01

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

12. 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…

13. ASTP ranging system mathematical model

NASA Technical Reports Server (NTRS)

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

1973-01-01

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

14. 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…

15. 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…

16. 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.

17. Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

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

18. 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…

19. Mathematical Modelling with Young Children

ERIC Educational Resources Information Center

English, Lyn D.; Watters, James J.

2004-01-01

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

20. Mathematical modeling of biological ensembles

SciTech Connect

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

1986-07-01

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

1. 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…

2. 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…

3. Mathematical Modeling in the High School Curriculum

ERIC Educational Resources Information Center

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

2016-01-01

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

4. Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

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

2005-01-01

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

5. 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…

6. 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.

7. Mathematical modeling of drug delivery.

PubMed

Siepmann, J; Siepmann, F

2008-12-08

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

8. 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…

9. Mathematical Modelling of Folate Metabolism

PubMed Central

Panetta, John C.; Paugh, Steven W.

2013-01-01

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

10. Mathematical modelling of hepatic lipid metabolism.

PubMed

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

2015-04-01

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

11. 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.

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

PubMed

Tian, Tianhai; Song, Jiangning

2012-01-01

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

PubMed

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

2015-01-01

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

14. Mathematical Modeling of Kidney Transport

PubMed Central

Layton, Anita T.

2013-01-01

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

15. Mathematical Model for Mapping Students' Cognitive Capability

ERIC Educational Resources Information Center

Tambunan, Hardi

2016-01-01

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

16. Mathematical models of bipolar disorder

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.

17. 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.

18. Mathematical Models Of Turbulence In Hypersonic Flow

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

19. Personalized Orthodontic Accurate Tooth Arrangement System with Complete Teeth Model.

PubMed

Cheng, Cheng; Cheng, Xiaosheng; Dai, Ning; Liu, Yi; Fan, Qilei; Hou, Yulin; Jiang, Xiaotong

2015-09-01

The accuracy, validity and lack of relation information between dental root and jaw in tooth arrangement are key problems in tooth arrangement technology. This paper aims to describe a newly developed virtual, personalized and accurate tooth arrangement system based on complete information about dental root and skull. Firstly, a feature constraint database of a 3D teeth model is established. Secondly, for computed simulation of tooth movement, the reference planes and lines are defined by the anatomical reference points. The matching mathematical model of teeth pattern and the principle of the specific pose transformation of rigid body are fully utilized. The relation of position between dental root and alveolar bone is considered during the design process. Finally, the relative pose relationships among various teeth are optimized using the object mover, and a personalized therapeutic schedule is formulated. Experimental results show that the virtual tooth arrangement system can arrange abnormal teeth very well and is sufficiently flexible. The relation of position between root and jaw is favorable. This newly developed system is characterized by high-speed processing and quantitative evaluation of the amount of 3D movement of an individual tooth.

20. Mathematical analysis and algorithms for efficiently and accurately implementing stochastic simulations of short-term synaptic depression and facilitation.

PubMed

McDonnell, Mark D; Mohan, Ashutosh; Stricker, Christian

2013-01-01

The release of neurotransmitter vesicles after arrival of a pre-synaptic action potential (AP) at cortical synapses is known to be a stochastic process, as is the availability of vesicles for release. These processes are known to also depend on the recent history of AP arrivals, and this can be described in terms of time-varying probabilities of vesicle release. Mathematical models of such synaptic dynamics frequently are based only on the mean number of vesicles released by each pre-synaptic AP, since if it is assumed there are sufficiently many vesicle sites, then variance is small. However, it has been shown recently that variance across sites can be significant for neuron and network dynamics, and this suggests the potential importance of studying short-term plasticity using simulations that do generate trial-to-trial variability. Therefore, in this paper we study several well-known conceptual models for stochastic availability and release. We state explicitly the random variables that these models describe and propose efficient algorithms for accurately implementing stochastic simulations of these random variables in software or hardware. Our results are complemented by mathematical analysis and statement of pseudo-code algorithms.

1. Mathematical modeling of glycerol biotransformation

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.

2. 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.

3. A quick accurate model of nozzle backflow

NASA Technical Reports Server (NTRS)

Kuharski, R. A.

1991-01-01

Backflow from nozzles is a major source of contamination on spacecraft. If the craft contains any exposed high voltages, the neutral density produced by the nozzles in the vicinity of the craft needs to be known in order to assess the possibility of Paschen breakdown or the probability of sheath ionization around a region of the craft that collects electrons for the plasma. A model for backflow has been developed for incorporation into the Environment-Power System Analysis Tool (EPSAT) which quickly estimates both the magnitude of the backflow and the species makeup of the flow. By combining the backflow model with the Simons (1972) model for continuum flow it is possible to quickly estimate the density of each species from a nozzle at any position in space. The model requires only a few physical parameters of the nozzle and the gas as inputs and is therefore ideal for engineering applications.

4. 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.

5. Accurate spectral modeling for infrared radiation

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Gupta, S. K.

1977-01-01

Direct line-by-line integration and quasi-random band model techniques are employed to calculate the spectral transmittance and total band absorptance of 4.7 micron CO, 4.3 micron CO2, 15 micron CO2, and 5.35 micron NO bands. Results are obtained for different pressures, temperatures, and path lengths. These are compared with available theoretical and experimental investigations. For each gas, extensive tabulations of results are presented for comparative purposes. In almost all cases, line-by-line results are found to be in excellent agreement with the experimental values. The range of validity of other models and correlations are discussed.

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

PubMed

Smye, Stephen W; Clayton, Richard H

2002-11-01

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

7. Mathematical model for classification of EEG signals

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.

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

ERIC Educational Resources Information Center

Julie, Cyril

2002-01-01

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

9. 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…

10. 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…

11. Mathematical Modelling of Data: Software for Pedagogy.

ERIC Educational Resources Information Center

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

1993-01-01

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

12. Modelling and Optimizing Mathematics Learning in Children

ERIC Educational Resources Information Center

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

2013-01-01

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

13. Scaffolding Mathematical Modelling with a Solution Plan

ERIC Educational Resources Information Center

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

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

14. Mathematical Modeling of Cellular Metabolism.

PubMed

Berndt, Nikolaus; Holzhütter, Hermann-Georg

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

15. Rival approaches to mathematical modelling in immunology

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

2007-08-01

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

16. Mathematical modeling in soil science

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.

17. 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…

18. A Seminar in Mathematical Model-Building.

ERIC Educational Resources Information Center

Smith, David A.

1979-01-01

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

19. 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,…

20. New process model proves accurate in tests on catalytic reformer

SciTech Connect

Aguilar-Rodriguez, E.; Ancheyta-Juarez, J. )

1994-07-25

A mathematical model has been devised to represent the process that takes place in a fixed-bed, tubular, adiabatic catalytic reforming reactor. Since its development, the model has been applied to the simulation of a commercial semiregenerative reformer. The development of mass and energy balances for this reformer led to a model that predicts both concentration and temperature profiles along the reactor. A comparison of the model's results with experimental data illustrates its accuracy at predicting product profiles. Simple steps show how the model can be applied to simulate any fixed-bed catalytic reformer.

1. Study of Photovoltaic Cells Engineering Mathematical Model

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

2016-11-01

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

2. Establishing an Explanatory Model for Mathematics Identity.

PubMed

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

2015-04-01

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

3. Mathematical model insights into arsenic detoxification

PubMed Central

2011-01-01

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

4. Mathematical Models of College Myopia

PubMed Central

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

2015-01-01

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

5. 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…

6. 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,…

7. 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.

8. Cooking Potatoes: Experimentation and Mathematical Modeling.

ERIC Educational Resources Information Center

Chen, Xiao Dong

2002-01-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

10. 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.

11. Modelling Mathematical Reasoning in Physics Education

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

2012-04-01

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

12. Mathematical Modeling of Circadian and Homeostatic Interaction

DTIC Science & Technology

2011-11-16

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

13. 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…

14. 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…

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

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

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

16. 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.

17. Mathematical Modelling with 9-Year-Olds

ERIC Educational Resources Information Center

English, Lyn D.; Watters, James J.

2005-01-01

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

18. An Accurate and Dynamic Computer Graphics Muscle Model

NASA Technical Reports Server (NTRS)

Levine, David Asher

1997-01-01

A computer based musculo-skeletal model was developed at the University in the departments of Mechanical and Biomedical Engineering. This model accurately represents human shoulder kinematics. The result of this model is the graphical display of bones moving through an appropriate range of motion based on inputs of EMGs and external forces. The need existed to incorporate a geometric muscle model in the larger musculo-skeletal model. Previous muscle models did not accurately represent muscle geometries, nor did they account for the kinematics of tendons. This thesis covers the creation of a new muscle model for use in the above musculo-skeletal model. This muscle model was based on anatomical data from the Visible Human Project (VHP) cadaver study. Two-dimensional digital images from the VHP were analyzed and reconstructed to recreate the three-dimensional muscle geometries. The recreated geometries were smoothed, reduced, and sliced to form data files defining the surfaces of each muscle. The muscle modeling function opened these files during run-time and recreated the muscle surface. The modeling function applied constant volume limitations to the muscle and constant geometry limitations to the tendons.

19. 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

20. 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…

1. A mathematical model of a cloud

Wang, A. P.

1980-07-01

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

2. Mathematical Modeling in Continuum Mechanics

Temam, Roger; Miranville, Alain

2005-06-01

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

3. Accurate modelling of unsteady flows in collapsible tubes.

PubMed

Marchandise, Emilie; Flaud, Patrice

2010-01-01

The context of this paper is the development of a general and efficient numerical haemodynamic tool to help clinicians and researchers in understanding of physiological flow phenomena. We propose an accurate one-dimensional Runge-Kutta discontinuous Galerkin (RK-DG) method coupled with lumped parameter models for the boundary conditions. The suggested model has already been successfully applied to haemodynamics in arteries and is now extended for the flow in collapsible tubes such as veins. The main difference with cardiovascular simulations is that the flow may become supercritical and elastic jumps may appear with the numerical consequence that scheme may not remain monotone if no limiting procedure is introduced. We show that our second-order RK-DG method equipped with an approximate Roe's Riemann solver and a slope-limiting procedure allows us to capture elastic jumps accurately. Moreover, this paper demonstrates that the complex physics associated with such flows is more accurately modelled than with traditional methods such as finite difference methods or finite volumes. We present various benchmark problems that show the flexibility and applicability of the numerical method. Our solutions are compared with analytical solutions when they are available and with solutions obtained using other numerical methods. Finally, to illustrate the clinical interest, we study the emptying process in a calf vein squeezed by contracting skeletal muscle in a normal and pathological subject. We compare our results with experimental simulations and discuss the sensitivity to parameters of our model.

4. Constructing Meanings of Mathematical Registers Using Metaphorical Reasoning and Models

ERIC Educational Resources Information Center

Lai, Mun Yee

2013-01-01

Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This…

5. About a mathematical model of market

Kulikov, D. A.

2017-01-01

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

6. Comprehensive Mathematical Model Of Real Fluids

NASA Technical Reports Server (NTRS)

Anderson, Peter G.

1996-01-01

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

7. Mathematical model for predicting human vertebral fracture

NASA Technical Reports Server (NTRS)

Benedict, J. V.

1973-01-01

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

8. Mathematical 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.

9. 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.

10. Mathematical modeling relevant to closed artificial ecosystems.

PubMed

DeAngelis, Donald L

2003-01-01

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

11. Local Debonding and Fiber Breakage in Composite Materials Modeled Accurately

NASA Technical Reports Server (NTRS)

Bednarcyk, Brett A.; Arnold, Steven M.

2001-01-01

A prerequisite for full utilization of composite materials in aerospace components is accurate design and life prediction tools that enable the assessment of component performance and reliability. Such tools assist both structural analysts, who design and optimize structures composed of composite materials, and materials scientists who design and optimize the composite materials themselves. NASA Glenn Research Center's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) software package (http://www.grc.nasa.gov/WWW/LPB/mac) addresses this need for composite design and life prediction tools by providing a widely applicable and accurate approach to modeling composite materials. Furthermore, MAC/GMC serves as a platform for incorporating new local models and capabilities that are under development at NASA, thus enabling these new capabilities to progress rapidly to a stage in which they can be employed by the code's end users.

12. Mathematical and Numerical Techniques in Energy and Environmental Modeling

Chen, Z.; Ewing, R. E.

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

13. 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

14. An Accurate Temperature Correction Model for Thermocouple Hygrometers 1

PubMed Central

Savage, Michael J.; Cass, Alfred; de Jager, James M.

1982-01-01

Numerous water relation studies have used thermocouple hygrometers routinely. However, the accurate temperature correction of hygrometer calibration curve slopes seems to have been largely neglected in both psychrometric and dewpoint techniques. In the case of thermocouple psychrometers, two temperature correction models are proposed, each based on measurement of the thermojunction radius and calculation of the theoretical voltage sensitivity to changes in water potential. The first model relies on calibration at a single temperature and the second at two temperatures. Both these models were more accurate than the temperature correction models currently in use for four psychrometers calibrated over a range of temperatures (15-38°C). The model based on calibration at two temperatures is superior to that based on only one calibration. The model proposed for dewpoint hygrometers is similar to that for psychrometers. It is based on the theoretical voltage sensitivity to changes in water potential. Comparison with empirical data from three dewpoint hygrometers calibrated at four different temperatures indicates that these instruments need only be calibrated at, e.g. 25°C, if the calibration slopes are corrected for temperature. PMID:16662241

15. An accurate temperature correction model for thermocouple hygrometers.

PubMed

Savage, M J; Cass, A; de Jager, J M

1982-02-01

Numerous water relation studies have used thermocouple hygrometers routinely. However, the accurate temperature correction of hygrometer calibration curve slopes seems to have been largely neglected in both psychrometric and dewpoint techniques.In the case of thermocouple psychrometers, two temperature correction models are proposed, each based on measurement of the thermojunction radius and calculation of the theoretical voltage sensitivity to changes in water potential. The first model relies on calibration at a single temperature and the second at two temperatures. Both these models were more accurate than the temperature correction models currently in use for four psychrometers calibrated over a range of temperatures (15-38 degrees C). The model based on calibration at two temperatures is superior to that based on only one calibration.The model proposed for dewpoint hygrometers is similar to that for psychrometers. It is based on the theoretical voltage sensitivity to changes in water potential. Comparison with empirical data from three dewpoint hygrometers calibrated at four different temperatures indicates that these instruments need only be calibrated at, e.g. 25 degrees C, if the calibration slopes are corrected for temperature.

