Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

Some aspects of mathematical and chemical modeling of complex chemical processes

NASA Technical Reports Server (NTRS)

Nemes, I.; Botar, L.; Danoczy, E.; Vidoczy, T.; Gal, D.

1983-01-01

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

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…

Cognitive components of a mathematical processing network in 9-year-old children.

PubMed

Szűcs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-07-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular 'number sense'. We suggest an 'executive memory function centric' model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors.

Cognitive components of a mathematical processing network in 9-year-old children

PubMed Central

Szűcs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-01-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular ‘number sense’. We suggest an ‘executive memory function centric’ model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors. PMID:25089322

A Mathematical Model for the Middle Ear Ventilation

NASA Astrophysics Data System (ADS)

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

2008-09-01

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

PREDICTING SUBSURFACE CONTAMINANT TRANSPORT AND TRANSFORMATION: CONSIDERATIONS FOR MODEL SELECTION AND FIELD VALIDATION

EPA Science Inventory

Predicting subsurface contaminant transport and transformation requires mathematical models based on a variety of physical, chemical, and biological processes. The mathematical model is an attempt to quantitatively describe observed processes in order to permit systematic forecas...

A Case Study on Pre-Service Secondary School Mathematics Teachers' Cognitive-Metacognitive Behaviours in Mathematical Modelling Process

ERIC Educational Resources Information Center

Sagirli, Meryem Özturan

2016-01-01

The aim of the present study is to investigate pre-service secondary mathematics teachers' cognitive-metacognitive behaviours during the mathematical problem-solving process considering class level. The study, in which the case study methodology was employed, was carried out with eight pre-service mathematics teachers, enrolled at a university in…

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.

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…

Experimental research on mathematical modelling and unconventional control of clinker kiln in cement plants

NASA Astrophysics Data System (ADS)

Rusu-Anghel, S.

2017-01-01

Analytical modeling of the flow of manufacturing process of the cement is difficult because of their complexity and has not resulted in sufficiently precise mathematical models. In this paper, based on a statistical model of the process and using the knowledge of human experts, was designed a fuzzy system for automatic control of clinkering process.

Mathematical model and software for investigation of internal ballistic processes in high-speed projectile installations

NASA Astrophysics Data System (ADS)

Diachkovskii, A. S.; Zykova, A. I.; Ishchenko, A. N.; Kasimov, V. Z.; Rogaev, K. S.; Sidorov, A. D.

2017-11-01

This paper describes a software package that allows to explore the interior ballistics processes occurring in a shot scheme with bulk charges using propellant pasty substances at various loading schemes, etc. As a mathematical model, a model of a polydisperse mixture of non-deformable particles and a carrier gas phase is used in the quasi-one-dimensional approximation. Writing the equations of the mathematical model allows to use it to describe a broad class of interior ballistics processes. Features of the using approach are illustrated by calculating the ignition period for the charge of tubular propellant.

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…

Exploring Yellowstone National Park with Mathematical Modeling

ERIC Educational Resources Information Center

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

2017-01-01

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

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

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…

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.

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

ERIC Educational Resources Information Center

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

2014-01-01

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

Differential Psychological Processes Underlying the Skill-Development Model and Self-Enhancement Model across Mathematics and Science in 28 Countries

ERIC Educational Resources Information Center

Chiu, Mei-Shiu

2012-01-01

The skill-development model contends that achievements have an effect on academic self-confidences, while the self-enhancement model contends that self-confidences have an effect on achievements. Differential psychological processes underlying the 2 models across the domains of mathematics and science were posited and examined with structural…

Validation of a multi-phase plant-wide model for the description of the aeration process in a WWTP.

PubMed

Lizarralde, I; Fernández-Arévalo, T; Beltrán, S; Ayesa, E; Grau, P

2018-02-01

This paper introduces a new mathematical model built under the PC-PWM methodology to describe the aeration process in a full-scale WWTP. This methodology enables a systematic and rigorous incorporation of chemical and physico-chemical transformations into biochemical process models, particularly for the description of liquid-gas transfer to describe the aeration process. The mathematical model constructed is able to reproduce biological COD and nitrogen removal, liquid-gas transfer and chemical reactions. The capability of the model to describe the liquid-gas mass transfer has been tested by comparing simulated and experimental results in a full-scale WWTP. Finally, an exploration by simulation has been undertaken to show the potential of the mathematical model. Copyright © 2017 Elsevier Ltd. All rights reserved.

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…

Mathematical form models of tree trunks

Treesearch

Rudolfs Ozolins

2000-01-01

Assortment structure analysis of tree trunks is a characteristic and proper problem that can be solved by using mathematical modeling and standard computer programs. Mathematical form model of tree trunks consists of tapering curve equations and their parameters. Parameters for nine species were obtained by processing measurements of 2,794 model trees and studying the...

Teachers as Managers of the Modelling Process

ERIC Educational Resources Information Center

Lingefjard, Thomas; Meier, Stephanie

2010-01-01

The work in the Comenius Network project Developing Quality in Mathematics Education II (DQME II) has a main focus on development and evaluation of modelling tasks. One reason is the gap between what mathematical modelling is and what is taught in mathematical classrooms. This article deals with one modelling task and focuses on how two teachers…

Discrete Dynamical Modeling.

ERIC Educational Resources Information Center

Sandefur, James T.

1991-01-01

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

Mathematical Model of Nonstationary Separation Processes Proceeding in the Cascade of Gas Centrifuges in the Process of Separation of Multicomponent Isotope Mixtures

NASA Astrophysics Data System (ADS)

Orlov, A. A.; Ushakov, A. A.; Sovach, V. P.

2017-03-01

We have developed and realized on software a mathematical model of the nonstationary separation processes proceeding in the cascades of gas centrifuges in the process of separation of multicomponent isotope mixtures. With the use of this model the parameters of the separation process of germanium isotopes have been calculated. It has been shown that the model adequately describes the nonstationary processes in the cascade and is suitable for calculating their parameters in the process of separation of multicomponent isotope mixtures.

Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

ERIC Educational Resources Information Center

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

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

Mathematical models of ABE fermentation: review and analysis.

PubMed

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

2013-12-01

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

Methodology and Results of Mathematical Modelling of Complex Technological Processes

NASA Astrophysics Data System (ADS)

Mokrova, Nataliya V.

2018-03-01

The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

NASA Astrophysics Data System (ADS)

Winda, A.; Sufyani, P.; Elah, N.

2018-05-01

Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

A Mathematical Model for Continuous Fiber Reinforced Thermoplastic Composite in Melt Impregnation

NASA Astrophysics Data System (ADS)

Ren, Feng; Yu, Yang; Yang, Jianjun; Xin, Chunling; He, Yadong

2017-06-01

Through the combination of Reynolds equation and Darcy's law, a mathematical model was established to calculate the pressure distribution in wedge area, which contributed to the forecast effect of processing parameters on impregnation degree of the fiber bundle. The experiments were conducted to verify the capacity of the proposed model with satisfactory results, which means that the model is effective in predicting the influence of processing parameters on impregnation. From the mathematical model, it was known that the impregnation degree of the fiber bundle would be improved by increasing the processing temperature, number and radius of pins, or decreasing the pulling speed and the center distance of pins, which provided a possible solution to the difficulty of melt with high viscosity in melt impregnation and optimization of impregnation processing.

Multiobjective optimization and multivariable control of the beer fermentation process with the use of evolutionary algorithms.

PubMed

Andrés-Toro, B; Girón-Sierra, J M; Fernández-Blanco, P; López-Orozco, J A; Besada-Portas, E

2004-04-01

This paper describes empirical research on the model, optimization and supervisory control of beer fermentation. Conditions in the laboratory were made as similar as possible to brewery industry conditions. Since mathematical models that consider realistic industrial conditions were not available, a new mathematical model design involving industrial conditions was first developed. Batch fermentations are multiobjective dynamic processes that must be guided along optimal paths to obtain good results. The paper describes a direct way to apply a Pareto set approach with multiobjective evolutionary algorithms (MOEAs). Successful finding of optimal ways to drive these processes were reported. Once obtained, the mathematical fermentation model was used to optimize the fermentation process by using an intelligent control based on certain rules.

Rival approaches to mathematical modelling in immunology

NASA Astrophysics Data System (ADS)

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

2007-08-01

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

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.

The human body metabolism process mathematical simulation based on Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur

2017-08-01

The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Unraveling the Mystery of the Origin of Mathematical Problems: Using a Problem-Posing Framework with Prospective Mathematics Teachers

ERIC Educational Resources Information Center

Contreras, Jose

2007-01-01

In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and…

Mathematical modeling of forest fire initiation in three dimensional setting

Treesearch

Valeriy Perminov

2007-01-01

In this study, the assignment and theoretical investigations of the problems of forest fire initiation were carried out, including development of a mathematical model for description of heat and mass transfer processes in overterrestrial layer of atmosphere at crown forest fire initiation, taking into account their mutual influence. Mathematical model of forest fire...

Mathematical modeling of a process the rolling delivery

NASA Astrophysics Data System (ADS)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

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

A theory of drug tolerance and dependence II: the mathematical model.

PubMed

Peper, Abraham

2004-08-21

The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.

Physical and mathematical modeling of antimicrobial photodynamic therapy

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Adjustment of automatic control systems of production facilities at coal processing plants using multivariant physico- mathematical models

NASA Astrophysics Data System (ADS)

Evtushenko, V. F.; Myshlyaev, L. P.; Makarov, G. V.; Ivushkin, K. A.; Burkova, E. V.

2016-10-01

The structure of multi-variant physical and mathematical models of control system is offered as well as its application for adjustment of automatic control system (ACS) of production facilities on the example of coal processing plant.

Mathematical modelling and numerical simulation of forces in milling process

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Modeling in the quality by design environment: Regulatory requirements and recommendations for design space and control strategy appointment.

PubMed

Djuris, Jelena; Djuric, Zorica

2017-11-30

Mathematical models can be used as an integral part of the quality by design (QbD) concept throughout the product lifecycle for variety of purposes, including appointment of the design space and control strategy, continual improvement and risk assessment. Examples of different mathematical modeling techniques (mechanistic, empirical and hybrid) in the pharmaceutical development and process monitoring or control are provided in the presented review. In the QbD context, mathematical models are predominantly used to support design space and/or control strategies. Considering their impact to the final product quality, models can be divided into the following categories: high, medium and low impact models. Although there are regulatory guidelines on the topic of modeling applications, review of QbD-based submission containing modeling elements revealed concerns regarding the scale-dependency of design spaces and verification of models predictions at commercial scale of manufacturing, especially regarding real-time release (RTR) models. Authors provide critical overview on the good modeling practices and introduce concepts of multiple-unit, adaptive and dynamic design space, multivariate specifications and methods for process uncertainty analysis. RTR specification with mathematical model and different approaches to multivariate statistical process control supporting process analytical technologies are also presented. Copyright © 2017 Elsevier B.V. All rights reserved.

Use of Words and Visuals in Modelling Context of Annual Plant

ERIC Educational Resources Information Center

Park, Jungeun; DiNapoli, Joseph; Mixell, Robert A.; Flores, Alfinio

2017-01-01

This study looks at the various verbal and non-verbal representations used in a process of modelling the number of annual plants over time. Analysis focuses on how various representations such as words, diagrams, letters and mathematical equations evolve in the mathematization process of the modelling context. Our results show that (1) visual…

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…

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

ERIC Educational Resources Information Center

Lee, Kyeong-Hwa

2011-01-01

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

How Long is my Toilet Roll?--A Simple Exercise in Mathematical Modelling

ERIC Educational Resources Information Center

Johnston, Peter R.

2013-01-01

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

A Comparative Analysis of a Generalized Lanchester Equation Model and a Stochastic Computer Simulation Model.

DTIC Science & Technology

1987-03-01

model is one in which words or numerical descriptions are used to represent an entity or process. An example of a symbolic model is a mathematical ...are the third type of model used in modeling combat attrition. Analytical models are symbolic models which use mathematical symbols and equations to...simplicity and the ease of tracing through the mathematical computations. In this section I will discuss some of the shortcoming which have been

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,…

Milestones of mathematical model for business process management related to cost estimate documentation in petroleum industry

NASA Astrophysics Data System (ADS)

Khamidullin, R. I.

2018-05-01

The paper is devoted to milestones of the optimal mathematical model for a business process related to cost estimate documentation compiled during construction and reconstruction of oil and gas facilities. It describes the study and analysis of fundamental issues in petroleum industry, which are caused by economic instability and deterioration of a business strategy. Business process management is presented as business process modeling aimed at the improvement of the studied business process, namely main criteria of optimization and recommendations for the improvement of the above-mentioned business model.

The Spectrum of Mathematical Models.

ERIC Educational Resources Information Center

Karplus, Walter J.

1983-01-01

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

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.

PubMed

Flegg, Jennifer A; Menon, Shakti N; Maini, Philip K; McElwain, D L Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

PubMed Central

Flegg, Jennifer A.; Menon, Shakti N.; Maini, Philip K.; McElwain, D. L. Sean

2015-01-01

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration. PMID:26483695

The Specific Features of design and process engineering in branch of industrial enterprise

NASA Astrophysics Data System (ADS)

Sosedko, V. V.; Yanishevskaya, A. G.

2017-06-01

Production output of industrial enterprise is organized in debugged working mechanisms at each stage of product’s life cycle from initial design documentation to product and finishing it with utilization. The topic of article is mathematical model of the system design and process engineering in branch of the industrial enterprise, statistical processing of estimated implementation results of developed mathematical model in branch, and demonstration of advantages at application at this enterprise. During the creation of model a data flow about driving of information, orders, details and modules in branch of enterprise groups of divisions were classified. Proceeding from the analysis of divisions activity, a data flow, details and documents the state graph of design and process engineering was constructed, transitions were described and coefficients are appropriated. To each condition of system of the constructed state graph the corresponding limiting state probabilities were defined, and also Kolmogorov’s equations are worked out. When integration of sets of equations of Kolmogorov the state probability of system activity the specified divisions and production as function of time in each instant is defined. On the basis of developed mathematical model of uniform system of designing and process engineering and manufacture, and a state graph by authors statistical processing the application of mathematical model results was carried out, and also advantage at application at this enterprise is shown. Researches on studying of loading services probability of branch and third-party contractors (the orders received from branch within a month) were conducted. The developed mathematical model of system design and process engineering and manufacture can be applied to definition of activity state probability of divisions and manufacture as function of time in each instant that will allow to keep account of loading of performance of work in branches of the enterprise.

Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

PubMed Central

Geary, David C.

2011-01-01

The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

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.

The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process

NASA Astrophysics Data System (ADS)

Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko

2012-06-01

A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.

Explicit Pharmacokinetic Modeling: Tools for Documentation, Verification, and Portability

EPA Science Inventory

Quantitative estimates of tissue dosimetry of environmental chemicals due to multiple exposure pathways require the use of complex mathematical models, such as physiologically-based pharmacokinetic (PBPK) models. The process of translating the abstract mathematics of a PBPK mode...

Multilevel modeling of damage accumulation processes in metals

NASA Astrophysics Data System (ADS)

Kurmoiartseva, K. A.; Trusov, P. V.; Kotelnikova, N. V.

2017-12-01

To predict the behavior of components and constructions it is necessary to develop the methods and mathematical models which take into account the self-organization of microstructural processes and the strain localization. The damage accumulation processes and the evolution of material properties during deformation are important to take into account. The heterogeneity of the process of damage accumulation is due to the appropriate physical mechanisms at the scale levels, which are lower than the macro-level. The purpose of this work is to develop a mathematical model for analyzing the behavior of polycrystalline materials that allows describing the damage accumulation processes. Fracture is the multistage and multiscale process of the build-up of micro- and mesodefects over the wide range of loading rates. The formation of microcracks by mechanisms is caused by the interactions of the dislocations of different slip systems, barriers, boundaries and the inclusions of the secondary phase. This paper provides the description of some of the most well-known models of crack nucleation and also suggests the structure of a mathematical model based on crystal plasticity and dislocation models of crack nucleation.

A theory of drug tolerance and dependence I: a conceptual analysis.

PubMed

Peper, Abraham

2004-08-21

A mathematical model of drug tolerance and its underlying theory is presented. The model extends a first approach, published previously. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behavior to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes. In addition, it establishes a relation between the drug dose at any moment, and the resulting drug effect and relates the magnitude of the reactions following withdrawal to the rate of tolerance and other parameters involved in the tolerance process. The present paper analyses the concept behind the model. The next paper discusses the mathematical model.

Gaining control: changing relations between executive control and processing speed and their relevance for mathematics achievement over course of the preschool period

PubMed Central

Clark, Caron A. C.; Nelson, Jennifer Mize; Garza, John; Sheffield, Tiffany D.; Wiebe, Sandra A.; Espy, Kimberly Andrews

2014-01-01

Early executive control (EC) predicts a range of academic outcomes and shows particularly strong associations with children's mathematics achievement. Nonetheless, a major challenge for EC research lies in distinguishing EC from related cognitive constructs that also are linked to achievement outcomes. Developmental cascade models suggest that children's information processing speed is a driving mechanism in cognitive development that supports gains in working memory, inhibitory control and associated cognitive abilities. Accordingly, individual differences in early executive task performance and their relation to mathematics may reflect, at least in part, underlying variation in children's processing speed. The aims of this study were to: (1) examine the degree of overlap between EC and processing speed at different preschool age points; and (2) determine whether EC uniquely predicts children's mathematics achievement after accounting for individual differences in processing speed. As part of a longitudinal, cohort-sequential study, 388 children (50% boys; 44% from low income households) completed the same battery of EC tasks at ages 3, 3.75, 4.5, and 5.25 years. Several of the tasks incorporated baseline speeded naming conditions with minimal EC demands. Multidimensional latent models were used to isolate the variance in executive task performance that did not overlap with baseline processing speed, covarying for child language proficiency. Models for separate age points showed that, while EC did not form a coherent latent factor independent of processing speed at age 3 years, it did emerge as a distinct factor by age 5.25. Although EC at age 3 showed no distinct relation with mathematics achievement independent of processing speed, EC at ages 3.75, 4.5, and 5.25 showed independent, prospective links with mathematics achievement. Findings suggest that EC and processing speed are tightly intertwined in early childhood. As EC becomes progressively decoupled from processing speed with age, it begins to take on unique, discriminative importance for children's mathematics achievement. PMID:24596563

Examining the Mathematical Modeling Processes of Primary School 4th-Grade Students: Shopping Problem

ERIC Educational Resources Information Center

Ulu, Mustafa

2017-01-01

The purpose of this study is to identify primary school students' thinking processes within the mathematical modeling process and the challenges they encounter, if any. This is a basic qualitative research study conducted in a primary school in the city of Kütahya in the academic year of 2015-2016. The study group of the research was composed of…

(Fish) Food for Thought: Authority Shifts in the Interaction between Mathematics and Reality

ERIC Educational Resources Information Center

Peled, Irit

2010-01-01

This theoretical paper explores the decision-making process involved in modelling and mathematizing situations during problem solving. Specifically, it focuses on the authority behind these choices (i.e., what or who determines the chosen mathematical models). We show that different types of situations involve different sources of authority,…

Neutral model analysis of landscape patterns from mathematical morphology

Treesearch

Kurt H. Riitters; Peter Vogt; Pierre Soille; Jacek Kozak; Christine Estreguil

2007-01-01

Mathematical morphology encompasses methods for characterizing land-cover patterns in ecological research and biodiversity assessments. This paper reports a neutral model analysis of patterns in the absence of a structuring ecological process, to help set standards for comparing and interpreting patterns identified by mathematical morphology on real land-cover maps. We...

A consistent modelling methodology for secondary settling tanks in wastewater treatment.

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

Connecting Biology and Mathematics: First Prepare the Teachers

PubMed Central

2010-01-01

Developing the connection between biology and mathematics is one of the most important ways to shift the paradigms of both established science disciplines. However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models. I propose a model of pedagogical mathematical biological content knowledge as a feasible starting point for connecting biology and mathematics in schools and universities. The process of connecting these disciplines should start as early as possible in the educational process, in order to produce prepared minds that will be able to combine both disciplines at graduate and postgraduate levels of study. Because teachers are a crucial factor in introducing innovations in education, the first step toward such a goal should be the education of prospective and practicing elementary and secondary school teachers. PMID:20810951

Computer-Based Mathematics Instructions for Engineering Students

NASA Technical Reports Server (NTRS)

Khan, Mustaq A.; Wall, Curtiss E.

1996-01-01

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

Introduction to a special section on ecohydrology of semiarid environments: Confronting mathematical models with ecosystem complexity

NASA Astrophysics Data System (ADS)

Svoray, Tal; Assouline, Shmuel; Katul, Gabriel

2015-11-01

Current literature provides large number of publications about ecohydrological processes and their effect on the biota in drylands. Given the limited laboratory and field experiments in such systems, many of these publications are based on mathematical models of varying complexity. The underlying implicit assumption is that the data set used to evaluate these models covers the parameter space of conditions that characterize drylands and that the models represent the actual processes with acceptable certainty. However, a question raised is to what extent these mathematical models are valid when confronted with observed ecosystem complexity? This Introduction reviews the 16 papers that comprise the Special Section on Eco-hydrology of Semiarid Environments: Confronting Mathematical Models with Ecosystem Complexity. The subjects studied in these papers include rainfall regime, infiltration and preferential flow, evaporation and evapotranspiration, annual net primary production, dispersal and invasion, and vegetation greening. The findings in the papers published in this Special Section show that innovative mathematical modeling approaches can represent actual field measurements. Hence, there are strong grounds for suggesting that mathematical models can contribute to greater understanding of ecosystem complexity through characterization of space-time dynamics of biomass and water storage as well as their multiscale interactions. However, the generality of the models and their low-dimensional representation of many processes may also be a "curse" that results in failures when particulars of an ecosystem are required. It is envisaged that the search for a unifying "general" model, while seductive, may remain elusive in the foreseeable future. It is for this reason that improving the merger between experiments and models of various degrees of complexity continues to shape the future research agenda.

The Material Supply Adjustment Process in RAMF-SM, Step 2

DTIC Science & Technology

2016-06-01

contain. The Risk Assessment and Mitigation Framework for Strategic Materials (RAMF-SM) is a suite of mathematical models and databases that has been...Risk Assessment and Mitigation Framework for Strategic Materials (RAMF-SM) is a suite of mathematical models and databases used to support the...and computes material shortfalls.1 Several mathematical models and dozens of databases, encompassing thousands of data items, support the

Application of Mathematical and Three-Dimensional Computer Modeling Tools in the Planning of Processes of Fuel and Energy Complexes

NASA Astrophysics Data System (ADS)

Aksenova, Olesya; Nikolaeva, Evgenia; Cehlár, Michal

2017-11-01

This work aims to investigate the effectiveness of mathematical and three-dimensional computer modeling tools in the planning of processes of fuel and energy complexes at the planning and design phase of a thermal power plant (TPP). A solution for purification of gas emissions at the design development phase of waste treatment systems is proposed employing mathematical and three-dimensional computer modeling - using the E-nets apparatus and the development of a 3D model of the future gas emission purification system. Which allows to visualize the designed result, to select and scientifically prove economically feasible technology, as well as to ensure the high environmental and social effect of the developed waste treatment system. The authors present results of a treatment of planned technological processes and the system for purifying gas emissions in terms of E-nets. using mathematical modeling in the Simulink application. What allowed to create a model of a device from the library of standard blocks and to perform calculations. A three-dimensional model of a system for purifying gas emissions has been constructed. It allows to visualize technological processes and compare them with the theoretical calculations at the design phase of a TPP and. if necessary, make adjustments.

Modelling Mathematics Problem Solving Item Responses Using a Multidimensional IRT Model

ERIC Educational Resources Information Center

Wu, Margaret; Adams, Raymond

2006-01-01

This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring…

On the Modeling of Vacuum Arc Remelting Process in Titanium Alloys

NASA Astrophysics Data System (ADS)

Patel, Ashish; Fiore, Daniel

2016-07-01

Mathematical modeling is routinely used in the process development and production of advanced aerospace alloys to gain greater insight into the effect of process parameters on final properties. This article describes the application of a 2-D mathematical VAR model presented at previous LMPC meetings. The impact of process parameters on melt pool geometry, solidification behavior, fluid-flow and chemistry in a Ti-6Al-4V ingot is discussed. Model predictions are validated against published data from a industrial size ingot, and results of a parametric study on particle dissolution are also discussed.

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

Neves, R.; Neves, M. L.; Teodoro, V.

2011-12-01

Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

Friction-Stir Welding and Mathematical Modeling

NASA Technical Reports Server (NTRS)

Rostant, Victor D.

1999-01-01

The friction-stir welding process is a remarkable way for making butt and lap joints in aluminum alloys. This process operates by passing a rotating tool between two closely butted plates. Through this process it generates a lot of heat and heated material is stirred from both sides of the plates in which the outcome will one high quality weld. My research has been done to study the FSW through mathematical modeling, and using modeling to better understand what take place during the friction-stir weld.

The study of thermal processes in control systems of heat consumption of buildings

NASA Astrophysics Data System (ADS)

Tsynaeva, E.; A, Tsynaeva

2017-11-01

The article discusses the main thermal processes in the automated control systems for heat consumption (ACSHC) of buildings, schematic diagrams of these systems, mathematical models used for description of thermal processes in ACSHC. Conducted verification represented by mathematical models. It was found that the efficiency of the operation of ACSHC depend from the external and internal factors. Numerical study of dynamic modes of operation of ACSHC.

Physical-mathematical model of condensation process of the sub-micron dust capture in sprayer scrubber

NASA Astrophysics Data System (ADS)

Shilyaev, M. I.; Khromova, E. M.; Grigoriev, A. V.; Tumashova, A. V.

2011-09-01

A physical-mathematical model of the heat and mass exchange process and condensation capture of sub-micron dust particles on the droplets of dispersed liquid in a sprayer scrubber is proposed and analysed. A satisfactory agreement of computed results and experimental data on soot capturing from the cracking gases is obtained.

An Onto-Semiotic Analysis of Combinatorial Problems and the Solving Processes by University Students

ERIC Educational Resources Information Center

Godino, Juan D.; Batanero, Carmen; Roa, Rafael

2005-01-01

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of…

Modeling Water Filtration

ERIC Educational Resources Information Center

Parks, Melissa

2014-01-01

Model-eliciting activities (MEAs) are not new to those in engineering or mathematics, but they were new to Melissa Parks. Model-eliciting activities are simulated real-world problems that integrate engineering, mathematical, and scientific thinking as students find solutions for specific scenarios. During this process, students generate solutions…

Can a Mathematical Model Predict an Individual’s Trait-like Response to Both Total and Partial Sleep Loss?

DTIC Science & Technology

2015-01-01

Can a mathematical model predict an individual’s trait-like response to both total and partial sleep loss? SR IDHAR RAMAKR I SHNAN 1 , WE I LU 1 , SR...biomathematical model, psychomotor vigilance task, sleep -loss phenotype, trait preservation, two-process model Correspondence Jaques Reifman, PhD...trait-like response to sleep loss. However, it is not known whether this trait-like response can be captured by a mathemat- ical model from only one

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Mathematical models of cell motility.

PubMed

Flaherty, Brendan; McGarry, J P; McHugh, P E

2007-01-01

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

Inssues for Consideration by Mathematics Educators: Selected Papers.

ERIC Educational Resources Information Center

Denmark, Tom, Ed.

This set of papers, selected from presentations at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics, are of primary interest to mathematics educators. In the first paper, Romberg describes a model for diagnosing mathematical learning difficulties which extends the diagnostic process beyond…

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

NASA Astrophysics Data System (ADS)

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 of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

Process development of a New Haemophilus influenzae type b conjugate vaccine and the use of mathematical modeling to identify process optimization possibilities.

PubMed

Hamidi, Ahd; Kreeftenberg, Hans; V D Pol, Leo; Ghimire, Saroj; V D Wielen, Luuk A M; Ottens, Marcel

2016-05-01

Vaccination is one of the most successful public health interventions being a cost-effective tool in preventing deaths among young children. The earliest vaccines were developed following empirical methods, creating vaccines by trial and error. New process development tools, for example mathematical modeling, as well as new regulatory initiatives requiring better understanding of both the product and the process are being applied to well-characterized biopharmaceuticals (for example recombinant proteins). The vaccine industry is still running behind in comparison to these industries. A production process for a new Haemophilus influenzae type b (Hib) conjugate vaccine, including related quality control (QC) tests, was developed and transferred to a number of emerging vaccine manufacturers. This contributed to a sustainable global supply of affordable Hib conjugate vaccines, as illustrated by the market launch of the first Hib vaccine based on this technology in 2007 and concomitant price reduction of Hib vaccines. This paper describes the development approach followed for this Hib conjugate vaccine as well as the mathematical modeling tool applied recently in order to indicate options for further improvements of the initial Hib process. The strategy followed during the process development of this Hib conjugate vaccine was a targeted and integrated approach based on prior knowledge and experience with similar products using multi-disciplinary expertise. Mathematical modeling was used to develop a predictive model for the initial Hib process (the 'baseline' model) as well as an 'optimized' model, by proposing a number of process changes which could lead to further reduction in price. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:568-580, 2016. © 2016 American Institute of Chemical Engineers.

Identifiability Of Systems With Modeling Errors

NASA Technical Reports Server (NTRS)

Hadaegh, Yadolah " fred" ; Bekey, George A.

1988-01-01

Advances in theory of modeling errors reported. Recent paper on errors in mathematical models of deterministic linear or weakly nonlinear systems. Extends theoretical work described in NPO-16661 and NPO-16785. Presents concrete way of accounting for difference in structure between mathematical model and physical process or system that it represents.

[Mathematical calculation of strength of the vertebral column in surgical treatment of unstable fractures of the spine].

PubMed

Orlov, S V; Kanykin, A Iu; Moskalev, V P; Shchedrenok, V V; Sedov, R L

2009-01-01

A mathematical model of a three-vertebra complex was developed in order to make an exact calculation of loss of supporting ability of the vertebral column in trauma. Mathematical description of the dynamic processes was based on Lagrange differential equation of the second order. The degree of compression and instability of the three-vertebra complex, established using mathematical modeling, determines the decision on the surgical treatment and might be considered as a prognostic criterion of the course of the compression trauma of the spine. The method of mathematical modeling of supporting ability of the vertebral column was used in 72 patients.

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…

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.

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.

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.

Mathematics for understanding disease.

PubMed

Bies, R R; Gastonguay, M R; Schwartz, S L

2008-06-01

The application of mathematical models to reflect the organization and activity of biological systems can be viewed as a continuum of purpose. The far left of the continuum is solely the prediction of biological parameter values, wherein an understanding of the underlying biological processes is irrelevant to the purpose. At the far right of the continuum are mathematical models, the purposes of which are a precise understanding of those biological processes. No models in present use fall at either end of the continuum. Without question, however, the emphasis in regards to purpose has been on prediction, e.g., clinical trial simulation and empirical disease progression modeling. Clearly the model that ultimately incorporates a universal understanding of biological organization will also precisely predict biological events, giving the continuum the logical form of a tautology. Currently that goal lies at an immeasurable distance. Nonetheless, the motive here is to urge movement in the direction of that goal. The distance traveled toward understanding naturally depends upon the nature of the scientific question posed with respect to comprehending and/or predicting a particular disease process. A move toward mathematical models implies a move away from static empirical modeling and toward models that focus on systems biology, wherein modeling entails the systematic study of the complex pattern of organization inherent in biological systems.

A mathematical model for ethanol fermentation from oil palm trunk sap using Saccharomyces cerevisiae

NASA Astrophysics Data System (ADS)

Sultana, S.; Jamil, Norazaliza Mohd; Saleh, E. A. M.; Yousuf, A.; Faizal, Che Ku M.

2017-09-01

This paper presents a mathematical model and solution strategy of ethanol fermentation for oil palm trunk (OPT) sap by considering the effect of substrate limitation, substrate inhibition product inhibition and cell death. To investigate the effect of cell death rate on the fermentation process we extended and improved the current mathematical model. The kinetic parameters of the model were determined by nonlinear regression using maximum likelihood function. The temporal profiles of sugar, cell and ethanol concentrations were modelled by a set of ordinary differential equations, which were solved numerically by the 4th order Runge-Kutta method. The model was validated by the experimental data and the agreement between the model and experimental results demonstrates that the model is reasonable for prediction of the dynamic behaviour of the fermentation process.

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.

A hybrid modeling system designed to support decision making in the optimization of extrusion of inhomogeneous materials

NASA Astrophysics Data System (ADS)

Kryuchkov, D. I.; Zalazinsky, A. G.

2017-12-01

Mathematical models and a hybrid modeling system are developed for the implementation of the experimental-calculation method for the engineering analysis and optimization of the plastic deformation of inhomogeneous materials with the purpose of improving metal-forming processes and machines. The created software solution integrates Abaqus/CAE, a subroutine for mathematical data processing, with the use of Python libraries and the knowledge base. Practical application of the software solution is exemplified by modeling the process of extrusion of a bimetallic billet. The results of the engineering analysis and optimization of the extrusion process are shown, the material damage being monitored.

Use of Angle Model to Understand Addition and Subtraction of Fractions

ERIC Educational Resources Information Center

Mukwambo, Muzwangowenyu; Ngcoza, Kenneth; Ramasike, Lineo Florence

2018-01-01

Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and…

An Analysis of the Reasoning Skills of Pre-Service Teachers in the Context of Mathematical Thinking

ERIC Educational Resources Information Center

Yavuz Mumcu, Hayal; Aktürk, Tolga

2017-01-01

The aim of this study is to address and analyse pre-service teachers' mathematical reasoning skills in relation to mathematical thinking processes. For these purposes, pre-service teachers' mathematical reasoning skills namely generalising/abstraction/modelling, ratiocination, development and creative thinking skills and the relationships among…

Fracking: Drilling into Math and Social Justice

ERIC Educational Resources Information Center

Hendrickson, Katie A.

2015-01-01

Mathematical modeling, a focus of the Common Core State Standards for School Mathematics (CCSSI 2010) and one of the Standards for Mathematical Practice, is generally considered to be the process of exploring a real-world situation and making sense of it using mathematics (Lesh and Zawojewski 2007). Teachers need to create opportunities for…

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

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

Choice of mathematical models for technological process of glass rod drawing

NASA Astrophysics Data System (ADS)

Alekseeva, L. B.

2017-10-01

The technological process of drawing glass rods (light guides) is considered. Automated control of the drawing process is reduced to the process of making decisions to ensure a given quality. The drawing process is considered as a control object, including the drawing device (control device) and the optical fiber forming zone (control object). To study the processes occurring in the formation zone, mathematical models are proposed, based on the continuum mechanics basics. To assess the influence of disturbances, a transfer function is obtained from the basis of the wave equation. Obtaining the regression equation also adequately describes the drawing process.

Integrating Mathematical Modeling for Undergraduate Pre-Service Science Education Learning and Instruction in Middle School Classrooms

ERIC Educational Resources Information Center

Carrejo, David; Robertson, William H.

2011-01-01

Computer-based mathematical modeling in physics is a process of constructing models of concepts and the relationships between them in the scientific characteristics of work. In this manner, computer-based modeling integrates the interactions of natural phenomenon through the use of models, which provide structure for theories and a base for…

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

Application of a Model for Simulating the Vacuum Arc Remelting Process in Titanium Alloys

NASA Astrophysics Data System (ADS)

Patel, Ashish; Tripp, David W.; Fiore, Daniel

Mathematical modeling is routinely used in the process development and production of advanced aerospace alloys to gain greater insight into system dynamics and to predict the effect of process modifications or upsets on final properties. This article describes the application of a 2-D mathematical VAR model presented in previous LMPC meetings. The impact of process parameters on melt pool geometry, solidification behavior, fluid-flow and chemistry in Ti-6Al-4V ingots will be discussed. Model predictions were first validated against the measured characteristics of industrially produced ingots, and process inputs and model formulation were adjusted to match macro-etched pool shapes. The results are compared to published data in the literature. Finally, the model is used to examine ingot chemistry during successive VAR melts.

Developing teachers' models for assessing students' competence in mathematical modelling through lesson study

NASA Astrophysics Data System (ADS)

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent

2017-08-01

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers' difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers' knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers' knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.

The Characterization of Cognitive Processes Involved in Chemical Kinetics Using a Blended Processing Framework

ERIC Educational Resources Information Center

Bain, Kinsey; Rodriguez, Jon-Marc G.; Moon, Alena; Towns, Marcy H.

2018-01-01

Chemical kinetics is a highly quantitative content area that involves the use of multiple mathematical representations to model processes and is a context that is under-investigated in the literature. This qualitative study explored undergraduate student integration of chemistry and mathematics during problem solving in the context of chemical…

Mathematical models in simulation process in rehabilitation of persons with disabilities

NASA Astrophysics Data System (ADS)

Gorie, Nina; Dolga, Valer; Mondoc, Alina

2012-11-01

The problems of people with disability are varied. A disability may be physical, cognitive, mental, sensory, emotional, developmental or some combination of these. The major disabilities which can appear in people's lives are: the blindness, the deafness, the limb-girdle muscular dystrophy, the orthopedic impairment, the visual impairment. A disability is an umbrella term, covering impairments, activity limitations and participation restrictions. A disability may occur during a person's lifetime or may be present from birth. The authors conclude that some of these disabilities like physical, cognitive, mental, sensory, emotional, developmental can be rehabilitated. Starting from this state of affairs the authors present briefly the possibility of using certain mechatronic systems for rehabilitation of persons with different disabilities. The authors focus their presentation on alternative calling the Stewart platform in order to achieve the proposed goal. The authors present a mathematical model of systems theory approach under the parallel system and described its contents can. The authors analyze in a meaningful mathematical model describing the procedure of rehabilitation process. From the affected function biomechanics and taking into account medical recommendations the authors illustrate the mathematical models of rehabilitation work. The authors assemble a whole mathematical model of parallel structure and the rehabilitation process and making simulation and highlighting the results estimated. The authors present in the end work the results envisaged in the end analysis work, conclusions and steps for future work program..

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

PubMed

Gilbert, Scott F

2018-01-31

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

Mathematical model of the loan portfolio dynamics in the form of Markov chain considering the process of new customers attraction

NASA Astrophysics Data System (ADS)

Bozhalkina, Yana

2017-12-01

Mathematical model of the loan portfolio structure change in the form of Markov chain is explored. This model considers in one scheme both the process of customers attraction, their selection based on the credit score, and loans repayment. The model describes the structure and volume of the loan portfolio dynamics, which allows to make medium-term forecasts of profitability and risk. Within the model corrective actions of bank management in order to increase lending volumes or to reduce the risk are formalized.

Towards a Dialogical Pedagogy: Some Characteristics of a Community of Mathematical Inquiry

ERIC Educational Resources Information Center

Kennedy, Nadia Stoyanova

2009-01-01

This paper discusses a teaching model called community of mathematical inquiry (CMI), characterized by dialogical and inquiry-driven communication and a dynamic structure of intertwined cognitive processes including distributed thinking, mathematical argumentation, integrated reasoning, conceptual transformation, internalization of critical…

Nonlinear and Digital Man-machine Control Systems Modeling

NASA Technical Reports Server (NTRS)

Mekel, R.

1972-01-01

An adaptive modeling technique is examined by which controllers can be synthesized to provide corrective dynamics to a human operator's mathematical model in closed loop control systems. The technique utilizes a class of Liapunov functions formulated for this purpose, Liapunov's stability criterion and a model-reference system configuration. The Liapunov function is formulated to posses variable characteristics to take into consideration the identification dynamics. The time derivative of the Liapunov function generate the identification and control laws for the mathematical model system. These laws permit the realization of a controller which updates the human operator's mathematical model parameters so that model and human operator produce the same response when subjected to the same stimulus. A very useful feature is the development of a digital computer program which is easily implemented and modified concurrent with experimentation. The program permits the modeling process to interact with the experimentation process in a mutually beneficial way.

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

PubMed

Ganusov, Vitaly V

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Preliminary Evaluation Report on the Los Angeles City Schools SB 28 Demonstration Program in Mathematics. CSE Working Paper No. 1.

ERIC Educational Resources Information Center

Gordon, C. Wayne

The objectives of the Los Angeles Model Mathematics Project (LAMMP) are stated by the administration as improvement of mathematical skills and understanding of mathematical concepts; improvement of the pupils' self-image; identification of specific assets and limitations relating to the learning process; development and use of special…

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

PubMed Central

Ganusov, Vitaly V.

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

Mathematical modelling of tissue formation in chondrocyte filter cultures.

PubMed

Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J

2011-12-17

In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

Mathematical Abstraction: Constructing Concept of Parallel Coordinates

NASA Astrophysics Data System (ADS)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2017-09-01

Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

Mathematical modeling and hydrodynamics of Electrochemical deburring process

NASA Astrophysics Data System (ADS)

Prabhu, Satisha; Abhishek Kumar, K., Dr

2018-04-01

The electrochemical deburring (ECD) is a variation of electrochemical machining is considered as one of the efficient methods for deburring of intersecting features and internal parts. Since manual deburring costs are comparatively high one can potentially use this method in both batch production and flow production. The other advantage of this process is that time of deburring as is on the order of seconds as compared to other methods. In this paper, the mathematical modeling of Electrochemical deburring is analysed from its deburring time and base metal removal point of view. Simultaneously material removal rate is affected by electrolyte temperature and bubble formation. The mathematical model and hydrodynamics of the process throw limelight upon optimum velocity calculations which can be theoretically determined. The analysis can be the powerful tool for prediction of the above-mentioned parameters by experimentation.

Mathematical modeling in biological populations through branching processes. Application to salmonid populations.

PubMed

Molina, Manuel; Mota, Manuel; Ramos, Alfonso

2015-01-01

This work deals with mathematical modeling through branching processes. We consider sexually reproducing animal populations where, in each generation, the number of progenitor couples is determined in a non-predictable environment. By using a class of two-sex branching processes, we describe their demographic dynamics and provide several probabilistic and inferential contributions. They include results about the extinction of the population and the estimation of the offspring distribution and its main moments. We also present an application to salmonid populations.

Real-time control data wrangling for development of mathematical control models of technological processes

NASA Astrophysics Data System (ADS)

Vasilyeva, N. V.; Koteleva, N. I.; Fedorova, E. R.

2018-05-01

The relevance of the research is due to the need to stabilize the composition of the melting products of copper-nickel sulfide raw materials in the Vanyukov furnace. The goal of this research is to identify the most suitable methods for the aggregation of the real time data for the development of a mathematical model for control of the technological process of melting copper-nickel sulfide raw materials in the Vanyukov furnace. Statistical methods of analyzing the historical data of the real technological object and the correlation analysis of process parameters are described. Factors that exert the greatest influence on the main output parameter (copper content in matte) and ensure the physical-chemical transformations are revealed. An approach to the processing of the real time data for the development of a mathematical model for control of the melting process is proposed. The stages of processing the real time information are considered. The adopted methodology for the aggregation of data suitable for the development of a control model for the technological process of melting copper-nickel sulfide raw materials in the Vanyukov furnace allows us to interpret the obtained results for their further practical application.

Mathematical Modeling of Thermofrictional Milling Process Using ANSYS WB Software

NASA Astrophysics Data System (ADS)

Sherov, K. T.; Sikhimbayev, M. R.; Sherov, A. K.; Donenbayev, B. S.; Rakishev, A. K.; Mazdubai, A. B.; Musayev, M. M.; Abeuova, A. M.

2017-06-01

This article presents ANSYS WB-based mathematical modelling of the thermofrictional milling process, which allowed studying the dynamics of thermal and physical processes occurring during the processing. The technique used also allows determination of the optimal cutting conditions of thermofrictional milling for processing various materials, in particular steel 40CN2MA, 30CGSA, 45, 3sp. In our study, from among a number of existing models of cutting fracture, we chose the criterion first proposed by prof. V. L. Kolmogorov. In order to increase the calculations performance, a mathematical model was proposed, that used only two objects: a parallelepiped-shaped workpiece and a cutting insert in the form of a pentagonal prism. In addition, the work takes into account the friction coefficient between a cutting insert and a workpiece taken equal to 0.4 mm. To determine the temperature in the subcontact layer of the workpiece, we introduced the coordinates of nine characteristic points with the same interval in the local coordinate system. As a result, the temperature values were obtained for different materials at the studied points during the cutter speed change. The research results showed the possibility of controlling thermal processes during processing by choosing the optimum cutting modes.

Studies on mathematical modeling of the leaching process in order to efficiently recover lead from the sulfate/oxide lead paste.

PubMed

Buzatu, Traian; Ghica, Gabriel Valeriu; Petrescu, Ionuţ Mircea; Iacob, Gheorghe; Buzatu, Mihai; Niculescu, Florentina

2017-02-01

Increasing global lead consumption has been mainly supported by the acid battery manufacturing industry. As the lead demand will continue to grow, to provide the necessary lead will require an efficient approach to recycling lead acid batteries. In this paper was performed a mathematical modeling of the process parameters for lead recovery from spent lead-acid batteries. The results of the mathematical modeling compare well with the experimental data. The experimental method applied consists in the solubilisation of the sulfate/oxide paste with sodium hydroxide solutions followed by electrolytic processing for lead recovery. The parameters taken into considerations were NaOH molarity (4M, 6M and 8M), solid/liquid ratio - S/L (1/10, 1/30 and 1/50) and temperature (40°C, 60°C and 80°C). The optimal conditions resulted by mathematical modeling of the electrolytic process of lead deposition from alkaline solutions have been established by using a second-order orthogonal program, in order to obtain a maximum efficiency of current without exceeding an imposed energy specific consumption. The optimum value for the leaching recovery efficiency, obtained through mathematical modeling, was 89.647%, with an error of δ y =3.623 which leads to a maximum recovery efficiency of 86.024%. The optimum values for each variable that ensure the lead extraction efficiency equal to 89.647% are the following: 3M - NaOH, 1/35 - S/L, 70°C - temperature. Copyright © 2016 Elsevier Ltd. All rights reserved.

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…

Developing the Mathematics Learning Management Model for Improving Creative Thinking in Thailand

ERIC Educational Resources Information Center

Sriwongchai, Arunee; Jantharajit, Nirat; Chookhampaeng, Sumalee

2015-01-01

The study purposes were: 1) To study current states and problems of relevant secondary students in developing mathematics learning management model for improving creative thinking, 2) To evaluate the effectiveness of model about: a) efficiency of learning process, b) comparisons of pretest and posttest on creative thinking and achievement of…

Teachers' Use of Computational Tools to Construct and Explore Dynamic Mathematical Models

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron

2011-01-01

To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…

Modeling of processing technologies in food industry

NASA Astrophysics Data System (ADS)

Korotkov, V. G.; Sagitov, R. F.; Popov, V. P.; Bachirov, V. D.; Akhmadieva, Z. R.; TSirkaeva, E. A.

2018-03-01

Currently, the society is facing an urgent need to solve the problems of nutrition (products with increased nutrition value) and to develop energy-saving technologies for food products. A mathematical modeling of heat and mass transfer of polymer materials in the extruder is rather successful these days. Mathematical description of movement and heat exchange during extrusion of gluten-protein-starch-containing material similar to pasta dough in its structure, were taken as a framework for the mathematical model presented in this paper.

[Rational bases for cooperation between epidemiologists and mathematicians].

PubMed

Favorova, L A; Shatrov, I I

1977-10-01

The authors consider rational foundations underlying creatin of realistic models. The principal condition for the successful mathematical modelling is obtaining of the most full value primary materials on the course of the epidemic process. For this purpose the authors suggest definite principles of the methodical approach to the mathematical modelling. Possibilities of the use of mathematical methods for various groups of infections are consideder. Particular attention is paid to the works on the study of the infection risk in "small" collective bodies.

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plechac, Petr

2016-03-01

The overall objective of this project was to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics and developing rigorous mathematical techniques and computational algorithms to study such models. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

PubMed

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

The system-resonance approach in modeling genetic structures.

PubMed

Petoukhov, Sergey V

2016-01-01

The founder of the theory of resonance in structural chemistry Linus Pauling established the importance of resonance patterns in organization of living systems. Any living organism is a great chorus of coordinated oscillatory processes. From the formal point of view, biological organism is an oscillatory system with a great number of degrees of freedom. Such systems are studied in the theory of oscillations using matrix mathematics of their resonance characteristics. This study is devoted to a new approach for modeling genetically inherited structures and processes in living organisms using mathematical tools of the theory of resonances. This approach reveals hidden relationships in a number of genetic phenomena and gives rise to a new class of bio-mathematical models, which contribute to a convergence of biology with physics and informatics. In addition some relationships of molecular-genetic ensembles with mathematics of noise-immunity coding of information in modern communications technology are shown. Perspectives of applications of the phenomena of vibrational mechanics for modeling in biology are discussed. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Obtaining mathematical models for assessing efficiency of dust collectors using integrated system of analysis and data management STATISTICA Design of Experiments

NASA Astrophysics Data System (ADS)

Azarov, A. V.; Zhukova, N. S.; Kozlovtseva, E. Yu; Dobrinsky, D. R.

2018-05-01

The article considers obtaining mathematical models to assess the efficiency of the dust collectors using an integrated system of analysis and data management STATISTICA Design of Experiments. The procedure for obtaining mathematical models and data processing is considered by the example of laboratory studies on a mounted installation containing a dust collector in counter-swirling flows (CSF) using gypsum dust of various fractions. Planning of experimental studies has been carried out in order to reduce the number of experiments and reduce the cost of experimental research. A second-order non-position plan (Box-Bencken plan) was used, which reduced the number of trials from 81 to 27. The order of statistical data research of Box-Benken plan using standard tools of integrated system for analysis and data management STATISTICA Design of Experiments is considered. Results of statistical data processing with significance estimation of coefficients and adequacy of mathematical models are presented.

The Evolvement of Numeracy and Mathematical Literacy Curricula and the Construction of Hierarchies of Numerate or Mathematically Literate Subjects

ERIC Educational Resources Information Center

Jablonka, Eva

2015-01-01

This contribution briefly sketches the evolvement of numeracy or mathematical literacy as models for mathematics curricula, which will be described as driven by a weakening of the insulation between discourses, that is, as a process of "declassification". The question then arises as to whether and how coherence of new forms of initially…

Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

NASA Astrophysics Data System (ADS)

Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

2012-11-01

Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

Mathematical modeling of fluid flow in aluminum ladles for degasification with impeller - injector

NASA Astrophysics Data System (ADS)

Ramos-Gómez, E.; González-Rivera, C.; Ramírez-Argáez, M. A.

2012-09-01

In this work a fundamental Eulerian mathematical model was developed to simulate fluid flow in a water physical model of an aluminum ladle equipped with impeller for degassing treatment. The effect of critical process parameters such as rotor speed, gas flow rate on the fluid flow and vortex formation was analyzed with this model. Commercial CFD code PHOENICS 3.4 was used to solve all conservation equations governing the process for this twophase fluid flow system. The mathematical model was successfully validated against experimentally measured liquid velocity and turbulent profiles in a physical model. From the results it was concluded that the angular speed of the impeller is the most important parameter promoting better stirred baths. Pumping effect of the impeller is increased as impeller rotation speed increases. Gas flow rate is detrimental on bath stirring and diminishes pumping effect of impeller.

On MTE-Model of Mathematics Teaching: Studying the Problems Related to a Plane Division Using the MTE-Model

ERIC Educational Resources Information Center

Bodroza-Pantic, O.; Matic-Kekic, Snezana; Jakovljev, Bogdanka; Markovic, Doko

2008-01-01

In this paper the didactically-methodological procedure named the MTE-model of mathematics teaching (Motivation test-Teaching-Examination test) is suggested and recommended when the teacher has subsequent lessons. This model is presented in detail through the processing of a nonstandard theme--the theme of decomposition of planes. Its efficiency…

Terrestrial implications of mathematical modeling developed for space biomedical research

NASA Technical Reports Server (NTRS)

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

1988-01-01

This paper summarizes several related research projects supported by NASA which seek to apply computer models to space medicine and physiology. These efforts span a wide range of activities, including mathematical models used for computer simulations of physiological control systems; power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and computer-aided diagnosis programs.

Mathematical Modelling of Bacterial Populations in Bio-remediation Processes

NASA Astrophysics Data System (ADS)

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

2011-09-01

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

Analysis of mathematical literacy ability based on goal orientation in model eliciting activities learning with murder strategy

NASA Astrophysics Data System (ADS)

Wijayanti, R.; Waluya, S. B.; Masrukan

2018-03-01

The purpose of this research are (1) to analyze the learning quality of MEAs with MURDER strategy, (2) to analyze students’ mathematical literacy ability based on goal orientation in MEAs learning with MURDER strategy. This research is a mixed method research of concurrent embedded type where qualitative method as the primary method. The data were obtained using the methods of scale, observation, test and interviews. The results showed that (1) MEAs Learning with MURDER strategy on students' mathematical literacy ability is qualified, (2) Students who have mastery goal characteristics are able to master the seven components of mathematical literacy process although there are still two components that the solution is less than the maximum. Students who have performance goal characteristics have not mastered the components of mathematical literacy process with the maximum, they are only able to master the ability of using mathematics tool and the other components of mathematical literacy process is quite good.

Guided Inquiry as a Model for Curricular Resources in Mathematics

ERIC Educational Resources Information Center

Debritz, Christine; Horne, Rhonda

2013-01-01

Research and the Australian Curriculum both indicate the importance of teaching students to apply their mathematical knowledge to real world problems. When developing curriculum resources for Queensland state school teachers from Prep to Year 9, the Department's mathematics team identified the significance of embedding the inquiry process in these…

AMERICAN-SOVIET SYMPOSIUM ON USE OF MATHEMATICAL MODELS TO OPTIMIZE WATER QUALITY MANAGEMENT HELD AT KHARKOV AND ROSTOV-ON-DON, USSR ON DECEMBER 9-16, 1975

EPA Science Inventory

The American-Soviet Symposium on Use of Mathematical Models to Optimize Water Quality Management examines methodological questions related to simulation and optimization modeling of processes that determine water quality of river basins. Discussants describe the general state of ...

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues.

PubMed

Kim, Munju; Gillies, Robert J; Rejniak, Katarzyna A

2013-11-18

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

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

A mathematical study of a random process proposed as an atmospheric turbulence model

NASA Technical Reports Server (NTRS)

Sidwell, K.

1977-01-01

A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

Investigation of the Bitumen Modification Process Regime Parameters Influence on Polymer-Bitumen Bonding Qualitative Indicators

NASA Astrophysics Data System (ADS)

Belyaev, P. S.; Mishchenko, S. V.; Belyaev, V. P.; Belousov, O. A.; Frolov, V. A.

2018-04-01

The objects of this study are petroleum road bitumen and polymeric bituminous binder for road surfaces obtained by polymer materials. The subject of the study is monitoring the polymer-bitumen binder quality changes as a result of varying the bitumen modification process. The purpose of the work is to identify the patterns of the modification process and build a mathematical model that provides the ability to calculate and select technological equipment. It is shown that the polymer-bitumen binder production with specified quality parameters can be ensured in apparatuses with agitators in turbulent mode without the colloidal mills use. Bitumen mix and modifying additives limiting indicators which can be used as restrictions in the form of mathematical model inequalities are defined. A mathematical model for the polymer-bitumen binder preparation has been developed and its adequacy has been confirmed.

Mathematical model of silicon smelting process basing on pelletized charge from technogenic raw materials

NASA Astrophysics Data System (ADS)

Nemchinova, N. V.; Tyutrin, A. A.; Salov, V. M.

2018-03-01

The silicon production process in the electric arc reduction furnaces (EAF) is studied using pelletized charge as an additive to the standard on the basis of the generated mathematical model. The results obtained due to the model will contribute to the analysis of the charge components behavior during melting with the achievement of optimum final parameters of the silicon production process. The authors proposed using technogenic waste as a raw material for the silicon production in a pelletized form using liquid glass and aluminum production dust from the electrostatic precipitators as a binder. The method of mathematical modeling with the help of the ‘Selector’ software package was used as a basis for the theoretical study. A model was simulated with the imitation of four furnace temperature zones and a crystalline silicon phase (25 °C). The main advantage of the created model is the ability to analyze the behavior of all burden materials (including pelletized charge) in the carbothermic process. The behavior analysis is based on the thermodynamic probability data of the burden materials interactions in the carbothermic process. The model accounts for 17 elements entering the furnace with raw materials, electrodes and air. The silicon melt, obtained by the modeling, contained 91.73 % wt. of the target product. The simulation results showed that in the use of the proposed combined charge, the recovery of silicon reached 69.248 %, which is in good agreement with practical data. The results of the crystalline silicon chemical composition modeling are compared with the real silicon samples of chemical analysis data, which showed the results of convergence. The efficiency of the mathematical modeling methods in the studying of the carbothermal silicon obtaining process with complex interphase transformations and the formation of numerous intermediate compounds using a pelletized charge as an additive to the traditional one is shown.

Automatic mathematical modeling for real time simulation system

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1988-01-01

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

Advances in multi-scale modeling of solidification and casting processes

NASA Astrophysics Data System (ADS)

Liu, Baicheng; Xu, Qingyan; Jing, Tao; Shen, Houfa; Han, Zhiqiang

2011-04-01

The development of the aviation, energy and automobile industries requires an advanced integrated product/process R&D systems which could optimize the product and the process design as well. Integrated computational materials engineering (ICME) is a promising approach to fulfill this requirement and make the product and process development efficient, economic, and environmentally friendly. Advances in multi-scale modeling of solidification and casting processes, including mathematical models as well as engineering applications are presented in the paper. Dendrite morphology of magnesium and aluminum alloy of solidification process by using phase field and cellular automaton methods, mathematical models of segregation of large steel ingot, and microstructure models of unidirectionally solidified turbine blade casting are studied and discussed. In addition, some engineering case studies, including microstructure simulation of aluminum casting for automobile industry, segregation of large steel ingot for energy industry, and microstructure simulation of unidirectionally solidified turbine blade castings for aviation industry are discussed.

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.

Correlated receptor transport processes buffer single-cell heterogeneity

PubMed Central

Kallenberger, Stefan M.; Unger, Anne L.; Legewie, Stefan; Lymperopoulos, Konstantinos; Eils, Roland

2017-01-01

Cells typically vary in their response to extracellular ligands. Receptor transport processes modulate ligand-receptor induced signal transduction and impact the variability in cellular responses. Here, we quantitatively characterized cellular variability in erythropoietin receptor (EpoR) trafficking at the single-cell level based on live-cell imaging and mathematical modeling. Using ensembles of single-cell mathematical models reduced parameter uncertainties and showed that rapid EpoR turnover, transport of internalized EpoR back to the plasma membrane, and degradation of Epo-EpoR complexes were essential for receptor trafficking. EpoR trafficking dynamics in adherent H838 lung cancer cells closely resembled the dynamics previously characterized by mathematical modeling in suspension cells, indicating that dynamic properties of the EpoR system are widely conserved. Receptor transport processes differed by one order of magnitude between individual cells. However, the concentration of activated Epo-EpoR complexes was less variable due to the correlated kinetics of opposing transport processes acting as a buffering system. PMID:28945754

Birth and Death Process Modeling Leads to the Poisson Distribution: A Journey Worth Taking

ERIC Educational Resources Information Center

Rash, Agnes M.; Winkel, Brian J.

2009-01-01

This paper describes details of development of the general birth and death process from which we can extract the Poisson process as a special case. This general process is appropriate for a number of courses and units in courses and can enrich the study of mathematics for students as it touches and uses a diverse set of mathematical topics, e.g.,…

A new process sensitivity index to identify important system processes under process model and parametric uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dai, Heng; Ye, Ming; Walker, Anthony P.

Hydrological models are always composed of multiple components that represent processes key to intended model applications. When a process can be simulated by multiple conceptual-mathematical models (process models), model uncertainty in representing the process arises. While global sensitivity analysis methods have been widely used for identifying important processes in hydrologic modeling, the existing methods consider only parametric uncertainty but ignore the model uncertainty for process representation. To address this problem, this study develops a new method to probe multimodel process sensitivity by integrating the model averaging methods into the framework of variance-based global sensitivity analysis, given that the model averagingmore » methods quantify both parametric and model uncertainty. A new process sensitivity index is derived as a metric of relative process importance, and the index includes variance in model outputs caused by uncertainty in both process models and model parameters. For demonstration, the new index is used to evaluate the processes of recharge and geology in a synthetic study of groundwater reactive transport modeling. The recharge process is simulated by two models that converting precipitation to recharge, and the geology process is also simulated by two models of different parameterizations of hydraulic conductivity; each process model has its own random parameters. The new process sensitivity index is mathematically general, and can be applied to a wide range of problems in hydrology and beyond.« less

Controlled grafting of vinylic monomers on polyolefins: a robust mathematical modeling approach

PubMed Central

Saeb, Mohammad Reza; Rezaee, Babak; Shadman, Alireza; Formela, Krzysztof; Ahmadi, Zahed; Hemmati, Farkhondeh; Kermaniyan, Tayebeh Sadat; Mohammadi, Yousef

2017-01-01

Abstract Experimental and mathematical modeling analyses were used for controlling melt free-radical grafting of vinylic monomers on polyolefins and, thereby, reducing the disturbance of undesired cross-linking of polyolefins. Response surface, desirability function, and artificial intelligence methodologies were blended to modeling/optimization of grafting reaction in terms of vinylic monomer content, peroxide initiator concentration, and melt-processing time. An in-house code was developed based on artificial neural network that learns and mimics processing torque and grafting of glycidyl methacrylate (GMA) typical vinylic monomer on high-density polyethylene (HDPE). Application of response surface and desirability function enabled concurrent optimization of processing torque and GMA grafting on HDPE, through which we quantified for the first time competition between parallel reactions taking place during melt processing: (i) desirable grafting of GMA on HDPE; (ii) undesirable cross-linking of HDPE. The proposed robust mathematical modeling approach can precisely learn the behavior of grafting reaction of vinylic monomers on polyolefins and be placed into practice in finding exact operating condition needed for efficient grafting of reactive monomers on polyolefins. PMID:29491797

Controlled grafting of vinylic monomers on polyolefins: a robust mathematical modeling approach.

PubMed

Saeb, Mohammad Reza; Rezaee, Babak; Shadman, Alireza; Formela, Krzysztof; Ahmadi, Zahed; Hemmati, Farkhondeh; Kermaniyan, Tayebeh Sadat; Mohammadi, Yousef

2017-01-01

Experimental and mathematical modeling analyses were used for controlling melt free-radical grafting of vinylic monomers on polyolefins and, thereby, reducing the disturbance of undesired cross-linking of polyolefins. Response surface, desirability function, and artificial intelligence methodologies were blended to modeling/optimization of grafting reaction in terms of vinylic monomer content, peroxide initiator concentration, and melt-processing time. An in-house code was developed based on artificial neural network that learns and mimics processing torque and grafting of glycidyl methacrylate (GMA) typical vinylic monomer on high-density polyethylene (HDPE). Application of response surface and desirability function enabled concurrent optimization of processing torque and GMA grafting on HDPE, through which we quantified for the first time competition between parallel reactions taking place during melt processing: (i) desirable grafting of GMA on HDPE; (ii) undesirable cross-linking of HDPE. The proposed robust mathematical modeling approach can precisely learn the behavior of grafting reaction of vinylic monomers on polyolefins and be placed into practice in finding exact operating condition needed for efficient grafting of reactive monomers on polyolefins.

Two-dimensional coupled mathematical modeling of fluvial processes with intense sediment transport and rapid bed evolution

NASA Astrophysics Data System (ADS)

Yue, Zhiyuan; Cao, Zhixian; Li, Xin; Che, Tao

2008-09-01

Alluvial rivers may experience intense sediment transport and rapid bed evolution under a high flow regime, for which traditional decoupled mathematical river models based on simplified conservation equations are not applicable. A two-dimensional coupled mathematical model is presented, which is generally applicable to the fluvial processes with either intense or weak sediment transport. The governing equations of the model comprise the complete shallow water hydrodynamic equations closed with Manning roughness for boundary resistance and empirical relationships for sediment exchange with the erodible bed. The second-order Total-Variation-Diminishing version of the Weighted-Average-Flux method, along with the HLLC approximate Riemann Solver, is adapted to solve the governing equations, which can properly resolve shock waves and contact discontinuities. The model is applied to the pilot study of the flooding due to a sudden outburst of a real glacial-lake.

The mathematical and computer modeling of the worm tool shaping

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Ayusheev, T. V.

2017-06-01

Traditionally mathematical profiling of the worm tool is carried out on the first T. Olivier method, known in the theory of gear gearings, with receiving an intermediate surface of the making lath. It complicates process of profiling and its realization by means of computer 3D-modeling. The purpose of the work is the improvement of mathematical model of profiling and its realization based on the methods of 3D-modeling. Research problems are: receiving of the mathematical model of profiling which excludes the presence of the making lath in it; realization of the received model by means of frame and superficial modeling; development and approbation of technology of solid-state modeling for the solution of the problem of profiling. As the basic, the kinematic method of research of the mutually envelope surfaces is accepted. Computer research is executed by means of CAD based on the methods of 3D-modeling. We have developed mathematical model of profiling of the worm tool; frame, superficial and solid-state models of shaping of the mutually enveloping surfaces of the detail and the tool are received. The offered mathematical models and the technologies of 3D-modeling of shaping represent tools for theoretical and experimental profiling of the worm tool. The results of researches can be used at design of metal-cutting tools.

Modelling in Action. Examining How Students Approach Modelling Real Life Situations. Three Case Studies. Model of the Movement of an Elevator

ERIC Educational Resources Information Center

Rivas, Eugenia Marmolejo

2015-01-01

By means of three case studies, we will present two mathematical modelling activities that are suitable for students enrolled in senior high school and the first year of mathematics at university level. The activities have been designed to enrich the learning process and promote the formation of vital modelling skills. In case studies one and two,…

Mathematical Modeling of Renal Hemodynamics in Physiology and Pathophysiology

PubMed Central

Sgouralis, Ioannis; Layton, Anita T.

2015-01-01

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. PMID:25765886

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

Mathematical and Computational Modeling in Complex Biological Systems.

PubMed

Ji, Zhiwei; Yan, Ke; Li, Wenyang; Hu, Haigen; 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.

Mathematizing Process of Junior High School Students to Improve Mathematics Literacy Refers PISA on RCP Learning

NASA Astrophysics Data System (ADS)

Wardono; Mariani, S.; Hendikawati, P.; Ikayani

2017-04-01

Mathematizing process (MP) is the process of modeling a phenomenon mathematically or establish the concept of a phenomenon. There are two mathematizing that is Mathematizing Horizontal (MH) and Mathematizing Vertical (MV). MH as events changes contextual problems into mathematical problems, while MV is the process of formulation of the problem into a variety of settlement mathematics by using some appropriate rules. Mathematics Literacy (ML) is the ability to formulate, implement and interpret mathematics in various contexts, including the capacity to perform reasoning mathematically and using the concepts, procedures, and facts to describe, explain or predict phenomena incident. If junior high school students are conditioned continuously to conduct mathematizing activities on RCP (RME-Card Problem) learning, it will be able to improve ML that refers PISA. The purpose of this research is to know the capability of the MP grade VIII on ML content shape and space with the matter of the cube and beams with RCP learning better than the scientific learning, upgrade MP grade VIII in the issue of the cube and beams with RCP learning better than the scientific learning in terms of cognitive styles reflective and impulsive the MP grade VIII with the approach of the RCP learning in terms of cognitive styles reflective and impulsive This research is the mixed methods model concurrent embedded. The population in this study, i.e., class VIII SMPN 1 Batang with sample two class. Data were taken with the observation, interviews, and tests and analyzed with a different test average of one party the right qualitative and descriptive. The results of this study demonstrate the capability of the MP student with RCP learning better than the scientific learning, upgrade MP with RCP learning better compare with scientific learning in term cognitive style of reflective and impulsive. The subject of the reflective group top, middle, and bottom can meet all the process of MH indicators are then the subject of the reflective upper and intermediate group can meet all the MV indicators but to lower groups can only fulfill some MV indicators. The subject is impulsive upper and middle group can meet all the MH indicators but to lower groups can only meet some MH indicator, then the subject is impulsive group can meet all the MV indicators but for middle and the bottom group can only fulfill some MV indicators.

DOE Office of Scientific and Technical Information (OSTI.GOV)

M. A. Wasiolek

The purpose of this report is to document the biosphere model, the Environmental Radiation Model for Yucca Mountain, Nevada (ERMYN), which describes radionuclide transport processes in the biosphere and associated human exposure that may arise as the result of radionuclide release from the geologic repository at Yucca Mountain. The biosphere model is one of the process models that support the Yucca Mountain Project (YMP) Total System Performance Assessment (TSPA) for the license application (LA), the TSPA-LA. The ERMYN model provides the capability of performing human radiation dose assessments. This report documents the biosphere model, which includes: (1) Describing the referencemore » biosphere, human receptor, exposure scenarios, and primary radionuclides for each exposure scenario (Section 6.1); (2) Developing a biosphere conceptual model using site-specific features, events, and processes (FEPs), the reference biosphere, the human receptor, and assumptions (Section 6.2 and Section 6.3); (3) Building a mathematical model using the biosphere conceptual model and published biosphere models (Sections 6.4 and 6.5); (4) Summarizing input parameters for the mathematical model, including the uncertainty associated with input values (Section 6.6); (5) Identifying improvements in the ERMYN model compared with the model used in previous biosphere modeling (Section 6.7); (6) Constructing an ERMYN implementation tool (model) based on the biosphere mathematical model using GoldSim stochastic simulation software (Sections 6.8 and 6.9); (7) Verifying the ERMYN model by comparing output from the software with hand calculations to ensure that the GoldSim implementation is correct (Section 6.10); and (8) Validating the ERMYN model by corroborating it with published biosphere models; comparing conceptual models, mathematical models, and numerical results (Section 7).« less

A Novel Approach to Develop the Lower Order Model of Multi-Input Multi-Output System

NASA Astrophysics Data System (ADS)

Rajalakshmy, P.; Dharmalingam, S.; Jayakumar, J.

2017-10-01

A mathematical model is a virtual entity that uses mathematical language to describe the behavior of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines like physics, biology, and electrical engineering as well as in the social sciences like economics, sociology and political science. Physicists, Engineers, Computer scientists, and Economists use mathematical models most extensively. With the advent of high performance processors and advanced mathematical computations, it is possible to develop high performing simulators for complicated Multi Input Multi Ouptut (MIMO) systems like Quadruple tank systems, Aircrafts, Boilers etc. This paper presents the development of the mathematical model of a 500 MW utility boiler which is a highly complex system. A synergistic combination of operational experience, system identification and lower order modeling philosophy has been effectively used to develop a simplified but accurate model of a circulation system of a utility boiler which is a MIMO system. The results obtained are found to be in good agreement with the physics of the process and with the results obtained through design procedure. The model obtained can be directly used for control system studies and to realize hardware simulators for boiler testing and operator training.

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?" Copyright © 2014 Elsevier Inc. All rights reserved.

The Development from Effortful to Automatic Processing in Mathematical Cognition.

ERIC Educational Resources Information Center

Kaye, Daniel B.; And Others

This investigation capitalizes upon the information processing models that depend upon measurement of latency of response to a mathematical problem and the decomposition of reaction time (RT). Simple two term addition problems were presented with possible solutions for true-false verification, and accuracy and RT to response were recorded. Total…

Mathematical Development: The Role of Broad Cognitive Processes

ERIC Educational Resources Information Center

Calderón-Tena, Carlos O.

2016-01-01

This study investigated the role of broad cognitive processes in the development of mathematics skills among children and adolescents. Four hundred and forty-seven students (age mean [M] = 10.23 years, 73% boys and 27% girls) from an elementary school district in the US southwest participated. Structural equation modelling tests indicated that…

Process models as tools in forestry research and management

Treesearch

Kurt Johnsen; Lisa Samuelson; Robert Teskey; Steve McNulty; Tom Fox

2001-01-01

Forest process models are mathematical representations of biological systems that incorporate our understanding of physiological and ecological mechanisms into predictive algorithms. These models were originally designed and used for research purposes, but are being developed for use in practical forest management. Process models designed for research...