16. More-Accurate Model of Flows in Rocket Injectors

NASA Technical Reports Server (NTRS)

Hosangadi, Ashvin; Chenoweth, James; Brinckman, Kevin; Dash, Sanford

2011-01-01

An improved computational model for simulating flows in liquid-propellant injectors in rocket engines has been developed. Models like this one are needed for predicting fluxes of heat in, and performances of, the engines. An important part of predicting performance is predicting fluctuations of temperature, fluctuations of concentrations of chemical species, and effects of turbulence on diffusion of heat and chemical species. Customarily, diffusion effects are represented by parameters known in the art as the Prandtl and Schmidt numbers. Prior formulations include ad hoc assumptions of constant values of these parameters, but these assumptions and, hence, the formulations, are inaccurate for complex flows. In the improved model, these parameters are neither constant nor specified in advance: instead, they are variables obtained as part of the solution. Consequently, this model represents the effects of turbulence on diffusion of heat and chemical species more accurately than prior formulations do, and may enable more-accurate prediction of mixing and flows of heat in rocket-engine combustion chambers. The model has been implemented within CRUNCH CFD, a proprietary computational fluid dynamics (CFD) computer program, and has been tested within that program. The model could also be implemented within other CFD programs.

17. 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…

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

SciTech Connect

Du, Qiang

2014-11-12

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

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

Shen, Ganghui; Xia, Yuanqing; Sun, Haoran

2015-04-01

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

20. The (Mathematical) Modeling Process in Biosciences.

PubMed

Torres, Nestor V; Santos, Guido

2015-01-01

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

1. 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

2. 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.

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

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

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

4. Mathematical Modeling of Wildfire Dynamics

Del Bene, Kevin; Drew, Donald

2012-11-01

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

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

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

2014-01-01

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

6. 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.

7. 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…

8. 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.

9. Identification of the noise using mathematical modelling

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.

10. Fast and Accurate Circuit Design Automation through Hierarchical Model Switching.

PubMed

Huynh, Linh; Tagkopoulos, Ilias

2015-08-21

In computer-aided biological design, the trifecta of characterized part libraries, accurate models and optimal design parameters is crucial for producing reliable designs. As the number of parts and model complexity increase, however, it becomes exponentially more difficult for any optimization method to search the solution space, hence creating a trade-off that hampers efficient design. To address this issue, we present a hierarchical computer-aided design architecture that uses a two-step approach for biological design. First, a simple model of low computational complexity is used to predict circuit behavior and assess candidate circuit branches through branch-and-bound methods. Then, a complex, nonlinear circuit model is used for a fine-grained search of the reduced solution space, thus achieving more accurate results. Evaluation with a benchmark of 11 circuits and a library of 102 experimental designs with known characterization parameters demonstrates a speed-up of 3 orders of magnitude when compared to other design methods that provide optimality guarantees.

11. 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.

12. Mathematical models for principles of gyroscope theory

Usubamatov, Ryspek

2017-01-01

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

13. 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…

14. 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…

15. Accurate pressure gradient calculations in hydrostatic atmospheric models

NASA Technical Reports Server (NTRS)

Carroll, John J.; Mendez-Nunez, Luis R.; Tanrikulu, Saffet

1987-01-01

A method for the accurate calculation of the horizontal pressure gradient acceleration in hydrostatic atmospheric models is presented which is especially useful in situations where the isothermal surfaces are not parallel to the vertical coordinate surfaces. The present method is shown to be exact if the potential temperature lapse rate is constant between the vertical pressure integration limits. The technique is applied to both the integration of the hydrostatic equation and the computation of the slope correction term in the horizontal pressure gradient. A fixed vertical grid and a dynamic grid defined by the significant levels in the vertical temperature distribution are employed.

16. Mouse models of human AML accurately predict chemotherapy response

PubMed Central

Zuber, Johannes; Radtke, Ina; Pardee, Timothy S.; Zhao, Zhen; Rappaport, Amy R.; Luo, Weijun; McCurrach, Mila E.; Yang, Miao-Miao; Dolan, M. Eileen; Kogan, Scott C.; Downing, James R.; Lowe, Scott W.

2009-01-01

The genetic heterogeneity of cancer influences the trajectory of tumor progression and may underlie clinical variation in therapy response. To model such heterogeneity, we produced genetically and pathologically accurate mouse models of common forms of human acute myeloid leukemia (AML) and developed methods to mimic standard induction chemotherapy and efficiently monitor therapy response. We see that murine AMLs harboring two common human AML genotypes show remarkably diverse responses to conventional therapy that mirror clinical experience. Specifically, murine leukemias expressing the AML1/ETO fusion oncoprotein, associated with a favorable prognosis in patients, show a dramatic response to induction chemotherapy owing to robust activation of the p53 tumor suppressor network. Conversely, murine leukemias expressing MLL fusion proteins, associated with a dismal prognosis in patients, are drug-resistant due to an attenuated p53 response. Our studies highlight the importance of genetic information in guiding the treatment of human AML, functionally establish the p53 network as a central determinant of chemotherapy response in AML, and demonstrate that genetically engineered mouse models of human cancer can accurately predict therapy response in patients. PMID:19339691

17. Mouse models of human AML accurately predict chemotherapy response.

PubMed

Zuber, Johannes; Radtke, Ina; Pardee, Timothy S; Zhao, Zhen; Rappaport, Amy R; Luo, Weijun; McCurrach, Mila E; Yang, Miao-Miao; Dolan, M Eileen; Kogan, Scott C; Downing, James R; Lowe, Scott W

2009-04-01

The genetic heterogeneity of cancer influences the trajectory of tumor progression and may underlie clinical variation in therapy response. To model such heterogeneity, we produced genetically and pathologically accurate mouse models of common forms of human acute myeloid leukemia (AML) and developed methods to mimic standard induction chemotherapy and efficiently monitor therapy response. We see that murine AMLs harboring two common human AML genotypes show remarkably diverse responses to conventional therapy that mirror clinical experience. Specifically, murine leukemias expressing the AML1/ETO fusion oncoprotein, associated with a favorable prognosis in patients, show a dramatic response to induction chemotherapy owing to robust activation of the p53 tumor suppressor network. Conversely, murine leukemias expressing MLL fusion proteins, associated with a dismal prognosis in patients, are drug-resistant due to an attenuated p53 response. Our studies highlight the importance of genetic information in guiding the treatment of human AML, functionally establish the p53 network as a central determinant of chemotherapy response in AML, and demonstrate that genetically engineered mouse models of human cancer can accurately predict therapy response in patients.

18. Turbulence Models for Accurate Aerothermal Prediction in Hypersonic Flows

Zhang, Xiang-Hong; Wu, Yi-Zao; Wang, Jiang-Feng

Accurate description of the aerodynamic and aerothermal environment is crucial to the integrated design and optimization for high performance hypersonic vehicles. In the simulation of aerothermal environment, the effect of viscosity is crucial. The turbulence modeling remains a major source of uncertainty in the computational prediction of aerodynamic forces and heating. In this paper, three turbulent models were studied: the one-equation eddy viscosity transport model of Spalart-Allmaras, the Wilcox k-ω model and the Menter SST model. For the k-ω model and SST model, the compressibility correction, press dilatation and low Reynolds number correction were considered. The influence of these corrections for flow properties were discussed by comparing with the results without corrections. In this paper the emphasis is on the assessment and evaluation of the turbulence models in prediction of heat transfer as applied to a range of hypersonic flows with comparison to experimental data. This will enable establishing factor of safety for the design of thermal protection systems of hypersonic vehicle.

19. Mathematical models of malaria - a review

PubMed Central

2011-01-01

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

20. An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

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

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

ERIC Educational Resources Information Center

Lingefjard, Thomas

2002-01-01

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

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

ERIC Educational Resources Information Center

Swetz, Frank

1991-01-01

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

3. Voters' Fickleness:. a Mathematical Model

Boccara, Nino

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

4. Mathematical Modelling of Turbidity Currents

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

2011-12-01

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

5. Mathematical Models Of Turbulence In Transonic Flow

NASA Technical Reports Server (NTRS)

Rubesin, Morris W.; Viegas, John R.

1989-01-01

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

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. Generating Facial Expressions Using an Anatomically Accurate Biomechanical Model.

PubMed

Wu, Tim; Hung, Alice; Mithraratne, Kumar

2014-11-01

This paper presents a computational framework for modelling the biomechanics of human facial expressions. A detailed high-order (Cubic-Hermite) finite element model of the human head was constructed using anatomical data segmented from magnetic resonance images. The model includes a superficial soft-tissue continuum consisting of skin, the subcutaneous layer and the superficial Musculo-Aponeurotic system. Embedded within this continuum mesh, are 20 pairs of facial muscles which drive facial expressions. These muscles were treated as transversely-isotropic and their anatomical geometries and fibre orientations were accurately depicted. In order to capture the relative composition of muscles and fat, material heterogeneity was also introduced into the model. Complex contact interactions between the lips, eyelids, and between superficial soft tissue continuum and deep rigid skeletal bones were also computed. In addition, this paper investigates the impact of incorporating material heterogeneity and contact interactions, which are often neglected in similar studies. Four facial expressions were simulated using the developed model and the results were compared with surface data obtained from a 3D structured-light scanner. Predicted expressions showed good agreement with the experimental data.

8. A stochastic model of kinetochore-microtubule attachment accurately describes fission yeast chromosome segregation.

PubMed

Gay, Guillaume; Courtheoux, Thibault; Reyes, Céline; Tournier, Sylvie; Gachet, Yannick

2012-03-19

In fission yeast, erroneous attachments of spindle microtubules to kinetochores are frequent in early mitosis. Most are corrected before anaphase onset by a mechanism involving the protein kinase Aurora B, which destabilizes kinetochore microtubules (ktMTs) in the absence of tension between sister chromatids. In this paper, we describe a minimal mathematical model of fission yeast chromosome segregation based on the stochastic attachment and detachment of ktMTs. The model accurately reproduces the timing of correct chromosome biorientation and segregation seen in fission yeast. Prevention of attachment defects requires both appropriate kinetochore orientation and an Aurora B-like activity. The model also reproduces abnormal chromosome segregation behavior (caused by, for example, inhibition of Aurora B). It predicts that, in metaphase, merotelic attachment is prevented by a kinetochore orientation effect and corrected by an Aurora B-like activity, whereas in anaphase, it is corrected through unbalanced forces applied to the kinetochore. These unbalanced forces are sufficient to prevent aneuploidy.

9. 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.

10. A mathematical model of the UH-60 helicopter

NASA Technical Reports Server (NTRS)

Hilbert, K. B.

1984-01-01

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

11. 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…

12. 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…

13. "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…

14. Mathematical modelling of the lower urinary tract.

PubMed

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

2013-03-01

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

15. 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.

16. 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.

17. 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)

18. Inverter Modeling For Accurate Energy Predictions Of Tracking HCPV Installations

Bowman, J.; Jensen, S.; McDonald, Mark

2010-10-01

High efficiency high concentration photovoltaic (HCPV) solar plants of megawatt scale are now operational, and opportunities for expanded adoption are plentiful. However, effective bidding for sites requires reliable prediction of energy production. HCPV module nameplate power is rated for specific test conditions; however, instantaneous HCPV power varies due to site specific irradiance and operating temperature, and is degraded by soiling, protective stowing, shading, and electrical connectivity. These factors interact with the selection of equipment typically supplied by third parties, e.g., wire gauge and inverters. We describe a time sequence model accurately accounting for these effects that predicts annual energy production, with specific reference to the impact of the inverter on energy output and interactions between system-level design decisions and the inverter. We will also show two examples, based on an actual field design, of inverter efficiency calculations and the interaction between string arrangements and inverter selection.

19. 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…

20. Mathematical Programming Model for Fighter Training Squadron Pilot Scheduling

DTIC Science & Technology

2007-03-01

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

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

PubMed

Tomlin, Claire J; Axelrod, Jeffrey D

2007-05-01

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

2. Accurate SHAPE-directed RNA secondary structure modeling, including pseudoknots

PubMed Central

Hajdin, Christine E.; Bellaousov, Stanislav; Huggins, Wayne; Leonard, Christopher W.; Mathews, David H.; Weeks, Kevin M.

2013-01-01

A pseudoknot forms in an RNA when nucleotides in a loop pair with a region outside the helices that close the loop. Pseudoknots occur relatively rarely in RNA but are highly overrepresented in functionally critical motifs in large catalytic RNAs, in riboswitches, and in regulatory elements of viruses. Pseudoknots are usually excluded from RNA structure prediction algorithms. When included, these pairings are difficult to model accurately, especially in large RNAs, because allowing this structure dramatically increases the number of possible incorrect folds and because it is difficult to search the fold space for an optimal structure. We have developed a concise secondary structure modeling approach that combines SHAPE (selective 2′-hydroxyl acylation analyzed by primer extension) experimental chemical probing information and a simple, but robust, energy model for the entropic cost of single pseudoknot formation. Structures are predicted with iterative refinement, using a dynamic programming algorithm. This melded experimental and thermodynamic energy function predicted the secondary structures and the pseudoknots for a set of 21 challenging RNAs of known structure ranging in size from 34 to 530 nt. On average, 93% of known base pairs were predicted, and all pseudoknots in well-folded RNAs were identified. PMID:23503844

3. Towards Accurate Molecular Modeling of Plastic Bonded Explosives

Chantawansri, T. L.; Andzelm, J.; Taylor, D.; Byrd, E.; Rice, B.

2010-03-01

There is substantial interest in identifying the controlling factors that influence the susceptibility of polymer bonded explosives (PBXs) to accidental initiation. Numerous Molecular Dynamics (MD) simulations of PBXs using the COMPASS force field have been reported in recent years, where the validity of the force field in modeling the solid EM fill has been judged solely on its ability to reproduce lattice parameters, which is an insufficient metric. Performance of the COMPASS force field in modeling EMs and the polymeric binder has been assessed by calculating structural, thermal, and mechanical properties, where only fair agreement with experimental data is obtained. We performed MD simulations using the COMPASS force field for the polymer binder hydroxyl-terminated polybutadiene and five EMs: cyclotrimethylenetrinitramine, 1,3,5,7-tetranitro-1,3,5,7-tetra-azacyclo-octane, 2,4,6,8,10,12-hexantirohexaazazisowurzitane, 2,4,6-trinitro-1,3,5-benzenetriamine, and pentaerythritol tetranitate. Predicted EM crystallographic and molecular structural parameters, as well as calculated properties for the binder will be compared with experimental results for different simulation conditions. We also present novel simulation protocols, which improve agreement between experimental and computation results thus leading to the accurate modeling of PBXs.

4. Mathematics.

ERIC Educational Resources Information Center

Costellano, Janet; Scaffa, Matthew

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

5. Mathematical modeling of deformation during hot rolling

SciTech Connect

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

1994-12-31

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

6. Mathematical models of human african trypanosomiasis epidemiology.

PubMed

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

2015-03-01

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

7. 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.

8. Aircraft engine mathematical model - linear system approach

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.

9. Evaluating Longitudinal Mathematics Achievement Growth: Modeling and Measurement Considerations for Assessing Academic Progress

ERIC Educational Resources Information Center

Shanley, Lina

2016-01-01

Accurately measuring and modeling academic achievement growth is critical to support educational policy and practice. Using a nationally representative longitudinal data set, this study compared various models of mathematics achievement growth on the basis of both practical utility and optimal statistical fit and explored relationships within and…

10. 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…

11. 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…

12. Declarative representation of uncertainty in mathematical models.

PubMed

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

2012-01-01

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

13. Mathematical Modeling of an Oscillating Droplet

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

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

PubMed

Loveday, S M; Winger, R J

2007-07-25

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

15. Mathematical modelling of submarine landslide motion

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.

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 modeling of the coating process.

PubMed

Toschkoff, Gregor; Khinast, Johannes G

2013-12-05

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

18. Predictive mathematical models of cancer signalling pathways.

PubMed

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

2012-02-01

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

19. Mathematical model of laser PUVA psoriasis treatment

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.

20. Mathematical modelling of risk reduction in reinsurance

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

2017-01-01

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

1. A Weibull statistics-based lignocellulose saccharification model and a built-in parameter accurately predict lignocellulose hydrolysis performance.

PubMed

Wang, Mingyu; Han, Lijuan; Liu, Shasha; Zhao, Xuebing; Yang, Jinghua; Loh, Soh Kheang; Sun, Xiaomin; Zhang, Chenxi; Fang, Xu

2015-09-01

Renewable energy from lignocellulosic biomass has been deemed an alternative to depleting fossil fuels. In order to improve this technology, we aim to develop robust mathematical models for the enzymatic lignocellulose degradation process. By analyzing 96 groups of previously published and newly obtained lignocellulose saccharification results and fitting them to Weibull distribution, we discovered Weibull statistics can accurately predict lignocellulose saccharification data, regardless of the type of substrates, enzymes and saccharification conditions. A mathematical model for enzymatic lignocellulose degradation was subsequently constructed based on Weibull statistics. Further analysis of the mathematical structure of the model and experimental saccharification data showed the significance of the two parameters in this model. In particular, the λ value, defined the characteristic time, represents the overall performance of the saccharification system. This suggestion was further supported by statistical analysis of experimental saccharification data and analysis of the glucose production levels when λ and n values change. In conclusion, the constructed Weibull statistics-based model can accurately predict lignocellulose hydrolysis behavior and we can use the λ parameter to assess the overall performance of enzymatic lignocellulose degradation. Advantages and potential applications of the model and the λ value in saccharification performance assessment were discussed.

2. A mathematical model of aortic aneurysm formation

PubMed Central

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

2017-01-01

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

3. Mathematical modeling of human brain physiological data

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

2013-12-01

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

4. Mathematical modeling of infectious disease dynamics

PubMed Central

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

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

5. A mathematical model of aortic aneurysm formation.

PubMed

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

2017-01-01

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

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

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

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

7. A mathematical model of elastic fin micromotors

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

2000-08-01

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

8. A mathematical model of leptin resistance.

PubMed

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

2015-09-01

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

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

PubMed

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

2007-06-01

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

10. 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.…

11. Improved mathematical models of flat-plate solar collectors

SciTech Connect

Siegler, M.

1986-01-01

This thesis examines various mathematical models of flat-plate solar collectors with the intent of analyzing their strengths and weaknesses and investigating various possible improvements. The purpose is to seek the simplest models that can provide sufficient accuracy for efficient control and design of the collector and for reliable estimation of system parameters. The first part of the thesis investigates the effects of the diffusivity of the collector fluid under steady-state operating conditions. It is shown that under zero flow conditions this diffusivity must be included in the model to accurately describe the rapid changes in the temperatures between adjacent components of the system. The second part of the thesis investigates the relationship between two well-known models for the temperature within the flat-plate solar collector. The simpler of the two models determines the temperature of the collector fluid alone and assumes the collector plate is at the same temperature as the fluid. The other model was separate state equations for the fluid and the collector. Finally, through a frequency analysis of these two different models for the flat-plate collector, it is shown how the thermal effects of the two-temperature model can be imitated by the one-temperature model by adding an artificial diffusion term into the one-temperature model.

12. Missing the Promise of Mathematical Modeling

ERIC Educational Resources Information Center

Meyer, Dan

2015-01-01

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

13. Teaching Mathematical Modelling for Earth Sciences via Case Studies

Yang, Xin-She

2010-05-01

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

14. Using a Functional Model to Develop a Mathematical Formula

ERIC Educational Resources Information Center

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

2008-01-01

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

15. Mathematical modeling of acid-base physiology

PubMed Central

Occhipinti, Rossana; Boron, Walter F.

2015-01-01

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

16. Optimal Cluster Mill Pass Scheduling With an Accurate and Rapid New Strip Crown Model

Malik, Arif S.; Grandhi, Ramana V.; Zipf, Mark E.

2007-05-01

Besides the requirement to roll coiled sheet at high levels of productivity, the optimal pass scheduling of cluster-type reversing cold mills presents the added challenge of assigning mill parameters that facilitate the best possible strip flatness. The pressures of intense global competition, and the requirements for increasingly thinner, higher quality specialty sheet products that are more difficult to roll, continue to force metal producers to commission innovative flatness-control technologies. This means that during the on-line computerized set-up of rolling mills, the mathematical model should not only determine the minimum total number of passes and maximum rolling speed, it should simultaneously optimize the pass-schedule so that desired flatness is assured, either by manual or automated means. In many cases today, however, on-line prediction of strip crown and corresponding flatness for the complex cluster-type rolling mills is typically addressed either by trial and error, by approximate deflection models for equivalent vertical roll-stacks, or by non-physical pattern recognition style models. The abundance of the aforementioned methods is largely due to the complexity of cluster-type mill configurations and the lack of deflection models with sufficient accuracy and speed for on-line use. Without adequate assignment of the pass-schedule set-up parameters, it may be difficult or impossible to achieve the required strip flatness. In this paper, we demonstrate optimization of cluster mill pass-schedules using a new accurate and rapid strip crown model. This pass-schedule optimization includes computations of the predicted strip thickness profile to validate mathematical constraints. In contrast to many of the existing methods for on-line prediction of strip crown and flatness on cluster mills, the demonstrated method requires minimal prior tuning and no extensive training with collected mill data. To rapidly and accurately solve the multi-contact problem

17. Mathematical Model for Addiction: Application to Multiple Risk Factor Intervention Trial Data for Smoking.

ERIC Educational Resources Information Center

Fan, David P.; Elketroussi, Mehdi

1989-01-01

Describes habituation and addiction, both psychological and physiological, using simple equations of mathematical model of ideodynamics, optimized to smoking data from Multiple Risk Factor Intervention Trial (MRFIT) program. With only four constant parameters, it was possible to calculate accurate time trends for recidivism to smoking among…

18. Incorporating neurophysiological concepts in mathematical thermoregulation models

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.

19. Mathematical model of tumor-immune surveillance.

PubMed

2016-09-07

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

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

PubMed

Morgenroth, E; Arvin, E; Vanrolleghem, P

2002-01-01

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

1. Fast and accurate analytical model to solve inverse problem in SHM using Lamb wave propagation

Poddar, Banibrata; Giurgiutiu, Victor

2016-04-01

Lamb wave propagation is at the center of attention of researchers for structural health monitoring of thin walled structures. This is due to the fact that Lamb wave modes are natural modes of wave propagation in these structures with long travel distances and without much attenuation. This brings the prospect of monitoring large structure with few sensors/actuators. However the problem of damage detection and identification is an "inverse problem" where we do not have the luxury to know the exact mathematical model of the system. On top of that the problem is more challenging due to the confounding factors of statistical variation of the material and geometric properties. Typically this problem may also be ill posed. Due to all these complexities the direct solution of the problem of damage detection and identification in SHM is impossible. Therefore an indirect method using the solution of the "forward problem" is popular for solving the "inverse problem". This requires a fast forward problem solver. Due to the complexities involved with the forward problem of scattering of Lamb waves from damages researchers rely primarily on numerical techniques such as FEM, BEM, etc. But these methods are slow and practically impossible to be used in structural health monitoring. We have developed a fast and accurate analytical forward problem solver for this purpose. This solver, CMEP (complex modes expansion and vector projection), can simulate scattering of Lamb waves from all types of damages in thin walled structures fast and accurately to assist the inverse problem solver.

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

ERIC Educational Resources Information Center

Akgün, Levent

2015-01-01

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

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

ERIC Educational Resources Information Center

Jacobini, Otavio Roberto; Wodewotzki, Maria Lucia L.

2006-01-01

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

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

ERIC Educational Resources Information Center

Rash, Agnes M.; Zurbach, E. Peter

2004-01-01

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

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

ERIC Educational Resources Information Center

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

2014-01-01

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

6. Mathematical model for contemplative amoeboid locomotion

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

2011-02-01

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

7. Mathematical 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

2016-08-08

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.

8. Mathematical foundations of the dendritic growth models.

PubMed

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

2007-11-01

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

9. Genetic demographic networks: Mathematical model and applications.

PubMed

Kimmel, Marek; Wojdyła, Tomasz

2016-10-01

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

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. Mathematical Modeling of the Origins of Life

NASA Technical Reports Server (NTRS)

Pohorille, Andrew

2006-01-01

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

12. Some Reflections on the Teaching of Mathematical Modeling

ERIC Educational Resources Information Center

Warwick, Jon

2007-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

14. The Aircraft Availability Model: Conceptual Framework and Mathematics

DTIC Science & Technology

1983-06-01

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

15. Noise in restaurants: levels and mathematical model.

PubMed

To, Wai Ming; Chung, Andy

2014-01-01

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

16. Mathematical modeling plasma transport in tokamaks

SciTech Connect

Quiang, Ji

1997-01-01

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

17. Mathematical Model for the Mineralization of Bone

NASA Technical Reports Server (NTRS)

Martin, Bruce

1994-01-01

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

18. Mathematical Model for the Mineralization of Bone

NASA Technical Reports Server (NTRS)

Martin, Bruce

1994-01-01

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

19. Cocaine addiction and personality: a mathematical model.

PubMed

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

2010-05-01

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

20. Mathematical modelling of animate and intentional motion.

PubMed Central

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

2003-01-01

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

1. Searching for new mathematical growth model approaches for Listeria monocytogenes.

PubMed

Valero, A; Hervás, C; García-Gimeno, R M; Zurera, G

2007-01-01

Different secondary modeling approaches for the estimation of Listeria monocytogenes growth rate as a function of temperature (4 to 30 degrees C), citric acid (0% to 0.4% w/v), and ascorbic acid (0% to 0.4% w/v) are presented. Response surface (RS) and square-root (SR) models are proposed together with different artificial neural networks (ANN) based on product functions units (PU), sigmoidal functions units (SU), and a novel approach based on the use of hybrid functions units (PSU), which results from a combination of PU and SU. In this study, a significantly better goodness-of-fit was obtained in the case of the ANN models presented, reflected by the lower SEP values obtained (< 24.23 for both training and generalization datasets). Among these models, the SU model provided the best generalization capacity, displaying lower RMSE and SEP values, with fewer parameters compared to the PU and PSU models. The bias factor (B(f)) and accuracy factor (A(f)) of the mathematical validation dataset were above 1 in all cases, providing fail-safe predictions. The balance between generalization properties and the ease of use is the main consideration when applying secondary modeling approaches to achieve accurate predictions about the behavior of microorganisms.

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

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

3. Turbulent motion of mass flows. Mathematical modeling

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

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

ERIC Educational Resources Information Center

Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

2016-01-01

Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

5. On Mathematical Modeling Of Quantum Systems

SciTech Connect

Achuthan, P.; Narayanankutty, Karuppath

2009-07-02

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

6. On Mathematical Modeling Of Quantum Systems

Achuthan, P.; Narayanankutty, Karuppath

2009-07-01

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

7. Mathematical Models of Cardiac Pacemaking Function

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

2013-10-01

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

8. Mathematical Modeling of Electrochemical Flow Capacitors

SciTech Connect

Hoyt, NC; Wainright, JS; Savinell, RF

2015-01-13

9. Modelling Mathematical Reasoning in Physics Education

ERIC Educational Resources Information Center

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

2012-01-01

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

10. Model Learner Outcomes for Mathematics Education.

ERIC Educational Resources Information Center

Halvorson, Judith K.; Stenglein, Sharon M.