Mathematical Modeling of Protein Misfolding Mechanisms in Neurological Diseases: A Historical Overview.

PubMed

Carbonell, Felix; Iturria-Medina, Yasser; Evans, Alan C

2018-01-01

Protein misfolding refers to a process where proteins become structurally abnormal and lose their specific 3-dimensional spatial configuration. The histopathological presence of misfolded protein (MP) aggregates has been associated as the primary evidence of multiple neurological diseases, including Prion diseases, Alzheimer's disease, Parkinson's disease, and Creutzfeldt-Jacob disease. However, the exact mechanisms of MP aggregation and propagation, as well as their impact in the long-term patient's clinical condition are still not well understood. With this aim, a variety of mathematical models has been proposed for a better insight into the kinetic rate laws that govern the microscopic processes of protein aggregation. Complementary, another class of large-scale models rely on modern molecular imaging techniques for describing the phenomenological effects of MP propagation over the whole brain. Unfortunately, those neuroimaging-based studies do not take full advantage of the tremendous capabilities offered by the chemical kinetics modeling approach. Actually, it has been barely acknowledged that the vast majority of large-scale models have foundations on previous mathematical approaches that describe the chemical kinetics of protein replication and propagation. The purpose of the current manuscript is to present a historical review about the development of mathematical models for describing both microscopic processes that occur during the MP aggregation and large-scale events that characterize the progression of neurodegenerative MP-mediated diseases.

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

ERIC Educational Resources Information Center

Marshall, Neil; Buteau, Chantal

2014-01-01

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

Determination of thermophysical characteristics of vulcanizable rubber products by the mathematical modeling method

NASA Astrophysics Data System (ADS)

Tikhomirov, S. G.; Pyatakov, Y. V.; Karmanova, O. V.; Maslov, A. A.

2018-03-01

The studies of the vulcanization kinetics of elastomers were carried out using a Truck tyre tread rubber compound. The formal kinetic scheme of vulcanization of rubbers sulfur-accelerator curing system was used which generalizes the set of reactions occurring in the curing process. A mathematical model is developed for determining the thermal parameters vulcanizable mixture comprising algorithms for solving direct and inverse problems for system of equations of heat conduction and kinetics of the curing process. The performance of the model is confirmed by the results of numerical experiments on model examples.

Modeling and Analysis of Power Processing Systems (MAPPS). Volume 1: Technical report

NASA Technical Reports Server (NTRS)

Lee, F. C.; Rahman, S.; Carter, R. A.; Wu, C. H.; Yu, Y.; Chang, R.

1980-01-01

Computer aided design and analysis techniques were applied to power processing equipment. Topics covered include: (1) discrete time domain analysis of switching regulators for performance analysis; (2) design optimization of power converters using augmented Lagrangian penalty function technique; (3) investigation of current-injected multiloop controlled switching regulators; and (4) application of optimization for Navy VSTOL energy power system. The generation of the mathematical models and the development and application of computer aided design techniques to solve the different mathematical models are discussed. Recommendations are made for future work that would enhance the application of the computer aided design techniques for power processing systems.

Computational and mathematical methods in brain atlasing.

PubMed

Nowinski, Wieslaw L

2017-12-01

Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.

The mathematical modeling of rapid solidification processing. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Gutierrez-Miravete, E.

1986-01-01

The detailed formulation of and the results obtained from a continuum mechanics-based mathematical model of the planar flow melt spinning (PFMS) rapid solidification system are presented and discussed. The numerical algorithm proposed is capable of computing the cooling and freezing rates as well as the fluid flow and capillary phenomena which take place inside the molten puddle formed in the PFMS process. The FORTRAN listings of some of the most useful computer programs and a collection of appendices describing the basic equations used for the modeling are included.

Mathematical modeling of gene expression: a guide for the perplexed biologist

PubMed Central

Ay, Ahmet; Arnosti, David N.

2011-01-01

The detailed analysis of transcriptional networks holds a key for understanding central biological processes, and interest in this field has exploded due to new large-scale data acquisition techniques. Mathematical modeling can provide essential insights, but the diversity of modeling approaches can be a daunting prospect to investigators new to this area. For those interested in beginning a transcriptional mathematical modeling project we provide here an overview of major types of models and their applications to transcriptional networks. In this discussion of recent literature on thermodynamic, Boolean and differential equation models we focus on considerations critical for choosing and validating a modeling approach that will be useful for quantitative understanding of biological systems. PMID:21417596

A Mathematical Model of the Illinois Interlibrary Loan Network: Project Report Number 2.

ERIC Educational Resources Information Center

Rouse, William B.; And Others

The development of a mathematical model of the Illinois Library and Information Network (ILLINET) is described. Based on queueing network theory, the model predicts the probability of a request being satisfied, the average time from the initiation of a request to the receipt of the desired resources, the costs, and the processing loads. Using a…

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.

Using mathematics to solve real world problems: the role of enablers

NASA Astrophysics Data System (ADS)

Geiger, Vincent; Stillman, Gloria; Brown, Jill; Galbriath, Peter; Niss, Mogens

2018-03-01

The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of "enablers" within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students' development as modellers.

Mathematical modeling of the heat transfer during pyrolysis process used for end-of-life tires treatment

NASA Astrophysics Data System (ADS)

Zheleva, I.; Georgiev, I.; Filipova, M.; Menseidov, D.

2017-10-01

Mathematical modeling of the heat transfer during the pyrolysis process used for the treatment of the End-of-Lifetires (EOLT) is presented in this paper. The pyrolysis process is 3D and non-stationary and because of this it is very complicated for modeling and studying. To simplify the modeling here a hierarchy of 2D models for the temperature which describe the non-stationary heat transfer in such a pyrolysis station is created. An algorithm for solving the model equations, based on MATLAB software is developed. The results for the temperature for some characteristic periods of operation of pyrolysis station are presented and commented in the paper. The results from this modeling can be used in the real pyrolysis station for more precise displacement of measurement devices and for designing of automated management of the process.

On dependency properties of the ISIs generated by a two-compartmental neuronal model.

PubMed

Benedetto, Elisa; Sacerdote, Laura

2013-02-01

One-dimensional leaky integrate and fire neuronal models describe interspike intervals (ISIs) of a neuron as a renewal process and disregarding the neuron geometry. Many multi-compartment models account for the geometrical features of the neuron but are too complex for their mathematical tractability. Leaky integrate and fire two-compartment models seem a good compromise between mathematical tractability and an improved realism. They indeed allow to relax the renewal hypothesis, typical of one-dimensional models, without introducing too strong mathematical difficulties. Here, we pursue the analysis of the two-compartment model studied by Lansky and Rodriguez (Phys D 132:267-286, 1999), aiming of introducing some specific mathematical results used together with simulation techniques. With the aid of these methods, we investigate dependency properties of ISIs for different values of the model parameters. We show that an increase of the input increases the strength of the dependence between successive ISIs.

Mathematical modeling of the integrated process of mercury bioremediation in the industrial bioreactor.

PubMed

Głuszcz, Paweł; Petera, Jerzy; Ledakowicz, Stanisław

2011-03-01

The mathematical model of the integrated process of mercury contaminated wastewater bioremediation in a fixed-bed industrial bioreactor is presented. An activated carbon packing in the bioreactor plays the role of an adsorbent for ionic mercury and at the same time of a carrier material for immobilization of mercury-reducing bacteria. The model includes three basic stages of the bioremediation process: mass transfer in the liquid phase, adsorption of mercury onto activated carbon and ionic mercury bioreduction to Hg(0) by immobilized microorganisms. Model calculations were verified using experimental data obtained during the process of industrial wastewater bioremediation in the bioreactor of 1 m³ volume. It was found that the presented model reflects the properties of the real system quite well. Numerical simulation of the bioremediation process confirmed the experimentally observed positive effect of the integration of ionic mercury adsorption and bioreduction in one apparatus.

A Double Layer Model of the Electromagnetic and Thermal Processes in Induction Heating of Ferromagnetic Material

NASA Astrophysics Data System (ADS)

Gilev, B.; Kraev, G.; Venkov, G. I.

2007-10-01

This paper presents the modeling of electromagnetic and heating processes in an inductor, where cylindrical ferromagnetic material has been placed. In the first part the electromagnetic mathematical problem is solved, as a result the power density is obtained. The power density takes part in the heat conduction equation. In the second part the thermal mathematical problem is solved, as a result the alteration of the temperature of the ferromagnetic material during the heating process is obtained. The parameters in both mathematical problems depend on the temperature. Because of that the stitching method is used for their finding. In [3, 4] the same mathematical problems are solved by the finite elements method. Comparing our results to those from [3] shows that they are similar. In contrast to [3, 4] our method allows the continuation of the analysis with the finding of the load power during the heating process. Thus result permits the determination of the load power alteration in the supplying inverter [1]. It is well-known that during the induction hardening it is necessary to maintain constant current amplitude in the load circuit of the inverter. So the next aim of this research is to build up a controller, based on the developed model, which will procure the necessary mode.

Review on experiment-based two- and three-dimensional models for wound healing

PubMed Central

Gefen, Amit

2016-01-01

Traumatic and chronic wounds are a considerable medical challenge that affects many populations and their treatment is a monetary and time-consuming burden in an ageing society to the medical systems. Because wounds are very common and their treatment is so costly, approaches to reveal the responses of a specific wound type to different medical procedures and treatments could accelerate healing and reduce patient suffering. The effects of treatments can be forecast using mathematical modelling that has the predictive power to quantify the effects of induced changes to the wound-healing process. Wound healing involves a diverse and complex combination of biophysical and biomechanical processes. We review a wide variety of contemporary approaches of mathematical modelling of gap closure and wound-healing-related processes, such as angiogenesis. We provide examples of the understanding and insights that may be garnered using those models, and how those relate to experimental evidence. Mathematical modelling-based simulations can provide an important visualization tool that can be used for illustrational purposes for physicians, patients and researchers. PMID:27708762

Designing Online Learning for Developing Pre-Service Teachers' Capabilities in Mathematical Modelling and Applications

ERIC Educational Resources Information Center

Geiger, Vince; Date-Huxtable, Liz; Ahlip, Rehez; Herberstein, Marie; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian; Mulligan, Joanne

2016-01-01

The purpose of this paper is to describe the processes utilised to develop an online learning module within the Opening Real Science (ORS) project--"Modelling the present: Predicting the future." The module was realised through an interdisciplinary collaboration, among mathematicians, scientists and mathematics and science educators that…

Evaluation of Turkish and Mathematics Curricula According to Value-Based Evaluation Model

ERIC Educational Resources Information Center

Duman, Serap Nur; Akbas, Oktay

2017-01-01

This study evaluated secondary school seventh-grade Turkish and mathematics programs using the Context-Input-Process-Product Evaluation Model based on student, teacher, and inspector views. The convergent parallel mixed method design was used in the study. Student values were identified using the scales for socio-level identification, traditional…

Elementary Modeling: Connecting Counting with Sharing

ERIC Educational Resources Information Center

Wickstrom, Megan H.; Aytes, Tracy

2018-01-01

Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

Exploring Student Reflective Practice during a Mathematical Modelling Challenge

ERIC Educational Resources Information Center

Redmond, Trevor; Sheehy, Joanne; Brown, Raymond; Kanasa, Harry

2012-01-01

This paper seeks to compare the reflective writings of two cohorts of students (Year 4/5 and Year 8/9) participating in mathematical modelling challenges. Whilst the reflections of the younger cohort were results oriented, the older cohort's reflections spoke more to the affective domain, group processes, the use of technology and the acquisition…

Growth in Mathematical Understanding: How Can We Characterise It and How Can We Represent It?

ERIC Educational Resources Information Center

Pirie, Susan; Kieren, Thomas

1994-01-01

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

Mathematics, Thermodynamics, and Modeling to Address Ten Common Misconceptions about Protein Structure, Folding, and Stability

ERIC Educational Resources Information Center

Robic, Srebrenka

2010-01-01

To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative…

Improving students’ mathematical representational ability through RME-based progressive mathematization

NASA Astrophysics Data System (ADS)

Warsito; Darhim; Herman, T.

2018-01-01

This study aims to determine the differences in the improving of mathematical representation ability based on progressive mathematization with realistic mathematics education (PMR-MP) with conventional learning approach (PB). The method of research is quasi-experiments with non-equivalent control group designs. The study population is all students of class VIII SMPN 2 Tangerang consisting of 6 classes, while the sample was taken two classes with purposive sampling technique. The experimental class is treated with PMR-MP while the control class is treated with PB. The instruments used are test of mathematical representation ability. Data analysis was done by t-test, ANOVA test, post hoc test, and descriptive analysis. The result of analysis can be concluded that: 1) there are differences of mathematical representation ability improvement between students treated by PMR-MP and PB, 2) no interaction between learning approach (PMR-MP, PB) and prior mathematics knowledge (PAM) to improve students’ mathematical representation; 3) Students’ mathematical representation improvement in the level of higher PAM is better than medium, and low PAM students. Thus, based on the process of mathematization, it is very important when the learning direction of PMR-MP emphasizes on the process of building mathematics through a mathematical model.

Information modeling system for blast furnace control

NASA Astrophysics Data System (ADS)

Spirin, N. A.; Gileva, L. Y.; Lavrov, V. V.

2016-09-01

Modern Iron & Steel Works as a rule are equipped with powerful distributed control systems (DCS) and databases. Implementation of DSC system solves the problem of storage, control, protection, entry, editing and retrieving of information as well as generation of required reporting data. The most advanced and promising approach is to use decision support information technologies based on a complex of mathematical models. The model decision support system for control of blast furnace smelting is designed and operated. The basis of the model system is a complex of mathematical models created using the principle of natural mathematical modeling. This principle provides for construction of mathematical models of two levels. The first level model is a basic state model which makes it possible to assess the vector of system parameters using field data and blast furnace operation results. It is also used to calculate the adjustment (adaptation) coefficients of the predictive block of the system. The second-level model is a predictive model designed to assess the design parameters of the blast furnace process when there are changes in melting conditions relative to its current state. Tasks for which software is developed are described. Characteristics of the main subsystems of the blast furnace process as an object of modeling and control - thermal state of the furnace, blast, gas dynamic and slag conditions of blast furnace smelting - are presented.

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Improving Mathematics Achievement of Indonesian 5th Grade Students through Guided Discovery Learning

ERIC Educational Resources Information Center

Yurniwati; Hanum, Latipa

2017-01-01

This research aims to find information about the improvement of mathematics achievement of grade five student through guided discovery learning. This research method is classroom action research using Kemmis and Taggart model consists of three cycles. Data used in this study is learning process and learning results. Learning process data is…

Modeling Scientific Processes with Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving

ERIC Educational Resources Information Center

Schuchardt, Anita M.; Schunn, Christian D.

2016-01-01

Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K-12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However,…

Models of Individual Trajectories in Computer-Assisted Instruction for Deaf Students. Technical Report No. 214.

ERIC Educational Resources Information Center

Suppes, P.; And Others

From some simple and schematic assumptions about information processing, a stochastic differential equation is derived for the motion of a student through a computer-assisted elementary mathematics curriculum. The mathematics strands curriculum of the Institute for Mathematical Studies in the Social Sciences is used to test: (1) the theory and (2)…

Modelling the human immunodeficiency virus (HIV) epidemic: A review of the substance and role of models in South Africa

PubMed Central

2018-01-01

We review key mathematical models of the South African human immunodeficiency virus (HIV) epidemic from the early 1990s onwards. In our descriptions, we sometimes differentiate between the concepts of a model world and its mathematical or computational implementation. The model world is the conceptual realm in which we explicitly declare the rules – usually some simplification of ‘real world’ processes as we understand them. Computing details of informative scenarios in these model worlds is a task requiring specialist knowledge, but all other aspects of the modelling process, from describing the model world to identifying the scenarios and interpreting model outputs, should be understandable to anyone with an interest in the epidemic. PMID:29568647

Mathematical Modeling of Resonant Processes in Confined Geometry of Atomic and Atom-Ion Traps

NASA Astrophysics Data System (ADS)

Melezhik, Vladimir S.

2018-02-01

We discuss computational aspects of the developed mathematical models for resonant processes in confined geometry of atomic and atom-ion traps. The main attention is paid to formulation in the nondirect product discrete-variable representation (npDVR) of the multichannel scattering problem with nonseparable angular part in confining traps as the boundary-value problem. Computational efficiency of this approach is demonstrated in application to atomic and atom-ion confinement-induced resonances we predicted recently.

Mathematical modeling of the gas extraction from the gas hydrate deposit taking into account the replacement technology

NASA Astrophysics Data System (ADS)

Musakaev, N. G.; Khasanov, M. K.; Borodin, S. L.

2018-03-01

In the work on the basis of methods and equations of mechanics of multiphase systems the mathematical model of the process of carbon dioxide burial in the reservoir saturated with methane hydrate is proposed. Estimates are obtained that allow for this problem to neglect diffusion mixing of carbon dioxide and methane. The features of the process of methane displacement from CH4 hydrate by filling them with carbon dioxide are studied.

Application of a mathematical model for ergonomics in lean manufacturing.

PubMed

Botti, Lucia; Mora, Cristina; Regattieri, Alberto

2017-10-01

The data presented in this article are related to the research article "Integrating ergonomics and lean manufacturing principles in a hybrid assembly line" (Botti et al., 2017) [1]. The results refer to the application of the mathematical model for the design of lean processes in hybrid assembly lines, meeting both the lean principles and the ergonomic requirements for safe assembly work. Data show that the success of a lean strategy is possible when ergonomics of workers is a parameter of the assembly process design.

Cellular automata-based modelling and simulation of biofilm structure on multi-core computers.

PubMed

Skoneczny, Szymon

2015-01-01

The article presents a mathematical model of biofilm growth for aerobic biodegradation of a toxic carbonaceous substrate. Modelling of biofilm growth has fundamental significance in numerous processes of biotechnology and mathematical modelling of bioreactors. The process following double-substrate kinetics with substrate inhibition proceeding in a biofilm has not been modelled so far by means of cellular automata. Each process in the model proposed, i.e. diffusion of substrates, uptake of substrates, growth and decay of microorganisms and biofilm detachment, is simulated in a discrete manner. It was shown that for flat biofilm of constant thickness, the results of the presented model agree with those of a continuous model. The primary outcome of the study was to propose a mathematical model of biofilm growth; however a considerable amount of focus was also placed on the development of efficient algorithms for its solution. Two parallel algorithms were created, differing in the way computations are distributed. Computer programs were created using OpenMP Application Programming Interface for C++ programming language. Simulations of biofilm growth were performed on three high-performance computers. Speed-up coefficients of computer programs were compared. Both algorithms enabled a significant reduction of computation time. It is important, inter alia, in modelling and simulation of bioreactor dynamics.

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. Copyright © 2015 Elsevier Inc. All rights reserved.

Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling.

PubMed

Powathil, Gibin G; Swat, Maciej; Chaplain, Mark A J

2015-02-01

The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life. Copyright © 2014 Elsevier Ltd. All rights reserved.

The use of mathematical models to inform influenza pandemic preparedness and response

PubMed Central

Wu, Joseph T; Cowling, Benjamin J

2011-01-01

Summary Influenza pandemics have occurred throughout history and were associated with substantial excess mortality and morbidity. Mathematical models of infectious diseases permit quantitative description of epidemic processes based on the underlying biological mechanisms. Mathematical models have been widely used in the past decade to aid pandemic planning by allowing detailed predictions of the speed of spread of an influenza pandemic and the likely effectiveness of alternative control strategies. During the initial waves of the 2009 influenza pandemic, mathematical models were used to track the spread of the virus, predict the time course of the pandemic and assess the likely impact of large-scale vaccination. While mathematical modeling has made substantial contributions to influenza pandemic preparedness, its use as a real-time tool for pandemic control is currently limited by the lack of essential surveillance information such as serologic data. Mathematical modeling provided a useful framework for analyzing and interpreting surveillance data during the 2009 influenza pandemic, for highlighting limitations in existing pandemic surveillance systems, and for guiding how these systems should be strengthened in order to cope with future epidemics of influenza or other emerging infectious diseases. PMID:21727183

Differential equations with applications in cancer diseases.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2013-01-01

Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Simulating carbon capture by enhanced weathering with croplands: an overview of key processes highlighting areas of future model development

PubMed Central

Quegan, Shaun; Banwart, Steven A.

2017-01-01

Enhanced weathering (EW) aims to amplify a natural sink for CO2 by incorporating powdered silicate rock with high reactive surface area into agricultural soils. The goal is to achieve rapid dissolution of minerals and release of alkalinity with accompanying dissolution of CO2 into soils and drainage waters. EW could counteract phosphorus limitation and greenhouse gas (GHG) emissions in tropical soils, and soil acidification, a common agricultural problem studied with numerical process models over several decades. Here, we review the processes leading to soil acidification in croplands and how the soil weathering CO2 sink is represented in models. Mathematical models capturing the dominant processes and human interventions governing cropland soil chemistry and GHG emissions neglect weathering, while most weathering models neglect agricultural processes. We discuss current approaches to modelling EW and highlight several classes of model having the potential to simulate EW in croplands. Finally, we argue for further integration of process knowledge in mathematical models to capture feedbacks affecting both longer-term CO2 consumption and crop growth and yields. PMID:28381633

Mathematical model with autoregressive process for electrocardiogram signals

NASA Astrophysics Data System (ADS)

Evaristo, Ronaldo M.; Batista, Antonio M.; Viana, Ricardo L.; Iarosz, Kelly C.; Szezech, José D., Jr.; Godoy, Moacir F. de

2018-04-01

The cardiovascular system is composed of the heart, blood and blood vessels. Regarding the heart, cardiac conditions are determined by the electrocardiogram, that is a noninvasive medical procedure. In this work, we propose autoregressive process in a mathematical model based on coupled differential equations in order to obtain the tachograms and the electrocardiogram signals of young adults with normal heartbeats. Our results are compared with experimental tachogram by means of Poincaré plot and dentrended fluctuation analysis. We verify that the results from the model with autoregressive process show good agreement with experimental measures from tachogram generated by electrical activity of the heartbeat. With the tachogram we build the electrocardiogram by means of coupled differential equations.

A discrete in continuous mathematical model of cardiac progenitor cells formation and growth as spheroid clusters (Cardiospheres).

PubMed

Di Costanzo, Ezio; Giacomello, Alessandro; Messina, Elisa; Natalini, Roberto; Pontrelli, Giuseppe; Rossi, Fabrizio; Smits, Robert; Twarogowska, Monika

2018-03-14

We propose a discrete in continuous mathematical model describing the in vitro growth process of biophsy-derived mammalian cardiac progenitor cells growing as clusters in the form of spheres (Cardiospheres). The approach is hybrid: discrete at cellular scale and continuous at molecular level. In the present model, cells are subject to the self-organizing collective dynamics mechanism and, additionally, they can proliferate and differentiate, also depending on stochastic processes. The two latter processes are triggered and regulated by chemical signals present in the environment. Numerical simulations show the structure and the development of the clustered progenitors and are in a good agreement with the results obtained from in vitro experiments.

Will big data yield new mathematics? An evolving synergy with neuroscience

PubMed Central

Feng, S.; Holmes, P.

2016-01-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics. PMID:27516705

Will big data yield new mathematics? An evolving synergy with neuroscience.

PubMed

Feng, S; Holmes, P

2016-06-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

Examples as an Instructional Tool in Mathematics and Science Classrooms: Teachers' Perceptions and Attitudes

ERIC Educational Resources Information Center

Huang, Xiaoxia; Cribbs, Jennifer

2017-01-01

This study examined mathematics and science teachers' perceptions and use of four types of examples, including typical textbook examples (standard worked examples) and erroneous worked examples in the written form as well as mastery modelling examples and peer modelling examples involving the verbalization of the problem-solving process. Data…

[Mathematical models and epidemiological analysis].

PubMed

Gerasimov, A N

2010-01-01

The limited use of mathematical simulation in epidemiology is due not only to the difficulty of monitoring the epidemic process and identifying its parameters but also to the application of oversimplified models. It is shown that realistic reproduction of actual morbidity dynamics requires taking into account heterogeneity and finiteness of the population and seasonal character of pathogen transmission mechanism.

Mathematical modeling of a radio-frequency path for IEEE 802.11ah based wireless sensor networks

NASA Astrophysics Data System (ADS)

Tyshchenko, Igor; Cherepanov, Alexander; Dmitrii, Vakhnin; Popova, Mariia

2017-09-01

This article discusses the process of creating the mathematical model of a radio-frequency path for an IEEE 802.11ah based wireless sensor networks using M atLab Simulink CAD tools. In addition, it describes occurring perturbing effects and determining the presence of a useful signal in the received mixture.

Model-Based Design of Biochemical Microreactors

PubMed Central

Elbinger, Tobias; Gahn, Markus; Neuss-Radu, Maria; Hante, Falk M.; Voll, Lars M.; Leugering, Günter; Knabner, Peter

2016-01-01

Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction. These microreactors consist of compartments separated by membranes carrying specific transporters for the input of substrates and export of products. Inside the compartments of the reactor multienzyme complexes assembled on nano-beads by peptide adapters are used to carry out metabolic reactions. The spatially resolved mathematical model describing the ongoing processes consists of a system of diffusion equations together with boundary and initial conditions. The boundary conditions model the exchange of metabolites with the neighboring compartments and the reactions at the surface of the nano-beads carrying the multienzyme complexes. Efficient and accurate approaches for numerical simulation of the mathematical model and for optimal design of the microreactor are developed. As a proof-of-concept scenario, a synthetic pathway for the conversion of sucrose to glucose-6-phosphate (G6P) was chosen. In this context, the mathematical model is employed to compute the spatio-temporal distributions of the metabolite concentrations, as well as application relevant quantities like the outflow rate of G6P. These computations are performed for different scenarios, where the number of beads as well as their loading capacity are varied. The computed metabolite distributions show spatial patterns, which differ for different experimental arrangements. Furthermore, the total output of G6P increases for scenarios where microcompartimentation of enzymes occurs. These results show that spatially resolved models are needed in the description of the conversion processes. Finally, the enzyme stoichiometry on the nano-beads is determined, which maximizes the production of glucose-6-phosphate. PMID:26913283

A Hilbert Space Representation of Generalized Observables and Measurement Processes in the ESR Model

NASA Astrophysics Data System (ADS)

Sozzo, Sandro; Garola, Claudio

2010-12-01

The extended semantic realism ( ESR) model recently worked out by one of the authors embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the generalized observables introduced by the ESR model that satisfy a simple physical condition, propose a generalization of the projection postulate, and suggest a possible mathematical description of the measurement process in terms of evolution of the compound system made up of the measured system and the measuring apparatus.

Modelling Of Flotation Processes By Classical Mathematical Methods - A Review

NASA Astrophysics Data System (ADS)

Jovanović, Ivana; Miljanović, Igor

2015-12-01

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

An engineering approach to modelling, decision support and control for sustainable systems.

PubMed

Day, W; Audsley, E; Frost, A R

2008-02-12

Engineering research and development contributes to the advance of sustainable agriculture both through innovative methods to manage and control processes, and through quantitative understanding of the operation of practical agricultural systems using decision models. This paper describes how an engineering approach, drawing on mathematical models of systems and processes, contributes new methods that support decision making at all levels from strategy and planning to tactics and real-time control. The ability to describe the system or process by a simple and robust mathematical model is critical, and the outputs range from guidance to policy makers on strategic decisions relating to land use, through intelligent decision support to farmers and on to real-time engineering control of specific processes. Precision in decision making leads to decreased use of inputs, less environmental emissions and enhanced profitability-all essential to sustainable systems.

Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Khramushin, Vasily

2016-02-01

The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.

Mathematical model of bone drilling for virtual surgery system

NASA Astrophysics Data System (ADS)

Alaytsev, Innokentiy K.; Danilova, Tatyana V.; Manturov, Alexey O.; Mareev, Gleb O.; Mareev, Oleg V.

2018-04-01

The bone drilling is an essential part of surgeries in ENT and Dentistry. A proper training of drilling machine handling skills is impossible without proper modelling of the drilling process. Utilization of high precision methods like FEM is limited due to the requirement of 1000 Hz update rate for haptic feedback. The study presents a mathematical model of the drilling process that accounts the properties of materials, the geometry and the rotation rate of a burr to compute the removed material volume. The simplicity of the model allows for integrating it in the high-frequency haptic thread. The precision of the model is enough for a virtual surgery system targeted on the training of the basic surgery skills.

Mathematics Pedagogical Standards: A Suggested Model of Instruction in Enhancing the Mathematics Teacher’s Quality of Instruction

NASA Astrophysics Data System (ADS)

Saad, N. S.; Jemali, M.; Zakaria, Z. Hj; Yusof, Q.

2018-01-01

The paper aims at identifying the standards for teaching and learning of mathematics based on National Council of Teacher of Mathematics (NCTM, 2000), The Australian Association of Mathematics Teachers (AAMT, 2006) and Training and Development Agency for School (TDA, 2007). These known standards were used as a guide in identifying the constructs of the mathematics teacher’s instruction in the classroom. The survey method used in which a questionnaire instrument encompassed on the four identified constructs on the standards for teaching and learning of mathematics, namely professional practices, professional attributes, professional knowledge, and professional instructional processes. The instrument was tested during a pilot study and a Cronbach’s Alpha reliability index of greater than 0.85 was obtained. The actual research was carried out in Peninsular Malaysia involving 224 secondary schools with 1.120 mathematics teachers and 108 primary schools with 540 mathematics teachers. From the selected schools, only 820 secondary mathematics teachers (73.2%) and 361 primary teachers (66.9%) gave a response to the mailed questionnaires. The findings of the study revealed that the secondary and primary mathematics teachers strongly agreed on three constructs; professional practices, professional attributes and professional instructional processes.

Data-Based Detection of Potential Terrorist Attacks: Statistical and Graphical Methods

DTIC Science & Technology

2010-06-01

Naren; Vasquez-Robinet, Cecilia; Watkinson, Jonathan: "A General Probabilistic Model of the PCR Process," Applied Mathematics and Computation 182(1...September 2006. Seminar, Measuring the effect of Length biased sampling, Mathematical Sciences Section, National Security Agency, 19 September 2006...Committee on National Statistics, 9 February 2007. Invited seminar, Statistical Tests for Bullet Lead Comparisons, Department of Mathematics , Butler

Structure and Maintenance of a Mathematical Creative Lesson as a Mean of Pupils' Meta-Subject Results Achievement

ERIC Educational Resources Information Center

Gorev, Pavel M.; Aydar M. Kalimullin

2017-01-01

The purpose of the research is to study and change the structure of a mathematical lesson to improve quality of pupils' mathematical training and design mechanisms of inclusion the systems of open type tasks in educational process considering specifics of pupils' creative personality development. The leading method is modeling of a mathematical…

Identification of mathematical model of human breathing in system “Artificial lungs – self-contained breathing apparatus”

NASA Astrophysics Data System (ADS)

Onevsky, P. M.; Onevsky, M. P.; Pogonin, V. A.

2018-03-01

The structure and mathematical models of the main subsystems of the control system of the “Artificial Lungs” are presented. This structure implements the process of imitation of human external respiration in the system “Artificial lungs - self-contained breathing apparatus”. A presented algorithm for parametric identification of the model is based on spectral operators, which allows using it in real time.

Mathematical Model of Bone Regeneration in a Porous Implant

NASA Astrophysics Data System (ADS)

Maslov, L. B.

2017-07-01

A mathematical model of the reparative regeneration of bone tissue governed by the law of cell differentiation and action of an external periodic mechanical loading is presented. The model allows one to study the recovery processes of injured human locomotor system elements under a dynamic loading and to theoretically substantiate the choice of an optimum periodic impact on the defective tissues for their fastest and steady healing.

Mathematical modeling for resource and energy saving control of extruders in multi-assortment productions of polymeric films

NASA Astrophysics Data System (ADS)

Polosin, A. N.; Chistyakova, T. B.

2018-05-01

In this article, the authors describe mathematical modeling of polymer processing in extruders of various types used in extrusion and calender productions of film materials. The method consists of the synthesis of a static model for calculating throughput, energy consumption of the extruder, extrudate quality indices, as well as a dynamic model for evaluating polymer residence time in the extruder, on which the quality indices depend. Models are adjusted according to the extruder type (single-screw, reciprocating, twin-screw), its screw and head configuration, extruder’s work temperature conditions, and the processed polymer type. Models enable creating extruder screw configurations and determining extruder controlling action values that provide the extrudate of required quality while satisfying extruder throughput and energy consumption requirements. Model adequacy has been verified using polyolefins’ and polyvinylchloride processing data in different extruders. The program complex, based on mathematical models, has been developed in order to control extruders of various types in order to ensure resource and energy saving in multi-assortment productions of polymeric films. Using the program complex in the control system for the extrusion stage of the polymeric film productions enables improving film quality, reducing spoilage, lessening the time required for production line change-over to other throughput and film type assignment.

Power efficiency improvements of the industrial processes at application of thermochemical recuperation of heath of the leaving gases with use of microchannel reactors

NASA Astrophysics Data System (ADS)

Tararykov, A. V.; Garyaev, A. B.

2017-11-01

The possibility of increasing the energy efficiency of production processes by converting the initial fuel - natural gas to synthesized fuel using the heat of the exhaust gases of plants involved in production is considered. Possible applications of this technology are given. A mathematical model of the processes of heat and mass transfer occurring in a thermochemical reactor is developed taking into account the nonequilibrium nature of the course of chemical reactions of fuel conversion. The possibility of using microchannel reaction elements and facilities for methane conversion in order to intensify the process and reduce the overall dimensions of plants is considered. The features of the course of heat and mass transfer processes under flow conditions in microchannel reaction elements are described. Additions have been made to the mathematical model, which makes it possible to use it for microchannel installations. With the help of a mathematical model, distribution of the parameters of mixtures along the length of the reaction element of the reactor-temperature, the concentration of the reacting components, the velocity, and the values of the heat fluxes are obtained. The calculations take into account the change in the thermophysical properties of the mix-ture, the type of the catalytic element, the rate of the reactions, the heat exchange processes by radiation, and the lon-gitudinal heat transfer along the flow of the reacting mixture. The reliability of the results of the application of the mathematical model is confirmed by their comparison with the experimental data obtained by Grasso G., Schaefer G., Schuurman Y., Mirodatos C., Kuznetsov V.V., Vitovsky O.V. on similar installations.

Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models

PubMed Central

Rejniak, Katarzyna A.; Gerlee, Philip

2013-01-01

Summary In this review we summarize our recent efforts using mathematical modeling and computation to simulate cancer invasion, with a special emphasis on the tumor microenvironment. We consider cancer progression as a complex multiscale process and approach it with three single-cell based mathematical models that examine the interactions between tumor microenvironment and cancer cells at several scales. The models exploit distinct mathematical and computational techniques, yet they share core elements and can be compared and/or related to each other. The overall aim of using mathematical models is to uncover the fundamental mechanisms that lend cancer progression its direction towards invasion and metastasis. The models effectively simulate various modes of cancer cell adaptation to the microenvironment in a growing tumor. All three point to a general mechanism underlying cancer invasion: competition for adaptation between distinct cancer cell phenotypes, driven by a tumor microenvironment with scarce resources. These theoretical predictions pose an intriguing experimental challenge: test the hypothesis that invasion is an emergent property of cancer cell populations adapting to selective microenvironment pressure, rather than culmination of cancer progression producing cells with the “invasive phenotype”. In broader terms, we propose that fundamental insights into cancer can be achieved by experimentation interacting with theoretical frameworks provided by computational and mathematical modeling. PMID:18524624

Mathematics and Information Retrieval.