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

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

ERIC Educational Resources Information Center

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

2010-01-01

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

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

NASA Technical Reports Server (NTRS)

Solomon, A. D.

1980-01-01

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

13. 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…

14. iSTEM: Promoting Fifth Graders' Mathematical Modeling

ERIC Educational Resources Information Center

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. 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…

16. 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…

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

ERIC Educational Resources Information Center

Çelik, H. Coskun

2017-01-01

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

18. Clarifying types of uncertainty: when are models accurate, and uncertainties small?

PubMed

Cox, Louis Anthony Tony

2011-10-01

Professor Aven has recently noted the importance of clarifying the meaning of terms such as "scientific uncertainty" for use in risk management and policy decisions, such as when to trigger application of the precautionary principle. This comment examines some fundamental conceptual challenges for efforts to define "accurate" models and "small" input uncertainties by showing that increasing uncertainty in model inputs may reduce uncertainty in model outputs; that even correct models with "small" input uncertainties need not yield accurate or useful predictions for quantities of interest in risk management (such as the duration of an epidemic); and that accurate predictive models need not be accurate causal models.

19. Accurate Modeling of Scaffold Hopping Transformations in Drug Discovery.

PubMed

Wang, Lingle; Deng, Yuqing; Wu, Yujie; Kim, Byungchan; LeBard, David N; Wandschneider, Dan; Beachy, Mike; Friesner, Richard A; Abel, Robert

2017-01-10

The accurate prediction of protein-ligand binding free energies remains a significant challenge of central importance in computational biophysics and structure-based drug design. Multiple recent advances including the development of greatly improved protein and ligand molecular mechanics force fields, more efficient enhanced sampling methods, and low-cost powerful GPU computing clusters have enabled accurate and reliable predictions of relative protein-ligand binding free energies through the free energy perturbation (FEP) methods. However, the existing FEP methods can only be used to calculate the relative binding free energies for R-group modifications or single-atom modifications and cannot be used to efficiently evaluate scaffold hopping modifications to a lead molecule. Scaffold hopping or core hopping, a very common design strategy in drug discovery projects, is critical not only in the early stages of a discovery campaign where novel active matter must be identified but also in lead optimization where the resolution of a variety of ADME/Tox problems may require identification of a novel core structure. In this paper, we introduce a method that enables theoretically rigorous, yet computationally tractable, relative protein-ligand binding free energy calculations to be pursued for scaffold hopping modifications. We apply the method to six pharmaceutically interesting cases where diverse types of scaffold hopping modifications were required to identify the drug molecules ultimately sent into the clinic. For these six diverse cases, the predicted binding affinities were in close agreement with experiment, demonstrating the wide applicability and the significant impact Core Hopping FEP may provide in drug discovery projects.

20. Mathematical modeling of Chikungunya fever control

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.

1. Mathematical model I. Electron and quantum mechanics

2011-03-01

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

2. A Mathematical Model of Forgetting and Amnesia

PubMed Central

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

2013-01-01

We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in strength (2) while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i) the temporal gradient of retrograde amnesia (Ribot’s Law), (ii) forgetting curves with and without anterograde amnesia, and (iii) learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff’s Disease, Alzheimer’s Dementia, Huntington’s Disease, and other disorders. PMID:23450438

3. Functional mathematical model of dual pathway AV nodal conduction.

PubMed

Climent, A M; Guillem, M S; Zhang, Y; Millet, J; Mazgalev, T N

2011-04-01

Dual atrioventricular (AV) nodal pathway physiology is described as two different wave fronts that propagate from the atria to the His bundle: one with a longer effective refractory period [fast pathway (FP)] and a second with a shorter effective refractory period [slow pathway (SP)]. By using His electrogram alternance, we have developed a mathematical model of AV conduction that incorporates dual AV nodal pathway physiology. Experiments were performed on five rabbit atrial-AV nodal preparations to develop and test the presented model. His electrogram alternances from the inferior margin of the His bundle were used to identify fast and slow wave front propagations. The ability to predict AV conduction time and the interaction between FP and SP wave fronts have been analyzed during regular and irregular atrial rhythms (e.g., atrial fibrillation). In addition, the role of dual AV nodal pathway wave fronts in the generation of Wenckebach periodicities has been illustrated. Finally, AV node ablative modifications have been evaluated. The model accurately reproduced interactions between FP and SP during regular and irregular atrial pacing protocols. In all experiments, specificity and sensitivity higher than 85% were obtained in the prediction of the pathway responsible for conduction. It has been shown that, during atrial fibrillation, the SP ablation significantly increased the mean HH interval (204 ± 39 vs. 274 ± 50 ms, P < 0.05), whereas FP ablation did not produce significant slowing of ventricular rate. The presented mathematical model can help in understanding some of the intriguing AV node mechanisms and should be considered as a step forward in the studies of AV nodal conduction.

4. A parallel high-order accurate finite element nonlinear Stokes ice sheet model and benchmark experiments: A PARALLEL FEM STOKES ICE SHEET MODEL

SciTech Connect

Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd

2012-01-04

The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.

5. Etch modeling for accurate full-chip process proximity correction

Beale, Daniel F.; Shiely, James P.

2005-05-01

The challenges of the 65 nm node and beyond require new formulations of the compact convolution models used in OPC. In addition to simulating more optical and resist effects, these models must accommodate pattern distortions due to etch which can no longer be treated as small perturbations on photo-lithographic effects. (Methods for combining optical and process modules while optimizing the speed/accuracy tradeoff were described in "Advanced Model Formulations for Optical and Process Proximity Correction", D. Beale et al, SPIE 2004.) In this paper, we evaluate new physics-based etch model formulations that differ from the convolution-based process models used previously. The new models are expressed within the compact modeling framework described by J. Stirniman et al. in SPIE, vol. 3051, p469, 1997, and thus can be used for high-speed process simulation during full-chip OPC.

6. A General Pairwise Interaction Model Provides an Accurate Description of In Vivo Transcription Factor Binding Sites

PubMed Central

Santolini, Marc; Mora, Thierry; Hakim, Vincent

2014-01-01

The identification of transcription factor binding sites (TFBSs) on genomic DNA is of crucial importance for understanding and predicting regulatory elements in gene networks. TFBS motifs are commonly described by Position Weight Matrices (PWMs), in which each DNA base pair contributes independently to the transcription factor (TF) binding. However, this description ignores correlations between nucleotides at different positions, and is generally inaccurate: analysing fly and mouse in vivo ChIPseq data, we show that in most cases the PWM model fails to reproduce the observed statistics of TFBSs. To overcome this issue, we introduce the pairwise interaction model (PIM), a generalization of the PWM model. The model is based on the principle of maximum entropy and explicitly describes pairwise correlations between nucleotides at different positions, while being otherwise as unconstrained as possible. It is mathematically equivalent to considering a TF-DNA binding energy that depends additively on each nucleotide identity at all positions in the TFBS, like the PWM model, but also additively on pairs of nucleotides. We find that the PIM significantly improves over the PWM model, and even provides an optimal description of TFBS statistics within statistical noise. The PIM generalizes previous approaches to interdependent positions: it accounts for co-variation of two or more base pairs, and predicts secondary motifs, while outperforming multiple-motif models consisting of mixtures of PWMs. We analyse the structure of pairwise interactions between nucleotides, and find that they are sparse and dominantly located between consecutive base pairs in the flanking region of TFBS. Nonetheless, interactions between pairs of non-consecutive nucleotides are found to play a significant role in the obtained accurate description of TFBS statistics. The PIM is computationally tractable, and provides a general framework that should be useful for describing and predicting TFBSs beyond

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

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

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

8. Mathematical Modeling Tools to Study Preharvest Food Safety.

PubMed

Lanzas, Cristina; Chen, Shi

2016-08-01

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

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

PubMed

Kaznessis, Yiannis N

2011-01-01

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

10. 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

11. A simple, closed-form, mathematical model for gas exchange in microchannel artificial lungs.

PubMed

Potkay, Joseph A

2013-06-01

Microfabrication techniques are attractive for constructing artificial lungs due to the ability to create features similar in size to those in the natural lung. However, a simple and intuitive mathematical model capable of accurately predicting the gas exchange performance of microchannel artificial lungs does not currently exist. Such a model is critical to understanding and optimizing these devices. Here, we describe a simple, closed-form mathematical model for gas exchange in microchannel artificial lungs and qualify it through application to experimental data from several research groups. We utilize lumped parameters and several assumptions to obtain a closed-form set of equations that describe gas exchange. This work is intended to augment computational models by providing a more intuitive, albeit potentially less accurate, understanding of the operation and trade-offs inherent in microchannel artificial lung devices.

12. The roughness surface expressed by the mathematical model

Macurova, Anna

2010-07-01

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

13. Towards an Accurate Performance Modeling of Parallel SparseFactorization

SciTech Connect

Grigori, Laura; Li, Xiaoye S.

2006-05-26

We present a performance model to analyze a parallel sparseLU factorization algorithm on modern cached-based, high-end parallelarchitectures. Our model characterizes the algorithmic behavior bytakingaccount the underlying processor speed, memory system performance, aswell as the interconnect speed. The model is validated using theSuperLU_DIST linear system solver, the sparse matrices from realapplications, and an IBM POWER3 parallel machine. Our modelingmethodology can be easily adapted to study performance of other types ofsparse factorizations, such as Cholesky or QR.

14. A Mathematical Model for Suppression Subtractive Hybridization

PubMed Central

Gadgil, Chetan; Rink, Anette; Beattie, Craig

2002-01-01

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

15. Mathematical modelling for nanotube bundle oscillators

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

2009-07-01

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

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

ERIC Educational Resources Information Center

Bunge, Annette L.; Miller, Ronald L.

1997-01-01

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

17. Mathematical modeling of MILD combustion of pulverized coal

SciTech Connect

Schaffel, N.; Mancini, M.; Weber, R.; Szlek, A.

2009-09-15

MILD (flameless) combustion is a new rapidly developing technology. The IFRF trials have demonstrated high potential of this technology also for N-containing fuels. In this work the IFRF experiments are analyzed using the CFD-based mathematical model. Both the Chemical Percolation Devolatilization (CPD) model and the char combustion intrinsic reactivity model have been adapted to Guasare coal combusted. The flow-field as well as the temperature and the oxygen fields have been accurately predicted by the CFD-based model. The predicted temperature and gas composition fields have been uniform demonstrating that slow combustion occurs in the entire furnace volume. The CFD-based predictions have highlighted the NO{sub x} reduction potential of MILD combustion through the following mechanism. Before the coal devolatilization proceeds, the coal jet entrains a substantial amount of flue gas so that its oxygen content is typically not higher than 3-5%. The volatiles are given off in a highly sub-stoichiometric environment and their N-containing species are preferentially converted to molecular nitrogen rather than to NO. Furthermore, there exists a strong NO-reburning mechanism within the fuel jet and in the air jet downstream of the position where these two jets merge. In other words, less NO is formed from combustion of volatiles and stronger NO-reburning mechanisms exist in the MILD combustion if compared to conventional coal combustion technology. (author)

18. How Accurate Is A Hydraulic Model? | Science Inventory | US ...

EPA Pesticide Factsheets

Symposium paper Network hydraulic models are widely used, but their overall accuracy is often unknown. Models are developed to give utilities better insight into system hydraulic behavior, and increasingly the ability to predict the fate and transport of chemicals. Without an accessible and consistent means of validating a given model against the system it is meant to represent, the value of those supposed benefits should be questioned. Supervisory Control And Data Acquisition (SCADA) databases, though ubiquitous, are underused data sources for this type of task. Integrating a network model with a measurement database would offer professionals the ability to assess the model’s assumptions in an automated fashion by leveraging enormous amounts of data.

19. Accurate 3D Modeling of Breast Deformation for Temporal Mammogram Registration

DTIC Science & Technology

2008-09-01

SUPPLEMENTARY NOTES 14. ABSTRACT In this research project, we have developed mathematical model of breast deformation to simulate breast compression during...proposed to simulate and analyze breast deformation that can significantly improve the accuracy of matching in temporal mammograms and thus, the...performance of diagnosis and treatment. In this research project, we have developed a mathematical model of breast deformation to simulate breast

20. Modeling for accurate dimensional scanning electron microscope metrology: then and now.

PubMed

Postek, Michael T; Vladár, András E

2011-01-01

A review of the evolution of modeling for accurate dimensional scanning electron microscopy is presented with an emphasis on developments in the Monte Carlo technique for modeling the generation of the electrons used for imaging and measurement. The progress of modeling for accurate metrology is discussed through a schematic technology timeline. In addition, a discussion of a future vision for accurate SEM dimensional metrology and the requirements to achieve it are presented.

1. ACCURATE LOW-MASS STELLAR MODELS OF KOI-126

SciTech Connect

Feiden, Gregory A.; Chaboyer, Brian; Dotter, Aaron

2011-10-10

The recent discovery of an eclipsing hierarchical triple system with two low-mass stars in a close orbit (KOI-126) by Carter et al. appeared to reinforce the evidence that theoretical stellar evolution models are not able to reproduce the observational mass-radius relation for low-mass stars. We present a set of stellar models for the three stars in the KOI-126 system that show excellent agreement with the observed radii. This agreement appears to be due to the equation of state implemented by our code. A significant dispersion in the observed mass-radius relation for fully convective stars is demonstrated; indicative of the influence of physics currently not incorporated in standard stellar evolution models. We also predict apsidal motion constants for the two M dwarf companions. These values should be observationally determined to within 1% by the end of the Kepler mission.

2. Accurate two-equation modelling of falling film flows

Ruyer-Quil, Christian

2015-11-01

The low-dimensional modeling of the wave dynamics of a falling liquid film on an inclined plane is revisited. The advantages and shortcomings of existing modelling approaches: weighted residual method, center-manifold analysis, consistent Saint-Venant approach are discussed and contrasted. A novel formulation of a two-equation consistent model is proposed. The proposed formulation cures the principal limitations of previous approaches: (i) apart from surface tension terms, it admits a conservative form which enables to make use of efficient numerical schemes, (ii) it recovers with less than 1 percent of error the asymptotic speed of solitary waves in the inertial regime found by DNS, (iii) it adequately captures the velocity field under the waves and in particular the wall drag. Research supported by Insitut Universitaire de France.