ERIC Educational Resources Information Center

Salton, Gerald

1979-01-01

Examines the main mathematical approaches to information retrieval, including both algebraic and probabilistic models, and describes difficulties which impede formalization of information retrieval processes. A number of developments are covered where new theoretical understandings have directly led to improved retrieval techniques and operations.…

Mathematical Modeling to Reduce Waste of Compounded Sterile Products in Hospital Pharmacies

PubMed Central

Dobson, Gregory; Haas, Curtis E.; Tilson, David

2014-01-01

Abstract In recent years, many US hospitals embarked on “lean” projects to reduce waste. One advantage of the lean operational improvement methodology is that it relies on process observation by those engaged in the work and requires relatively little data. However, the thoughtful analysis of the data captured by operational systems allows the modeling of many potential process options. Such models permit the evaluation of likely waste reductions and financial savings before actual process changes are made. Thus the most promising options can be identified prospectively, change efforts targeted accordingly, and realistic targets set. This article provides one example of such a datadriven process redesign project focusing on waste reduction in an in-hospital pharmacy. A mathematical model of the medication prepared and delivered by the pharmacy is used to estimate the savings from several potential redesign options (rescheduling the start of production, scheduling multiple batches, or reordering production within a batch) as well as the impact of information system enhancements. The key finding is that mathematical modeling can indeed be a useful tool. In one hospital setting, it estimated that waste could be realistically reduced by around 50% by using several process changes and that the greatest benefit would be gained by rescheduling the start of production (for a single batch) away from the period when most order cancellations are made. PMID:25477580

Developing teaching process for enhancing students' mathematical problem solving in the 21st century through STEM education

NASA Astrophysics Data System (ADS)

Prawvichien, Sutthaporn; Siripun, Kulpatsorn; Yuenyong, Chokchai

2018-01-01

The STEM education could provide the context for students' learning in the 21st century. The Mathematical problem solving requires a context which simulates real life in order to give students experience of the power of mathematics in the world around them. This study aimed to develop the teaching process for enhancing students' mathematical problem solving in the 21st century through STEM education. The paper will clarify the STEM learning activities about graph theories regarding on the 6 steps of engineering design process. These include identify a challenge, exploring ideas, designing and planning, doing and developing, test and evaluate, and present the solution. The learning activities will start from the Identify a challenge stage which provides the northern part of Thailand flooding situation in order to set the students' tasks of develop the solutions of providing the routes of fastest moving people away from the flooding areas. The explore ideas stage will provide activities for enhance students to learn some knowledge based for designing the possible solutions. This knowledge based could focus on measuring, geometry, graph theory, and mathematical process. The design and plan stage will ask students to model the city based on the map and then provide the possible routes. The doing and development stage will ask students to develop the routes based on their possible model. The test and evaluating will ask students to clarify how to test and evaluate the possible routes, and then test it. The present solution stage will ask students to present the whole process of designing routes. Then, the paper will discuss how these learning activities could enhance students' mathematical problem solving. The paper may have implication for STEM education in school setting.

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

Forest forming process and dynamic vegetation models under global change

Treesearch

A. Shvidenko; E. Gustafson

2009-01-01

The paper analyzes mathematical models that are used to project the dynamics of forest ecosystems on different spatial and temporal scales. Landscape disturbance and succession models (LDSMs) are of a particular interest for studying the forest forming process in Northern Eurasia. They have a solid empirical background and are able to model ecological processes under...

Modeling Processes of 4th-Year Middle-School Students and the Difficulties Encountered

ERIC Educational Resources Information Center

Eraslan, Ali; Kant, Sinem

2015-01-01

Mathematics teachers have recently begun to stress the need for teaching models and modeling approaches that encompass cognitive and meta-cognitive thought processes for every level of schooling, starting from primary school through to higher education. The objective of this study is to examine modeling processes with the help of modeling…

Improving science and mathematics education with computational modelling in interactive engagement environments

NASA Astrophysics Data System (ADS)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.

Two-Dimensional Mathematical Modeling of the Pack Carburizing Process

NASA Astrophysics Data System (ADS)

Sarkar, S.; Gupta, G. S.

2008-10-01

Pack carburization is the oldest method among the case-hardening treatments, and sufficient attempts have not been made to understand this process in terms of heat and mass transfer, effect of alloying elements, dimensions of the sample, etc. Thus, a two-dimensional mathematical model in cylindrical coordinate is developed for simulating the pack carburization process for chromium-bearing steel in this study. Heat and mass balance equations are solved simultaneously, where the surface temperature of the sample varies with time, but the carbon potential at the surface during the process remains constant. The fully implicit finite volume technique is used to solve the governing equations. Good agreement has been found between the predicted and published data. The effect of temperature, carburizing time, dimensions of the sample, etc. on the pack carburizing process shows some interesting results. It is found that the two-dimensional model gives better insight into understanding the carburizing process.

Agent based simulations in disease modeling Comment on "Towards a unified approach in the modeling of fibrosis: A review with research perspectives" by Martine Ben Amar and Carlo Bianca

NASA Astrophysics Data System (ADS)

Pappalardo, Francesco; Pennisi, Marzio

2016-07-01

Fibrosis represents a process where an excessive tissue formation in an organ follows the failure of a physiological reparative or reactive process. Mathematical and computational techniques may be used to improve the understanding of the mechanisms that lead to the disease and to test potential new treatments that may directly or indirectly have positive effects against fibrosis [1]. In this scenario, Ben Amar and Bianca [2] give us a broad picture of the existing mathematical and computational tools that have been used to model fibrotic processes at the molecular, cellular, and tissue levels. Among such techniques, agent based models (ABM) can give a valuable contribution in the understanding and better management of fibrotic diseases.

Automated Welding System

NASA Technical Reports Server (NTRS)

Bayless, E. O.; Lawless, K. G.; Kurgan, C.; Nunes, A. C.; Graham, B. F.; Hoffman, D.; Jones, C. S.; Shepard, R.

1993-01-01

Fully automated variable-polarity plasma arc VPPA welding system developed at Marshall Space Flight Center. System eliminates defects caused by human error. Integrates many sensors with mathematical model of the weld and computer-controlled welding equipment. Sensors provide real-time information on geometry of weld bead, location of weld joint, and wire-feed entry. Mathematical model relates geometry of weld to critical parameters of welding process.

The Enhancement of Mathematical Critical Thinking Ability of Aliyah Madrasas Student Model Using Gorontalo by Interactive Learning Setting Cooperative Model

ERIC Educational Resources Information Center

Husnaeni

2016-01-01

Critical thinking ability of students' mathematical is a component that must be mastered by the student. Learn to think critically means using mental processes, such as attention, categorize, selection, and rate/decide. Critical thinking ability in giving proper guidance in thinking and working, and assist in determining the relationship between…

Mathematical Creative Process Wallas Model in Students Problem Posing with Lesson Study Approach

ERIC Educational Resources Information Center

Nuha, Muhammad 'Azmi; Waluya, S. B.; Junaedi, Iwan

2018-01-01

Creative thinking is very important in the modern era so that it should be improved by doing efforts such as making a lesson that train students to pose their own problems. The purposes of this research are (1) to give an initial description of students about mathematical creative thinking level in Problem Posing Model with Lesson Study approach…

Ordinary differential equations with applications in molecular biology.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

Basin-scale hydrogeologic modeling

NASA Astrophysics Data System (ADS)

Person, Mark; Raffensperger, Jeff P.; Ge, Shemin; Garven, Grant

1996-02-01

Mathematical modeling of coupled groundwater flow, heat transfer, and chemical mass transport at the sedimentary basin scale has been increasingly used by Earth scientists studying a wide range of geologic processes including the formation of excess pore pressures, infiltration-driven metamorphism, heat flow anomalies, nuclear waste isolation, hydrothermal ore genesis, sediment diagenesis, basin tectonics, and petroleum generation and migration. These models have provided important insights into the rates and pathways of groundwater migration through basins, the relative importance of different driving mechanisms for fluid flow, and the nature of coupling between the hydraulic, thermal, chemical, and stress regimes. The mathematical descriptions of basin transport processes, the analytical and numerical solution methods employed, and the application of modeling to sedimentary basins around the world are the subject of this review paper. The special considerations made to represent coupled transport processes at the basin scale are emphasized. Future modeling efforts will probably utilize three-dimensional descriptions of transport processes, incorporate greater information regarding natural geological heterogeneity, further explore coupled processes, and involve greater field applications.

Mathematical modeling of simultaneous carbon-nitrogen-sulfur removal from industrial wastewater.

PubMed

Xu, Xi-Jun; Chen, Chuan; Wang, Ai-Jie; Ni, Bing-Jie; Guo, Wan-Qian; Yuan, Ye; Huang, Cong; Zhou, Xu; Wu, Dong-Hai; Lee, Duu-Jong; Ren, Nan-Qi

2017-01-05

A mathematical model of carbon, nitrogen and sulfur removal (C-N-S) from industrial wastewater was constructed considering the interactions of sulfate-reducing bacteria (SRB), sulfide-oxidizing bacteria (SOB), nitrate-reducing bacteria (NRB), facultative bacteria (FB), and methane producing archaea (MPA). For the kinetic network, the bioconversion of C-N by heterotrophic denitrifiers (NO 3 - →NO 2 - →N 2 ), and that of C-S by SRB (SO 4 2- →S 2- ) and SOB (S 2- →S 0 ) was proposed and calibrated based on batch experimental data. The model closely predicted the profiles of nitrate, nitrite, sulfate, sulfide, lactate, acetate, methane and oxygen under both anaerobic and micro-aerobic conditions. The best-fit kinetic parameters had small 95% confidence regions with mean values approximately at the center. The model was further validated using independent data sets generated under different operating conditions. This work was the first successful mathematical modeling of simultaneous C-N-S removal from industrial wastewater and more importantly, the proposed model was proven feasible to simulate other relevant processes, such as sulfate-reducing, sulfide-oxidizing process (SR-SO) and denitrifying sulfide removal (DSR) process. The model developed is expected to enhance our ability to predict the treatment of carbon-nitrogen-sulfur contaminated industrial wastewater. Copyright © 2016 Elsevier B.V. All rights reserved.

Numerical simulation of the coaxial magneto-plasma accelerator and non-axisymmetric radio frequency discharge

NASA Astrophysics Data System (ADS)

Kuzenov, V. V.; Ryzhkov, S. V.; Frolko, P. A.

2017-05-01

The paper presents the results of mathematical modeling of physical processes in electronic devices such as helicon discharge and coaxial pulsed plasma thruster. A mathematical model of coaxial magneto-plasma accelerator (with a preionization helicon discharge), which allows estimating the transformation of one form of energy to another, as well as to evaluate the level of the contribution of different types of energy, the increase in mass of the accelerated plasmoid in the process of changing the speed. Main plasma parameters with experimental data were compared.

Mathematical modeling of the process of filling a mold during injection molding of ceramic products

NASA Astrophysics Data System (ADS)

Kulkov, S. N.; Korobenkov, M. V.; Bragin, N. A.

2015-10-01

Using the software package Fluent it have been predicted of the filling of a mold in injection molding of ceramic products is of great importance, because the strength of the final product is directly related to the presence of voids in the molding, making possible early prediction of inaccuracies in the mold prior to manufacturing. The calculations were performed in the formulation of mathematical modeling of hydrodynamic turbulent process of filling a predetermined volume of a viscous liquid. The model used to determine the filling forms evaluated the influence of density and viscosity of the feedstock, and the injection pressure on the mold filling process to predict the formation of voids in the area caused by the shape defect geometry.

Theoretical models for supercritical fluid extraction.

PubMed

Huang, Zhen; Shi, Xiao-Han; Jiang, Wei-Juan

2012-08-10

For the proper design of supercritical fluid extraction processes, it is essential to have a sound knowledge of the mass transfer mechanism of the extraction process and the appropriate mathematical representation. In this paper, the advances and applications of kinetic models for describing supercritical fluid extraction from various solid matrices have been presented. The theoretical models overviewed here include the hot ball diffusion, broken and intact cell, shrinking core and some relatively simple models. Mathematical representations of these models have been in detail interpreted as well as their assumptions, parameter identifications and application examples. Extraction process of the analyte solute from the solid matrix by means of supercritical fluid includes the dissolution of the analyte from the solid, the analyte diffusion in the matrix and its transport to the bulk supercritical fluid. Mechanisms involved in a mass transfer model are discussed in terms of external mass transfer resistance, internal mass transfer resistance, solute-solid interactions and axial dispersion. The correlations of the external mass transfer coefficient and axial dispersion coefficient with certain dimensionless numbers are also discussed. Among these models, the broken and intact cell model seems to be the most relevant mathematical model as it is able to provide realistic description of the plant material structure for better understanding the mass-transfer kinetics and thus it has been widely employed for modeling supercritical fluid extraction of natural matters. Copyright © 2012 Elsevier B.V. All rights reserved.

Specific modes of vibratory technological machines: mathematical models, peculiarities of interaction of system elements

NASA Astrophysics Data System (ADS)

Eliseev, A. V.; Sitov, I. S.; Eliseev, S. V.

2018-03-01

The methodological basis of constructing mathematical models of vibratory technological machines is developed in the article. An approach is proposed that makes it possible to introduce a vibration table in a specific mode that provides conditions for the dynamic damping of oscillations for the zone of placement of a vibration exciter while providing specified vibration parameters in the working zone of the vibration table. The aim of the work is to develop methods of mathematical modeling, oriented to technological processes with long cycles. The technologies of structural mathematical modeling are used with structural schemes, transfer functions and amplitude-frequency characteristics. The concept of the work is to test the possibilities of combining the conditions for reducing loads with working components of a vibration exciter while simultaneously maintaining sufficiently wide limits in variating the parameters of the vibrational field.

Mathematical modeling of ignition of woodlands resulted from accident on the pipeline

NASA Astrophysics Data System (ADS)

Perminov, V. A.; Loboda, E. L.; Reyno, V. V.

2014-11-01

Accidents occurring at the sites of pipelines, accompanied by environmental damage, economic loss, and sometimes loss of life. In this paper we calculated the sizes of the possible ignition zones in emergency situations on pipelines located close to the forest, accompanied by the appearance of fireballs. In this paper, using the method of mathematical modeling calculates the maximum size of the ignition zones of vegetation as a result of accidental releases of flammable substances. The paper suggested in the context of the general mathematical model of forest fires give a new mathematical setting and method of numerical solution of a problem of a forest fire modeling. The boundary-value problem is solved numerically using the method of splitting according to physical processes. The dependences of the size of the forest fuel for different amounts of leaked flammable substances and moisture content of vegetation.

A comparison of mixed-integer linear programming models for workforce scheduling with position-dependent processing times

NASA Astrophysics Data System (ADS)

Moreno-Camacho, Carlos A.; Montoya-Torres, Jairo R.; Vélez-Gallego, Mario C.

2018-06-01

Only a few studies in the available scientific literature address the problem of having a group of workers that do not share identical levels of productivity during the planning horizon. This study considers a workforce scheduling problem in which the actual processing time is a function of the scheduling sequence to represent the decline in workers' performance, evaluating two classical performance measures separately: makespan and maximum tardiness. Several mathematical models are compared with each other to highlight the advantages of each approach. The mathematical models are tested with randomly generated instances available from a public e-library.

Brief Report: Preliminary Proposal of a Conceptual Model of a Digital Environment for Developing Mathematical Reasoning in Students with Autism Spectrum Disorders.

PubMed

Santos, Maria Isabel; Breda, Ana; Almeida, Ana Margarida

2015-08-01

There is clear evidence that in typically developing children reasoning and sense-making are essential in all mathematical learning and understanding processes. In children with autism spectrum disorders (ASD), however, these become much more significant, considering their importance to successful independent living. This paper presents a preliminary proposal of a digital environment, specifically targeted to promote the development of mathematical reasoning in students with ASD. Given the diversity of ASD, the prototyping of this environment requires the study of dynamic adaptation processes and the development of activities adjusted to each user's profile. We present the results obtained during the first phase of this ongoing research, describing a conceptual model of the proposed digital environment. Guidelines for future research are also discussed.

Pyroelectric effect in tryglicyne sulphate single crystals - Differential measurement method

NASA Astrophysics Data System (ADS)

Trybus, M.

2018-06-01

A simple mathematical model of the pyroelectric phenomenon was used to explain the electric response of the TGS (triglycine sulphate) samples in the linear heating process in ferroelectric and paraelectric phases. Experimental verification of mathematical model was realized. TGS single crystals were grown and four electrode samples were fabricated. Differential measurements of the pyroelectric response of two different regions of the samples were performed and the results were compared with data obtained from the model. Experimental results are in good agreement with model calculations.

Novel mathematic models for quantitative transitivity of quality-markers in extraction process of the Buyanghuanwu decoction.

PubMed

Zhang, Yu-Tian; Xiao, Mei-Feng; Deng, Kai-Wen; Yang, Yan-Tao; Zhou, Yi-Qun; Zhou, Jin; He, Fu-Yuan; Liu, Wen-Long

2018-06-01

Nowadays, to research and formulate an efficiency extraction system for Chinese herbal medicine, scientists have always been facing a great challenge for quality management, so that the transitivity of Q-markers in quantitative analysis of TCM was proposed by Prof. Liu recently. In order to improve the quality of extraction from raw medicinal materials for clinical preparations, a series of integrated mathematic models for transitivity of Q-markers in quantitative analysis of TCM were established. Buyanghuanwu decoction (BYHWD) was a commonly TCMs prescription, which was used to prevent and treat the ischemic heart and brain diseases. In this paper, we selected BYHWD as an extraction experimental subject to study the quantitative transitivity of TCM. Based on theory of Fick's Rule and Noyes-Whitney equation, novel kinetic models were established for extraction of active components. Meanwhile, fitting out kinetic equations of extracted models and then calculating the inherent parameters in material piece and Q-marker quantitative transfer coefficients, which were considered as indexes to evaluate transitivity of Q-markers in quantitative analysis of the extraction process of BYHWD. HPLC was applied to screen and analyze the potential Q-markers in the extraction process. Fick's Rule and Noyes-Whitney equation were adopted for mathematically modeling extraction process. Kinetic parameters were fitted and calculated by the Statistical Program for Social Sciences 20.0 software. The transferable efficiency was described and evaluated by potential Q-markers transfer trajectory via transitivity availability AUC, extraction ratio P, and decomposition ratio D respectively. The Q-marker was identified with AUC, P, D. Astragaloside IV, laetrile, paeoniflorin, and ferulic acid were studied as potential Q-markers from BYHWD. The relative technologic parameters were presented by mathematic models, which could adequately illustrate the inherent properties of raw materials preparation and affection of Q-markers transitivity in equilibrium processing. AUC, P, D for potential Q-markers of AST-IV, laetrile, paeoniflorin, and FA were obtained, with the results of 289.9 mAu s, 46.24%, 22.35%; 1730 mAu s, 84.48%, 1.963%; 5600 mAu s, 70.22%, 0.4752%; 7810 mAu s, 24.29%, 4.235%, respectively. The results showed that the suitable Q-markers were laetrile and paeoniflorin in our study, which exhibited acceptable traceability and transitivity in the extraction process of TCMs. Therefore, these novel mathematic models might be developed as a new standard to control TCMs quality process from raw medicinal materials to product manufacturing. Copyright © 2018 Elsevier GmbH. All rights reserved.

Implementation of cooperative learning model type STAD with RME approach to understanding of mathematical concept student state junior high school in Pekanbaru

NASA Astrophysics Data System (ADS)

Nurhayati, Dian Mita; Hartono

2017-05-01

This study aims to determine whether there is a difference in the ability of understanding the concept of mathematics between students who use cooperative learning model Student Teams Achievement Division type with Realistic Mathematic Education approach and students who use regular learning in seventh grade SMPN 35 Pekanbaru. This study was quasi experiments with Posttest-only Control Design. The populations in this research were all the seventh grade students in one of state junior high school in Pekanbaru. The samples were a class that is used as the experimental class and one other as the control class. The process of sampling is using purposive sampling technique. Retrieval of data in this study using the documentation, observation sheets, and test. The test use t-test formula to determine whether there is a difference in student's understanding of mathematical concepts. Before the t-test, should be used to test the homogeneity and normality. Based in the analysis of these data with t0 = 2.9 there is a difference in student's understanding of mathematical concepts between experimental and control class. Percentage of students experimental class with score more than 65 was 76.9% and 56.4% of students control class. Thus be concluded, the ability of understanding mathematical concepts students who use the cooperative learning model type STAD with RME approach better than students using the regular learning. So that cooperative learning model type STAD with RME approach is well used in learning process.

Reverse engineering of aircraft wing data using a partial differential equation surface model

NASA Astrophysics Data System (ADS)

Huband, Jacalyn Mann

Reverse engineering is a multi-step process used in industry to determine a production representation of an existing physical object. This representation is in the form of mathematical equations that are compatible with computer-aided design and computer-aided manufacturing (CAD/CAM) equipment. The four basic steps to the reverse engineering process are data acquisition, data separation, surface or curve fitting, and CAD/CAM production. The surface fitting step determines the design representation of the object, and thus is critical to the success or failure of the reverse engineering process. Although surface fitting methods described in the literature are used to model a variety of surfaces, they are not suitable for reversing aircraft wings. In this dissertation, we develop and demonstrate a new strategy for reversing a mathematical representation of an aircraft wing. The basis of our strategy is to take an aircraft design model and determine if an inverse model can be derived. A candidate design model for this research is the partial differential equation (PDE) surface model, proposed by Bloor and Wilson and used in the Rapid Airplane Parameter Input Design (RAPID) tool at the NASA-LaRC Geolab. There are several basic mathematical problems involved in reversing the PDE surface model: (i) deriving a computational approximation of the surface function; (ii) determining a radial parametrization of the wing; (iii) choosing mathematical models or classes of functions for representation of the boundary functions; (iv) fitting the boundary data points by the chosen boundary functions; and (v) simultaneously solving for the axial parameterization and the derivative boundary functions. The study of the techniques to solve the above mathematical problems has culminated in a reverse PDE surface model and two reverse PDE surface algorithms. One reverse PDE surface algorithm recovers engineering design parameters for the RAPID tool from aircraft wing data and the other generates a PDE surface model with spline boundary functions from an arbitrary set of grid points. Our numerical tests show that the reverse PDE surface model and the reverse PDE surface algorithms can be used for the reverse engineering of aircraft wing data.

Mathematical models used to inform study design or surveillance systems in infectious diseases: a systematic review.

PubMed

Herzog, Sereina A; Blaizot, Stéphanie; Hens, Niel

2017-12-18

Mathematical models offer the possibility to investigate the infectious disease dynamics over time and may help in informing design of studies. A systematic review was performed in order to determine to what extent mathematical models have been incorporated into the process of planning studies and hence inform study design for infectious diseases transmitted between humans and/or animals. We searched Ovid Medline and two trial registry platforms (Cochrane, WHO) using search terms related to infection, mathematical model, and study design from the earliest dates to October 2016. Eligible publications and registered trials included mathematical models (compartmental, individual-based, or Markov) which were described and used to inform the design of infectious disease studies. We extracted information about the investigated infection, population, model characteristics, and study design. We identified 28 unique publications but no registered trials. Focusing on compartmental and individual-based models we found 12 observational/surveillance studies and 11 clinical trials. Infections studied were equally animal and human infectious diseases for the observational/surveillance studies, while all but one between humans for clinical trials. The mathematical models were used to inform, amongst other things, the required sample size (n = 16), the statistical power (n = 9), the frequency at which samples should be taken (n = 6), and from whom (n = 6). Despite the fact that mathematical models have been advocated to be used at the planning stage of studies or surveillance systems, they are used scarcely. With only one exception, the publications described theoretical studies, hence, not being utilised in real studies.

Data-based mathematical modeling of vectorial transport across double-transfected polarized cells.

PubMed

Bartholomé, Kilian; Rius, Maria; Letschert, Katrin; Keller, Daniela; Timmer, Jens; Keppler, Dietrich

2007-09-01

Vectorial transport of endogenous small molecules, toxins, and drugs across polarized epithelial cells contributes to their half-life in the organism and to detoxification. To study vectorial transport in a quantitative manner, an in vitro model was used that includes polarized MDCKII cells stably expressing the recombinant human uptake transporter OATP1B3 in their basolateral membrane and the recombinant ATP-driven efflux pump ABCC2 in their apical membrane. These double-transfected cells enabled mathematical modeling of the vectorial transport of the anionic prototype substance bromosulfophthalein (BSP) that has frequently been used to examine hepatobiliary transport. Time-dependent analyses of (3)H-labeled BSP in the basolateral, intracellular, and apical compartments of cells cultured on filter membranes and efflux experiments in cells preloaded with BSP were performed. A mathematical model was fitted to the experimental data. Data-based modeling was optimized by including endogenous transport processes in addition to the recombinant transport proteins. The predominant contributions to the overall vectorial transport of BSP were mediated by OATP1B3 (44%) and ABCC2 (28%). Model comparison predicted a previously unrecognized endogenous basolateral efflux process as a negative contribution to total vectorial transport, amounting to 19%, which is in line with the detection of the basolateral efflux pump Abcc4 in MDCKII cells. Rate-determining steps in the vectorial transport were identified by calculating control coefficients. Data-based mathematical modeling of vectorial transport of BSP as a model substance resulted in a quantitative description of this process and its components. The same systems biology approach may be applied to other cellular systems and to different substances.

Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach.

PubMed

Campitelli, Guillermo; Gerrans, Paul

2014-04-01

We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research.

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

PubMed

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

2017-07-01

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

Mathematical modeling and characteristic analysis for over-under turbine based combined cycle engine

NASA Astrophysics Data System (ADS)

Ma, Jingxue; Chang, Juntao; Ma, Jicheng; Bao, Wen; Yu, Daren

2018-07-01

The turbine based combined cycle engine has become the most promising hypersonic airbreathing propulsion system for its superiority of ground self-starting, wide flight envelop and reusability. The simulation model of the turbine based combined cycle engine plays an important role in the research of performance analysis and control system design. In this paper, a turbine based combined cycle engine mathematical model is built on the Simulink platform, including a dual-channel air intake system, a turbojet engine and a ramjet. It should be noted that the model of the air intake system is built based on computational fluid dynamics calculation, which provides valuable raw data for modeling of the turbine based combined cycle engine. The aerodynamic characteristics of turbine based combined cycle engine in turbojet mode, ramjet mode and mode transition process are studied by the mathematical model, and the influence of dominant variables on performance and safety of the turbine based combined cycle engine is analyzed. According to the stability requirement of thrust output and the safety in the working process of turbine based combined cycle engine, a control law is proposed that could guarantee the steady output of thrust by controlling the control variables of the turbine based combined cycle engine in the whole working process.

Mathematics: Program Assessment and Improvement Planning Manual.

ERIC Educational Resources Information Center

Whitman, Nancy C.; And Others

This document provides a model for assessing a school's mathematics program and planning for program improvement. A systematic process for instructional improvement focuses upon students' needs and the identification of successful instructional strategies to meet these needs. The improvement plan and the implementation of intervention strategies…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua

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

Mathematical Modelling of Continuous Biotechnological Processes

ERIC Educational Resources Information Center

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

2003-01-01

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

Neural mechanisms of the mind, Aristotle, Zadeh, and fMRI.

PubMed

Perlovsky, Leonid I

2010-05-01

Processes in the mind: perception, cognition, concepts, instincts, emotions, and higher cognitive abilities for abstract thinking, beautiful music are considered here within a neural modeling fields (NMFs) paradigm. Its fundamental mathematical mechanism is a process "from vague-fuzzy to crisp," called dynamic logic (DL). This paper discusses why this paradigm is necessary mathematically, and relates it to a psychological description of the mind. Surprisingly, the process from "vague to crisp" corresponds to Aristotelian understanding of mental functioning. Recent functional magnetic resonance imaging (fMRI) measurements confirmed this process in neural mechanisms of perception.

Power Laws in Stochastic Processes for Social Phenomena: An Introductory Review

NASA Astrophysics Data System (ADS)

Kumamoto, Shin-Ichiro; Kamihigashi, Takashi

2018-03-01

Many phenomena with power laws have been observed in various fields of the natural and social sciences, and these power laws are often interpreted as the macro behaviors of systems that consist of micro units. In this paper, we review some basic mathematical mechanisms that are known to generate power laws. In particular, we focus on stochastic processes including the Yule process and the Simon process as well as some recent models. The main purpose of this paper is to explain the mathematical details of their mechanisms in a self-contained manner.

From biology to mathematical models and back: teaching modeling to biology students, and biology to math and engineering students.

PubMed

Chiel, Hillel J; McManus, Jeffrey M; Shaw, Kendrick M

2010-01-01

We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge that they find difficult. To give students a sense of mastery in each area, several complementary approaches are used in the course: 1) a "live" textbook that allows students to explore models and mathematical processes interactively; 2) benchmark problems providing key skills on which students make continuous progress; 3) assignment of students to teams of two throughout the semester; 4) regular one-on-one interactions with instructors throughout the semester; and 5) a term project in which students reconstruct, analyze, extend, and then write in detail about a recently published biological model. Based on student evaluations and comments, an attitude survey, and the quality of the students' term papers, the course has significantly increased the ability and willingness of biology students to use mathematical concepts and modeling tools to understand biological systems, and it has significantly enhanced engineering students' appreciation of biology.

[Mathematic concept model of accumulation of functional disorders associated with environmental factors].

PubMed

Zaĭtseva, N V; Trusov, P V; Kir'ianov, D A

2012-01-01

The mathematic concept model presented describes accumulation of functional disorders associated with environmental factors, plays predictive role and is designed for assessments of possible effects caused by heterogenous factors with variable exposures. Considering exposure changes with self-restoration process opens prospects of using the model to evaluate, analyse and manage occupational risks. To develop current theoretic approaches, the authors suggested a model considering age-related body peculiarities, systemic interactions of organs, including neuro-humoral regulation, accumulation of functional disorders due to external factors, rehabilitation of functions during treatment. General objective setting covers defining over a hundred unknow coefficients that characterize speed of various processes within the body. To solve this problem, the authors used iteration approach, successive identification, that starts from the certain primary approximation of the model parameters and processes subsequent updating on the basis of new theoretic and empirical knowledge.

Composite mathematical modeling of calcium signaling behind neuronal cell death in Alzheimer's disease.

PubMed

Ranjan, Bobby; Chong, Ket Hing; Zheng, Jie

2018-04-11

Alzheimer's disease (AD) is a progressive neurological disorder, recognized as the most common cause of dementia affecting people aged 65 and above. AD is characterized by an increase in amyloid metabolism, and by the misfolding and deposition of β-amyloid oligomers in and around neurons in the brain. These processes remodel the calcium signaling mechanism in neurons, leading to cell death via apoptosis. Despite accumulating knowledge about the biological processes underlying AD, mathematical models to date are restricted to depicting only a small portion of the pathology. Here, we integrated multiple mathematical models to analyze and understand the relationship among amyloid depositions, calcium signaling and mitochondrial permeability transition pore (PTP) related cell apoptosis in AD. The model was used to simulate calcium dynamics in the absence and presence of AD. In the absence of AD, i.e. without β-amyloid deposition, mitochondrial and cytosolic calcium level remains in the low resting concentration. However, our in silico simulation of the presence of AD with the β-amyloid deposition, shows an increase in the entry of calcium ions into the cell and dysregulation of Ca 2+ channel receptors on the Endoplasmic Reticulum. This composite model enabled us to make simulation that is not possible to measure experimentally. Our mathematical model depicting the mechanisms affecting calcium signaling in neurons can help understand AD at the systems level and has potential for diagnostic and therapeutic applications.

Problem solving in the borderland between mathematics and physics

NASA Astrophysics Data System (ADS)

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization.

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

Price-Dynamics of Shares and Bohmian Mechanics: Deterministic or Stochastic Model?

NASA Astrophysics Data System (ADS)

Choustova, Olga

2007-02-01

We apply the mathematical formalism of Bohmian mechanics to describe dynamics of shares. The main distinguishing feature of the financial Bohmian model is the possibility to take into account market psychology by describing expectations of traders by the pilot wave. We also discuss some objections (coming from conventional financial mathematics of stochastic processes) against the deterministic Bohmian model. In particular, the objection that such a model contradicts to the efficient market hypothesis which is the cornerstone of the modern market ideology. Another objection is of pure mathematical nature: it is related to the quadratic variation of price trajectories. One possibility to reply to this critique is to consider the stochastic Bohm-Vigier model, instead of the deterministic one. We do this in the present note.

The Local Brewery: A Project for Use in Differential Equations Courses

ERIC Educational Resources Information Center

Starling, James K.; Povich, Timothy J.; Findlay, Michael

2016-01-01

We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

A Mathematical Model for Pathogen Cross-Contamination Dynamics during the Postharvest Processing of Leafy Greens.

PubMed

Mokhtari, Amir; Oryang, David; Chen, Yuhuan; Pouillot, Regis; Van Doren, Jane

2018-01-08

We developed a probabilistic mathematical model for the postharvest processing of leafy greens focusing on Escherichia coli O157:H7 contamination of fresh-cut romaine lettuce as the case study. Our model can (i) support the investigation of cross-contamination scenarios, and (ii) evaluate and compare different risk mitigation options. We used an agent-based modeling framework to predict the pathogen prevalence and levels in bags of fresh-cut lettuce and quantify spread of E. coli O157:H7 from contaminated lettuce to surface areas of processing equipment. Using an unbalanced factorial design, we were able to propagate combinations of random values assigned to model inputs through different processing steps and ranked statistically significant inputs with respect to their impacts on selected model outputs. Results indicated that whether contamination originated on incoming lettuce heads or on the surface areas of processing equipment, pathogen prevalence among bags of fresh-cut lettuce and batches was most significantly impacted by the level of free chlorine in the flume tank and frequency of replacing the wash water inside the tank. Pathogen levels in bags of fresh-cut lettuce were most significantly influenced by the initial levels of contamination on incoming lettuce heads or surface areas of processing equipment. The influence of surface contamination on pathogen prevalence or levels in fresh-cut bags depended on the location of that surface relative to the flume tank. This study demonstrates that developing a flexible yet mathematically rigorous modeling tool, a "virtual laboratory," can provide valuable insights into the effectiveness of individual and combined risk mitigation options. © 2018 The Authors Risk Analysis published by Wiley Periodicals, Inc. on behalf of Society for Risk Analysis.

Mathematical model of rolling an elastic wheel over deformable support base

NASA Astrophysics Data System (ADS)

Volskaia, V. N.; Zhileykin, M. M.; Zakharov, A. Y.

2018-02-01

One of the main direction of economic growth in Russia remains to be a speedy development of north and northeast regions that are the constituents of the 60 percent of the country territory. The further development of these territories requires new methods and technologies for solving transport and technological problems when off-road transportation of cargoes and people is conducting. One of the fundamental methods of patency prediction is imitation modeling of wheeled vehicles movement in different operating conditions. Both deformable properties of tires and physical and mechanical properties of the ground: normal tire deflection and gauge depth; variation of contact patch area depending on the load and pressure of air in the tire; existence of hysteresis losses in the tire material which are influencing on the rolling resistance due to friction processes between tire and ground in the contact patch; existence of the tangential reaction from the ground by entire contact area influence on the tractive patency. Nowadays there are two main trends in theoretical research of interaction wheeled propulsion device with ground: analytical method involving mathematical description of explored process and finite element method based on computational modeling. Mathematical models of interaction tire with the ground are used both in processes of interaction individual wheeled propulsion device with ground and researches of mobile vehicle dynamical models operated in specific road and climate conditions. One of the most significant imperfection of these models is the description of interaction wheel with flat deformable support base whereas profile of real support base surface has essential height of unevenness which is commensurate with radius of the wheel. The description of processes taking place in the ground under influence of the wheeled propulsion device using the finite element method is relatively new but most applicable lately. The application of this method allows to provide the most accurate description of the interaction process of a wheeled propulsion devices and the ground, also this method allows to define tension in the ground, deformation of the ground and the tire and ground’s compression. However, the high laboriousness of computations is essential shortcoming of that method therefore it’s hard to use these models as part of the general motion model of multi-axis wheeled vehicles. The purpose of this research is the elaboration of mathematical model of elastic wheel rolling over deformable rough support base taking into account the contact patch deformation. The mathematical model of rectilinear rolling an elastic wheel over rough deformable support base, taking into account variation of contact patch area and variation in the direction of the radial and tangential reactions also load bearing capacity of the ground, is developed. The efficiency of developed mathematical model of rectilinear rolling an elastic wheel over rough deformable support base is proved by the simulation methods.

Multiple Scales in Fluid Dynamics and Meteorology: The DFG Priority Programme 1276 MetStröm

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

Geophysical fluid motions are characterized by a very wide range of length and time scales, and by a rich collection of varying physical phenomena. The mathematical description of these motions reflects this multitude of scales and mechanisms in that it involves strong non-linearities and various scale-dependent singular limit regimes. Considerable progress has been made in recent years in the mathematical modelling and numerical simulation of such flows in detailed process studies, numerical weather forecasting, and climate research. One task of outstanding importance in this context has been and will remain for the foreseeable future the subgrid scale parameterization of the net effects of non-resolved processes that take place on spacio-temporal scales not resolvable even by the largest most recent supercomputers. Since the advent of numerical weather forecasting some 60 years ago, one simple but efficient means to achieve improved forecasting skills has been increased spacio-temporal resolution. This seems quite consistent with the concept of convergence of numerical methods in Applied Mathematics and Computational Fluid Dynamics (CFD) at a first glance. Yet, the very notion of increased resolution in atmosphere-ocean science is very different from the one used in Applied Mathematics: For the mathematician, increased resolution provides the benefit of getting closer to the ideal of a converged solution of some given partial differential equations. On the other hand, the atmosphere-ocean scientist would naturally refine the computational grid and adjust his mathematical model, such that it better represents the relevant physical processes that occur at smaller scales. This conceptual contradiction remains largely irrelevant as long as geophysical flow models operate with fixed computational grids and time steps and with subgrid scale parameterizations being optimized accordingly. The picture changes fundamentally when modern techniques from CFD involving spacio-temporal grid adaptivity get invoked in order to further improve the net efficiency in exploiting the given computational resources. In the setting of geophysical flow simulation one must then employ subgrid scale parameterizations that dynamically adapt to the changing grid sizes and time steps, implement ways to judiciously control and steer the newly available flexibility of resolution, and invent novel ways of quantifying the remaining errors. The DFG priority program MetStröm covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of this priority programme is to provide simulation models which combine scale-dependent (mathematical) descriptions of key physical processes with adaptive flow discretization schemes. Deterministic continuous approaches and discrete and/or stochastic closures and their possible interplay are taken into consideration. Research focuses on the theory and methodology of multiscale meteorological-fluid mechanics modelling. Accompanying reference experiments support model validation.

Software and mathematical support of Kazakhstani star tracker

NASA Astrophysics Data System (ADS)

Akhmedov, D.; Yelubayev, S.; Ten, V.; Bopeyev, T.; Alipbayev, K.; Sukhenko, A.

2016-10-01

Currently the specialists of Kazakhstan have been developing the star tracker that is further planned to use on Kazakhstani satellites of various purposes. At the first stage it has been developed the experimental model of star tracker that has following characteristics: field of view 20°, update frequency 2 Hz, exclusion angle 40°, accuracy of attitude determination of optical axis/around optical axis 15/50 arcsec. Software and mathematical support are the most high technology parts of star tracker. The results of software and mathematical support development of experimental model of Kazakhstani star tracker are represented in this article. In particular, there are described the main mathematical models and algorithms that have been used as a basis for program units of preliminary image processing of starry sky, stars identification and star tracker attitude determination. The results of software and mathematical support testing with the help of program simulation complex using various configurations of defects including image sensor noises, point spread function modeling, optical system distortion up to 2% are presented. Analysis of testing results has shown that accuracy of attitude determination of star tracker is within the permissible range

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…

Simulation of Solar Energy Use in Livelihood of Buildings

NASA Astrophysics Data System (ADS)

Lvocich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2017-11-01

Solar energy can be considered as the most technological and economical type of renewable energy. The purpose of the paper is to increase the efficiency of solar energy utilization on the basis of the mathematical simulation of the solar collector. A mathematical model of the radiant heat transfer vacuum solar collector is clarified. The model was based on the process of radiative heat transfer between glass and copper walls with the defined blackness degrees. A mathematical model of the ether phase transition point is developed. The dependence of the reservoir walls temperature change on the ambient temperature over time is obtained. The results of the paper can be useful for the development of prospective sources using solar energy.

Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.

PubMed

Robin, Eric; Valle, Valéry; Brémand, Fabrice

2005-12-01

The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

Automated information system for analysis and prediction of production situations in blast furnace plant

NASA Astrophysics Data System (ADS)

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

2016-09-01

Advances in modern science and technology are inherently connected with the development, implementation, and widespread use of computer systems based on mathematical modeling. Algorithms and computer systems are gaining practical significance solving a range of process tasks in metallurgy of MES-level (Manufacturing Execution Systems - systems controlling industrial process) of modern automated information systems at the largest iron and steel enterprises in Russia. This fact determines the necessity to develop information-modeling systems based on mathematical models that will take into account the physics of the process, the basics of heat and mass exchange, the laws of energy conservation, and also the peculiarities of the impact of technological and standard characteristics of raw materials on the manufacturing process data. Special attention in this set of operations for metallurgic production is devoted to blast-furnace production, as it consumes the greatest amount of energy, up to 50% of the fuel used in ferrous metallurgy. The paper deals with the requirements, structure and architecture of BF Process Engineer's Automated Workstation (AWS), a computer decision support system of MES Level implemented in the ICS of the Blast Furnace Plant at Magnitogorsk Iron and Steel Works. It presents a brief description of main model subsystems as well as assumptions made in the process of mathematical modelling. Application of the developed system allows the engineering and process staff to analyze online production situations in the blast furnace plant, to solve a number of process tasks related to control of heat, gas dynamics and slag conditions of blast-furnace smelting as well as to calculate the optimal composition of blast-furnace slag, which eventually results in increasing technical and economic performance of blast-furnace production.

Statistical analysis of experimental data for mathematical modeling of physical processes in the atmosphere

NASA Astrophysics Data System (ADS)

Karpushin, P. A.; Popov, Yu B.; Popova, A. I.; Popova, K. Yu; Krasnenko, N. P.; Lavrinenko, A. V.

2017-11-01

In this paper, the probabilities of faultless operation of aerologic stations are analyzed, the hypothesis of normality of the empirical data required for using the Kalman filter algorithms is tested, and the spatial correlation functions of distributions of meteorological parameters are determined. The results of a statistical analysis of two-term (0, 12 GMT) radiosonde observations of the temperature and wind velocity components at some preset altitude ranges in the troposphere in 2001-2016 are presented. These data can be used in mathematical modeling of physical processes in the atmosphere.

Genetic programming-based mathematical modeling of influence of weather parameters in BOD5 removal by Lemna minor.

PubMed

Chandrasekaran, Sivapragasam; Sankararajan, Vanitha; Neelakandhan, Nampoothiri; Ram Kumar, Mahalakshmi

2017-11-04

This study, through extensive experiments and mathematical modeling, reveals that other than retention time and wastewater temperature (T w ), atmospheric parameters also play important role in the effective functioning of aquatic macrophyte-based treatment system. Duckweed species Lemna minor is considered in this study. It is observed that the combined effect of atmospheric temperature (T atm ), wind speed (U w ), and relative humidity (RH) can be reflected through one parameter, namely the "apparent temperature" (T a ). A total of eight different models are considered based on the combination of input parameters and the best mathematical model is arrived at which is validated through a new experimental set-up outside the modeling period. The validation results are highly encouraging. Genetic programming (GP)-based models are found to reveal deeper understandings of the wetland process.

Mathematic modeling of the Earth's surface and the process of remote sensing

NASA Technical Reports Server (NTRS)

Balter, B. M.

1979-01-01

It is shown that real data from remote sensing of the Earth from outer space are not best suited to the search for optimal procedures with which to process such data. To work out the procedures, it was proposed that data synthesized with the help of mathematical modeling be used. A criterion for simularity to reality was formulated. The basic principles for constructing methods for modeling the data from remote sensing are recommended. A concrete method is formulated for modeling a complete cycle of radiation transformations in remote sensing. A computer program is described which realizes the proposed method. Some results from calculations are presented which show that the method satisfies the requirements imposed on it.

Mathematical models to characterize early epidemic growth: A Review

PubMed Central

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

2016-01-01

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 2014-15 Ebola epidemic in West Africa. PMID:27451336

Mathematical models to characterize early epidemic growth: A review

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

Generalized mathematical model of red muds’ thickener of alumina production

NASA Astrophysics Data System (ADS)

Fedorova, E. R.; Vinogradova, A. A.

2018-03-01

The article describes the principle of a generalized mathematical model of the red mud’s thickener construction. The model of the red muds’ thickener of alumina production consists of sub-models of flocculation zones containing solid fraction feed slurry, free-fall and cramped sedimentation zones or effective sedimentation zones, bleaching zones. The generalized mathematical model of thickener allows predicting the content of solid fraction in the condensed product and in the upper discharge. The sub-model of solid phase aggregation allows one to count up average size of floccules, which is created during the flocculation process in feedwell. The sub-model of the free-fall and cramped sedimentation zone allows one to count up the concentration profile taking into account the variable cross-sectional area of the thickener. The sub-model of the bleaching zone is constructed on the basis of the theory of the precipitation of Kinc, supplemented by correction factors.

Mathematical model of design loading vessel

NASA Astrophysics Data System (ADS)

Budnik, V. Yu

2017-10-01

Transport by ferry is very important in our time. The paper shows the factors that affect the operation of the ferry. The constraints of the designed system were identified. The indicators of quality were articulated. It can be done by means of improving the decision-making process and the choice of the optimum loading options to ensure efficient functioning of Kerch strait ferry line. The algorithm and a mathematical model were developed.

The Poisson Random Process. Applications of Probability Theory to Operations Research. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 340.

ERIC Educational Resources Information Center

Wilde, Carroll O.

The Poisson probability distribution is seen to provide a mathematical model from which useful information can be obtained in practical applications. The distribution and some situations to which it applies are studied, and ways to find answers to practical questions are noted. The unit includes exercises and a model exam, and provides answers to…

Revisiting Dosing Regimen Using Pharmacokinetic/Pharmacodynamic Mathematical Modeling: Densification and Intensification of Combination Cancer Therapy.

PubMed

Meille, Christophe; Barbolosi, Dominique; Ciccolini, Joseph; Freyer, Gilles; Iliadis, Athanassios

2016-08-01

Controlling effects of drugs administered in combination is particularly challenging with a densified regimen because of life-threatening hematological toxicities. We have developed a mathematical model to optimize drug dosing regimens and to redesign the dose intensification-dose escalation process, using densified cycles of combined anticancer drugs. A generic mathematical model was developed to describe the main components of the real process, including pharmacokinetics, safety and efficacy pharmacodynamics, and non-hematological toxicity risk. This model allowed for computing the distribution of the total drug amount of each drug in combination, for each escalation dose level, in order to minimize the average tumor mass for each cycle. This was achieved while complying with absolute neutrophil count clinical constraints and without exceeding a fixed risk of non-hematological dose-limiting toxicity. The innovative part of this work was the development of densifying and intensifying designs in a unified procedure. This model enabled us to determine the appropriate regimen in a pilot phase I/II study in metastatic breast patients for a 2-week-cycle treatment of docetaxel plus epirubicin doublet, and to propose a new dose-ranging process. In addition to the present application, this method can be further used to achieve optimization of any combination therapy, thus improving the efficacy versus toxicity balance of such a regimen.

Bioprocess systems engineering: transferring traditional process engineering principles to industrial biotechnology.

PubMed

Koutinas, Michalis; Kiparissides, Alexandros; Pistikopoulos, Efstratios N; Mantalaris, Athanasios

2012-01-01

The complexity of the regulatory network and the interactions that occur in the intracellular environment of microorganisms highlight the importance in developing tractable mechanistic models of cellular functions and systematic approaches for modelling biological systems. To this end, the existing process systems engineering approaches can serve as a vehicle for understanding, integrating and designing biological systems and processes. Here, we review the application of a holistic approach for the development of mathematical models of biological systems, from the initial conception of the model to its final application in model-based control and optimisation. We also discuss the use of mechanistic models that account for gene regulation, in an attempt to advance the empirical expressions traditionally used to describe micro-organism growth kinetics, and we highlight current and future challenges in mathematical biology. The modelling research framework discussed herein could prove beneficial for the design of optimal bioprocesses, employing rational and feasible approaches towards the efficient production of chemicals and pharmaceuticals.

Bioprocess systems engineering: transferring traditional process engineering principles to industrial biotechnology

PubMed Central

Koutinas, Michalis; Kiparissides, Alexandros; Pistikopoulos, Efstratios N.; Mantalaris, Athanasios

2013-01-01

The complexity of the regulatory network and the interactions that occur in the intracellular environment of microorganisms highlight the importance in developing tractable mechanistic models of cellular functions and systematic approaches for modelling biological systems. To this end, the existing process systems engineering approaches can serve as a vehicle for understanding, integrating and designing biological systems and processes. Here, we review the application of a holistic approach for the development of mathematical models of biological systems, from the initial conception of the model to its final application in model-based control and optimisation. We also discuss the use of mechanistic models that account for gene regulation, in an attempt to advance the empirical expressions traditionally used to describe micro-organism growth kinetics, and we highlight current and future challenges in mathematical biology. The modelling research framework discussed herein could prove beneficial for the design of optimal bioprocesses, employing rational and feasible approaches towards the efficient production of chemicals and pharmaceuticals. PMID:24688682

Wave processes in the human cardiovascular system: The measuring complex, computing models, and diagnostic analysis

NASA Astrophysics Data System (ADS)

Ganiev, R. F.; Reviznikov, D. L.; Rogoza, A. N.; Slastushenskiy, Yu. V.; Ukrainskiy, L. E.

2017-03-01

A description of a complex approach to investigation of nonlinear wave processes in the human cardiovascular system based on a combination of high-precision methods of measuring a pulse wave, mathematical methods of processing the empirical data, and methods of direct numerical modeling of hemodynamic processes in an arterial tree is given.

Adaptive Neurons For Artificial Neural Networks

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1990-01-01

Training time decreases dramatically. In improved mathematical model of neural-network processor, temperature of neurons (in addition to connection strengths, also called weights, of synapses) varied during supervised-learning phase of operation according to mathematical formalism and not heuristic rule. Evidence that biological neural networks also process information at neuronal level.

The Relevance and Efficacy of Metacognition for Instructional Design in the Domain of Mathematics

ERIC Educational Resources Information Center

Baten, Elke; Praet, Magda; Desoete, Annemie

2017-01-01

The efficacy of metacognition as theory-based instructional principle or technique in general, and particularly in mathematics, is explored. Starting with an overview of different definitions, conceptualizations, assessment and training models originating from cognitive information processing theory, the role of metacognition in teaching and…

The Jukes-Cantor Model of Molecular Evolution

ERIC Educational Resources Information Center

Erickson, Keith

2010-01-01

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…

Exploring Social Equity Aspects in Integrating Technology in Primary Mathematics Education

ERIC Educational Resources Information Center

Stoilescu, Dorian

2014-01-01

This research focus on aspects of equity related to the introduction of using technology in classrooms. Technology has the potential to support mathematics pedagogy with visual representations and offer modelling and simulation facilities, increasing the creativity of the learning and teaching processes (Kaput, Ness, & Hoyles, 2008; Stoilescu…

Effective moisture diffusivity determination and mathematical modelling of drying curves of apple pomace

NASA Astrophysics Data System (ADS)

Kara, Cem; Doymaz, İbrahim

2015-07-01

Drying of apple pomace representing by-products from apple juice processing was studied. The results obtained show that moisture content of the pomace decreases with time and temperature. The Midilli et al. model was selected as the best mathematical model for describing the drying kinetics of the apple pomace. The effective moisture diffusivity varied from 1.73 × 10-10 to 4.40 × 10-10 m2/s and the activation energy was calculated to be 29.65 kJ/mol.

Development of mathematical techniques for the assimilation of remote sensing data into atmospheric models

NASA Technical Reports Server (NTRS)

Seinfeld, J. H. (Principal Investigator)

1982-01-01

The problem of the assimilation of remote sensing data into mathematical models of atmospheric pollutant species was investigated. The data assimilation problem is posed in terms of the matching of spatially integrated species burden measurements to the predicted three-dimensional concentration fields from atmospheric diffusion models. General conditions were derived for the reconstructability of atmospheric concentration distributions from data typical of remote sensing applications, and a computational algorithm (filter) for the processing of remote sensing data was developed.

Development of mathematical techniques for the assimilation of remote sensing data into atmospheric models

NASA Technical Reports Server (NTRS)

Seinfeld, J. H. (Principal Investigator)

1982-01-01

The problem of the assimilation of remote sensing data into mathematical models of atmospheric pollutant species was investigated. The problem is posed in terms of the matching of spatially integrated species burden measurements to the predicted three dimensional concentration fields from atmospheric diffusion models. General conditions are derived for the "reconstructability' of atmospheric concentration distributions from data typical of remote sensing applications, and a computational algorithm (filter) for the processing of remote sensing data is developed.

Numerical simulation of injection process of warm carbon dioxide into layer saturated with methane and its hydrate

NASA Astrophysics Data System (ADS)

Khasanov, M. K.; Stolpovsky, M. V.; Gimaltdinov, I. K.

2018-05-01

In this article, in a flat-one-dimensional approximation, a mathematical model is presented for injecting warm carbon dioxide into a methane hydrate formation of finite length. It is established that the model of formation of hydrate of carbon dioxide in the absence of an area saturated with methane and water, under certain parameters, leads to thermodynamic contradiction. The mathematical model of carbon dioxide injection with formation of the region saturated with methane and water is constructed.

Gravitational orientation of the orbital complex, Salyut-6--Soyuz

NASA Technical Reports Server (NTRS)

Grecho, G. M.; Sarychev, V. A.; Legostayev, V. P.; Sazonov, V. V.; Gansvind, I. N.

1983-01-01

A simple mathematical model is proposed for the Salyut-6-Soyuz orbital complex motion with respect to the center of mass under the one-axis gravity-gradient orientation regime. This model was used for processing the measurements of the orbital complex motion parameters when the above orientation region was implemented. Some actual satellite motions are simulated and the satellite's aerodynamic parameters are determined. Estimates are obtained for the accuracy of measurements as well as that of the mathematical model.

The Mathematics of Navigating the Solar System

NASA Technical Reports Server (NTRS)

Hintz, Gerald

2000-01-01

In navigating spacecraft throughout the solar system, the space navigator relies on three academic disciplines - optimization, estimation, and control - that work on mathematical models of the real world. Thus, the navigator determines the flight path that will consume propellant and other resources in an efficient manner, determines where the craft is and predicts where it will go, and transfers it onto the optimal trajectory that meets operational and mission constraints. Mission requirements, for example, demand that observational measurements be made with sufficient precision that relativity must be modeled in collecting and fitting (the estimation process) the data, and propagating the trajectory. Thousands of parameters are now determined in near real-time to model the gravitational forces acting on a spacecraft in the vicinity of an irregularly shaped body. Completing these tasks requires mathematical models, analyses, and processing techniques. Newton, Gauss, Lambert, Legendre, and others are justly famous for their contributions to the mathematics of these tasks. More recently, graduate students participated in research to update the gravity model of the Saturnian system, including higher order gravity harmonics, tidal effects, and the influence of the rings. This investigation was conducted for the Cassini project to incorporate new trajectory modeling features in the navigation software. The resulting trajectory model will be used in navigating the 4-year tour of the Saturnian satellites. Also, undergraduate students are determining the ephemerides (locations versus time) of asteroids that will be used as reference objects in navigating the New Millennium's Deep Space 1 spacecraft autonomously.

Modeling particulate matter emissions during mineral loading process under weak wind simulation.

PubMed

Zhang, Xiaochun; Chen, Weiping; Ma, Chun; Zhan, Shuifen

2013-04-01

The quantification of particulate matter emissions from mineral handling is an important problem for the quantification of global emissions on industrial sites. Mineral particulate matter emissions could adversely impact environmental quality in mining regions, transport regions, and even on a global scale. Mineral loading is an important process contributing to mineral particulate matter emissions, especially under weak wind conditions. Mathematical models are effective ways to evaluate particulate matter emissions during the mineral loading process. The currently used empirical models based on the form of a power function do not predict particulate matter emissions accurately under weak wind conditions. At low particulate matter emissions, the models overestimated, and at high particulate matter emissions, the models underestimated emission factors. We conducted wind tunnel experiments to evaluate the particulate matter emission factors for the mineral loading process. A new approach based on the mathematical form of a logistical function was developed and tested. It provided a realistic depiction of the particulate matter emissions during the mineral loading process, accounting for fractions of fine mineral particles, dropping height, and wind velocity. Copyright © 2013 Elsevier B.V. All rights reserved.

Evaluation of the mathematical and economic basis for conversion processes in the LEAP energy-economy model

NASA Astrophysics Data System (ADS)

Oblow, E. M.

1982-10-01

An evaluation was made of the mathematical and economic basis for conversion processes in the Long-term Energy Analysis Program (LEAP) energy economy model. Conversion processes are the main modeling subunit in LEAP used to represent energy conversion industries and are supposedly based on the classical economic theory of the firm. Questions about uniqueness and existence of LEAP solutions and their relation to classical equilibrium economic theory prompted the study. An analysis of classical theory and LEAP model equations was made to determine their exact relationship. The conclusions drawn from this analysis were that LEAP theory is not consistent with the classical theory of the firm. Specifically, the capacity factor formalism used by LEAP does not support a classical interpretation in terms of a technological production function for energy conversion processes. The economic implications of this inconsistency are suboptimal process operation and short term negative profits in years where plant operation should be terminated. A new capacity factor formalism, which retains the behavioral features of the original model, is proposed to resolve these discrepancies.

Comparison of mathematical models of fibrosis. Comment on "Towards a unified approach in the modeling of fibrosis: A review with research perspectives" by M. Ben Amar and C. Bianca

NASA Astrophysics Data System (ADS)

Kachapova, Farida

2016-07-01

Mathematical and computational models in biology and medicine help to improve diagnostics and medical treatments. Modeling of pathological fibrosis is reviewed by M. Ben Amar and C. Bianca in [4]. Pathological fibrosis is the process when excessive fibrous tissue is deposited on an organ or tissue during a wound healing and can obliterate their normal function. In [4] the phenomena of fibrosis are briefly explained including the causes, mechanism and management; research models of pathological fibrosis are described, compared and critically analyzed. Different models are suitable at different levels: molecular, cellular and tissue. The main goal of mathematical modeling of fibrosis is to predict long term behavior of the system depending on bifurcation parameters; there are two main trends: inhibition of fibrosis due to an active immune system and swelling of fibrosis because of a weak immune system.

Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions.

PubMed

Schmithorst, Vincent J; Brown, Rhonda Douglas

2004-07-01

The suitability of a previously hypothesized triple-code model of numerical processing, involving analog magnitude, auditory verbal, and visual Arabic codes of representation, was investigated for the complex mathematical task of the mental addition and subtraction of fractions. Functional magnetic resonance imaging (fMRI) data from 15 normal adult subjects were processed using exploratory group Independent Component Analysis (ICA). Separate task-related components were found with activation in bilateral inferior parietal, left perisylvian, and ventral occipitotemporal areas. These results support the hypothesized triple-code model corresponding to the activated regions found in the individual components and indicate that the triple-code model may be a suitable framework for analyzing the neuropsychological bases of the performance of complex mathematical tasks. Copyright 2004 Elsevier Inc.

The materials processing research base of the Materials Processing Center. Report for FY 1982

NASA Technical Reports Server (NTRS)

Flemings, M. C.

1983-01-01

The work described, while involving research in the broad field of materials processing, has two common features: the problems are closed related to space precessing of materials and have both practical and fundamental significance. An interesting and important feature of many of the projects is that the interdisciplinary nature of the problem mandates complementary analytical modeling/experimental approaches. An other important aspect of many of the projects is the increasing use of mathematical modeling techniques as one of the research tools. The predictive capability of these models, when tested against measurements, plays a very important role in both the planning of experimental programs and in the rational interpretation of the results. Many of the projects described have a space experiment as their ultimate objective. Mathematical models are proving to be extremely valuable in projecting the findings of ground - based experiments to microgravity conditions.

EVALUATING REGIONAL PREDICTIVE CAPACITY OF A PROCESS-BASED MERCURY EXPOSURE MODEL, REGIONAL-MERCURY CYCLING MODEL (R-MCM), APPLIED TO 91 VERMONT AND NEW HAMPSHIRE LAKES AND PONDS, USA

EPA Science Inventory

Regulatory agencies must develop fish consumption advisories for many lakes and rivers with limited resources. Process-based mathematical models are potentially valuable tools for developing regional fish advisories. The Regional Mercury Cycling model (R-MCM) was specifically d...

Predictive modeling of infrared radiative heating in tomato dry-peeling process: Part II. Model validation and sensitivity analysis

USDA-ARS?s Scientific Manuscript database

A predictive mathematical model was developed to simulate heat transfer in a tomato undergoing double sided infrared (IR) heating in a dry-peeling process. The aims of this study were to validate the developed model using experimental data and to investigate different engineering parameters that mos...

Investigation of approximate models of experimental temperature characteristics of machines

NASA Astrophysics Data System (ADS)

Parfenov, I. V.; Polyakov, A. N.

2018-05-01

This work is devoted to the investigation of various approaches to the approximation of experimental data and the creation of simulation mathematical models of thermal processes in machines with the aim of finding ways to reduce the time of their field tests and reducing the temperature error of the treatments. The main methods of research which the authors used in this work are: the full-scale thermal testing of machines; realization of various approaches at approximation of experimental temperature characteristics of machine tools by polynomial models; analysis and evaluation of modelling results (model quality) of the temperature characteristics of machines and their derivatives up to the third order in time. As a result of the performed researches, rational methods, type, parameters and complexity of simulation mathematical models of thermal processes in machine tools are proposed.

Black-Scholes model under subordination

NASA Astrophysics Data System (ADS)

Stanislavsky, A. A.

2003-02-01

In this paper, we consider a new mathematical extension of the Black-Scholes (BS) model in which the stochastic time and stock share price evolution is described by two independent random processes. The parent process is Brownian, and the directing process is inverse to the totally skewed, strictly α-stable process. The subordinated process represents the Brownian motion indexed by an independent, continuous and increasing process. This allows us to introduce the long-term memory effects in the classical BS model.

Mathematical models of the AIDS epidemic: An historical perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stanley, E.A.

1988-01-01

Researchers developing mathematical models of the spreading of HIV, the Human Immunodeficiency Virus that causes AIDS, hope to achieve a number of goals. These goals may be classified rather broadly into three categories: understanding, prediction, and control. Understanding which are the key biological and sociological processes spreading this epidemic and leading to the deaths of those infected will allow AIDS researchers to collect better data and to identify ways of slowing the epidemic. Predicting the groups at risk and future numbers of ill people will allow an appropriate allocation of health-care resources. Analysis and comparison of proposed control methods willmore » point out unexpected consequences and allow a better design of these programs. The processes which lead to the spread of HIV are biologically and sociologically complex. Mathematical models allow us to organize our knowledge into a coherent picture and examine the logical consequences, therefore they have the potential to be extremely useful in the search to control this disease. 24 refs., 3 figs.« less

Comparison of Mathematical Equation and Neural Network Modeling for Drying Kinetic of Mendong in Microwave Oven

NASA Astrophysics Data System (ADS)

Maulidah, Rifa'atul; Purqon, Acep

2016-08-01

Mendong (Fimbristylis globulosa) has a potentially industrial application. We investigate a predictive model for heat and mass transfer in drying kinetics during drying a Mendong. We experimentally dry the Mendong by using a microwave oven. In this study, we analyze three mathematical equations and feed forward neural network (FNN) with back propagation to describe the drying behavior of Mendong. Our results show that the experimental data and the artificial neural network model has a good agreement and better than a mathematical equation approach. The best FNN for the prediction is 3-20-1-1 structure with Levenberg- Marquardt training function. This drying kinetics modeling is potentially applied to determine the optimal parameters during mendong drying and to estimate and control of drying process.

Will the digital computer transform classical mathematics?

PubMed

Rotman, Brian

2003-08-15

Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plechac, Petr; Vlachos, Dionisios; Katsoulakis, Markos

2013-09-05

The overall objective of this project is to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals. Specific goals include: (i) Development of rigorous spatio-temporal coarse-grained kinetic Monte Carlo (KMC) mathematics and simulation for microscopic processes encountered in biomassmore » transformation. (ii) Development of hybrid multiscale simulation that links stochastic simulation to a deterministic partial differential equation (PDE) model for an entire reactor. (iii) Development of hybrid multiscale simulation that links KMC simulation with quantum density functional theory (DFT) calculations. (iv) Development of parallelization of models of (i)-(iii) to take advantage of Petaflop computing and enable real world applications of complex, multiscale models. In this NCE period, we continued addressing these objectives and completed the proposed work. Main initiatives, key results, and activities are outlined.« less

The Abstraction Process of Limit Knowledge

ERIC Educational Resources Information Center

Sezgin Memnun, Dilek; Aydin, Bünyamin; Özbilen, Ömer; Erdogan, Günes

2017-01-01

The RBC+C abstraction model is an effective model in mathematics education because it gives the opportunity to analyze research data through cognitive actions. For this reason, we aim to examine the abstraction process of the limit knowledge of two volunteer participant students using the RBC+C abstraction model. With this aim, the students'…

Simulation modeling of forest landscape disturbances: An overview

Treesearch

Ajith H. Perera; Brian R. Sturtevant; Lisa J. Buse

2015-01-01

Quantification of ecological processes and formulation of the mathematical expressions that describe those processes in computer models has been a cornerstone of landscape ecology research and its application. Consequently, the body of publications on simulation models in landscape ecology has grown rapidly in recent decades. This trend is also evident in the subfield...

Mathematical modeling of efficacy and safety for anticancer drugs clinical development.

PubMed

Lavezzi, Silvia Maria; Borella, Elisa; Carrara, Letizia; De Nicolao, Giuseppe; Magni, Paolo; Poggesi, Italo

2018-01-01

Drug attrition in oncology clinical development is higher than in other therapeutic areas. In this context, pharmacometric modeling represents a useful tool to explore drug efficacy in earlier phases of clinical development, anticipating overall survival using quantitative model-based metrics. Furthermore, modeling approaches can be used to characterize earlier the safety and tolerability profile of drug candidates, and, thus, the risk-benefit ratio and the therapeutic index, supporting the design of optimal treatment regimens and accelerating the whole process of clinical drug development. Areas covered: Herein, the most relevant mathematical models used in clinical anticancer drug development during the last decade are described. Less recent models were considered in the review if they represent a standard for the analysis of certain types of efficacy or safety measures. Expert opinion: Several mathematical models have been proposed to predict overall survival from earlier endpoints and validate their surrogacy in demonstrating drug efficacy in place of overall survival. An increasing number of mathematical models have also been developed to describe the safety findings. Modeling has been extensively used in anticancer drug development to individualize dosing strategies based on patient characteristics, and design optimal dosing regimens balancing efficacy and safety.

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Mathematical model of whole-process calculation for bottom-blowing copper smelting

NASA Astrophysics Data System (ADS)

Li, Ming-zhou; Zhou, Jie-min; Tong, Chang-ren; Zhang, Wen-hai; Li, He-song

2017-11-01

The distribution law of materials in smelting products is key to cost accounting and contaminant control. Regardless, the distribution law is difficult to determine quickly and accurately by mere sampling and analysis. Mathematical models for material and heat balance in bottom-blowing smelting, converting, anode furnace refining, and electrolytic refining were established based on the principles of material (element) conservation, energy conservation, and control index constraint in copper bottom-blowing smelting. Simulation of the entire process of bottom-blowing copper smelting was established using a self-developed MetCal software platform. A whole-process simulation for an enterprise in China was then conducted. Results indicated that the quantity and composition information of unknown materials, as well as heat balance information, can be quickly calculated using the model. Comparison of production data revealed that the model can basically reflect the distribution law of the materials in bottom-blowing copper smelting. This finding provides theoretical guidance for mastering the performance of the entire process.

Mathematical modeling of PDC bit drilling process based on a single-cutter mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wojtanowicz, A.K.; Kuru, E.

1993-12-01

An analytical development of a new mechanistic drilling model for polycrystalline diamond compact (PDC) bits is presented. The derivation accounts for static balance of forces acting on a single PDC cutter and is based on assumed similarity between bit and cutter. The model is fully explicit with physical meanings given to all constants and functions. Three equations constitute the mathematical model: torque, drilling rate, and bit life. The equations comprise cutter`s geometry, rock properties drilling parameters, and four empirical constants. The constants are used to match the model to a PDC drilling process. Also presented are qualitative and predictive verificationsmore » of the model. Qualitative verification shows that the model`s response to drilling process variables is similar to the behavior of full-size PDC bits. However, accuracy of the model`s predictions of PDC bit performance is limited primarily by imprecision of bit-dull evaluation. The verification study is based upon the reported laboratory drilling and field drilling tests as well as field data collected by the authors.« less

Thermomechanical Stresses Analysis of a Single Event Burnout Process

NASA Astrophysics Data System (ADS)

Tais, Carlos E.; Romero, Eduardo; Demarco, Gustavo L.

2009-06-01

This work analyzes the thermal and mechanical effects arising in a power Diffusion Metal Oxide Semiconductor (DMOS) during a Single Event Burnout (SEB) process. For studying these effects we propose a more detailed simulation structure than the previously used by other authors, solving the mathematical models by means of the Finite Element Method. We use a cylindrical heat generation region, with 5 W, 10 W, 50 W and 100 W for emulating the thermal phenomena occurring during SEB processes, avoiding the complexity of the mathematical treatment of the ion-semiconductor interaction.

Mathematical modeling of processes of heat and mass transfer in channels of water evaporating coolers

NASA Astrophysics Data System (ADS)

Gulevsky, V. A.; Ryazantsev, A. A.; Nikulichev, A. A.; Menzhulova, A. S.

2018-05-01

The variety of cooling systems is dictated by a wide range of demands placed on them. This is the price, operating costs, quality of work, ecological safety, etc. These requirements in a positive sense are put into correspondence by water evaporating plate coolers. Currently, their widespread use is limited by a lack of theoretical base. To solve this problem, the best method is mathematical modeling.

Theory, Modeling, Software and Hardware Development for Analytical and Computational Materials Science

NASA Technical Reports Server (NTRS)

Young, Gerald W.; Clemons, Curtis B.

2004-01-01

The focus of this Cooperative Agreement between the Computational Materials Laboratory (CML) of the Processing Science and Technology Branch of the NASA Glenn Research Center (GRC) and the Department of Theoretical and Applied Mathematics at The University of Akron was in the areas of system development of the CML workstation environment, modeling of microgravity and earth-based material processing systems, and joint activities in laboratory projects. These efforts complement each other as the majority of the modeling work involves numerical computations to support laboratory investigations. Coordination and interaction between the modelers, system analysts, and laboratory personnel are essential toward providing the most effective simulations and communication of the simulation results. Toward these means, The University of Akron personnel involved in the agreement worked at the Applied Mathematics Research Laboratory (AMRL) in the Department of Theoretical and Applied Mathematics while maintaining a close relationship with the personnel of the Computational Materials Laboratory at GRC. Network communication between both sites has been established. A summary of the projects we undertook during the time period 9/1/03 - 6/30/04 is included.

Theoretical studies in isoelectric focusing. [mathematical modeling and computer simulation for biologicals purification process

NASA Technical Reports Server (NTRS)

Mosher, R. A.; Palusinski, O. A.; Bier, M.

1982-01-01

A mathematical model has been developed which describes the steady state in an isoelectric focusing (IEF) system with ampholytes or monovalent buffers. The model is based on the fundamental equations describing the component dissociation equilibria, mass transport due to diffusion and electromigration, electroneutrality, and the conservation of charge. The validity and usefulness of the model has been confirmed by using it to formulate buffer systems in actual laboratory experiments. The model has been recently extended to include the evolution of transient states not only in IEF but also in other modes of electrophoresis.

From Biology to Mathematical Models and Back: Teaching Modeling to Biology Students, and Biology to Math and Engineering Students

PubMed Central

McManus, Jeffrey M.; Shaw, Kendrick M.