3. Building accurate geometric models from abundant range imaging information

SciTech Connect

Diegert, C.; Sackos, J.; Nellums, R.

1997-05-01

The authors define two simple metrics for accuracy of models built from range imaging information. They apply the metric to a model built from a recent range image taken at the Laser Radar Development and Evaluation Facility (LDERF), Eglin AFB, using a Scannerless Range Imager (SRI) from Sandia National Laboratories. They also present graphical displays of the residual information produced as a byproduct of this measurement, and discuss mechanisms that these data suggest for further improvement in the performance of this already impressive SRI.

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

PubMed

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

2015-11-01

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

5. Magnetic field models of nine CP stars from "accurate" measurements

Glagolevskij, Yu. V.

2013-01-01

The dipole models of magnetic fields in nine CP stars are constructed based on the measurements of metal lines taken from the literature, and performed by the LSD method with an accuracy of 10-80 G. The model parameters are compared with the parameters obtained for the same stars from the hydrogen line measurements. For six out of nine stars the same type of structure was obtained. Some parameters, such as the field strength at the poles B p and the average surface magnetic field B s differ considerably in some stars due to differences in the amplitudes of phase dependences B e (Φ) and B s (Φ), obtained by different authors. It is noted that a significant increase in the measurement accuracy has little effect on the modelling of the large-scale structures of the field. By contrast, it is more important to construct the shape of the phase dependence based on a fairly large number of field measurements, evenly distributed by the rotation period phases. It is concluded that the Zeeman component measurement methods have a strong effect on the shape of the phase dependence, and that the measurements of the magnetic field based on the lines of hydrogen are more preferable for modelling the large-scale structures of the field.

6. Inference Method for Developing Mathematical Models of Cell Signaling Pathways Using Proteomic Datasets.

PubMed

Tian, Tianhai; Song, Jiangning

2017-01-01

The progress in proteomics technologies has led to a rapid accumulation of large-scale proteomic datasets in recent years, which provides an unprecedented opportunity and valuable resources to understand how living organisms perform necessary functions at systems levels. This work presents a computational method for designing mathematical models based on proteomic datasets. Using the mitogen-activated protein (MAP) kinase pathway as the test system, we first develop a mathematical model including the cytosolic and nuclear subsystems. A key step of modeling is to apply a genetic algorithm to infer unknown model parameters. Then the robustness property of mathematical models is used as a criterion to select appropriate rate constants from the estimated candidates. Moreover, quantitative information such as the absolute protein concentrations is used to further refine the mathematical model. The successful application of this inference method to the MAP kinase pathway suggests that it is a useful and powerful approach for developing accurate mathematical models to gain important insights into the regulatory mechanisms of cell signaling pathways.

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

PubMed

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

2010-01-01

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

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

ERIC Educational Resources Information Center

Schoenfeld, Alan H.

2013-01-01

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

9. 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…

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

ERIC Educational Resources Information Center

Berlin, Donna F.; White, Arthur L.

1994-01-01

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

11. 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…

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. 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…

14. 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)

15. 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…

16. Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Martin, Michael A.; Nguyen, Huy H.; Greene, William D.; Seymout, David C.

2003-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

17. Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

2005-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

18. Accurate first principles model potentials for intermolecular interactions.

PubMed

Gordon, Mark S; Smith, Quentin A; Xu, Peng; Slipchenko, Lyudmila V

2013-01-01

The general effective fragment potential (EFP) method provides model potentials for any molecule that is derived from first principles, with no empirically fitted parameters. The EFP method has been interfaced with most currently used ab initio single-reference and multireference quantum mechanics (QM) methods, ranging from Hartree-Fock and coupled cluster theory to multireference perturbation theory. The most recent innovations in the EFP model have been to make the computationally expensive charge transfer term much more efficient and to interface the general EFP dispersion and exchange repulsion interactions with QM methods. Following a summary of the method and its implementation in generally available computer programs, these most recent new developments are discussed.

19. Light driven microactuators: Design, fabrication, and mathematical modeling

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.

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 in wound healing, bone regeneration and tissue engineering.

PubMed

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

2010-12-01

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

2. Accurate numerical solutions for elastic-plastic models. [LMFBR

SciTech Connect

Schreyer, H. L.; Kulak, R. F.; Kramer, J. M.

1980-03-01

The accuracy of two integration algorithms is studied for the common engineering condition of a von Mises, isotropic hardening model under plane stress. Errors in stress predictions for given total strain increments are expressed with contour plots of two parameters: an angle in the pi plane and the difference between the exact and computed yield-surface radii. The two methods are the tangent-predictor/radial-return approach and the elastic-predictor/radial-corrector algorithm originally developed by Mendelson. The accuracy of a combined tangent-predictor/radial-corrector algorithm is also investigated.

3. Mathematical Modeling and Simulation of Seated Stability

PubMed Central

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

2009-01-01

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

4. Accurate Force Field Development for Modeling Conjugated Polymers.

PubMed

DuBay, Kateri H; Hall, Michelle Lynn; Hughes, Thomas F; Wu, Chuanjie; Reichman, David R; Friesner, Richard A

2012-11-13

The modeling of the conformational properties of conjugated polymers entails a unique challenge for classical force fields. Conjugation imposes strong constraints upon bond rotation. Planar configurations are favored, but the concomitantly shortened bond lengths result in moieties being brought into closer proximity than usual. The ensuing steric repulsions are particularly severe in the presence of side chains, straining angles, and stretching bonds to a degree infrequently found in nonconjugated systems. We herein demonstrate the resulting inaccuracies by comparing the LMP2-calculated inter-ring torsion potentials for a series of substituted stilbenes and bithiophenes to those calculated using standard classical force fields. We then implement adjustments to the OPLS-2005 force field in order to improve its ability to model such systems. Finally, we show the impact of these changes on the dihedral angle distributions, persistence lengths, and conjugation length distributions observed during molecular dynamics simulations of poly[2-methoxy-5-(2'-ethylhexyloxy)-p-phenylene vinylene] (MEH-PPV) and poly 3-hexylthiophene (P3HT), two of the most widely used conjugated polymers.

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

PubMed

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

1981-01-01

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

6. An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models

Mead, A. J.; Peacock, J. A.; Heymans, C.; Joudaki, S.; Heavens, A. F.

2015-12-01

We present an optimized variant of the halo model, designed to produce accurate matter power spectra well into the non-linear regime for a wide range of cosmological models. To do this, we introduce physically motivated free parameters into the halo-model formalism and fit these to data from high-resolution N-body simulations. For a variety of Λ cold dark matter (ΛCDM) and wCDM models, the halo-model power is accurate to ≃ 5 per cent for k ≤ 10h Mpc-1 and z ≤ 2. An advantage of our new halo model is that it can be adapted to account for the effects of baryonic feedback on the power spectrum. We demonstrate this by fitting the halo model to power spectra from the OWLS (OverWhelmingly Large Simulations) hydrodynamical simulation suite via parameters that govern halo internal structure. We are able to fit all feedback models investigated at the 5 per cent level using only two free parameters, and we place limits on the range of these halo parameters for feedback models investigated by the OWLS simulations. Accurate predictions to high k are vital for weak-lensing surveys, and these halo parameters could be considered nuisance parameters to marginalize over in future analyses to mitigate uncertainty regarding the details of feedback. Finally, we investigate how lensing observables predicted by our model compare to those from simulations and from HALOFIT for a range of k-cuts and feedback models and quantify the angular scales at which these effects become important. Code to calculate power spectra from the model presented in this paper can be found at https://github.com/alexander-mead/hmcode.

7. Mathematical modeling of the circulation in the liver lobule.

PubMed

Bonfiglio, Andrea; Leungchavaphongse, Kritsada; Repetto, Rodolfo; Siggers, Jennifer H

2010-11-01

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which

8. a Discrete Mathematical Model to Simulate Malware Spreading

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. Mathematics of tsunami: modelling and identification

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

10. PREFACE: Physics-Based Mathematical Models for Nanotechnology

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

2008-03-01

in the cross-disciplinary research area: low-dimensional semiconductor nanostructures. Since the main properties of two-dimensional heterostructures (such as quantum wells) are now quite well understood, there has been a consistently growing interest in the mathematical physics community to further dimensionality reduction of semiconductor structures. Experimental achievements in realizing one-dimensional and quasi-zero-dimensional heterostructures have opened new opportunities for theory and applications of such low-dimensional semiconductor nanostructures. One of the most important implications of this process has been a critical re-examining of assumptions under which traditional quantum mechanical models have been derived in this field. Indeed, the formation of LDSNs, in particular quantum dots, is a competition between the surface energy in the structure and strain energy. However, current models for bandstructure calculations use quite a simplified analysis of strain relaxation effects, although such effects are in the heart of nanostructure formation. By now, it has been understood that traditional models in this field may not be adequate for modeling realistic objects based on LDSNs due to neglecting many effects that may profoundly influence optoelectronic properties of the nanostructures. Among such effects are electromechanical effects, including strain relaxation, piezoelectric effect, spontaneous polarization, and higher order nonlinear effects. Up to date, major efforts have been concentrated on the analysis of idealized, isolated quantum dots, while a typical self-assembled semiconductor quantum dot nanostructure is an array (or a molecule) of many individual quantum dots sitting on the same `substrate' known as the wetting layer. Each such dot contains several hundred thousand atoms. In order to account for quantum effects accurately in a situation like that, attempts can be made to apply ab initio or atomistic methodologies, but then one would face a

11. Adequate mathematical modelling of environmental processes

Chashechkin, Yu. D.

2012-04-01

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

12. 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,…

13. Key Concept Mathematics and Management Science Models

ERIC Educational Resources Information Center

Macbeth, Thomas G.; Dery, George C.

1973-01-01

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

14. Making Insulation Decisions through Mathematical Modeling

ERIC Educational Resources Information Center

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…

15. 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)

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

ERIC Educational Resources Information Center

1999-01-01

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

17. Mechanical-mathematical modeling for landslide process

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.

18. 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…

19. 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…

20. 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…

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

PubMed

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

2014-09-25

2. A Two-Phase Space Resection Model for Accurate Topographic Reconstruction from Lunar Imagery with PushbroomScanners

PubMed Central

Xu, Xuemiao; Zhang, Huaidong; Han, Guoqiang; Kwan, Kin Chung; Pang, Wai-Man; Fang, Jiaming; Zhao, Gansen

2016-01-01

Exterior orientation parameters’ (EOP) estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs) for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang’E-1, compared to the existing space resection model. PMID:27077855

3. A Two-Phase Space Resection Model for Accurate Topographic Reconstruction from Lunar Imagery with PushbroomScanners.

PubMed

Xu, Xuemiao; Zhang, Huaidong; Han, Guoqiang; Kwan, Kin Chung; Pang, Wai-Man; Fang, Jiaming; Zhao, Gansen

2016-04-11

Exterior orientation parameters' (EOP) estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs) for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang'E-1, compared to the existing space resection model.

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

PubMed

Men'shikov, D D; Enileev, R Kh

1989-03-01

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

5. 2016 KIVA-hpFE Development: A Robust and Accurate Engine Modeling Software

SciTech Connect

2016-10-25

Los Alamos National Laboratory and its collaborators are facilitating engine modeling by improving accuracy and robustness of the modeling, and improving the robustness of software. We also continue to improve the physical modeling methods. We are developing and implementing new mathematical algorithms, those that represent the physics within an engine. We provide software that others may use directly or that they may alter with various models e.g., sophisticated chemical kinetics, different turbulent closure methods or other fuel injection and spray systems.

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

PubMed

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

2014-08-28

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

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

PubMed Central

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

2014-01-01

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: “What is the value of a model?” PMID:25064823

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

ERIC Educational Resources Information Center

Charnes, A.; And Others

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

9. A Mathematical Model for the Middle Ear Ventilation

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

2008-09-01

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

10. 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.

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

PubMed

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

2009-10-01

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

12. Development of physical and mathematical models for the Porous Ceramic Tube Plant Nutrification System (PCTPNS)

NASA Technical Reports Server (NTRS)

Tsao, D. Teh-Wei; Okos, M. R.; Sager, J. C.; Dreschel, T. W.

1992-01-01

A physical model of the Porous Ceramic Tube Plant Nutrification System (PCTPNS) was developed through microscopic observations of the tube surface under various operational conditions. In addition, a mathematical model of this system was developed which incorporated the effects of the applied suction pressure, surface tension, and gravitational forces as well as the porosity and physical dimensions of the tubes. The flow of liquid through the PCTPNS was thus characterized for non-biological situations. One of the key factors in the verification of these models is the accurate and rapid measurement of the 'wetness' or holding capacity of the ceramic tubes. This study evaluated a thermistor based moisture sensor device and recommendations for future research on alternative sensing devices are proposed. In addition, extensions of the physical and mathematical models to include the effects of plant physiology and growth are also discussed for future research.

13. 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.

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

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

2016-09-01

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

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

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.

16. Mathematical model of layered metallurgical furnaces and units

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

2016-09-01

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

17. Nonlinear mathematical model for a biaxial MOEMS scanning mirror

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

2010-02-01

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

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

PubMed

Sgouralis, Ioannis; Layton, Anita T

2015-06-01

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

19. Mathematical Modeling of Primary Wood Processing

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).

20. Issues and Importance of "Good" Starting Points for Nonlinear Regression for Mathematical Modeling with Maple: Basic Model Fitting to Make Predictions with Oscillating Data

ERIC Educational Resources Information Center

Fox, William

2012-01-01

The purpose of our modeling effort is to predict future outcomes. We assume the data collected are both accurate and relatively precise. For our oscillating data, we examined several mathematical modeling forms for predictions. We also examined both ignoring the oscillations as an important feature and including the oscillations as an important…

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

PubMed

Seno, Hiromi; Kohno, Takahiro

2012-01-01

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

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

ERIC Educational Resources Information Center

Garland, May; Treisman, Uri

1993-01-01

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

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

PubMed

Millat, Thomas; Winzer, Klaus

2017-03-01

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

4. Mathematical and computational modeling simulation of solar drying Systems

Technology Transfer Automated Retrieval System (TEKTRAN)

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

5. 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…

6. Applicability of mathematical modeling to problems of environmental physiology

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

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

ERIC Educational Resources Information Center

Brown, John Seely; Burton, Richard R.