2010-01-01

We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge that they find difficult. To give students a sense of mastery in each area, several complementary approaches are used in the course: 1) a “live” textbook that allows students to explore models and mathematical processes interactively; 2) benchmark problems providing key skills on which students make continuous progress; 3) assignment of students to teams of two throughout the semester; 4) regular one-on-one interactions with instructors throughout the semester; and 5) a term project in which students reconstruct, analyze, extend, and then write in detail about a recently published biological model. Based on student evaluations and comments, an attitude survey, and the quality of the students' term papers, the course has significantly increased the ability and willingness of biology students to use mathematical concepts and modeling tools to understand biological systems, and it has significantly enhanced engineering students' appreciation of biology. PMID:20810957

Energy Survey of Machine Tools: Separating Power Information of the Main Transmission System During Machining Process

NASA Astrophysics Data System (ADS)

Liu, Shuang; Liu, Fei; Hu, Shaohua; Yin, Zhenbiao

The major power information of the main transmission system in machine tools (MTSMT) during machining process includes effective output power (i.e. cutting power), input power and power loss from the mechanical transmission system, and the main motor power loss. These information are easy to obtain in the lab but difficult to evaluate in a manufacturing process. To solve this problem, a separation method is proposed here to extract the MTSMT power information during machining process. In this method, the energy flow and the mathematical models of major power information of MTSMT during the machining process are set up first. Based on the mathematical models and the basic data tables obtained from experiments, the above mentioned power information during machining process can be separated just by measuring the real time total input power of the spindle motor. The operation program of this method is also given.

Adolescents' perceptions of socializers' beliefs, career-related conversations, and motivation in mathematics.

PubMed

Lazarides, Rebecca; Rubach, Charlott; Ittel, Angela

2017-03-01

Research based on the Eccles model of parent socialization demonstrated that parents are an important source of value and ability information for their children. Little is known, however, about the bidirectional effects between students' perceptions of their parents' beliefs and behaviors and the students' own domain-specific values. This study analyzed how students' perceptions of parents' beliefs and behaviors and students' mathematics values and mathematics-related career plans affect each other bidirectionally, and analyzed the role of students' gender as a moderator of these relations. Data from 475 students in 11th and 12th grade (girls: 50.3%; 31 classrooms; 12 schools), who participated in 2 waves of the study, were analyzed. Results of longitudinal structural equation models demonstrated that students' perceptions of their parents' mathematics value beliefs at Time 1 affected the students' own mathematics utility value at Time 2. Bidirectional effects were not shown in the full sample but were identified for boys. The paths within the tested model varied for boys and girls. For example, boys', not girls', mathematics intrinsic value predicted their reported conversations with their fathers about future occupational plans. Boys', not girls', perceived parents' mathematics value predicted the mathematics utility value. Findings are discussed in relation to their implications for parents and teachers, as well as in relation to gendered motivational processes. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Numerical modelling in biosciences using delay differential equations

NASA Astrophysics Data System (ADS)

Bocharov, Gennadii A.; Rihan, Fathalla A.

2000-12-01

Our principal purposes here are (i) to consider, from the perspective of applied mathematics, models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics, (ii) to review the application of numerical techniques to investigate these models. We show that there are prima facie reasons for using such models: (i) they have a richer mathematical framework (compared with ordinary differential equations) for the analysis of biosystem dynamics, (ii) they display better consistency with the nature of certain biological processes and predictive results. We analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics. We then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences, comparing them with those implemented by the bio-modellers.

Enhancing Manufacturing Process Education via Computer Simulation and Visualization

ERIC Educational Resources Information Center

Manohar, Priyadarshan A.; Acharya, Sushil; Wu, Peter

2014-01-01

Industrially significant metal manufacturing processes such as melting, casting, rolling, forging, machining, and forming are multi-stage, complex processes that are labor, time, and capital intensive. Academic research develops mathematical modeling of these processes that provide a theoretical framework for understanding the process variables…

Design, processing and testing of LSI arrays: Hybrid microelectronics task

NASA Technical Reports Server (NTRS)

Himmel, R. P.; Stuhlbarg, S. M.; Ravetti, R. G.; Zulueta, P. J.

1979-01-01

Mathematical cost factors were generated for both hybrid microcircuit and printed wiring board packaging methods. A mathematical cost model was created for analysis of microcircuit fabrication costs. The costing factors were refined and reduced to formulae for computerization. Efficient methods were investigated for low cost packaging of LSI devices as a function of density and reliability. Technical problem areas such as wafer bumping, inner/outer leading bonding, testing on tape, and tape processing, were investigated.

Numerical modeling of heat and mass transport processes in an evaporative thermal protection system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bobrov, I.N.; Kuryachii, A.P.

1992-08-01

We propose a mathematical model of heat and mass transport processes in a moist, porous material subject to capillary action. The material is in contact with a heated surface, and the processes take place while the liquid is evaporating in a cavity with a drainage hole. A sample calculation based on the model is presented. 45 refs., 4 figs.

Mathematical Modeling with MyMaps and Spreadsheets

ERIC Educational Resources Information Center

Weber, Victoria; Fortune, Nicholas; Williams, Derek; Whitehead, Ashley

2016-01-01

Software programs such as Tinkerplots ® or Geometer's Sketchpad ® can help students solve problems in mathematics classes, but may not be available to them after high school. In contrast, many students who become familiar with Internet tools and programs in office packages (word processing, spreadsheets, etc.) may use them daily to enhance their…

The mathematics of sexual attraction.

PubMed

Feijó, José A

2010-01-01

Pollen tubes follow attractants secreted by the ovules. In a recent paper in BMC Plant Biology, Stewman and colleagues have quantified the parameters of this attraction and used them to calibrate a mathematical model that reproduces the process and enables predictions on the nature of the female attractant and the mechanisms of the male response.

Statistics and Style. Mathematical Linguistics and Automatic Language Processing No. 6.

ERIC Educational Resources Information Center

Dolezel, Lubomir, Ed.; Bailey, Richard W., Ed.

This collection of 17 articles concerning the application of mathematical models and techniques to the study of literary style is an attempt to overcome the communication barriers that exist between scholars in the various fields that find their meeting ground in statistical stylistics. The articles selected were chosen to represent the best…

Toward User Interfaces and Data Visualization Criteria for Learning Design of Digital Textbooks

ERIC Educational Resources Information Center

Railean, Elena

2014-01-01

User interface and data visualisation criteria are central issues in digital textbooks design. However, when applying mathematical modelling of learning process to the analysis of the possible solutions, it could be observed that results differ. Mathematical learning views cognition in on the base on statistics and probability theory, graph…

Relations among Brief Measures of Mathematics, Reading, and Processing Speed: A Construct Validity Study

ERIC Educational Resources Information Center

Maynard, Jennifer Leigh

2012-01-01

Emphasis on regular mathematics skill assessment, intervention, and progress monitoring under the RTI model has created a need for the development of assessment instruments that are psychometrically sound, reliable, universal, and brief. Important factors to consider when developing or selecting assessments for the school environment include what…

A Constructivist Computational Platform to Support Mathematics Education in Elementary School

ERIC Educational Resources Information Center

Garcia, I.; Pacheco, C.

2013-01-01

Many courses for elementary school are based upon teacher presentation and explanation of basic topics, rather than allowing students to develop their own knowledge. This traditional model may turn elementary-level lessons into an extremely theoretical, boring and non-effective process. In this context, research in mathematics elementary education…

A Quantitative Analysis of Methods Used for Avoidance and Acceleration of Developmental Mathematics Sequences in Community College

ERIC Educational Resources Information Center

Travers, Steven T.

2017-01-01

Many developmental mathematics programs at community colleges in recent years have undergone a process of redesign in an attempt increase the historical poor rate of student successful completion of required developmental coursework. Various curriculum and instructional design models that incorporate methods of avoiding and accelerating the…

Experimental Analysis and Mathematical Modeling on Mg-Li Alloy Sheets with Three Crystal Structures during Cold Rolling and Heat Treatment.

PubMed

Tang, Yan; Le, Qichi; Wang, Tong; Chen, Xingrui

2017-10-12

The microstructural evolution, mechanical properties, and mathematical relationship of an α, α + β, and β phase Mg-Li alloy during the cold rolling and annealing process were investigated. The results showed that the increased Li element gradually transformed the Mg matrix structure from hcp to bcc. Simultaneously, the alloy plasticity was improved remarkably during cold rolling. In the annealing process, a sort of abnormal grain growth was found in Mg-11Li-3Al-2Zn-0.2Y, but was not detected in Mg-5Li-3Al-2Zn-0.2Y and Mg-8Li-3Al-2Zn-0.2Y. Moreover, the mechanical properties of alloy were evidently improved through a kind of solid solution in the β matrix. To accurately quantify this strengthening effect, the method of mathematical modeling was used to determine the relationship between strength and multiple factors.

Mathematical models applied to the Cr(III) and Cr(VI) breakthrough curves.

PubMed

Ramirez C, Margarita; Pereira da Silva, Mônica; Ferreira L, Selma G; Vasco E, Oscar

2007-07-19

Trivalent and hexavalent chromium continuous biosorption was studied using residual brewer Saccharomyces cerevisiae immobilized in volcanic rock. The columns used in the process had a diameter of 4.5 cm and a length of 140 cm, working at an inlet flow rate of 15 mL/min. Breakthrough curves were used to study the yeast biosorption behavior in the process. The saturation time (ts) was 21 and 45 h for Cr(III) and Cr(VI), respectively, and a breakthrough time (tb) of 4 h for Cr(III) and 5 h for Cr(VI). The uptake capacity of the biosorbent for Cr(III) and Cr(VI) were 48 and 60 mg/g, respectively. Two non-diffusional mathematical models with parameters t0 and sigma were used to adjust the experimental data obtained. Microsoft Excel tools were used for the mathematical solution of the two parameters used.

Application of the Cluster Expansion to a Mathematical Model of the Long Memory Phenomenon in a Financial Market

NASA Astrophysics Data System (ADS)

Kuroda, Koji; Maskawa, Jun-ichi; Murai, Joshin

2013-08-01

Empirical studies of the high frequency data in stock markets show that the time series of trade signs or signed volumes has a long memory property. In this paper, we present a discrete time stochastic process for polymer model which describes trader's trading strategy, and show that a scale limit of the process converges to superposition of fractional Brownian motions with Hurst exponents and Brownian motion, provided that the index γ of the time scale about the trader's investment strategy coincides with the index δ of the interaction range in the discrete time process. The main tool for the investigation is the method of cluster expansion developed in the mathematical study of statistical mechanics.

Modeling and simulation of enzymatic gluconic acid production using immobilized enzyme and CSTR-PFTR circulation reaction system.

PubMed

Li, Can; Lin, Jianqun; Gao, Ling; Lin, Huibin; Lin, Jianqiang

2018-04-01

Production of gluconic acid by using immobilized enzyme and continuous stirred tank reactor-plug flow tubular reactor (CSTR-PFTR) circulation reaction system. A production system is constructed for gluconic acid production, which consists of a continuous stirred tank reactor (CSTR) for pH control and liquid storage and a plug flow tubular reactor (PFTR) filled with immobilized glucose oxidase (GOD) for gluconic acid production. Mathematical model is developed for this production system and simulation is made for the enzymatic reaction process. The pH inhibition effect on GOD is modeled by using a bell-type curve. Gluconic acid can be efficiently produced by using the reaction system and the mathematical model developed for this system can simulate and predict the process well.

Mathematical modeling of a continuous alcoholic fermentation process in a two-stage tower reactor cascade with flocculating yeast recycle.

PubMed

de Oliveira, Samuel Conceição; de Castro, Heizir Ferreira; Visconti, Alexandre Eliseu Stourdze; Giudici, Reinaldo

2015-03-01

Experiments of continuous alcoholic fermentation of sugarcane juice with flocculating yeast recycle were conducted in a system of two 0.22-L tower bioreactors in series, operated at a range of dilution rates (D 1 = D 2 = 0.27-0.95 h(-1)), constant recycle ratio (α = F R /F = 4.0) and a sugar concentration in the feed stream (S 0) around 150 g/L. The data obtained in these experimental conditions were used to adjust the parameters of a mathematical model previously developed for the single-stage process. This model considers each of the tower bioreactors as a perfectly mixed continuous reactor and the kinetics of cell growth and product formation takes into account the limitation by substrate and the inhibition by ethanol and biomass, as well as the substrate consumption for cellular maintenance. The model predictions agreed satisfactorily with the measurements taken in both stages of the cascade. The major differences with respect to the kinetic parameters previously estimated for a single-stage system were observed for the maximum specific growth rate, for the inhibition constants of cell growth and for the specific rate of substrate consumption for cell maintenance. Mathematical models were validated and used to simulate alternative operating conditions as well as to analyze the performance of the two-stage process against that of the single-stage process.

An overview of the mathematical and statistical analysis component of RICIS

NASA Technical Reports Server (NTRS)

Hallum, Cecil R.

1987-01-01

Mathematical and statistical analysis components of RICIS (Research Institute for Computing and Information Systems) can be used in the following problem areas: (1) quantification and measurement of software reliability; (2) assessment of changes in software reliability over time (reliability growth); (3) analysis of software-failure data; and (4) decision logic for whether to continue or stop testing software. Other areas of interest to NASA/JSC where mathematical and statistical analysis can be successfully employed include: math modeling of physical systems, simulation, statistical data reduction, evaluation methods, optimization, algorithm development, and mathematical methods in signal processing.

Predicting plot soil loss by empirical and process-oriented approaches: A review

USDA-ARS?s Scientific Manuscript database

Soil erosion directly affects the quality of the soil, its agricultural productivity and its biological diversity. Many mathematical models have been developed to estimate plot soil erosion at different temporal scales. At present, empirical soil loss equations and process-oriented models are consid...

Concurrent processing simulation of the space station

NASA Technical Reports Server (NTRS)

Gluck, R.; Hale, A. L.; Sunkel, John W.

1989-01-01

The development of a new capability for the time-domain simulation of multibody dynamic systems and its application to the study of a large angle rotational maneuvers of the Space Station is described. The effort was divided into three sequential tasks, which required significant advancements of the state-of-the art to accomplish. These were: (1) the development of an explicit mathematical model via symbol manipulation of a flexible, multibody dynamic system; (2) the development of a methodology for balancing the computational load of an explicit mathematical model for concurrent processing; and (3) the implementation and successful simulation of the above on a prototype Custom Architectured Parallel Processing System (CAPPS) containing eight processors. The throughput rate achieved by the CAPPS operating at only 70 percent efficiency, was 3.9 times greater than that obtained sequentially by the IBM 3090 supercomputer simulating the same problem. More significantly, analysis of the results leads to the conclusion that the relative cost effectiveness of concurrent vs. sequential digital computation will grow substantially as the computational load is increased. This is a welcomed development in an era when very complex and cumbersome mathematical models of large space vehicles must be used as substitutes for full scale testing which has become impractical.

Computer Synthesis Approaches of Hyperboloid Gear Drives with Linear Contact

NASA Astrophysics Data System (ADS)

Abadjiev, Valentin; Kawasaki, Haruhisa

2014-09-01

The computer design has improved forming different type software for scientific researches in the field of gearing theory as well as performing an adequate scientific support of the gear drives manufacture. Here are attached computer programs that are based on mathematical models as a result of scientific researches. The modern gear transmissions require the construction of new mathematical approaches to their geometric, technological and strength analysis. The process of optimization, synthesis and design is based on adequate iteration procedures to find out an optimal solution by varying definite parameters. The study is dedicated to accepted methodology in the creation of soft- ware for the synthesis of a class high reduction hyperboloid gears - Spiroid and Helicon ones (Spiroid and Helicon are trademarks registered by the Illinois Tool Works, Chicago, Ill). The developed basic computer products belong to software, based on original mathematical models. They are based on the two mathematical models for the synthesis: "upon a pitch contact point" and "upon a mesh region". Computer programs are worked out on the basis of the described mathematical models, and the relations between them are shown. The application of the shown approaches to the synthesis of commented gear drives is illustrated.

On Mathematical Proving

NASA Astrophysics Data System (ADS)

Stefaneas, Petros; Vandoulakis, Ioannis M.

2015-12-01

This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

Investigating the impact of mindfulness meditation training on working memory: a mathematical modeling approach.

PubMed

van Vugt, Marieke K; Jha, Amishi P

2011-09-01

We investigated whether mindfulness training (MT) influences information processing in a working memory task with complex visual stimuli. Participants were tested before (T1) and after (T2) participation in an intensive one-month MT retreat, and their performance was compared with that of an age- and education-matched control group. Accuracy did not differ across groups at either time point. Response times were faster and significantly less variable in the MT versus the control group at T2. Since these results could be due to changes in mnemonic processes, speed-accuracy trade-off, or nondecisional factors (e.g., motor execution), we used a mathematical modeling approach to disentangle these factors. The EZ-diffusion model (Wagenmakers, van der Maas, & Grasman, Psychonomic Bulletin & Review 14:(1), 3-22, 2007) suggested that MT leads to improved information quality and reduced response conservativeness, with no changes in nondecisional factors. The noisy exemplar model further suggested that the increase in information quality reflected a decrease in encoding noise and not an increase in forgetting. Thus, mathematical modeling may help clarify the mechanisms by which MT produces salutary effects on performance.

Stochastic growth logistic model with aftereffect for batch fermentation process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Dynamic pathway modeling of signal transduction networks: a domain-oriented approach.

PubMed

Conzelmann, Holger; Gilles, Ernst-Dieter

2008-01-01

Mathematical models of biological processes become more and more important in biology. The aim is a holistic understanding of how processes such as cellular communication, cell division, regulation, homeostasis, or adaptation work, how they are regulated, and how they react to perturbations. The great complexity of most of these processes necessitates the generation of mathematical models in order to address these questions. In this chapter we provide an introduction to basic principles of dynamic modeling and highlight both problems and chances of dynamic modeling in biology. The main focus will be on modeling of s transduction pathways, which requires the application of a special modeling approach. A common pattern, especially in eukaryotic signaling systems, is the formation of multi protein signaling complexes. Even for a small number of interacting proteins the number of distinguishable molecular species can be extremely high. This combinatorial complexity is due to the great number of distinct binding domains of many receptors and scaffold proteins involved in signal transduction. However, these problems can be overcome using a new domain-oriented modeling approach, which makes it possible to handle complex and branched signaling pathways.

Comparing the cognitive differences resulting from modeling instruction: Using computer microworld and physical object instruction to model real world problems

NASA Astrophysics Data System (ADS)

Oursland, Mark David

This study compared the modeling achievement of students receiving mathematical modeling instruction using the computer microworld, Interactive Physics, and students receiving instruction using physical objects. Modeling instruction included activities where students applied the (a) linear model to a variety of situations, (b) linear model to two-rate situations with a constant rate, (c) quadratic model to familiar geometric figures. Both quantitative and qualitative methods were used to analyze achievement differences between students (a) receiving different methods of modeling instruction, (b) with different levels of beginning modeling ability, or (c) with different levels of computer literacy. Student achievement was analyzed quantitatively through a three-factor analysis of variance where modeling instruction, beginning modeling ability, and computer literacy were used as the three independent factors. The SOLO (Structure of the Observed Learning Outcome) assessment framework was used to design written modeling assessment instruments to measure the students' modeling achievement. The same three independent factors were used to collect and analyze the interviews and observations of student behaviors. Both methods of modeling instruction used the data analysis approach to mathematical modeling. The instructional lessons presented problem situations where students were asked to collect data, analyze the data, write a symbolic mathematical equation, and use equation to solve the problem. The researcher recommends the following practice for modeling instruction based on the conclusions of this study. A variety of activities with a common structure are needed to make explicit the modeling process of applying a standard mathematical model. The modeling process is influenced strongly by prior knowledge of the problem context and previous modeling experiences. The conclusions of this study imply that knowledge of the properties about squares improved the students' ability to model a geometric problem more than instruction in data analysis modeling. The uses of computer microworlds such as Interactive Physics in conjunction with cooperative groups are a viable method of modeling instruction.

Basic mathematical rules are encoded by primate prefrontal cortex neurons

PubMed Central

Bongard, Sylvia; Nieder, Andreas

2010-01-01

Mathematics is based on highly abstract principles, or rules, of how to structure, process, and evaluate numerical information. If and how mathematical rules can be represented by single neurons, however, has remained elusive. We therefore recorded the activity of individual prefrontal cortex (PFC) neurons in rhesus monkeys required to switch flexibly between “greater than” and “less than” rules. The monkeys performed this task with different numerical quantities and generalized to set sizes that had not been presented previously, indicating that they had learned an abstract mathematical principle. The most prevalent activity recorded from randomly selected PFC neurons reflected the mathematical rules; purely sensory- and memory-related activity was almost absent. These data show that single PFC neurons have the capacity to represent flexible operations on most abstract numerical quantities. Our findings support PFC network models implementing specific “rule-coding” units that control the flow of information between segregated input, memory, and output layers. We speculate that these neuronal circuits in the monkey lateral PFC could readily have been adopted in the course of primate evolution for syntactic processing of numbers in formalized mathematical systems. PMID:20133872

Microbiological fermentation of lignocellulosic biomass: current state and prospects of mathematical modeling.

PubMed

Lübken, Manfred; Gehring, Tito; Wichern, Marc

2010-02-01

The anaerobic fermentation process has achieved growing importance in practice in recent years. Anaerobic fermentation is especially valuable because its end product is methane, a renewable energy source. While the use of renewable energy sources has accelerated substantially in recent years, their potential has not yet been sufficiently exploited. This is especially true for biogas technology. Biogas is created in a multistage process in which different microorganisms use the energy stored in carbohydrates, fats, and proteins for their metabolism. In order to produce biogas, any organic substrate that is microbiologically accessible can be used. The microbiological process in itself is extremely complex and still requires substantial research in order to be fully understood. Technical facilities for the production of biogas are thus generally scaled in a purely empirical manner. The efficiency of the process, therefore, corresponds to the optimum only in the rarest cases. An optimal production of biogas, as well as a stable plant operation requires detailed knowledge of the biochemical processes in the fermenter. The use of mathematical models can help to achieve the necessary deeper understanding of the process. This paper reviews both the history of model development and current state of the art in modeling anaerobic digestion processes.

OPTIMIZATION OF COUNTERCURRENT STAGED PROCESSES.

DTIC Science & Technology

CHEMICAL ENGINEERING , OPTIMIZATION), (*DISTILLATION, OPTIMIZATION), INDUSTRIAL PRODUCTION, INDUSTRIAL EQUIPMENT, MATHEMATICAL MODELS, DIFFERENCE EQUATIONS, NONLINEAR PROGRAMMING, BOUNDARY VALUE PROBLEMS, NUMERICAL INTEGRATION

Legal Policy Optimizing Models

ERIC Educational Resources Information Center

Nagel, Stuart; Neef, Marian

1977-01-01

The use of mathematical models originally developed by economists and operations researchers is described for legal process research. Situations involving plea bargaining, arraignment, and civil liberties illustrate the applicability of decision theory, inventory modeling, and linear programming in operations research. (LBH)

8-Step Model Drawing: Singapore's Best Problem-Solving MATH Strategies

ERIC Educational Resources Information Center

Hogan, Bob; Forsten, Char

2007-01-01

In this book, Bob Hogan and Char Forsten introduce American mathematics educators to the model drawing process adapted from the much-acclaimed Singapore approach. They explain what model drawing is and why it's such an effective problem-solving tool. They show exactly how teachers can guide their students through the process, tell which key points…

EVALUATING THE REGIONAL PREDICTIVE CAPACITY OF A PROCESS-BASED MERCURY EXPOSURE MODEL (R-MCM) FOR LAKES ACROSS VERMONT AND NEW HAMPSHIRE, USA

EPA Science Inventory

Regulatory agencies are confronted with a daunting task of developing fish consumption advisories for a large number of lakes and rivers with little resources. A feasible mechanism to develop region-wide fish advisories is by using a process-based mathematical model. One model of...

Activation and Binding in Verbal Working Memory: A Dual-Process Model for the Recognition of Nonwords

ERIC Educational Resources Information Center

Oberauer, Klauss; Lange, Elke B.

2009-01-01

The article presents a mathematical model of short-term recognition based on dual-process models and the three-component theory of working memory [Oberauer, K. (2002). Access to information in working memory: Exploring the focus of attention. "Journal of Experimental Psychology: Learning, Memory, and Cognition, 28", 411-421]. Familiarity arises…

Inverse modeling approach for evaluation of kinetic parameters of a biofilm reactor using tabu search.

PubMed

Kumar, B Shiva; Venkateswarlu, Ch

2014-08-01

The complex nature of biological reactions in biofilm reactors often poses difficulties in analyzing such reactors experimentally. Mathematical models could be very useful for their design and analysis. However, application of biofilm reactor models to practical problems proves somewhat ineffective due to the lack of knowledge of accurate kinetic models and uncertainty in model parameters. In this work, we propose an inverse modeling approach based on tabu search (TS) to estimate the parameters of kinetic and film thickness models. TS is used to estimate these parameters as a consequence of the validation of the mathematical models of the process with the aid of measured data obtained from an experimental fixed-bed anaerobic biofilm reactor involving the treatment of pharmaceutical industry wastewater. The results evaluated for different modeling configurations of varying degrees of complexity illustrate the effectiveness of TS for accurate estimation of kinetic and film thickness model parameters of the biofilm process. The results show that the two-dimensional mathematical model with Edward kinetics (with its optimum parameters as mu(max)rho(s)/Y = 24.57, Ks = 1.352 and Ki = 102.36) and three-parameter film thickness expression (with its estimated parameters as a = 0.289 x 10(-5), b = 1.55 x 10(-4) and c = 15.2 x 10(-6)) better describes the biofilm reactor treating the industry wastewater.

Determination of the mass transfer limiting step of dye adsorption onto commercial adsorbent by using mathematical models.

PubMed

Marin, Pricila; Borba, Carlos Eduardo; Módenes, Aparecido Nivaldo; Espinoza-Quiñones, Fernando R; de Oliveira, Silvia Priscila Dias; Kroumov, Alexander Dimitrov

2014-01-01

Reactive blue 5G dye removal in a fixed-bed column packed with Dowex Optipore SD-2 adsorbent was modelled. Three mathematical models were tested in order to determine the limiting step of the mass transfer of the dye adsorption process onto the adsorbent. The mass transfer resistance was considered to be a criterion for the determination of the difference between models. The models contained information about the external, internal, or surface adsorption limiting step. In the model development procedure, two hypotheses were applied to describe the internal mass transfer resistance. First, the mass transfer coefficient constant was considered. Second, the mass transfer coefficient was considered as a function of the dye concentration in the adsorbent. The experimental breakthrough curves were obtained for different particle diameters of the adsorbent, flow rates, and feed dye concentrations in order to evaluate the predictive power of the models. The values of the mass transfer parameters of the mathematical models were estimated by using the downhill simplex optimization method. The results showed that the model that considered internal resistance with a variable mass transfer coefficient was more flexible than the other ones and this model described the dynamics of the adsorption process of the dye in the fixed-bed column better. Hence, this model can be used for optimization and column design purposes for the investigated systems and similar ones.

Mathematical models frame environmental dispute [Review of the article Useless arithmetic: Ten points to ponder when using mathematical models in environmental decision making

USGS Publications Warehouse

Lamb, Berton Lee; Burkardt, Nina

2008-01-01

When Linda Pilkey- Jarvis and Orrin Pilkey state in their article, "Useless Arithmetic," that "mathematical models are simplified, generalized representations of a process or system," they probably do not mean to imply that these models are simple. Rather, the models are simpler than nature and that is the heart of the problem with predictive models. We have had a long professional association with the developers and users of one of these simplifications of nature in the form of a mathematical model known as Physical Habitat Simulation (PHABSIM), which is part of the Instream Flow Incremental Methodology (IFIM). The IFIM is a suite of techniques, including PHABSIM, that allows the analyst to incorporate hydrology , hydraulics, habitat, water quality, stream temperature, and other variables into a tradeoff analysis that decision makers can use to design a flow regime to meet management objectives (Stalnaker et al. 1995). Although we are not the developers of the IFIM, we have worked with those who did design it, and we have tried to understand how the IFIM and PHABSIM are actually used in decision making (King, Burkardt, and Clark 2006; Lamb 1989).

Mathematical modeling of the MHD stability dependence on the interpole distance in the multianode aluminium electrolyser

NASA Astrophysics Data System (ADS)

Kuzmin, R. N.; Savenkova, N. P.; Shobukhov, A. V.; Kalmykov, A. V.

2018-03-01

The paper deals with investigation of the MHD-stability dependence on the depth of the anode immersion in the process of aluminium electrolysis. The proposed 3D three-phase mathematical model is based on the Navier-Stokes and Maxwell equation systems. This model makes it possible to simulate the distributions of the main physical fields both in horizontal and vertical planes. The suggested approach also allows to study the dynamics of the border between aluminium and electrolyte and the shape of the back oxidation zone.

Evaluation of the Triple Code Model of numerical processing-Reviewing past neuroimaging and clinical findings.

PubMed

Siemann, Julia; Petermann, Franz

2018-01-01

This review reconciles past findings on numerical processing with key assumptions of the most predominant model of arithmetic in the literature, the Triple Code Model (TCM). This is implemented by reporting diverse findings in the literature ranging from behavioral studies on basic arithmetic operations over neuroimaging studies on numerical processing to developmental studies concerned with arithmetic acquisition, with a special focus on developmental dyscalculia (DD). We evaluate whether these studies corroborate the model and discuss possible reasons for contradictory findings. A separate section is dedicated to the transfer of TCM to arithmetic development and to alternative accounts focusing on developmental questions of numerical processing. We conclude with recommendations for future directions of arithmetic research, raising questions that require answers in models of healthy as well as abnormal mathematical development. This review assesses the leading model in the field of arithmetic processing (Triple Code Model) by presenting knowledge from interdisciplinary research. It assesses the observed contradictory findings and integrates the resulting opposing viewpoints. The focus is on the development of arithmetic expertise as well as abnormal mathematical development. The original aspect of this article is that it points to a gap in research on these topics and provides possible solutions for future models. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mathematical modelling of methanogenic reactor start-up: Importance of volatile fatty acids degrading population.

PubMed

Jabłoński, Sławomir J; Łukaszewicz, Marcin

2014-12-01

Development of balanced community of microorganisms is one of the obligatory for stable anaerobic digestion. Application of mathematical models might be helpful in development of reliable procedures during the process start-up period. Yet, the accuracy of forecast depends on the quality of input and parameters. In this study, the specific anaerobic activity (SAA) tests were applied in order to estimate microbial community structure. Obtained data was applied as input conditions for mathematical model of anaerobic digestion. The initial values of variables describing the amount of acetate and propionate utilizing microorganisms could be calculated on the basis of SAA results. The modelling based on those optimized variables could successfully reproduce the behavior of a real system during the continuous fermentation. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Mathematical models of cell factories: moving towards the core of industrial biotechnology.

PubMed

Cvijovic, Marija; Bordel, Sergio; Nielsen, Jens

2011-09-01

Industrial biotechnology involves the utilization of cell factories for the production of fuels and chemicals. Traditionally, the development of highly productive microbial strains has relied on random mutagenesis and screening. The development of predictive mathematical models provides a new paradigm for the rational design of cell factories. Instead of selecting among a set of strains resulting from random mutagenesis, mathematical models allow the researchers to predict in silico the outcomes of different genetic manipulations and engineer new strains by performing gene deletions or additions leading to a higher productivity of the desired chemicals. In this review we aim to summarize the main modelling approaches of biological processes and illustrate the particular applications that they have found in the field of industrial microbiology. © 2010 The Authors. Journal compilation © 2010 Society for Applied Microbiology and Blackwell Publishing Ltd.

The stability of colorectal cancer mathematical models

NASA Astrophysics Data System (ADS)

Khairudin, Nur Izzati; Abdullah, Farah Aini

2013-04-01

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

Capability of GPGPU for Faster Thermal Analysis Used in Data Assimilation

NASA Astrophysics Data System (ADS)

Takaki, Ryoji; Akita, Takeshi; Shima, Eiji

A thermal mathematical model plays an important role in operations on orbit as well as spacecraft thermal designs. The thermal mathematical model has some uncertain thermal characteristic parameters, such as thermal contact resistances between components, effective emittances of multilayer insulation (MLI) blankets, discouraging make up efficiency and accuracy of the model. A particle filter which is one of successive data assimilation methods has been applied to construct spacecraft thermal mathematical models. This method conducts a lot of ensemble computations, which require large computational power. Recently, General Purpose computing in Graphics Processing Unit (GPGPU) has been attracted attention in high performance computing. Therefore GPGPU is applied to increase the computational speed of thermal analysis used in the particle filter. This paper shows the speed-up results by using GPGPU as well as the application method of GPGPU.

A mathematical model for adaptive transport network in path finding by true slime mold.

PubMed

Tero, Atsushi; Kobayashi, Ryo; Nakagaki, Toshiyuki

2007-02-21

We describe here a mathematical model of the adaptive dynamics of a transport network of the true slime mold Physarum polycephalum, an amoeboid organism that exhibits path-finding behavior in a maze. This organism possesses a network of tubular elements, by means of which nutrients and signals circulate through the plasmodium. When the organism is put in a maze, the network changes its shape to connect two exits by the shortest path. This process of path-finding is attributed to an underlying physiological mechanism: a tube thickens as the flux through it increases. The experimental evidence for this is, however, only qualitative. We constructed a mathematical model of the general form of the tube dynamics. Our model contains a key parameter corresponding to the extent of the feedback regulation between the thickness of a tube and the flux through it. We demonstrate the dependence of the behavior of the model on this parameter.

Clinical study and numerical simulation of brain cancer dynamics under radiotherapy

NASA Astrophysics Data System (ADS)

Nawrocki, S.; Zubik-Kowal, B.

2015-05-01

We perform a clinical and numerical study of the progression of brain cancer tumor growth dynamics coupled with the effects of radiotherapy. We obtained clinical data from a sample of brain cancer patients undergoing radiotherapy and compare it to our numerical simulations to a mathematical model of brain tumor cell population growth influenced by radiation treatment. We model how the body biologically receives a physically delivered dose of radiation to the affected tumorous area in the form of a generalized LQ model, modified to account for the conversion process of sublethal lesions into lethal lesions at high radiation doses. We obtain good agreement between our clinical data and our numerical simulations of brain cancer progression given by the mathematical model, which couples tumor growth dynamics and the effect of irradiation. The correlation, spanning a wide dataset, demonstrates the potential of the mathematical model to describe the dynamics of brain tumor growth influenced by radiotherapy.

Nonlinear-programming mathematical modeling of coal blending for power plant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang Longhua; Zhou Junhu; Yao Qiang

At present most of the blending works are guided by experience or linear-programming (LP) which can not reflect the coal complicated characteristics properly. Experimental and theoretical research work shows that most of the coal blend properties can not always be measured as a linear function of the properties of the individual coals in the blend. The authors introduced nonlinear functions or processes (including neural network and fuzzy mathematics), established on the experiments directed by the authors and other researchers, to quantitatively describe the complex coal blend parameters. Finally nonlinear-programming (NLP) mathematical modeling of coal blend is introduced and utilized inmore » the Hangzhou Coal Blending Center. Predictions based on the new method resulted in different results from the ones based on LP modeling. The authors concludes that it is very important to introduce NLP modeling, instead of NL modeling, into the work of coal blending.« less

A Weighted Difference of Anisotropic and Isotropic Total Variation Model for Image Processing

DTIC Science & Technology

2014-09-01

A WEIGHTED DIFFERENCE OF ANISOTROPIC AND ISOTROPIC TOTAL VARIATION MODEL FOR IMAGE PROCESSING YIFEI LOU∗, TIEYONG ZENG† , STANLEY OSHER‡ , AND JACK...grants DMS-0928427 and DMS-1222507. † Department of Mathematics, Hong Kong Baptist University, Kowloon Tong , Hong Kong. Email: zeng@hkbu.edu.hk. TZ is

Hierarchical analytical and simulation modelling of human-machine systems with interference

NASA Astrophysics Data System (ADS)

Braginsky, M. Ya; Tarakanov, D. V.; Tsapko, S. G.; Tsapko, I. V.; Baglaeva, E. A.