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

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

PubMed

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

2013-10-01

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

9. Mathematical modeling of steel fiber concrete under dynamic impact

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

2015-01-01

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

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

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.

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

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

2007-10-01

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

12. 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…

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

ERIC Educational Resources Information Center

Brown, R.

2002-01-01

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

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

PubMed

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

2017-02-01

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

15. Creation of Anatomically Accurate Computer-Aided Design (CAD) Solid Models from Medical Images

NASA Technical Reports Server (NTRS)

Stewart, John E.; Graham, R. Scott; Samareh, Jamshid A.; Oberlander, Eric J.; Broaddus, William C.

1999-01-01

Most surgical instrumentation and implants used in the world today are designed with sophisticated Computer-Aided Design (CAD)/Computer-Aided Manufacturing (CAM) software. This software automates the mechanical development of a product from its conceptual design through manufacturing. CAD software also provides a means of manipulating solid models prior to Finite Element Modeling (FEM). Few surgical products are designed in conjunction with accurate CAD models of human anatomy because of the difficulty with which these models are created. We have developed a novel technique that creates anatomically accurate, patient specific CAD solids from medical images in a matter of minutes.

16. The Mathematical Structure of Error Correction Models.

DTIC Science & Technology

1985-05-01

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

17. Facial plastic surgery area acquisition method based on point cloud mathematical model solution.

PubMed

Li, Xuwu; Liu, Fei

2013-09-01

It is one of the hot research problems nowadays to find a quick and accurate method of acquiring the facial plastic surgery area to provide sufficient but irredundant autologous or in vitro skin source for covering extensive wound, trauma, and burnt area. At present, the acquisition of facial plastic surgery area mainly includes model laser scanning, point cloud data acquisition, pretreatment of point cloud data, three-dimensional model reconstruction, and computation of area. By using this method, the area can be computed accurately, but it is hard to control the random error, and it requires a comparatively longer computation period. In this article, a facial plastic surgery area acquisition method based on point cloud mathematical model solution is proposed. This method applies symmetric treatment to the point cloud based on the pretreatment of point cloud data, through which the comparison diagram color difference map of point cloud error before and after symmetry is obtained. The slicing mathematical model of facial plastic area is got through color difference map diagram. By solving the point cloud data in this area directly, the facial plastic area is acquired. The point cloud data are directly operated in this method, which can accurately and efficiently complete the surgery area computation. The result of the comparative analysis shows the method is effective in facial plastic surgery area.

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

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.

19. Mathematically modelling proportions of Japanese populations by industry

Hirata, Yoshito

2016-10-01

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

20. Modeling eBook acceptance: A study on mathematics teachers

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.

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

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

2. 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.

3. Mathematical modelling in the computer-aided process planning

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.

4. Mathematical modeling and the neuroscience of metaphor

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

5. Fast and accurate calculation of dilute quantum gas using Uehling-Uhlenbeck model equation

Yano, Ryosuke

2017-02-01

The Uehling-Uhlenbeck (U-U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U-U model equation. DSMC analysis based on the U-U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U-U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculating the viscosity coefficient of a Bose gas on the basis of the Green-Kubo expression and the shock layer of a dilute Bose gas around a cylinder.

6. Assessing Mathematical Models of Influenza Infections Using Features of the Immune Response

PubMed Central

Dobrovolny, Hana M.; Reddy, Micaela B.; Kamal, Mohamed A.; Rayner, Craig R.; Beauchemin, Catherine A. A.

2013-01-01

The role of the host immune response in determining the severity and duration of an influenza infection is still unclear. In order to identify severity factors and more accurately predict the course of an influenza infection within a human host, an understanding of the impact of host factors on the infection process is required. Despite the lack of sufficiently diverse experimental data describing the time course of the various immune response components, published mathematical models were constructed from limited human or animal data using various strategies and simplifying assumptions. To assess the validity of these models, we assemble previously published experimental data of the dynamics and role of cytotoxic T lymphocytes, antibodies, and interferon and determined qualitative key features of their effect that should be captured by mathematical models. We test these existing models by confronting them with experimental data and find that no single model agrees completely with the variety of influenza viral kinetics responses observed experimentally when various immune response components are suppressed. Our analysis highlights the strong and weak points of each mathematical model and highlights areas where additional experimental data could elucidate specific mechanisms, constrain model design, and complete our understanding of the immune response to influenza. PMID:23468916

7. An efficient and accurate model of the coax cable feeding structure for FEM simulations

NASA Technical Reports Server (NTRS)

Gong, Jian; Volakis, John L.

1995-01-01

An efficient and accurate coax cable feed model is proposed for microstrip or cavity-backed patch antennas in the context of a hybrid finite element method (FEM). A TEM mode at the cavity-cable junction is assumed for the FEM truncation and system excitation. Of importance in this implementation is that the cavity unknowns are related to the model fields by enforcing an equipotential condition rather than field continuity. This scheme proved quite accurate and may be applied to other decomposed systems as a connectivity constraint. Comparisons of our predictions with input impedance measurements are presented and demonstrate the substantially improved accuracy of the proposed model.

8. 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.

9. 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.

10. Molecular modeling: An open invitation for applied mathematics

Mezey, Paul G.

2013-10-01

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

11. Mathematical modeling of lithium iodine discharge data

SciTech Connect

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

1980-01-01

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

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

PubMed

Lofgren, Eric T

2016-10-01

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

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

PubMed

Muñoz, Ana I; Tello, José Ignacio

2011-10-01

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

14. A Computational and Mathematical Model for Device Induced Thrombosis

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.

15. Bayesian parameter estimation of a k-ε model for accurate jet-in-crossflow simulations

SciTech Connect

Ray, Jaideep; Lefantzi, Sophia; Arunajatesan, Srinivasan; Dechant, Lawrence

2016-05-31

Reynolds-averaged Navier–Stokes models are not very accurate for high-Reynolds-number compressible jet-in-crossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-averaged Navier–Stokes model. In this study, the hypothesis is pursued that Reynolds-averaged Navier–Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.

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

PubMed

Li, Xuefang; Xu, Jian-Xin

2016-10-07

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

17. Mathematical Model of Estuarial Sediment Transport.

DTIC Science & Technology

1977-10-01

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

18. Mathematical Modelling of Laser/Material Interactions.

DTIC Science & Technology

1983-11-25

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

19. A mathematical model of intestinal oedema formation.

PubMed

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

2014-03-01

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

20. A mathematical model of intestinal oedema formation

PubMed Central

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

2014-01-01

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

1. 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…

2. 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.

3. Cancer evolution: mathematical models and computational inference.

PubMed

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

2015-01-01

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

4. 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

5. 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.

6. 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).

7. 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.

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

PubMed

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

2015-09-11

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

9. 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…

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

ERIC Educational Resources Information Center

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

2016-01-01

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

11. Mathematical model of cancer with competition

Chrobak, Joanna M.; Herrero, Henar

2009-05-01

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

12. 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.

13. Models of Intervention in Mathematics: Reweaving the Tapestry

ERIC Educational Resources Information Center

Fosnot, Catherine

2010-01-01

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

14. A Mathematical Model for HIV Drug-Resistance

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

2010-09-01

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

15. 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.

16. 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…

17. Mathematical modeling of the instability of viscous fluid films

Prokudina, L. A.

2016-08-01

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

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

ERIC Educational Resources Information Center

Berlin, Donna F.; White, Arthur L.

2001-01-01

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

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

PubMed

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

2016-08-01

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

20. 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.

1. 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…

2. 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.

3. Some mathematical models of intermolecular autophosphorylation.

PubMed

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

2015-04-07

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

4. Mathematical Modeling of Flow Through Vegetated Regions

DTIC Science & Technology

2013-08-01

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

5. Asymptotic properties of mathematical models of excitability.

PubMed

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

2006-05-15

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

6. Mathematical modeling of polymer electrolyte fuel cells

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.

7. Mathematical Model for the Behavior of Wildfires

Delbene, Kevin; Drew, Donald

2009-11-01

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

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

Chupin, Laurent

2017-01-01

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

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

Dawkins, Bryan A.; Laverty, Sean M.

2014-02-01

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

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

Grzymkowski, Radosław; Mochnacki, Bohdan; Suchy, Józef

1983-05-01

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

11. Improving light propagation Monte Carlo simulations with accurate 3D modeling of skin tissue

SciTech Connect

Paquit, Vincent C; Price, Jeffery R; Meriaudeau, Fabrice; Tobin Jr, Kenneth William

2008-01-01

In this paper, we present a 3D light propagation model to simulate multispectral reflectance images of large skin surface areas. In particular, we aim to simulate more accurately the effects of various physiological properties of the skin in the case of subcutaneous vein imaging compared to existing models. Our method combines a Monte Carlo light propagation model, a realistic three-dimensional model of the skin using parametric surfaces and a vision system for data acquisition. We describe our model in detail, present results from the Monte Carlo modeling and compare our results with those obtained with a well established Monte Carlo model and with real skin reflectance images.

12. A Fuzzy mathematical model to estimate the effects of global warming on the vitality of Laelia purpurata orchids.

PubMed

Putti, Fernando Ferrari; Filho, Luis Roberto Almeida Gabriel; Gabriel, Camila Pires Cremasco; Neto, Alfredo Bonini; Bonini, Carolina Dos Santos Batista; Rodrigues Dos Reis, André

2017-03-18

This study aimed to develop a fuzzy mathematical model to estimate the impacts of global warming on the vitality of Laelia purpurata growing in different Brazilian environmental conditions. In order to develop the mathematical model was considered as intrinsic factors the parameters: temperature, humidity and shade conditions to determine the vitality of plants. Fuzzy model results could accurately predict the optimal conditions for cultivation of Laelia purpurata in several sites of Brazil. Based on fuzzy model results, we found that higher temperatures and lacking of properly shading can reduce the vitality of orchids. Fuzzy mathematical model could precisely detect the effect of higher temperatures causing damages on vitality of plants as a consequence of global warming.

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

NASA Technical Reports Server (NTRS)

Shitzer, A.

1972-01-01

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

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. 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.

16. Comprehensive Mathematical Model for Simulating Electroslag Remelting

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.

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

PubMed

Ito, Makoto; Doya, Kenji

2008-07-01

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

18. Mathematical Model of Porous Medium Dynamics

Gerschuk, Peotr; Sapozhnikov, Anatoly

1999-06-01

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

19. Mathematical models for space shuttle ground systems

NASA Technical Reports Server (NTRS)

Tory, E. G.

1985-01-01

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

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

ERIC Educational Resources Information Center

Norton, Anderson H.; McCloskey, Andrea V.

2008-01-01

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

1. Using Archeological Data to Model Mathematics

ERIC Educational Resources Information Center

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

2014-01-01

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

2. Mathematical Modelling of the Infusion Test

Cieslicki, Krzysztof

2007-01-01

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

3. Mathematical modelling of avascular-tumour growth.

PubMed

Ward, J P; King, J R

1997-03-01

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

4. 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

5. Accurate modeling of high-repetition rate ultrashort pulse amplification in optical fibers

PubMed Central

Lindberg, Robert; Zeil, Peter; Malmström, Mikael; Laurell, Fredrik; Pasiskevicius, Valdas

2016-01-01

A numerical model for amplification of ultrashort pulses with high repetition rates in fiber amplifiers is presented. The pulse propagation is modeled by jointly solving the steady-state rate equations and the generalized nonlinear Schrödinger equation, which allows accurate treatment of nonlinear and dispersive effects whilst considering arbitrary spatial and spectral gain dependencies. Comparison of data acquired by using the developed model and experimental results prove to be in good agreement. PMID:27713496

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

PubMed

Nargund, Shilpa; Sriram, Ganesh

2014-01-01

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

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

PubMed

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

2006-09-01

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

8. Physical and mathematical modeling of antimicrobial photodynamic therapy

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

2014-07-01

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

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

PubMed

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

2011-01-01

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

10. Generalized mathematical models in design optimization

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

11. Mathematical Model of an Air Cushion Vehicle

DTIC Science & Technology

1975-05-01

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

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

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.

13. A mathematical model for late term cancer chemotherapy

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

2006-03-01

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

14. 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

15. A mathematical model of lung parenchyma.

PubMed

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

1980-05-01

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

16. Mathematical modeling of solid oxide fuel cells

NASA Technical Reports Server (NTRS)

Lu, Cheng-Yi; Maloney, Thomas M.

1988-01-01

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

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

PubMed

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

2010-09-07

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

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

PubMed Central

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

2015-01-01

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

19. 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.

20. Whole muscle length-tension relationships are accurately modeled as scaled sarcomeres in rabbit hindlimb muscles.

PubMed

Winters, Taylor M; Takahashi, Mitsuhiko; Lieber, Richard L; Ward, Samuel R

2011-01-04

An a priori model of the whole active muscle length-tension relationship was constructed utilizing only myofilament length and serial sarcomere number for rabbit tibialis anterior (TA), extensor digitorum longus (EDL), and extensor digitorum II (EDII) muscles. Passive tension was modeled with a two-element Hill-type model. Experimental length-tension relations were then measured for each of these muscles and compared to predictions. The model was able to accurately capture the active-tension characteristics of experimentally-measured data for all muscles (ICC=0.88 ± 0.03). Despite their varied architecture, no differences in predicted versus experimental correlations were observed among muscles. In addition, the model demonstrated that excursion, quantified by full-width-at-half-maximum (FWHM) of the active length-tension relationship, scaled linearly (slope=0.68) with normalized muscle fiber length. Experimental and theoretical FWHM values agreed well with an intraclass correlation coefficient of 0.99 (p<0.001). In contrast to active tension, the passive tension model deviated from experimentally-measured values and thus, was not an accurate predictor of passive tension (ICC=0.70 ± 0.07). These data demonstrate that modeling muscle as a scaled sarcomere provides accurate active functional but not passive functional predictions for rabbit TA, EDL, and EDII muscles and call into question the need for more complex modeling assumptions often proposed.

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

DOE PAGES

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

2014-12-18

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

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

SciTech Connect

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

2014-12-18

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

3. ICPSEF: a user's manual for the computer mathematical model of the ICPP purex solvent extraction system

SciTech Connect

Bendixsen, C L

1982-11-01

A computer-based mathematical program, ICPSEF, was developed for the first-cycle extraction system at the Idaho Chemical Processing Plant (ICPP). At the ICPP, spent nuclear fuels are processed to recover unfissioned uranium. The uranium is recovered from aqueous solutions in a pulse column, solvent extraction system using tributyl phosphate (TBP) solvent (purex process). A previously developed SEPHIS-MOD4 computer program was added to and modified to provide a model for the ICPP system. Major modifications included addition of: (1) partial theoretical stages to permit more accurate modeling of ICPP columns, (2) modeling ammonium hydroxide neutralization of nitric acid in a scrubbing column, and (3) equilibrium data for 5 to 10 vol % TBP. The model was verified by comparison with actual operating data. Detailed instructions for using the ICPSEF model and sample results of the model are included.

4. Aspects of Mathematical Modelling of Pressure Retarded Osmosis.

PubMed

Anissimov, Yuri G

2016-02-03

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

5. Aspects of Mathematical Modelling of Pressure Retarded Osmosis

PubMed Central

Anissimov, Yuri G.

2016-01-01

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

6. 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.

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

ERIC Educational Resources Information Center

Kim, Sun Hee; Kim, Soojin

2010-01-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

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

ERIC Educational Resources Information Center

Chitera, Nancy

2011-01-01

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

10. Accurate protein structure modeling using sparse NMR data and homologous structure information.

PubMed

Thompson, James M; Sgourakis, Nikolaos G; Liu, Gaohua; Rossi, Paolo; Tang, Yuefeng; Mills, Jeffrey L; Szyperski, Thomas; Montelione, Gaetano T; Baker, David

2012-06-19

While information from homologous structures plays a central role in X-ray structure determination by molecular replacement, such information is rarely used in NMR structure determination because it can be incorrect, both locally and globally, when evolutionary relationships are inferred incorrectly or there has been considerable evolutionary structural divergence. Here we describe a method that allows robust modeling of protein structures of up to 225 residues by combining (1)H(N), (13)C, and (15)N backbone and (13)Cβ chemical shift data, distance restraints derived from homologous structures, and a physically realistic all-atom energy function. Accurate models are distinguished from inaccurate models generated using incorrect sequence alignments by requiring that (i) the all-atom energies of models generated using the restraints are lower than models generated in unrestrained calculations and (ii) the low-energy structures converge to within 2.0 Å backbone rmsd over 75% of the protein. Benchmark calculations on known structures and blind targets show that the method can accurately model protein structures, even with very remote homology information, to a backbone rmsd of 1.2-1.9 Å relative to the conventional determined NMR ensembles and of 0.9-1.6 Å relative to X-ray structures for well-defined regions of the protein structures. This approach facilitates the accurate modeling of protein structures using backbone chemical shift data without need for side-chain resonance assignments and extensive analysis of NOESY cross-peak assignments.

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

Michelsen, Claus

2015-07-01

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

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

PubMed

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

2016-07-08

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

13. Mathematical models of continuous flow electrophoresis: Electrophoresis technology

NASA Technical Reports Server (NTRS)

Saville, Dudley A.

1986-01-01

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

14. Mathematical and computer modeling of component surface shaping

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.

15. Fast and accurate focusing analysis of large photon sieve using pinhole ring diffraction model.

PubMed

Liu, Tao; Zhang, Xin; Wang, Lingjie; Wu, Yanxiong; Zhang, Jizhen; Qu, Hemeng

2015-06-10

In this paper, we developed a pinhole ring diffraction model for the focusing analysis of a large photon sieve. Instead of analyzing individual pinholes, we discuss the focusing of all of the pinholes in a single ring. An explicit equation for the diffracted field of individual pinhole ring has been proposed. We investigated the validity range of this generalized model and analytically describe the sufficient conditions for the validity of this pinhole ring diffraction model. A practical example and investigation reveals the high accuracy of the pinhole ring diffraction model. This simulation method could be used for fast and accurate focusing analysis of a large photon sieve.

16. Mathematical modeling provides kinetic details of the human immune response to vaccination

PubMed Central

Le, Dustin; Miller, Joseph D.; Ganusov, Vitaly V.

2015-01-01

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data. PMID:25621280

17. Mathematical modeling provides kinetic details of the human immune response to vaccination.

PubMed

Le, Dustin; Miller, Joseph D; Ganusov, Vitaly V

2014-01-01

With major advances in experimental techniques to track antigen-specific immune responses many basic questions on the kinetics of virus-specific immunity in humans remain unanswered. To gain insights into kinetics of T and B cell responses in human volunteers we combined mathematical models and experimental data from recent studies employing vaccines against yellow fever and smallpox. Yellow fever virus-specific CD8 T cell population expanded slowly with the average doubling time of 2 days peaking 2.5 weeks post immunization. Interestingly, we found that the peak of the yellow fever-specific CD8 T cell response was determined by the rate of T cell proliferation and not by the precursor frequency of antigen-specific cells as has been suggested in several studies in mice. We also found that while the frequency of virus-specific T cells increased slowly, the slow increase could still accurately explain clearance of yellow fever virus in the blood. Our additional mathematical model described well the kinetics of virus-specific antibody-secreting cell and antibody response to vaccinia virus in vaccinated individuals suggesting that most of antibodies in 3 months post immunization were derived from the population of circulating antibody-secreting cells. Taken together, our analysis provided novel insights into mechanisms by which live vaccines induce immunity to viral infections and highlighted challenges of applying methods of mathematical modeling to the current, state-of-the-art yet limited immunological data.

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

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

2014-06-01

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

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

PubMed

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

2013-03-01

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

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

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

2016-11-01

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

1. Mathematical modeling and simulation of a thermal system

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

2016-12-01

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

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

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

2011-09-01

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

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

Bobak, Carly; Kunze, Herb

2017-01-01

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

4. Development of modified cable models to simulate accurate neuronal active behaviors

PubMed Central

2014-01-01

In large network and single three-dimensional (3-D) neuron simulations, high computing speed dictates using reduced cable models to simulate neuronal firing behaviors. However, these models are unwarranted under active conditions and lack accurate representation of dendritic active conductances that greatly shape neuronal firing. Here, realistic 3-D (R3D) models (which contain full anatomical details of dendrites) of spinal motoneurons were systematically compared with their reduced single unbranched cable (SUC, which reduces the dendrites to a single electrically equivalent cable) counterpart under passive and active conditions. The SUC models matched the R3D model's passive properties but failed to match key active properties, especially active behaviors originating from dendrites. For instance, persistent inward currents (PIC) hysteresis, frequency-current (FI) relationship secondary range slope, firing hysteresis, plateau potential partial deactivation, staircase currents, synaptic current transfer ratio, and regional FI relationships were not accurately reproduced by the SUC models. The dendritic morphology oversimplification and lack of dendritic active conductances spatial segregation in the SUC models caused significant underestimation of those behaviors. Next, SUC models were modified by adding key branching features in an attempt to restore their active behaviors. The addition of primary dendritic branching only partially restored some active behaviors, whereas the addition of secondary dendritic branching restored most behaviors. Importantly, the proposed modified models successfully replicated the active properties without sacrificing model simplicity, making them attractive candidates for running R3D single neuron and network simulations with accurate firing behaviors. The present results indicate that using reduced models to examine PIC behaviors in spinal motoneurons is unwarranted. PMID:25277743

5. Models in biology: ‘accurate descriptions of our pathetic thinking’

PubMed Central

2014-01-01

In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as ‘predictive’, in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders. PMID:24886484

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

PubMed

Afenya, Evans K

2005-07-01

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

7. A Mathematical Model for Simulating Infrared Images of Ships

DTIC Science & Technology

1986-12-01

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

8. Mathematical Model of the Jet Engine Fuel System

Klimko, Marek

2015-05-01

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

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

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

2016-01-01

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

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

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

2012-10-01

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

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

ERIC Educational Resources Information Center

2015-01-01

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

12. A Mathematical Model Coupling Tumor Growth and Angiogenesis

PubMed Central

Gomez, Hector

2016-01-01

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

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

NASA Technical Reports Server (NTRS)

Kelkar, Atul, G.

1994-01-01

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

14. A Mathematical Model of the Thermo-Anemometric Flowmeter

PubMed Central

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

2015-01-01

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

15. Mathematical model of a lithium/polypyrrole cell

NASA Technical Reports Server (NTRS)

Yeu, Taewhan; White, Ralph E.

1990-01-01

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

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

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

2017-04-01

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

17. Enhancing the Fever Workup Utilizing a Multi-Technique Modeling Approach to Diagnose Infections More Accurately

PubMed Central

2012-01-01

Abstract Background Differentiation between infectious and non-infectious etiologies of the systemic inflammatory response syndrome (SIRS) in trauma patients remains elusive. We hypothesized that mathematical modeling in combination with computerized clinical decision support would assist with this differentiation. The purpose of this study was to determine the capability of various mathematical modeling techniques to predict infectious complications in critically ill trauma patients and compare the performance of these models with a standard fever workup practice (identifying infections on the basis of fever or leukocytosis). Methods An 18-mo retrospective database was created using information collected daily from critically ill trauma patients admitted to an academic surgical and trauma intensive care unit. Two hundred forty-three non-infected patient-days were chosen randomly to combine with the 243 infected-days, which created a modeling sample of 486 patient-days. Utilizing ten variables known to be associated with infectious complications, decision trees, neural networks, and logistic regression analysis models were created to predict the presence of urinary tract infections (UTIs), bacteremia, and respiratory tract infections (RTIs). The data sample was split into a 70% training set and a 30% testing set. Models were compared by calculating sensitivity, specificity, positive predictive value, negative predictive value, overall accuracy, and discrimination. Results Decision trees had the best modeling performance, with a sensitivity of 83%, an accuracy of 82%, and a discrimination of 0.91 for identifying infections. Both neural networks and decision trees outperformed logistic regression analysis. A second analysis was performed utilizing the same 243 infected days and only those non-infected patient-days associated with negative microbiologic cultures (n = 236). Decision trees again had the best modeling performance for infection identification, with a

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

PubMed

Mason, I G

2006-01-01

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

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

PubMed

Jorgensen, Stephanie N; Sanders, Jonathan R

2016-09-01

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

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

ERIC Educational Resources Information Center

Brown, Jill Patricia; Stillman, Gloria Ann

2017-01-01

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

1. Accurate path integration in continuous attractor network models of grid cells.

PubMed

Burak, Yoram; Fiete, Ila R

2009-02-01

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

2. Mathematical model of radiation effects on thrombopoiesis in rhesus macaques and humans.

PubMed

Wentz, J M; Vainstein, V; Oldson, D; Gluzman-Poltorak, Z; Basile, L A; Stricklin, D

2015-10-21

A mathematical model that describes the effects of acute radiation exposure on thrombopoiesis in primates and humans is presented. Thrombopoiesis is a complex multistage dynamic process with potential differences between species. Due to known differences in cellular radiosensitivities, nadir times, and cytopenia durations, direct extrapolation from rhesus to human platelet dynamics is unrealistic. Developing mathematical models of thrombopoiesis for both humans and primates allows for the comparison of the system's response across species. Thus, data obtained in primate experiments can be extrapolated to predictions in humans. Parameter values for rhesus macaques and humans were obtained either from direct experimental measurements or through optimization procedures using dynamic data on platelet counts following radiation exposure. Model simulations accurately predict trends observed in platelet dynamics: at low radiation doses platelet counts decline after a time lag, and nadir depth is dose dependent. The models were validated using data that was not used during the parameterization process. In particular, additional experimental data was used for rhesus, and accident and platelet donor data was used for humans. The model aims to simulate the average response in rhesus and humans following irradiation. Variation in platelet dynamics due to individual variability can be modeled using Monte Carlo simulations in which parameter values are sampled from distributions. This model provides insight into the time course of the physiological effects of radiation exposure, information which could be valuable for disaster planning and survivability analysis and help in drug development of radiation medical countermeasures.

3. Can phenological models predict tree phenology accurately under climate change conditions?

Chuine, Isabelle; Bonhomme, Marc; Legave, Jean Michel; García de Cortázar-Atauri, Inaki; Charrier, Guillaume; Lacointe, André; Améglio, Thierry

2014-05-01

The onset of the growing season of trees has been globally earlier by 2.3 days/decade during the last 50 years because of global warming and this trend is predicted to continue according to climate forecast. The effect of temperature on plant phenology is however not linear because temperature has a dual effect on bud development. On one hand, low temperatures are necessary to break bud dormancy, and on the other hand higher temperatures are necessary to promote bud cells growth afterwards. Increasing phenological changes in temperate woody species have strong impacts on forest trees distribution and productivity, as well as crops cultivation areas. Accurate predictions of trees phenology are therefore a prerequisite to understand and foresee the impacts of climate change on forests and agrosystems. Different process-based models have been developed in the last two decades to predict the date of budburst or flowering of woody species. They are two main families: (1) one-phase models which consider only the ecodormancy phase and make the assumption that endodormancy is always broken before adequate climatic conditions for cell growth occur; and (2) two-phase models which consider both the endodormancy and ecodormancy phases and predict a date of dormancy break which varies from year to year. So far, one-phase models have been able to predict accurately tree bud break and flowering under historical climate. However, because they do not consider what happens prior to ecodormancy, and especially the possible negative effect of winter temperature warming on dormancy break, it seems unlikely that they can provide accurate predictions in future climate conditions. It is indeed well known that a lack of low temperature results in abnormal pattern of bud break and development in temperate fruit trees. An accurate modelling of the dormancy break date has thus become a major issue in phenology modelling. Two-phases phenological models predict that global warming should delay

4. Mathematical and Computational Modeling in Complex Biological Systems

PubMed Central

Li, Wenyang; Zhu, Xiaoliang

2017-01-01

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

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

PubMed

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

2016-02-07

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

6. Final Report for "Accurate Numerical Models of the Secondary Electron Yield from Grazing-incidence Collisions".

SciTech Connect

Seth A Veitzer

2008-10-21

Effects of stray electrons are a main factor limiting performance of many accelerators. Because heavy-ion fusion (HIF) accelerators will operate in regimes of higher current and with walls much closer to the beam than accelerators operating today, stray electrons might have a large, detrimental effect on the performance of an HIF accelerator. A primary source of stray electrons is electrons generated when halo ions strike the beam pipe walls. There is some research on these types of secondary electrons for the HIF community to draw upon, but this work is missing one crucial ingredient: the effect of grazing incidence. The overall goal of this project was to develop the numerical tools necessary to accurately model the effect of grazing incidence on the behavior of halo ions in a HIF accelerator, and further, to provide accurate models of heavy ion stopping powers with applications to ICF, WDM, and HEDP experiments.