2017-01-01

The article considers the principles of building the analytical and simulation model of the human operator and the industrial control system hardware and software. E-networks as the extension of Petri nets are used as the mathematical apparatus. This approach allows simulating complex parallel distributed processes in human-machine systems. The structural and hierarchical approach is used as the building method for the mathematical model of the human operator. The upper level of the human operator is represented by the logical dynamic model of decision making based on E-networks. The lower level reflects psychophysiological characteristics of the human-operator.

Integration of multiple theories for the simulation of laser interference lithography processes

NASA Astrophysics Data System (ADS)

Lin, Te-Hsun; Yang, Yin-Kuang; Fu, Chien-Chung

2017-11-01

The periodic structure of laser interference lithography (LIL) fabrication is superior to other lithography technologies. In contrast to traditional lithography, LIL has the advantages of being a simple optical system with no mask requirements, low cost, high depth of focus, and large patterning area in a single exposure. Generally, a simulation pattern for the periodic structure is obtained through optical interference prior to its fabrication through LIL. However, the LIL process is complex and combines the fields of optical and polymer materials; thus, a single simulation theory cannot reflect the real situation. Therefore, this research integrates multiple theories, including those of optical interference, standing waves, and photoresist characteristics, to create a mathematical model for the LIL process. The mathematical model can accurately estimate the exposure time and reduce the LIL process duration through trial and error.

Integration of multiple theories for the simulation of laser interference lithography processes.

PubMed

Lin, Te-Hsun; Yang, Yin-Kuang; Fu, Chien-Chung

2017-11-24

The periodic structure of laser interference lithography (LIL) fabrication is superior to other lithography technologies. In contrast to traditional lithography, LIL has the advantages of being a simple optical system with no mask requirements, low cost, high depth of focus, and large patterning area in a single exposure. Generally, a simulation pattern for the periodic structure is obtained through optical interference prior to its fabrication through LIL. However, the LIL process is complex and combines the fields of optical and polymer materials; thus, a single simulation theory cannot reflect the real situation. Therefore, this research integrates multiple theories, including those of optical interference, standing waves, and photoresist characteristics, to create a mathematical model for the LIL process. The mathematical model can accurately estimate the exposure time and reduce the LIL process duration through trial and error.

Mathematical Description Development of Reactions of Metallic Gallium Using Kinetic Block Diagram

NASA Astrophysics Data System (ADS)

Yakovleva, A. A.; Soboleva, V. G.; Filatova, E. G.

2018-05-01

A kinetic block diagram based on a logical sequence of actions in the mathematical processing of a kinetic data is used. A type of reactions of metallic gallium in hydrochloric acid solutions is determined. It has been established that the reactions of the formation of gallium oxide and its salts proceed independently and in the absence of the diffusion resistance. Kinetic models connecting the constants of the reaction rate with the activation energy and describing the evolution of the process are obtained.

Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine.

PubMed

Erdem, Mustafa; Safan, Muntaser; Castillo-Chavez, Carlos

2017-07-01

The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.

Modeling birds on wires.

PubMed

Aydoğdu, A; Frasca, P; D'Apice, C; Manzo, R; Thornton, J M; Gachomo, B; Wilson, T; Cheung, B; Tariq, U; Saidel, W; Piccoli, B

2017-02-21

In this paper we introduce a mathematical model to study the group dynamics of birds resting on wires. The model is agent-based and postulates attraction-repulsion forces between the interacting birds: the interactions are "topological", in the sense that they involve a given number of neighbors irrespective of their distance. The model is first mathematically analyzed and then simulated to study its main properties: we observe that the model predicts birds to be more widely spaced near the borders of each group. We compare the results from the model with experimental data, derived from the analysis of pictures of pigeons and starlings taken in New Jersey: two different image elaboration protocols allow us to establish a good agreement with the model and to quantify its main parameters. We also discuss the potential handedness of the birds, by analyzing the group organization features and the group dynamics at the arrival of new birds. Finally, we propose a more refined mathematical model that describes landing and departing birds by suitable stochastic processes. Copyright © 2016 Elsevier Ltd. All rights reserved.

Development of syntax of intuition-based learning model in solving mathematics problems

NASA Astrophysics Data System (ADS)

Yeni Heryaningsih, Nok; Khusna, Hikmatul

2018-01-01

The aim of the research was to produce syntax of Intuition Based Learning (IBL) model in solving mathematics problem for improving mathematics students’ achievement that valid, practical and effective. The subject of the research were 2 classes in grade XI students of SMAN 2 Sragen, Central Java. The type of the research was a Research and Development (R&D). Development process adopted Plomp and Borg & Gall development model, they were preliminary investigation step, design step, realization step, evaluation and revision step. Development steps were as follow: (1) Collected the information and studied of theories in Preliminary Investigation step, studied about intuition, learning model development, students condition, and topic analysis, (2) Designed syntax that could bring up intuition in solving mathematics problem and then designed research instruments. They were several phases that could bring up intuition, Preparation phase, Incubation phase, Illumination phase and Verification phase, (3) Realized syntax of Intuition Based Learning model that has been designed to be the first draft, (4) Did validation of the first draft to the validator, (5) Tested the syntax of Intuition Based Learning model in the classrooms to know the effectiveness of the syntax, (6) Conducted Focus Group Discussion (FGD) to evaluate the result of syntax model testing in the classrooms, and then did the revision on syntax IBL model. The results of the research were produced syntax of IBL model in solving mathematics problems that valid, practical and effective. The syntax of IBL model in the classroom were, (1) Opening with apperception, motivations and build students’ positive perceptions, (2) Teacher explains the material generally, (3) Group discussion about the material, (4) Teacher gives students mathematics problems, (5) Doing exercises individually to solve mathematics problems with steps that could bring up students’ intuition: Preparations, Incubation, Illumination, and Verification, (6) Closure with the review of students have learned or giving homework.

Simulation of friction stir drilling process

NASA Astrophysics Data System (ADS)

Vijayabaskar, P.; Hynes, N. Rajesh Jesudoss

2018-05-01

The project is the study of the thermal drilling process. The process is a hole forming process in the sheet metals using the heat generated by means of friction. The main advantage of the process over the conventional drilling process is that the holes formed using this process does not need any backing arrangements such as weld nuts, rivet nuts etc. Because the extruded bush itself acts as a supporting structure for the fasteners. This eliminates the need for the access to the backside of the work material for fastening operations. The major factors contributing the thermal drilling operation are the spindle speed and the thrust force required for forming a hole. The process of finding out the suitable thrust force and the speed for drilling a particular material with particular thickness is a tedious process. The process can be simplified by forming a mathematical model by combining the empirical formulae from the literature. These formulae were derived in the literature from the experimental trials by following certain assumptions. In this paper a suitable mathematical model is formed by replicating the experiments and tried to be validated by the results from numerical analysis. The numerical analysis of the model is done using the ANSYS software.

CFD Modeling of Flow, Temperature, and Concentration Fields in a Pilot-Scale Rotary Hearth Furnace

NASA Astrophysics Data System (ADS)

Liu, Ying; Su, Fu-Yong; Wen, Zhi; Li, Zhi; Yong, Hai-Quan; Feng, Xiao-Hong

2014-01-01

A three-dimensional mathematical model for simulation of flow, temperature, and concentration fields in a pilot-scale rotary hearth furnace (RHF) has been developed using a commercial computational fluid dynamics software, FLUENT. The layer of composite pellets under the hearth is assumed to be a porous media layer with CO source and energy sink calculated by an independent mathematical model. User-defined functions are developed and linked to FLUENT to process the reduction process of the layer of composite pellets. The standard k-ɛ turbulence model in combination with standard wall functions is used for modeling of gas flow. Turbulence-chemistry interaction is taken into account through the eddy-dissipation model. The discrete ordinates model is used for modeling of radiative heat transfer. A comparison is made between the predictions of the present model and the data from a test of the pilot-scale RHF, and a reasonable agreement is found. Finally, flow field, temperature, and CO concentration fields in the furnace are investigated by the model.

Catastrophic event modeling. [lithium thionyl chloride batteries

NASA Technical Reports Server (NTRS)

Frank, H. A.

1981-01-01

A mathematical model for the catastrophic failures (venting or explosion of the cell) in lithium thionyl chloride batteries is presented. The phenomenology of the various processes leading to cell failure is reviewed.

Mathematical modelling of disintegration-limited co-digestion of OFMSW and sewage sludge.

PubMed

Esposito, G; Frunzo, L; Panico, A; d'Antonio, G

2008-01-01

This paper presents a mathematical model able to simulate under dynamic conditions the physical, chemical and biological processes prevailing in a OFMSW and sewage sludge anaerobic digestion system. The model proposed is based on differential mass balance equations for substrates, products and bacterial groups involved in the co-digestion process and includes the biochemical reactions of the substrate conversion and the kinetics of microbial growth and decay. The main peculiarity of the model is the surface based kinetic description of the OFMSW disintegration process, whereas the pH determination is based on a nine-order polynomial equation derived by acid-base equilibria. The model can be applied to simulate the co-digestion process for several purposes, such as the evaluation of the optimal process conditions in terms of OFMSW/sewage sludge ratio, temperature, OFMSW particle size, solid mixture retention time, reactor stirring rate, etc. Biogas production and composition can also be evaluated to estimate the potential energy production under different process conditions. In particular, model simulations reported in this paper show the model capability to predict the OFMSW amount which can be treated in the digester of an existing MWWTP and to assess the OFMSW particle size diminution pre-treatment required to increase the rate of the disintegration process, which otherwise can highly limit the co-digestion system. Copyright IWA Publishing 2008.

Covariation between Variables in a Modelling Process: The ACODESA (Collaborative Learning, Scientific Debate and Self-Reflection) Method

ERIC Educational Resources Information Center

Hitt, Fernando; González-Martín, Alejandro S.

2015-01-01

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

Mathematical modeling and Monte Carlo simulation of thermal inactivation of non-proteolytic Clostridium botulinum spores during continuous microwave-assisted pasteurization

USDA-ARS?s Scientific Manuscript database

The objective of this study is to develop a mathematical method to simulate the internal temperature history of products processed in a prototype microwave-assisted pasteurization system (MAPS) developed by Washington State University. Two products (10 oz. beef meatball trays and 16 oz. salmon fill...

Planning for Mathematics Instruction: A Model of Experienced Teachers' Planning Processes in the Context of a Reform Mathematics Curriculum

ERIC Educational Resources Information Center

Superfine, Alison Castro

2008-01-01

Planning is an important phase of teaching, during which teachers make decisions about various aspects of instruction that ultimately shape students' opportunities to learn. Prior research on teacher planning, however, fails to adequately describe experienced teachers' planning decisions, and is unclear about the extent to which teachers use…

From particle systems to learning processes. Comment on "Collective learning modeling based on the kinetic theory of active particles" by Diletta Burini, Silvana De Lillo, and Livio Gibelli

NASA Astrophysics Data System (ADS)

Lachowicz, Mirosław

2016-03-01

The very stimulating paper [6] discusses an approach to perception and learning in a large population of living agents. The approach is based on a generalization of kinetic theory methods in which the interactions between agents are described in terms of game theory. Such an approach was already discussed in Ref. [2-4] (see also references therein) in various contexts. The processes of perception and learning are based on the interactions between agents and therefore the general kinetic theory is a suitable tool for modeling them. However the main question that rises is how the perception and learning processes may be treated in the mathematical modeling. How may we precisely deliver suitable mathematical structures that are able to capture various aspects of perception and learning?

An analysis of the Petri net based model of the human body iron homeostasis process.

PubMed

Sackmann, Andrea; Formanowicz, Dorota; Formanowicz, Piotr; Koch, Ina; Blazewicz, Jacek

2007-02-01

In the paper a Petri net based model of the human body iron homeostasis is presented and analyzed. The body iron homeostasis is an important but not fully understood complex process. The modeling of the process presented in the paper is expressed in the language of Petri net theory. An application of this theory to the description of biological processes allows for very precise analysis of the resulting models. Here, such an analysis of the body iron homeostasis model from a mathematical point of view is given.

Trade-offs mathematical modelling of 3DCE in new product development: real three dimensions and directions for development

NASA Astrophysics Data System (ADS)

Ilhami, M. A.; Subagyo; Masruroh, N. A.

2018-04-01

In the last two decades, coordinating product, process, and supply chain has become the main focus in recent years as a growing body of research, which mathematical modelling is leading technique used in the early phase design. In this paper, we aim to conduct a comprehensive literature review of published paper and propose directions for future research, especially in mathematical modelling. Our findings exhibit fact that evidently there are only a few papers coordinate “real three dimensions”. The other papers, in fact, show simply two dimensions. Finally, some suggestions are proposed such as paying more attention to “real three dimensions” research-based and more focus on minimizing time to market, product life cycle consideration, and product rollover.

SeSBench - An initiative to benchmark reactive transport models for environmental subsurface processes

NASA Astrophysics Data System (ADS)

Jacques, Diederik

2017-04-01

As soil functions are governed by a multitude of interacting hydrological, geochemical and biological processes, simulation tools coupling mathematical models for interacting processes are needed. Coupled reactive transport models are a typical example of such coupled tools mainly focusing on hydrological and geochemical coupling (see e.g. Steefel et al., 2015). Mathematical and numerical complexity for both the tool itself or of the specific conceptual model can increase rapidly. Therefore, numerical verification of such type of models is a prerequisite for guaranteeing reliability and confidence and qualifying simulation tools and approaches for any further model application. In 2011, a first SeSBench -Subsurface Environmental Simulation Benchmarking- workshop was held in Berkeley (USA) followed by four other ones. The objective is to benchmark subsurface environmental simulation models and methods with a current focus on reactive transport processes. The final outcome was a special issue in Computational Geosciences (2015, issue 3 - Reactive transport benchmarks for subsurface environmental simulation) with a collection of 11 benchmarks. Benchmarks, proposed by the participants of the workshops, should be relevant for environmental or geo-engineering applications; the latter were mostly related to radioactive waste disposal issues - excluding benchmarks defined for pure mathematical reasons. Another important feature is the tiered approach within a benchmark with the definition of a single principle problem and different sub problems. The latter typically benchmarked individual or simplified processes (e.g. inert solute transport, simplified geochemical conceptual model) or geometries (e.g. batch or one-dimensional, homogeneous). Finally, three codes should be involved into a benchmark. The SeSBench initiative contributes to confidence building for applying reactive transport codes. Furthermore, it illustrates the use of those type of models for different environmental and geo-engineering applications. SeSBench will organize new workshops to add new benchmarks in a new special issue. Steefel, C. I., et al. (2015). "Reactive transport codes for subsurface environmental simulation." Computational Geosciences 19: 445-478.

Mathematical model of a DIC position sensing system within an optical trap

NASA Astrophysics Data System (ADS)

Wulff, Kurt D.; Cole, Daniel G.; Clark, Robert L.

2005-08-01

The quantitative study of displacements and forces of motor proteins and processes that occur at the microscopic level and below require a high level of sensitivity. For optical traps, two techniques for position sensing have been accepted and used quite extensively: quadrant photodiodes and an interferometric position sensing technique based on DIC imaging. While quadrant photodiodes have been studied in depth and mathematically characterized, a mathematical characterization of the interferometric position sensor has not been presented to the authors' knowledge. The interferometric position sensing method works off of the DIC imaging capabilities of a microscope. Circularly polarized light is sent into the microscope and the Wollaston prism used for DIC imaging splits the beam into its orthogonal components, displacing them by a set distance determined by the user. The distance between the axes of the beams is set so the beams overlap at the specimen plane and effectively share the trapped microsphere. A second prism then recombines the light beams and the exiting laser light's polarization is measured and related to position. In this paper we outline the mathematical characterization of a microsphere suspended in an optical trap using a DIC position sensing method. The sensitivity of this mathematical model is then compared to the QPD model. The mathematical model of a microsphere in an optical trap can serve as a calibration curve for an experimental setup.

A Gambler's Model of Natural Selection.

ERIC Educational Resources Information Center

Nolan, Michael J.; Ostrovsky, David S.

1996-01-01

Presents an activity that highlights the mechanism and power of natural selection. Allows students to think in terms of modeling a biological process and instills an appreciation for a mathematical approach to biological problems. (JRH)

Mathematics ability and related skills in preschoolers born very preterm.

PubMed

Hasler, Holly M; Akshoomoff, Natacha

2017-12-12

Children born very preterm (VPT) are at risk for academic, behavioral, and/or emotional problems. Mathematics is a particular weakness and better understanding of the relationship between preterm birth and early mathematics ability is needed, particularly as early as possible to aid in early intervention. Preschoolers born VPT (n = 58) and those born full term (FT; n = 29) were administered a large battery of measures within 6 months of beginning kindergarten. A multiple-mediation model was utilized to characterize the difference in skills underlying mathematics ability between groups. Children born VPT performed significantly worse than FT-born children on a measure of mathematics ability as well as full-scale IQ, verbal skills, visual-motor integration, phonological awareness, phonological working memory, motor skills, and executive functioning. Mathematics was significantly correlated with verbal skills, visual-motor integration, phonological processing, and motor skills across both groups. When entered into the mediation model, verbal skills, visual-motor integration, and phonological awareness were significant mediators of the group differences. This analysis provides insights into the pre-academic skills that are weak in preschoolers born VPT and their relationship to mathematics. It is important to identify children who will have difficulties as early as possible, particularly for VPT children who are at higher risk for academic difficulties. Therefore, this model may be used in evaluating VPT children for emerging difficulties as well as an indicator that if other weaknesses are found, an assessment of mathematics should be conducted.

MAESTRO: Mathematics and Earth Science Teachers' Resource Organization

NASA Astrophysics Data System (ADS)

Courtier, A. M.; Pyle, E. J.; Fichter, L.; Lucas, S.; Jackson, A.

2013-12-01

The Mathematics and Earth Science Teachers' Resource Organization (MAESTRO) partnership between James Madison University and Harrisonburg City and Page County Public Schools, funded through NSF-GEO. The partnership aims to transform mathematics and Earth science instruction in middle and high schools by developing an integrated mathematics and Earth systems science approach to instruction. This curricular integration is intended to enhance the mathematical skills and confidence of students through concrete, Earth systems-based examples, while increasing the relevance and rigor of Earth science instruction via quantification and mathematical modeling of Earth system phenomena. MAESTRO draws heavily from the Earth Science Literacy Initiative (2009) and is informed by criterion-level standardized test performance data in both mathematics and Earth science. The project has involved two summer professional development workshops, academic year Lesson Study (structured teacher observation and reflection), and will incorporate site-based case studies with direct student involvement. Participating teachers include Grade 6 Science and Mathematics teachers, and Grade 9 Earth Science and Algebra teachers. It is anticipated that the proposed integration across grade bands will first strengthen students' interests in mathematics and science (a problem in middle school) and subsequently reinforce the relevance of mathematics and other sciences (a problem in high school), both in support of Earth systems literacy. MAESTRO's approach to the integration of math and science focuses on using box models to emphasize the interconnections among the geo-, atmo-, bio-, and hydrospheres, and demonstrates the positive and negative feedback processes that connect their mutual evolution. Within this framework we explore specific relationships that can be described both qualitatively and mathematically, using mathematical operations appropriate for each grade level. Site-based case studies, developed in collaboration between teachers and JMU faculty members, provide a tangible, relevant setting in which students can apply and understand mathematical applications and scientific processes related to evolving Earth systems. Initial results from student questionnaires and teacher focus groups suggest that the anticipated impacts of MAESTRO on students are being realized, including increased valuing of mathematics and Earth science in society and transfer between mathematics and science courses. As a high percentage of students in the MAESTRO schools are of low socio-economic status, they also face the prospect of becoming first-generation college students, hopefully considering STEM academic pathways. MAESTRO will drive the development of challenging and engaging instruction designed to draw a larger pool of students into STEM career pathways.

The study of heat penetration of kimchi soup on stationary and rotary retorts.

PubMed

Cho, Won-Il; Park, Eun-Ji; Cheon, Hee Soon; Chung, Myong-Soo

2015-03-01

The aim of this study was to determine the heat-penetration characteristics using stationary and rotary retorts to manufacture Kimchi soup. Both heat-penetration tests and computer simulation based on mathematical modeling were performed. The sterility was measured at five different positions in the pouch. The results revealed only a small deviation of F 0 among the different positions, and the rate of heat transfer was increased by rotation of the retort. The thermal processing of retort-pouched Kimchi soup was analyzed mathematically using a finite-element model, and optimum models for predicting the time course of the temperature and F 0 were developed. The mathematical models could accurately predict the actual heat penetration of retort-pouched Kimchi soup. The average deviation of the temperature between the experimental and mathematical predicted model was 2.46% (R(2)=0.975). The changes in nodal temperature and F 0 caused by microbial inactivation in the finite-element model predicted using the NISA program were very similar to that of the experimental data of for the retorted Kimchi soup during sterilization with rotary retorts. The correlation coefficient between the simulation using the NISA program and the experimental data was very high, at 99%.

The Study of Heat Penetration of Kimchi Soup on Stationary and Rotary Retorts

PubMed Central

Cho, Won-Il; Park, Eun-Ji; Cheon, Hee Soon; Chung, Myong-Soo

2015-01-01

The aim of this study was to determine the heat-penetration characteristics using stationary and rotary retorts to manufacture Kimchi soup. Both heat-penetration tests and computer simulation based on mathematical modeling were performed. The sterility was measured at five different positions in the pouch. The results revealed only a small deviation of F0 among the different positions, and the rate of heat transfer was increased by rotation of the retort. The thermal processing of retort-pouched Kimchi soup was analyzed mathematically using a finite-element model, and optimum models for predicting the time course of the temperature and F0 were developed. The mathematical models could accurately predict the actual heat penetration of retort-pouched Kimchi soup. The average deviation of the temperature between the experimental and mathematical predicted model was 2.46% (R2=0.975). The changes in nodal temperature and F0 caused by microbial inactivation in the finite-element model predicted using the NISA program were very similar to that of the experimental data of for the retorted Kimchi soup during sterilization with rotary retorts. The correlation coefficient between the simulation using the NISA program and the experimental data was very high, at 99%. PMID:25866751

A new standard model for milk yield in dairy cows based on udder physiology at the milking-session level.

PubMed

Gasqui, Patrick; Trommenschlager, Jean-Marie

2017-08-21

Milk production in dairy cow udders is a complex and dynamic physiological process that has resisted explanatory modelling thus far. The current standard model, Wood's model, is empirical in nature, represents yield in daily terms, and was published in 1967. Here, we have developed a dynamic and integrated explanatory model that describes milk yield at the scale of the milking session. Our approach allowed us to formally represent and mathematically relate biological features of known relevance while accounting for stochasticity and conditional elements in the form of explicit hypotheses, which could then be tested and validated using real-life data. Using an explanatory mathematical and biological model to explore a physiological process and pinpoint potential problems (i.e., "problem finding"), it is possible to filter out unimportant variables that can be ignored, retaining only those essential to generating the most realistic model possible. Such modelling efforts are multidisciplinary by necessity. It is also helpful downstream because model results can be compared with observed data, via parameter estimation using maximum likelihood and statistical testing using model residuals. The process in its entirety yields a coherent, robust, and thus repeatable, model.

Semantic Processing of Mathematical Gestures

ERIC Educational Resources Information Center

Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.

2009-01-01

Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…

Blooms' separation of the final exam of Engineering Mathematics II: Item reliability using Rasch measurement model

NASA Astrophysics Data System (ADS)

Fuaad, Norain Farhana Ahmad; Nopiah, Zulkifli Mohd; Tawil, Norgainy Mohd; Othman, Haliza; Asshaari, Izamarlina; Osman, Mohd Hanif; Ismail, Nur Arzilah

2014-06-01

In engineering studies and researches, Mathematics is one of the main elements which express physical, chemical and engineering laws. Therefore, it is essential for engineering students to have a strong knowledge in the fundamental of mathematics in order to apply the knowledge to real life issues. However, based on the previous results of Mathematics Pre-Test, it shows that the engineering students lack the fundamental knowledge in certain topics in mathematics. Due to this, apart from making improvements in the methods of teaching and learning, studies on the construction of questions (items) should also be emphasized. The purpose of this study is to assist lecturers in the process of item development and to monitor the separation of items based on Blooms' Taxonomy and to measure the reliability of the items itself usingRasch Measurement Model as a tool. By using Rasch Measurement Model, the final exam questions of Engineering Mathematics II (Linear Algebra) for semester 2 sessions 2012/2013 were analysed and the results will provide the details onthe extent to which the content of the item providesuseful information about students' ability. This study reveals that the items used in Engineering Mathematics II (Linear Algebra) final exam are well constructed but the separation of the items raises concern as it is argued that it needs further attention, as there is abig gap between items at several levels of Blooms' cognitive skill.

Modeling of Geometric Error in Linear Guide Way to Improved the vertical three-axis CNC Milling machine’s accuracy

NASA Astrophysics Data System (ADS)

Kwintarini, Widiyanti; Wibowo, Agung; Arthaya, Bagus M.; Yuwana Martawirya, Yatna

2018-03-01

The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

Mathematical Simulation of the Process of Aerobic Treatment of Wastewater under Conditions of Diffusion and Mass Transfer Perturbations

NASA Astrophysics Data System (ADS)

Bomba, A. Ya.; Safonik, A. P.

2018-05-01

A mathematical model of the process of aerobic treatment of wastewater has been refined. It takes into account the interaction of bacteria, as well as of organic and biologically nonoxidizing substances under conditions of diffusion and mass transfer perturbations. An algorithm of the solution of the corresponding nonlinear perturbed problem of convection-diffusion-mass transfer type has been constructed, with a computer experiment carried out based on it. The influence of the concentration of oxygen and of activated sludge on the quality of treatment is shown. Within the framework of the model suggested, a possibility of automated control of the process of deposition of impurities in a biological filter depending on the initial parameters of the water medium is suggested.

Simulation and automation of thermal processes in oil well

NASA Astrophysics Data System (ADS)

Kostarev, N. A.; Trufanova, N. M.

2018-03-01

The paper presents a two-dimensional mathematical model and a numerical analysis of heat and mass transfer processes in an oil well. The proposed and implemented mathematical model of the process of heat and mass transfer in an oil well allows analyzing the temperature field in the whole space of an oil well and is suitable for any fields equipped with an electric centrifugal pump. Temperature and velocity fields were obtained, as well as the distribution of temperature on the wall of the pump tubing along the depth of the well. On the basis of the obtained temperature fields, the modes of periodic heating of the well by the heating cable were developed. Recommendations are given on the choice of power parameters and the time of warming up the well.

Mathematical Simulation of the Process of Aerobic Treatment of Wastewater under Conditions of Diffusion and Mass Transfer Perturbations

NASA Astrophysics Data System (ADS)

Bomba, A. Ya.; Safonik, A. P.

2018-03-01

A mathematical model of the process of aerobic treatment of wastewater has been refined. It takes into account the interaction of bacteria, as well as of organic and biologically nonoxidizing substances under conditions of diffusion and mass transfer perturbations. An algorithm of the solution of the corresponding nonlinear perturbed problem of convection-diffusion-mass transfer type has been constructed, with a computer experiment carried out based on it. The influence of the concentration of oxygen and of activated sludge on the quality of treatment is shown. Within the framework of the model suggested, a possibility of automated control of the process of deposition of impurities in a biological filter depending on the initial parameters of the water medium is suggested.

Development of mathematical models for automation of strength calculation during plastic deformation processing

NASA Astrophysics Data System (ADS)

Steposhina, S. V.; Fedonin, O. N.

2018-03-01

Dependencies that make it possible to automate the force calculation during surface plastic deformation (SPD) processing and, thus, to shorten the time for technological preparation of production have been developed.

The Effect of Teaching Model ‘Learning Cycles 5E’ toward Students’ Achievement in Learning Mathematic at X Years Class SMA Negeri 1 Banuhampu 2013/2014 Academic Year

NASA Astrophysics Data System (ADS)

Yeni, N.; Suryabayu, E. P.; Handayani, T.

2017-02-01

Based on the survey showed that mathematics teacher still dominated in teaching and learning process. The process of learning is centered on the teacher while the students only work based on instructions provided by the teacher without any creativity and activities that stimulate students to explore their potential. Realized the problem above the writer interested in finding the solution by applying teaching model ‘Learning Cycles 5E’. The purpose of his research is to know whether teaching model ‘Learning Cycles 5E’ is better than conventional teaching in teaching mathematic. The type of the research is quasi experiment by Randomized Control test Group Only Design. The population in this research were all X years class students. The sample is chosen randomly after doing normality, homogeneity test and average level of students’ achievement. As the sample of this research was X.7’s class as experiment class used teaching model learning cycles 5E and X.8’s class as control class used conventional teaching. The result showed us that the students achievement in the class that used teaching model ‘Learning Cycles 5E’ is better than the class which did not use the model.

On the development of nugget growth model for resistance spot welding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Kang, E-mail: zhoukang326@126.com, E-mail: melcai@ust.hk; Cai, Lilong, E-mail: zhoukang326@126.com, E-mail: melcai@ust.hk

2014-04-28

In this paper, we developed a general mathematical model to estimate the nugget growth process based on the heat energy delivered into the welds by the resistance spot welding. According to the principles of thermodynamics and heat transfer, and the effect of electrode force during the welding process, the shape of the nugget can be estimated. Then, a mathematical model between heat energy absorbed and nugget diameter can be obtained theoretically. It is shown in this paper that the nugget diameter can be precisely described by piecewise fractal polynomial functions. Experiments were conducted with different welding operation conditions, such asmore » welding currents, workpiece thickness, and widths, to validate the model and the theoretical analysis. All the experiments confirmed that the proposed model can predict the nugget diameters with high accuracy based on the input heat energy to the welds.« less

Modelling and simulating reaction-diffusion systems using coloured Petri nets.

PubMed

Liu, Fei; Blätke, Mary-Ann; Heiner, Monika; Yang, Ming

2014-10-01

Reaction-diffusion systems often play an important role in systems biology when developmental processes are involved. Traditional methods of modelling and simulating such systems require substantial prior knowledge of mathematics and/or simulation algorithms. Such skills may impose a challenge for biologists, when they are not equally well-trained in mathematics and computer science. Coloured Petri nets as a high-level and graphical language offer an attractive alternative, which is easily approachable. In this paper, we investigate a coloured Petri net framework integrating deterministic, stochastic and hybrid modelling formalisms and corresponding simulation algorithms for the modelling and simulation of reaction-diffusion processes that may be closely coupled with signalling pathways, metabolic reactions and/or gene expression. Such systems often manifest multiscaleness in time, space and/or concentration. We introduce our approach by means of some basic diffusion scenarios, and test it against an established case study, the Brusselator model. Copyright © 2014 Elsevier Ltd. All rights reserved.

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

PubMed Central

Santonja, F.; Chen-Charpentier, B.

2012-01-01

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model. PMID:22927889

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.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1987-01-01

A general mathematical model and solution methodologies are being developed for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic, or static thermomechanical loads. Among the system responses, which were associated with these load conditions, were thermal buckling, creep buckling, and ratcheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution process.

Mathematic Model of Digital Control System with PID Regulator and Regular Step of Quantization with Information Transfer via the Channel of Plural Access

NASA Astrophysics Data System (ADS)

Abramov, G. V.; Emeljanov, A. E.; Ivashin, A. L.

Theoretical bases for modeling a digital control system with information transfer via the channel of plural access and a regular quantization cycle are submitted. The theory of dynamic systems with random changes of the structure including elements of the Markov random processes theory is used for a mathematical description of a network control system. The characteristics of similar control systems are received. Experimental research of the given control systems is carried out.

Evaluation of leaf litter leaching kinetics through commonly-used mathematical models

NASA Astrophysics Data System (ADS)

Montoya, J. V.; Bastianoni, A.; Mendez, C.; Paolini, J.

2012-04-01

Leaching is defined as the abiotic process by which soluble compounds of the litter are released into the water. Most studies dealing with leaf litter breakdown and leaching kinetics apply the single exponential decay model since it corresponds well with the understanding of the biology of decomposition. However, during leaching important mass losses occur and mathematical models often fail in describing this process adequately. During the initial hours of leaching leaf litter experience high decay rates which are not properly modelled. Adjusting leaching losses to mathematical models has not been investigated thoroughly and the use of models assuming constant decay rates leads to inappropriate assessments of leaching kinetics. We aim to describe, assess, and compare different leaching kinetics models fitted to leaf litter mass losses from six Neotropical riparian forest species. Leaf litter from each species was collected in the lower reaches of San Miguel stream in Northern Venezuela. Air-dried leaves from each species were incubated in 250 ml of water in the dark at room temperature. At 1h, 6h, 1d, 2d, 4d, 8d and 15d, three jars were removed from the assay in a no-replacement experimental design. At each time leaves from each jar were removed and oven-dried. Afterwards, dried up leaves were weighed and remaining dry mass was determined and expressed as ash-free dry mass. Mass losses of leaf litter showed steep declines for the first two days followed by a steady decrease in mass loss. Data was fitted to three different models: single-exponential, power and rational. Our results showed that the mass loss predicted with the single-exponential model did not reflect the real data at any stage of the leaching process. The power model showed a better adjustment, but fails predicting successfully the behavior during leaching's early stages. To evaluate the performance of our models we used three criteria: Adj-R2, Akaike's Information Criteria (AIC), and residual distribution. Higher Adj-R2 were obtained for the power and the rational-type models. However, when AIC and residuals distribution were used, the only model that could satisfactory predict the behavior of our dataset was the rational-type. Even if the Adj-R2 was higher for some species when using the power model compared to the rational-type; our results showed that this criterion alone cannot demonstrate the predicting performance of any model. Usually Adj-R2 is used when assessing the goodness of fit for any mathematical model disregarding the fact that a good Adj-R2 could be obtained even when statistical assumptions required for the validity of the model are not satisfied. Our results showed that sampling at the initial stages of leaching is necessary to adequately describe this process. We also provided evidence that using traditional mathematical models is not the best option to evaluate leaching kinetics because of its mathematical inability to properly describe the abrupt changes that occur during the early stages of leaching. We also found useful applying different criteria to evaluate the goodness-of-fit and performance of any model considered taking into account both statistical and biological meaning of the results.

A mathematical model of the chevron-like wave pattern on a weld piece

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dowden, J.; Kapadia, P.

1996-12-31

In welding processes in general the surface of a metallic weld displays a chevron-like pattern. Such a pattern is also clearly seen to be present if welding is carried out using a laser beam. In the welding process a laser beam is directed normally on the metal undergoing translation and usually penetrates it to form a keyhole. The keyhole is surrounded by a molten region, the weld pool. Even if a CO{sub 2} laser is used, there are numerous fluctuations and instabilities that occur, so that the keyhole imposes forcing frequencies on the molten weld pool, additional to vibrations attendantmore » on the process of translation. The weld pool in turn responds by supporting a spectrum of waves of different frequencies involving the natural frequency of the weld pool as well as various forcing frequencies. These waves are surface tension-type capillary waves and previous publications have attempted to model their behavior mathematically, although not all aspects of the problem have always been included. The wave pattern that is manifested in the chevron-like pattern seen on the weld piece is, however, not necessarily identical to the wave pattern present in the weld pool. This is because the chevron-like wave pattern forms as a result of several complicating effects that arise as the weld specimen cools on its surface immediately after the weld has been formed. This process involves the waves on the surface of the weld pool freezing to form the chevron-like wave pattern. A feature that is often ignored is the fact that the waves on the weld pool can only be regarded as irrotational if the translation speed is sufficiently low. This paper describes mathematically the formation of the chevron-like wave pattern based on suitable simplifying assumptions to model the process. The mathematical description of the way in which this chevron-like pattern forms is a step toward a more comprehensive understanding of this process.« less

Mathematical modeling of high-pH chemical flooding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhuyan, D.; Lake, L.W.; Pope, G.A.

1990-05-01

This paper describes a generalized compositional reservoir simulator for high-pH chemical flooding processes. This simulator combines the reaction chemistry associated with these processes with the extensive physical- and flow-property modeling schemes of an existing micellar/polymer flood simulator, UTCHEM. Application of the model is illustrated for cases from a simple alkaline preflush to surfactant-enhanced alkaline-polymer flooding.

A mathematical model and computational framework for three-dimensional chondrocyte cell growth in a porous tissue scaffold placed inside a bi-directional flow perfusion bioreactor.