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

Lu, Jay W.; Chen, Falin

1997-02-01

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

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

Cotfas, Nicolae

2005-09-01

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

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

PubMed Central

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

2009-01-01

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

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

PubMed

Lundengård, Karin; Cedersund, Gunnar; Sten, Sebastian; Leong, Felix; Smedberg, Alexander; Elinder, Fredrik; Engström, Maria

2016-06-01

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

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

PubMed Central

Lundengård, Karin; Cedersund, Gunnar; Sten, Sebastian; Leong, Felix; Smedberg, Alexander; Elinder, Fredrik

2016-01-01

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

12. Accurate and efficient halo-based galaxy clustering modelling with simulations

Zheng, Zheng; Guo, Hong

2016-06-01

Small- and intermediate-scale galaxy clustering can be used to establish the galaxy-halo connection to study galaxy formation and evolution and to tighten constraints on cosmological parameters. With the increasing precision of galaxy clustering measurements from ongoing and forthcoming large galaxy surveys, accurate models are required to interpret the data and extract relevant information. We introduce a method based on high-resolution N-body simulations to accurately and efficiently model the galaxy two-point correlation functions (2PCFs) in projected and redshift spaces. The basic idea is to tabulate all information of haloes in the simulations necessary for computing the galaxy 2PCFs within the framework of halo occupation distribution or conditional luminosity function. It is equivalent to populating galaxies to dark matter haloes and using the mock 2PCF measurements as the model predictions. Besides the accurate 2PCF calculations, the method is also fast and therefore enables an efficient exploration of the parameter space. As an example of the method, we decompose the redshift-space galaxy 2PCF into different components based on the type of galaxy pairs and show the redshift-space distortion effect in each component. The generalizations and limitations of the method are discussed.

13. An analytic model for accurate spring constant calibration of rectangular atomic force microscope cantilevers.

PubMed

Li, Rui; Ye, Hongfei; Zhang, Weisheng; Ma, Guojun; Su, Yewang

2015-10-29

Spring constant calibration of the atomic force microscope (AFM) cantilever is of fundamental importance for quantifying the force between the AFM cantilever tip and the sample. The calibration within the framework of thin plate theory undoubtedly has a higher accuracy and broader scope than that within the well-established beam theory. However, thin plate theory-based accurate analytic determination of the constant has been perceived as an extremely difficult issue. In this paper, we implement the thin plate theory-based analytic modeling for the static behavior of rectangular AFM cantilevers, which reveals that the three-dimensional effect and Poisson effect play important roles in accurate determination of the spring constants. A quantitative scaling law is found that the normalized spring constant depends only on the Poisson's ratio, normalized dimension and normalized load coordinate. Both the literature and our refined finite element model validate the present results. The developed model is expected to serve as the benchmark for accurate calibration of rectangular AFM cantilevers.

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

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

1993-04-01

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

15. 5D model for accurate representation and visualization of dynamic cardiac structures

Lin, Wei-te; Robb, Richard A.

2000-05-01

Accurate cardiac modeling is challenging due to the intricate structure and complex contraction patterns of myocardial tissues. Fast imaging techniques can provide 4D structural information acquired as a sequence of 3D images throughout the cardiac cycle. To mode. The beating heart, we created a physics-based surface model that deforms between successive time point in the cardiac cycle. 3D images of canine hearts were acquired during one complete cardiac cycle using the DSR and the EBCT. The left ventricle of the first time point is reconstructed as a triangular mesh. A mass-spring physics-based deformable mode,, which can expand and shrink with local contraction and stretching forces distributed in an anatomically accurate simulation of cardiac motion, is applied to the initial mesh and allows the initial mesh to deform to fit the left ventricle in successive time increments of the sequence. The resulting 4D model can be interactively transformed and displayed with associated regional electrical activity mapped onto anatomic surfaces, producing a 5D model, which faithfully exhibits regional cardiac contraction and relaxation patterns over the entire heart. The model faithfully represents structural changes throughout the cardiac cycle. Such models provide the framework for minimizing the number of time points required to usefully depict regional motion of myocardium and allow quantitative assessment of regional myocardial motion. The electrical activation mapping provides spatial and temporal correlation within the cardiac cycle. In procedures which as intra-cardiac catheter ablation, visualization of the dynamic model can be used to accurately localize the foci of myocardial arrhythmias and guide positioning of catheters for optimal ablation.

16. Monte Carlo modeling provides accurate calibration factors for radionuclide activity meters.

PubMed

Zagni, F; Cicoria, G; Lucconi, G; Infantino, A; Lodi, F; Marengo, M

2014-12-01

Accurate determination of calibration factors for radionuclide activity meters is crucial for quantitative studies and in the optimization step of radiation protection, as these detectors are widespread in radiopharmacy and nuclear medicine facilities. In this work we developed the Monte Carlo model of a widely used activity meter, using the Geant4 simulation toolkit. More precisely the "PENELOPE" EM physics models were employed. The model was validated by means of several certified sources, traceable to primary activity standards, and other sources locally standardized with spectrometry measurements, plus other experimental tests. Great care was taken in order to accurately reproduce the geometrical details of the gas chamber and the activity sources, each of which is different in shape and enclosed in a unique container. Both relative calibration factors and ionization current obtained with simulations were compared against experimental measurements; further tests were carried out, such as the comparison of the relative response of the chamber for a source placed at different positions. The results showed a satisfactory level of accuracy in the energy range of interest, with the discrepancies lower than 4% for all the tested parameters. This shows that an accurate Monte Carlo modeling of this type of detector is feasible using the low-energy physics models embedded in Geant4. The obtained Monte Carlo model establishes a powerful tool for first instance determination of new calibration factors for non-standard radionuclides, for custom containers, when a reference source is not available. Moreover, the model provides an experimental setup for further research and optimization with regards to materials and geometrical details of the measuring setup, such as the ionization chamber itself or the containers configuration.

17. Tumor Angiogenesis and Vascular Patterning: A Mathematical Model

PubMed Central

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

2011-01-01

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

18. Mathematical modeling the radiation effects on humoral immunity

Smirnova, O. A.

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

19. Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

Everett, R. A.; Packer, A. M.; Kuang, Y.

2014-04-01

Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

20. Can Mathematical Models Predict the Outcomes of Prostate Cancer Patients Undergoing Intermittent Androgen Deprivation Therapy?

Everett, R. A.; Packer, A. M.; Kuang, Y.

Androgen deprivation therapy is a common treatment for advanced or metastatic prostate cancer. Like the normal prostate, most tumors depend on androgens for proliferation and survival but often develop treatment resistance. Hormonal treatment causes many undesirable side effects which significantly decrease the quality of life for patients. Intermittently applying androgen deprivation in cycles reduces the total duration with these negative effects and may reduce selective pressure for resistance. We extend an existing model which used measurements of patient testosterone levels to accurately fit measured serum prostate specific antigen (PSA) levels. We test the model's predictive accuracy, using only a subset of the data to find parameter values. The results are compared with those of an existing piecewise linear model which does not use testosterone as an input. Since actual treatment protocol is to re-apply therapy when PSA levels recover beyond some threshold value, we develop a second method for predicting the PSA levels. Based on a small set of data from seven patients, our results showed that the piecewise linear model produced slightly more accurate results while the two predictive methods are comparable. This suggests that a simpler model may be more beneficial for a predictive use compared to a more biologically insightful model, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting. Nevertheless, both models are an important step in this direction.

1. Mathematical model of a flexible space shuttle vehicle

NASA Technical Reports Server (NTRS)

Harvey, C. A.

1972-01-01

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

2. 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.

3. Mathematical Model Of Curing Behavior Of A Polymer

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

4. Mathematical model of depolarization mechanism of conducted vasoreactivity

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

2015-03-01

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

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

NASA Technical Reports Server (NTRS)

1983-01-01

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

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

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

2005-11-01

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

7. Mathematical modeling of bent-axis hydraulic piston motors

NASA Technical Reports Server (NTRS)

Bartos, R. D.

1992-01-01

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

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

PubMed

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

2016-01-01

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

9. Using a highly accurate self-stop Cu-CMP model in the design flow

Izuha, Kyoko; Sakairi, Takashi; Shibuki, Shunichi; Bora, Monalisa; Hatem, Osama; Ghulghazaryan, Ruben; Strecker, Norbert; Wilson, Jeff; Takeshita, Noritsugu

2010-03-01

An accurate model for the self-stop copper chemical mechanical polishing (Cu-CMP) process has been developed using CMP modeling technology from Mentor Graphics. This technology was applied on data from Sony to create and optimize copper electroplating (ECD), Cu-CMP, and barrier metal polishing (BM-CMP) process models. These models take into account layout pattern dependency, long range diffusion and planarization effects, as well as microloading from local pattern density. The developed ECD model accurately predicted erosion and dishing over the entire range of width and space combinations present on the test chip. Then, the results of the ECD model were used as an initial structure to model the Cu-CMP step. Subsequently, the result of Cu-CMP was used for the BM-CMP model creation. The created model was successful in reproducing the measured data, including trends for a broad range of metal width and densities. Its robustness is demonstrated by the fact that it gives acceptable prediction of final copper thickness data although the calibration data included noise from line scan measurements. Accuracy of the Cu-CMP model has a great impact on the prediction results for BM-CMP. This is a critical feature for the modeling of high precision CMP such as self-stop Cu-CMP. Finally, the developed model could successfully extract planarity hotspots that helped identify potential problems in production chips before they were manufactured. The output thickness values of metal and dielectric can be used to drive layout enhancement tools and improve the accuracy of timing analysis.

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

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

2013-12-01

In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students. Participants developed simple mathematical models for everyday life problems with an open-ended answer. The format and content of the workshop are described and feedback from both students and participating teachers is provided. For nearly all participants, this workshop was an enjoyable experience which showed mathematics and other STEM components in a very positive way.

11. Coarse-grained red blood cell model with accurate mechanical properties, rheology and dynamics.

PubMed

Fedosov, Dmitry A; Caswell, Bruce; Karniadakis, George E

2009-01-01

We present a coarse-grained red blood cell (RBC) model with accurate and realistic mechanical properties, rheology and dynamics. The modeled membrane is represented by a triangular mesh which incorporates shear inplane energy, bending energy, and area and volume conservation constraints. The macroscopic membrane elastic properties are imposed through semi-analytic theory, and are matched with those obtained in optical tweezers stretching experiments. Rheological measurements characterized by time-dependent complex modulus are extracted from the membrane thermal fluctuations, and compared with those obtained from the optical magnetic twisting cytometry results. The results allow us to define a meaningful characteristic time of the membrane. The dynamics of RBCs observed in shear flow suggests that a purely elastic model for the RBC membrane is not appropriate, and therefore a viscoelastic model is required. The set of proposed analyses and numerical tests can be used as a complete model testbed in order to calibrate the modeled viscoelastic membranes to accurately represent RBCs in health and disease.

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

ERIC Educational Resources Information Center

Al Duwairi, Ahmed

2013-01-01

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

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

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

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

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

Boulanouar, Mohamed

2013-04-01

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

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

ERIC Educational Resources Information Center

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

2017-01-01

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

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

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

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

17. Yield-Ensuring DAC-Embedded Opamp Design Based on Accurate Behavioral Model Development

Jang, Yeong-Shin; Nguyen, Hoai-Nam; Ryu, Seung-Tak; Lee, Sang-Gug

An accurate behavioral model of a DAC-embedded opamp (DAC-opamp) is developed for a yield-ensuring LCD column driver design. A lookup table for the V-I curve of the unit differential pair in the DAC-opamp is extracted from a circuit simulation and is later manipulated through a random error insertion. Virtual ground assumption simplifies the output voltage estimation algorithm. The developed behavioral model of a 5-bit DAC-opamp shows good agreement with the circuit level simulation with less than 5% INL difference.

18. Time resolved diffuse optical spectroscopy with geometrically accurate models for bulk parameter recovery

PubMed Central

Guggenheim, James A.; Bargigia, Ilaria; Farina, Andrea; Pifferi, Antonio; Dehghani, Hamid

2016-01-01

A novel straightforward, accessible and efficient approach is presented for performing hyperspectral time-domain diffuse optical spectroscopy to determine the optical properties of samples accurately using geometry specific models. To allow bulk parameter recovery from measured spectra, a set of libraries based on a numerical model of the domain being investigated is developed as opposed to the conventional approach of using an analytical semi-infinite slab approximation, which is known and shown to introduce boundary effects. Results demonstrate that the method improves the accuracy of derived spectrally varying optical properties over the use of the semi-infinite approximation. PMID:27699137

19. 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

20. Body charge modelling for accurate simulation of small-signal behaviour in floating body SOI