PubMed

Shakhawath Hossain, Md; Bergstrom, D J; Chen, X B

2015-12-01

The in vitro chondrocyte cell culture for cartilage tissue regeneration in a perfusion bioreactor is a complex process. Mathematical modeling and computational simulation can provide important insights into the culture process, which would be helpful for selecting culture conditions to improve the quality of the developed tissue constructs. However, simulation of the cell culture process is a challenging task due to the complicated interaction between the cells and local fluid flow and nutrient transport inside the complex porous scaffolds. In this study, a mathematical model and computational framework has been developed to simulate the three-dimensional (3D) cell growth in a porous scaffold placed inside a bi-directional flow perfusion bioreactor. The model was developed by taking into account the two-way coupling between the cell growth and local flow field and associated glucose concentration, and then used to perform a resolved-scale simulation based on the lattice Boltzmann method (LBM). The simulation predicts the local shear stress, glucose concentration, and 3D cell growth inside the porous scaffold for a period of 30 days of cell culture. The predicted cell growth rate was in good overall agreement with the experimental results available in the literature. This study demonstrates that the bi-directional flow perfusion culture system can enhance the homogeneity of the cell growth inside the scaffold. The model and computational framework developed is capable of providing significant insight into the culture process, thus providing a powerful tool for the design and optimization of the cell culture process. © 2015 Wiley Periodicals, Inc.

Removal of antibiotics in a parallel-plate thin-film-photocatalytic reactor: Process modeling and evolution of transformation by-products and toxicity.

PubMed

Özkal, Can Burak; Frontistis, Zacharias; Antonopoulou, Maria; Konstantinou, Ioannis; Mantzavinos, Dionissios; Meriç, Süreyya

2017-10-01

Photocatalytic degradation of sulfamethoxazole (SMX) antibiotic has been studied under recycling batch and homogeneous flow conditions in a thin-film coated immobilized system namely parallel-plate (PPL) reactor. Experimentally designed, statistically evaluated with a factorial design (FD) approach with intent to provide a mathematical model takes into account the parameters influencing process performance. Initial antibiotic concentration, UV energy level, irradiated surface area, water matrix (ultrapure and secondary treated wastewater) and time, were defined as model parameters. A full of 2 5 experimental design was consisted of 32 random experiments. PPL reactor test experiments were carried out in order to set boundary levels for hydraulic, volumetric and defined defined process parameters. TTIP based thin-film with polyethylene glycol+TiO 2 additives were fabricated according to pre-described methodology. Antibiotic degradation was monitored by High Performance Liquid Chromatography analysis while the degradation products were specified by LC-TOF-MS analysis. Acute toxicity of untreated and treated SMX solutions was tested by standard Daphnia magna method. Based on the obtained mathematical model, the response of the immobilized PC system is described with a polynomial equation. The statistically significant positive effects are initial SMX concentration, process time and the combined effect of both, while combined effect of water matrix and irradiated surface area displays an adverse effect on the rate of antibiotic degradation by photocatalytic oxidation. Process efficiency and the validity of the acquired mathematical model was also verified for levofloxacin and cefaclor antibiotics. Immobilized PC degradation in PPL reactor configuration was found capable of providing reduced effluent toxicity by simultaneous degradation of SMX parent compound and TBPs. Copyright © 2017. Published by Elsevier B.V.

A mathematical model for foreign body reactions in 2D.

PubMed

Su, Jianzhong; Gonzales, Humberto Perez; Todorov, Michail; Kojouharov, Hristo; Tang, Liping

2011-02-01

The foreign body reactions are commonly referred to the network of immune and inflammatory reactions of human or animals to foreign objects placed in tissues. They are basic biological processes, and are also highly relevant to bioengineering applications in implants, as fibrotic tissue formations surrounding medical implants have been found to substantially reduce the effectiveness of devices. Despite of intensive research on determining the mechanisms governing such complex responses, few mechanistic mathematical models have been developed to study such foreign body reactions. This study focuses on a kinetics-based predictive tool in order to analyze outcomes of multiple interactive complex reactions of various cells/proteins and biochemical processes and to understand transient behavior during the entire period (up to several months). A computational model in two spatial dimensions is constructed to investigate the time dynamics as well as spatial variation of foreign body reaction kinetics. The simulation results have been consistent with experimental data and the model can facilitate quantitative insights for study of foreign body reaction process in general.

An improvement in the calculation of the efficiency of oxidative phosphorylation and rate of energy dissipation in mitochondria

NASA Astrophysics Data System (ADS)

Ghafuri, Mohazabeh; Golfar, Bahareh; Nosrati, Mohsen; Hoseinkhani, Saman

2014-12-01

The process of ATP production is one of the most vital processes in living cells which happens with a high efficiency. Thermodynamic evaluation of this process and the factors involved in oxidative phosphorylation can provide a valuable guide for increasing the energy production efficiency in research and industry. Although energy transduction has been studied qualitatively in several researches, there are only few brief reviews based on mathematical models on this subject. In our previous work, we suggested a mathematical model for ATP production based on non-equilibrium thermodynamic principles. In the present study, based on the new discoveries on the respiratory chain of animal mitochondria, Golfar's model has been used to generate improved results for the efficiency of oxidative phosphorylation and the rate of energy loss. The results calculated from the modified coefficients for the proton pumps of the respiratory chain enzymes are closer to the experimental results and validate the model.

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

NASA Astrophysics Data System (ADS)

Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia

2018-02-01

Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

Energy-technological complex with reactor for torrefaction

NASA Astrophysics Data System (ADS)

Kuzmina, J. S.; Director, L. B.; Zaichenko, V. M.

2016-11-01

To eliminate shortcomings of raw plant materials pelletizing process with thermal treatment (low-temperature pyrolysis or torrefaction) can be applied. This paper presents a mathematical model of energy-technological complex (ETC) for combined production of heat, electricity and solid biofuels torrefied pellets. According to the structure the mathematical model consists of mathematical models of main units of ETC and the relationships between them and equations of energy and material balances. The equations describe exhaust gas straining action through a porous medium formed by pellets. Decomposition rate of biomass was calculated by using the gross-reaction diagram, which is responsible for the disintegration of raw material. A mathematical model has been tested according to bench experiments on one reactor module. From nomographs, designed for a particular configuration of ETC it is possible to determine the basic characteristics of torrefied pellets (rate of weight loss, heating value and heat content) specifying only two parameters (temperature and torrefaction time). It is shown that the addition of reactor for torrefaction to gas piston engine can improve the energy efficiency of power plant.

The Mathematical Modeling and Computer Simulation of Electrochemical Micromachining Using Ultrashort Pulses

NASA Astrophysics Data System (ADS)

Kozak, J.; Gulbinowicz, D.; Gulbinowicz, Z.

2009-05-01

The need for complex and accurate three dimensional (3-D) microcomponents is increasing rapidly for many industrial and consumer products. Electrochemical machining process (ECM) has the potential of generating desired crack-free and stress-free surfaces of microcomponents. This paper reports a study of pulse electrochemical micromachining (PECMM) using ultrashort (nanoseconds) pulses for generating complex 3-D microstructures of high accuracy. A mathematical model of the microshaping process with taking into consideration unsteady phenomena in electrical double layer has been developed. The software for computer simulation of PECM has been developed and the effects of machining parameters on anodic localization and final shape of machined surface are presented.

Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW Processes

PubMed Central

Liu, Wenji; Li, Liangyu; Hong, Ying; Yue, Jianfeng

2017-01-01

Arc sensors have been used in seam tracking and widely studied since the 80s and commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because the arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and weaving or rotate speed. PMID:28335425

Mathematics, thermodynamics, and modeling to address ten common misconceptions about protein structure, folding, and stability.

PubMed

Robic, Srebrenka

2010-01-01

To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative phenomena in undergraduate classes. In the process of learning about these topics, students often form incorrect ideas. For example, by learning about protein folding in the context of protein synthesis, students may come to an incorrect conclusion that once synthesized on the ribosome, a protein spends its entire cellular life time in its fully folded native confirmation. This is clearly not true; proteins are dynamic structures that undergo both local fluctuations and global unfolding events. To prevent and address such misconceptions, basic concepts of protein science can be introduced in the context of simple mathematical models and hands-on explorations of publicly available data sets. Ten common misconceptions about proteins are presented, along with suggestions for using equations, models, sequence, structure, and thermodynamic data to help students gain a deeper understanding of basic concepts relating to protein structure, folding, and stability.

Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW Processes.

PubMed

Liu, Wenji; Li, Liangyu; Hong, Ying; Yue, Jianfeng

2017-03-14

Arc sensors have been used in seam tracking and widely studied since the 80s and commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because the arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and weaving or rotate speed.

An attempt at the computer-aided management of HIV infection

NASA Astrophysics Data System (ADS)

Ida, A.; Oharu, Y.; Sankey, O.

2007-07-01

The immune system is a complex and diverse system in the human body and HIV virus disrupts and destroys it through extremely complicated but surprisingly logical process. The purpose of this paper is to make an attempt to present a method for the computer-aided management of HIV infection process by means of a mathematical model describing the dynamics of the host pathogen interaction with HIV-1. Treatments for the AIDS disease must be changed to more efficient ones in accordance with the disease progression and the status of the immune system. The level of progression and the status are represented by parameters which are governed by our mathematical model. It is then exhibited that our model is numerically stable and uniquely solvable. With this knowledge, our mathematical model for HIV disease progression is formulated and physiological interpretations are provided. The results of our numerical simulations are visualized, and it is seen that our results agree with medical aspects from the point of view of antiretroviral therapy. It is then expected that our approach will take to address practical clinical issues and will be applied to the computer-aided management of antiretroviral therapies.

Methods for Maximizing the Learning Process: A Theoretical and Experimental Analysis.

ERIC Educational Resources Information Center

Atkinson, Richard C.

This research deals with optimizing the instructional process. The approach adopted was to limit consideration to simple learning tasks for which adequate mathematical models could be developed. Optimal or suitable suboptimal instructional strategies were developed for the models. The basic idea was to solve for strategies that either maximize the…

Modeling as a Decision-Making Process

ERIC Educational Resources Information Center

Bleiler-Baxter, Sarah K.; Stephens, D. Christopher; Baxter, Wesley A.; Barlow, Angela T.

2017-01-01

The goal in this article is to support teachers in better understanding what it means to model with mathematics by focusing on three key decision-making processes: Simplification, Relationship Mapping, and Situation Analysis. The authors use the Theme Park task to help teachers develop a vision of how students engage in these three decision-making…

Modellus: Learning Physics with Mathematical Modelling

NASA Astrophysics Data System (ADS)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations--differential equations--are the most important mathematical objects used for modelling Natural phenomena. In traditional approaches, they are introduced only at advanced level, because it takes a long time for students to be introduced to the fundamental principles of Calculus. With the new proposed approach, rates of change can be introduced also at early stages on learning if teachers stress semi-quantitative reasoning and use adequate computer tools. In this thesis, there is also presented Modellus, a computer tool for modelling and experimentation. This computer tool has a user interface that allows students to start doing meaningful conceptual and empirical experiments without the need to learn new syntax, as is usual with established tools. The different steps in the process of constructing and exploring models can be done with Modellus, both from physical points of view and from mathematical points of view. Modellus activities show how mathematics and physics have a unity that is very difficult to see with traditional approaches. Mathematical models are treated as concrete-abstract objects: concrete in the sense that they can be manipulated directly with a computer and abstract in the sense that they are representations of relations between variables. Data gathered from two case studies, one with secondary school students and another with first year undergraduate students support the main ideas of the thesis. Also data gathered from teachers (from college and secondary schools), mainly through an email structured questionnaire, shows that teachers agree on the potential of modelling in the learning of physics (and mathematics) and of the most important aspects of the proposed framework to integrate modelling as an essential component of the curriculum. Schools, as all institutions, change at a very slow rate. There are a multitude of reasons for this. And traditional curricula, where the emphasis is on rote learning of facts, can only be changed if schools have access to new and powerful views of learning and to new tools, that support meaningful conceptual learning and are as common and easy to use as pencil and paper.

A dynamic dual process model of risky decision making.

PubMed

Diederich, Adele; Trueblood, Jennifer S

2018-03-01

Many phenomena in judgment and decision making are often attributed to the interaction of 2 systems of reasoning. Although these so-called dual process theories can explain many types of behavior, they are rarely formalized as mathematical or computational models. Rather, dual process models are typically verbal theories, which are difficult to conclusively evaluate or test. In the cases in which formal (i.e., mathematical) dual process models have been proposed, they have not been quantitatively fit to experimental data and are often silent when it comes to the timing of the 2 systems. In the current article, we present a dynamic dual process model framework of risky decision making that provides an account of the timing and interaction of the 2 systems and can explain both choice and response-time data. We outline several predictions of the model, including how changes in the timing of the 2 systems as well as time pressure can influence behavior. The framework also allows us to explore different assumptions about how preferences are constructed by the 2 systems as well as the dynamic interaction of the 2 systems. In particular, we examine 3 different possible functional forms of the 2 systems and 2 possible ways the systems can interact (simultaneously or serially). We compare these dual process models with 2 single process models using risky decision making data from Guo, Trueblood, and Diederich (2017). Using this data, we find that 1 of the dual process models significantly outperforms the other models in accounting for both choices and response times. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Mathematical model of organic substrate degradation in solid waste windrow composting.

PubMed

Seng, Bunrith; Kristanti, Risky Ayu; Hadibarata, Tony; Hirayama, Kimiaki; Katayama-Hirayama, Keiko; Kaneko, Hidehiro

2016-01-01

Organic solid waste composting is a complex process that involves many coupled physical, chemical and biological mechanisms. To understand this complexity and to ease in planning, design and management of the composting plant, mathematical model for simulation is usually applied. The aim of this paper is to develop a mathematical model of organic substrate degradation and its performance evaluation in solid waste windrow composting system. The present model is a biomass-dependent model, considering biological growth processes under the limitation of moisture, oxygen and substrate contents, and temperature. The main output of this model is substrate content which was divided into two categories: slowly and rapidly degradable substrates. To validate the model, it was applied to a laboratory scale windrow composting of a mixture of wood chips and dog food. The wastes were filled into a cylindrical reactor of 6 cm diameter and 1 m height. The simulation program was run for 3 weeks with 1 s stepwise. The simulated results were in reasonably good agreement with the experimental results. The MC and temperature of model simulation were found to be matched with those of experiment, but limited for rapidly degradable substrates. Under anaerobic zone, the degradation of rapidly degradable substrate needs to be incorporated into the model to achieve full simulation of a long period static pile composting. This model is a useful tool to estimate the changes of substrate content during composting period, and acts as a basic model for further development of a sophisticated model.

Availability Control for Means of Transport in Decisive Semi-Markov Models of Exploitation Process

NASA Astrophysics Data System (ADS)

Migawa, Klaudiusz

2012-12-01

The issues presented in this research paper refer to problems connected with the control process for exploitation implemented in the complex systems of exploitation for technical objects. The article presents the description of the method concerning the control availability for technical objects (means of transport) on the basis of the mathematical model of the exploitation process with the implementation of the decisive processes by semi-Markov. The presented method means focused on the preparing the decisive for the exploitation process for technical objects (semi-Markov model) and after that specifying the best control strategy (optimal strategy) from among possible decisive variants in accordance with the approved criterion (criteria) of the activity evaluation of the system of exploitation for technical objects. In the presented method specifying the optimal strategy for control availability in the technical objects means a choice of a sequence of control decisions made in individual states of modelled exploitation process for which the function being a criterion of evaluation reaches the extreme value. In order to choose the optimal control strategy the implementation of the genetic algorithm was chosen. The opinions were presented on the example of the exploitation process of the means of transport implemented in the real system of the bus municipal transport. The model of the exploitation process for the means of transports was prepared on the basis of the results implemented in the real transport system. The mathematical model of the exploitation process was built taking into consideration the fact that the model of the process constitutes the homogenous semi-Markov process.

Non-Lipschitz Dynamics Approach to Discrete Event Systems

NASA Technical Reports Server (NTRS)

Zak, M.; Meyers, R.

1995-01-01

This paper presents and discusses a mathematical formalism for simulation of discrete event dynamics (DED) - a special type of 'man- made' system designed to aid specific areas of information processing. A main objective is to demonstrate that the mathematical formalism for DED can be based upon the terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.

Epistemological Beliefs of Prospective Preschool Teachers and Their Relation to Knowledge, Perception, and Planning Abilities in the Field of Mathematics: A Process Model

ERIC Educational Resources Information Center

Dunekacke, Simone; Jenßen, Lars; Eilerts, Katja; Blömeke, Sigrid

2016-01-01

Teacher competence is a multi-dimensional construct that includes beliefs as well as knowledge. The present study investigated the structure of prospective preschool teachers' mathematics-related beliefs and their relation to content knowledge and pedagogical content knowledge. In addition, prospective preschool teachers' perception and planning…

Brief Report: Preliminary Proposal of a Conceptual Model of a Digital Environment for Developing Mathematical Reasoning in Students with Autism Spectrum Disorders

ERIC Educational Resources Information Center

Santos, Maria Isabel; Breda, Ana; Almeida, Ana Margarida

2015-01-01

There is clear evidence that in typically developing children reasoning and sense-making are essential in all mathematical learning and understanding processes. In children with autism spectrum disorders (ASD), however, these become much more significant, considering their importance to successful independent living. This paper presents a…

Do Teachers Make Decisions Like Firefighters? Applying Naturalistic Decision-Making Methods to Teachers' In-Class Decision Making in Mathematics

ERIC Educational Resources Information Center

Jazby, Dan

2014-01-01

Research into human decision making (DM) processes from outside of education paint a different picture of DM than current DM models in education. This pilot study assesses the use of critical decision method (CDM)--developed from observations of firefighters' DM -- in the context of primary mathematics teachers' in-class DM. Preliminary results…

Thermal Capacitance (Slug) Calorimeter Theory Including Heat Losses and Other Decaying Processes

NASA Technical Reports Server (NTRS)

Hightower, T. Mark; Olivares, Ricardo A.; Philippidis, Daniel

2008-01-01

A mathematical model, termed the Slug Loss Model, has been developed for describing thermal capacitance (slug) calorimeter behavior when heat losses and other decaying processes are not negligible. This model results in the temperature time slope taking the mathematical form of exponential decay. When data is found to fit well to this model, it allows a heat flux value to be calculated that corrects for the losses and may be a better estimate of the cold wall fully catalytic heat flux, as is desired in arc jet testing. The model was applied to the data from a copper slug calorimeter inserted during a particularly severe high heating rate arc jet run to illustrate its use. The Slug Loss Model gave a cold wall heat flux 15% higher than the value of 2,250 W/sq cm obtained from the conventional approach to processing the data (where no correction is made for losses). For comparison, a Finite Element Analysis (FEA) model was created and applied to the same data, where conduction heat losses from the slug were simulated. The heat flux determined by the FEA model was found to be in close agreement with the heat flux determined by the Slug Loss Model.

Performance evaluation of functioning of natural-industrial system of mining-processing complex with help of analytical and mathematical models

NASA Astrophysics Data System (ADS)

Bosikov, I. I.; Klyuev, R. V.; Revazov, V. Ch; Pilieva, D. E.

2018-03-01

The article describes research and analysis of hazardous processes occurring in the natural-industrial system and effectiveness assessment of its functioning using mathematical models. Studies of the functioning regularities of the natural and industrial system are becoming increasingly relevant in connection with the formulation of the task of modernizing production and the economy of Russia as a whole. In connection with a significant amount of poorly structured data, it is complicated by regulations for the effective functioning of production processes, social and natural complexes, under which a sustainable development of the natural-industrial system of the mining and processing complex would be ensured. Therefore, the scientific and applied problems, the solution of which allows one to formalize the hidden structural functioning patterns of the natural-industrial system and to make managerial decisions of organizational and technological nature to improve the efficiency of the system, are very relevant.

Development of Mathematic Model of Cold Welding at Drawing-up the Flange Joint of Pneumohydraulic Systems

NASA Astrophysics Data System (ADS)

Boyko, Y. S.

2002-01-01

Provision of high airtightness of joints of pipe- lines of pneumohydraulic systems (PHS) operating under high pressure, is an important task for designing and operation of launch vehicles. In the process of assembly and tests of PHS of launch vehicles, it was found that detachable flange joints do not lose their airtightness after removal of fastening elements, even in conditions of standard loads. The task of this work is in studying a phenomenon connected with initiation of the observed effect of adhesion and also stresses in the zone of contact at drawing- up the flange detachable joints with a plastic gasket. Investigations have shown that density of the joint is kept due to cold welding, as the created conditions are helpful for that process. As a result of the investigations performed, we have developed a mathematic model which is based on application of the theory of metal bonds; that theory explains the essence of the effect observed. Basic factors which provide optimum mode of cold welding, are effort which can cause microplastic deformation and form maximum contact, and also quality of processing the material of the surfaces joined. Strength of all- metal joint depends on factual area of contact. So, surface processing quality defines a configuration of microbulges which come into contact not simultaneously, and their stressed state is different, and it influences the character of dependence of the contact area on loading. Results of calculations by the mathematic model are expressed by dependencies of factual area of contact and a single diameter of the contact spot on the load applied which compresses the materials with various physical properties, and on the surface processing quality. The mathematic model allows to explain the common character of the cold welding process in detachable flange joints with the plastic gasket, to determine the nature and the character of acting forces, to define kinetics and the mechanism of formation of cold welding of detachable joints. It also helps to analyze the state of airtightness and to metal welding technology in the plastic state at drawing- up of detachable flange joints with a plastic gasket and to review cold welding as a positive phenomenon.

Informations in Models of Evolutionary Dynamics

NASA Astrophysics Data System (ADS)

Rivoire, Olivier

2016-03-01

Biological organisms adapt to changes by processing informations from different sources, most notably from their ancestors and from their environment. We review an approach to quantify these informations by analyzing mathematical models of evolutionary dynamics and show how explicit results are obtained for a solvable subclass of these models. In several limits, the results coincide with those obtained in studies of information processing for communication, gambling or thermodynamics. In the most general case, however, information processing by biological populations shows unique features that motivate the analysis of specific models.

Design of a robust fuzzy controller for the arc stability of CO(2) welding process using the Taguchi method.

PubMed

Kim, Dongcheol; Rhee, Sehun

2002-01-01

CO(2) welding is a complex process. Weld quality is dependent on arc stability and minimizing the effects of disturbances or changes in the operating condition commonly occurring during the welding process. In order to minimize these effects, a controller can be used. In this study, a fuzzy controller was used in order to stabilize the arc during CO(2) welding. The input variable of the controller was the Mita index. This index estimates quantitatively the arc stability that is influenced by many welding process parameters. Because the welding process is complex, a mathematical model of the Mita index was difficult to derive. Therefore, the parameter settings of the fuzzy controller were determined by performing actual control experiments without using a mathematical model of the controlled process. The solution, the Taguchi method was used to determine the optimal control parameter settings of the fuzzy controller to make the control performance robust and insensitive to the changes in the operating conditions.

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

Sriyudthsak, Kansuporn; Iwata, Michio; Hirai, Masami Yokota; Shiraishi, Fumihide

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

Dose- and time-dependence of the host-mediated response to paclitaxel therapy: a mathematical modeling approach.

PubMed

Benguigui, Madeleine; Alishekevitz, Dror; Timaner, Michael; Shechter, Dvir; Raviv, Ziv; Benzekry, Sebastien; Shaked, Yuval

2018-01-05

It has recently been suggested that pro-tumorigenic host-mediated processes induced in response to chemotherapy counteract the anti-tumor activity of therapy, and thereby decrease net therapeutic outcome. Here we use experimental data to formulate a mathematical model describing the host response to different doses of paclitaxel (PTX) chemotherapy as well as the duration of the response. Three previously described host-mediated effects are used as readouts for the host response to therapy. These include the levels of circulating endothelial progenitor cells in peripheral blood and the effect of plasma derived from PTX-treated mice on migratory and invasive properties of tumor cells in vitro . A first set of mathematical models, based on basic principles of pharmacokinetics/pharmacodynamics, did not appropriately describe the dose-dependence and duration of the host response regarding the effects on invasion. We therefore provide an alternative mathematical model with a dose-dependent threshold, instead of a concentration-dependent one, that describes better the data. This model is integrated into a global model defining all three host-mediated effects. It not only precisely describes the data, but also correctly predicts host-mediated effects at different doses as well as the duration of the host response. This mathematical model may serve as a tool to predict the host response to chemotherapy in cancer patients, and therefore may be used to design chemotherapy regimens with improved therapeutic outcome by minimizing host mediated effects.

Computational modelling of the scaffold-free chondrocyte regeneration: a two-way coupling between the cell growth and local fluid flow and nutrient concentration.

PubMed

Hossain, Md Shakhawath; Bergstrom, D J; Chen, X B

2015-11-01

The in vitro chondrocyte cell culture process in a perfusion bioreactor provides enhanced nutrient supply as well as the flow-induced shear stress that may have a positive influence on the cell growth. Mathematical and computational modelling of such a culture process, by solving the coupled flow, mass transfer and cell growth equations simultaneously, can provide important insight into the biomechanical environment of a bioreactor and the related cell growth process. To do this, a two-way coupling between the local flow field and cell growth is required. Notably, most of the computational and mathematical models to date have not taken into account the influence of the cell growth on the local flow field and nutrient concentration. The present research aimed at developing a mathematical model and performing a numerical simulation using the lattice Boltzmann method to predict the chondrocyte cell growth without a scaffold on a flat plate placed inside a perfusion bioreactor. The model considers the two-way coupling between the cell growth and local flow field, and the simulation has been performed for 174 culture days. To incorporate the cell growth into the model, a control-volume-based surface growth modelling approach has been adopted. The simulation results show the variation of local fluid velocity, shear stress and concentration distribution during the culture period due to the growth of the cell phase and also illustrate that the shear stress can increase the cell volume fraction to a certain extent.

Safety Verification of the Small Aircraft Transportation System Concept of Operations

NASA Technical Reports Server (NTRS)

Carreno, Victor; Munoz, Cesar

2005-01-01

A critical factor in the adoption of any new aeronautical technology or concept of operation is safety. Traditionally, safety is accomplished through a rigorous process that involves human factors, low and high fidelity simulations, and flight experiments. As this process is usually performed on final products or functional prototypes, concept modifications resulting from this process are very expensive to implement. This paper describe an approach to system safety that can take place at early stages of a concept design. It is based on a set of mathematical techniques and tools known as formal methods. In contrast to testing and simulation, formal methods provide the capability of exhaustive state exploration analysis. We present the safety analysis and verification performed for the Small Aircraft Transportation System (SATS) Concept of Operations (ConOps). The concept of operations is modeled using discrete and hybrid mathematical models. These models are then analyzed using formal methods. The objective of the analysis is to show, in a mathematical framework, that the concept of operation complies with a set of safety requirements. It is also shown that the ConOps has some desirable characteristic such as liveness and absence of dead-lock. The analysis and verification is performed in the Prototype Verification System (PVS), which is a computer based specification language and a theorem proving assistant.

Young-age gender differences in mathematics mediated by independent control or uncontrollability.

PubMed

Zirk-Sadowski, Jan; Lamptey, Charlotte; Devine, Amy; Haggard, Mark; Szűcs, Dénes

2014-05-01

We studied whether the origins of math anxiety can be related to a biologically supported framework of stress induction: (un)controllability perception, here indicated by self-reported independent efforts in mathematics. Math anxiety was tested in 182 children (8- to 11-year-olds). Latent factor modeling was used to test hypotheses on plausible causal processes and mediations within competing models in quasi-experimental contrasts. Uncontrollability perception in mathematics, or (in)dependence of efforts, best fit the data as an antecedent of math anxiety. In addition, the relationship of math anxiety with gender was fully mediated by adaptive perception of control (i.e. controllability). That is, young boys differ from girls in terms of their experience of control in mathematics learning. These differences influence math anxiety. Our findings are consistent with recent suggestions in clinical literature according to which uncontrollability makes women more susceptible to fear and anxiety disorders. © 2014 John Wiley & Sons Ltd.

Evaluating a technical university's placement test using the Rasch measurement model

NASA Astrophysics Data System (ADS)

Salleh, Tuan Salwani; Bakri, Norhayati; Zin, Zalhan Mohd

2016-10-01

This study discusses the process of validating a mathematics placement test at a technical university. The main objective is to produce a valid and reliable test to measure students' prerequisite knowledge to learn engineering technology mathematics. It is crucial to have a valid and reliable test as the results will be used in a critical decision making to assign students into different groups of Technical Mathematics 1. The placement test which consists of 50 mathematics questions were tested on 82 new diplomas in engineering technology students at a technical university. This study employed rasch measurement model to analyze the data through the Winsteps software. The results revealed that there are ten test questions lower than less able students' ability. Nevertheless, all the ten questions satisfied infit and outfit standard values. Thus, all the questions can be reused in the future placement test at the technical university.

A Mathematical Model for Reactions During Top-Blowing in the AOD Process: Validation and Results

NASA Astrophysics Data System (ADS)

Visuri, Ville-Valtteri; Järvinen, Mika; Kärnä, Aki; Sulasalmi, Petri; Heikkinen, Eetu-Pekka; Kupari, Pentti; Fabritius, Timo

2017-06-01

In earlier work, a fundamental mathematical model was proposed for side-blowing operation in the argon oxygen decarburization (AOD) process. In the preceding part "Derivation of the Model," a new mathematical model was proposed for reactions during top-blowing in the AOD process. In this model it was assumed that reactions occur simultaneously at the surface of the cavity caused by the gas jet and at the surface of the metal droplets ejected from the metal bath. This paper presents validation and preliminary results with twelve industrial heats. In the studied heats, the last combined-blowing stage was altered so that oxygen was introduced from the top lance only. Four heats were conducted using an oxygen-nitrogen mixture (1:1), while eight heats were conducted with pure oxygen. Simultaneously, nitrogen or argon gas was blown via tuyères in order to provide mixing that is comparable to regular practice. The measured carbon content varied from 0.4 to 0.5 wt pct before the studied stage to 0.1 to 0.2 wt pct after the studied stage. The results suggest that the model is capable of predicting changes in metal bath composition and temperature with a reasonably high degree of accuracy. The calculations indicate that the top slag may supply oxygen for decarburization during top-blowing. Furthermore, it is postulated that the metal droplets generated by the shear stress of top-blowing create a large mass exchange area, which plays an important role in enabling the high decarburization rates observed during top-blowing in the AOD process. The overall rate of decarburization attributable to top-blowing in the last combined-blowing stage was found to be limited by the mass transfer of dissolved carbon.

Mathematical Modeling the Geometric Regularity in Proteus Mirabilis Colonies

NASA Astrophysics Data System (ADS)

Zhang, Bin; Jiang, Yi; Minsu Kim Collaboration

Proteus Mirabilis colony exhibits striking spatiotemporal regularity, with concentric ring patterns with alternative high and low bacteria density in space, and periodicity for repetition process of growth and swarm in time. We present a simple mathematical model to explain the spatiotemporal regularity of P. Mirabilis colonies. We study a one-dimensional system. Using a reaction-diffusion model with thresholds in cell density and nutrient concentration, we recreated periodic growth and spread patterns, suggesting that the nutrient constraint and cell density regulation might be sufficient to explain the spatiotemporal periodicity in P. Mirabilis colonies. We further verify this result using a cell based model.

Transmission dynamics of cholera: Mathematical modeling and control strategies

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Exponential Models of Legislative Turnover. [and] The Dynamics of Political Mobilization, I: A Model of the Mobilization Process, II: Deductive Consequences and Empirical Application of the Model. Applications of Calculus to American Politics. [and] Public Support for Presidents. Applications of Algebra to American Politics. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 296-300.

ERIC Educational Resources Information Center

Casstevens, Thomas W.; And Others

This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Mathematical concepts for modeling human behavior in complex man-machine systems

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1979-01-01

Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.

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.

A dynamic, climate-driven model of Rift Valley fever.

PubMed

Leedale, Joseph; Jones, Anne E; Caminade, Cyril; Morse, Andrew P

2016-03-31

Outbreaks of Rift Valley fever (RVF) in eastern Africa have previously occurred following specific rainfall dynamics and flooding events that appear to support the emergence of large numbers of mosquito vectors. As such, transmission of the virus is considered to be sensitive to environmental conditions and therefore changes in climate can impact the spatiotemporal dynamics of epizootic vulnerability. Epidemiological information describing the methods and parameters of RVF transmission and its dependence on climatic factors are used to develop a new spatio-temporal mathematical model that simulates these dynamics and can predict the impact of changes in climate. The Liverpool RVF (LRVF) model is a new dynamic, process-based model driven by climate data that provides a predictive output of geographical changes in RVF outbreak susceptibility as a result of the climate and local livestock immunity. This description of the multi-disciplinary process of model development is accessible to mathematicians, epidemiological modellers and climate scientists, uniting dynamic mathematical modelling, empirical parameterisation and state-of-the-art climate information.

Numerical Simulation of Rheological, Chemical and Hydromechanical Processes of Thrombolysis

NASA Astrophysics Data System (ADS)

Khramchenkov, E.; Khramchenkov, M.

2015-04-01

Mathematical model of clot lysis in blood vessels is developed on the basis of equations of convection-diffusion. Fibrin of the clot is considered stationary solid phase, and plasminogen, plasmin and plasminogen-activators - as dissolved fluid phases. As a result of numerical solution of the model predictions of lysis process are gained. Important influence of clot swelling on the process of lysis is revealed.

Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models?

PubMed

Ledzewicz, Urszula; Schättler, Heinz

2017-08-10

Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an eradication of all malignant cells, in a metronomic dosing the goal often lies in the long-term management of the disease when eradication proves elusive. Mathematical modeling and subsequent analysis (theoretical as well as numerical) have become an increasingly more valuable tool (in silico) both for determining conditions under which specific treatment strategies should be preferred and for numerically optimizing treatment regimens. While elaborate, computationally-driven patient specific schemes that would optimize the timing and drug dose levels are still a part of the future, such procedures may become instrumental in making chemotherapy effective in situations where it currently fails. Ideally, mathematical modeling and analysis will develop into an additional decision making tool in the complicated process that is the determination of efficient chemotherapy regimens. In this article, we review some of the results that have been obtained about metronomic chemotherapy from mathematical models and what they infer about the structure of optimal treatment regimens. Copyright © 2017 Elsevier B.V. All rights reserved.

Implications of conceptual channel representation on SWAT streamflow and sediment modeling

USDA-ARS?s Scientific Manuscript database

Hydrologic modeling outputs are influenced by how a watershed system is represented. Channel routing is a typical example of the mathematical conceptualization of watershed landscape and processes in hydrologic modeling. We investigated the sensitivity of accuracy, equifinality, and uncertainty of...

A MATHEMATICAL MODEL OF ELECTROSTATIC PRECIPITATION. (REVISION 1): VOLUME I. MODELING AND PROGRAMMING

EPA Science Inventory

The report briefly describes the fundamental mechanisms and limiting factors involved in the electrostatic precipitation process. It discusses theories and procedures used in the computer model to describe the physical mechanisms, and generally describes the major operations perf...

Does lake size matter? Combining morphology and process modeling to examine the contribution of lake classes to population-scale processes

USGS Publications Warehouse

Winslow, Luke A.; Read, Jordan S.; Hanson, Paul C.; Stanley, Emily H.

2014-01-01

With lake abundances in the thousands to millions, creating an intuitive understanding of the distribution of morphology and processes in lakes is challenging. To improve researchers’ understanding of large-scale lake processes, we developed a parsimonious mathematical model based on the Pareto distribution to describe the distribution of lake morphology (area, perimeter and volume). While debate continues over which mathematical representation best fits any one distribution of lake morphometric characteristics, we recognize the need for a simple, flexible model to advance understanding of how the interaction between morphometry and function dictates scaling across large populations of lakes. These models make clear the relative contribution of lakes to the total amount of lake surface area, volume, and perimeter. They also highlight the critical thresholds at which total perimeter, area and volume would be evenly distributed across lake size-classes have Pareto slopes of 0.63, 1 and 1.12, respectively. These models of morphology can be used in combination with models of process to create overarching “lake population” level models of process. To illustrate this potential, we combine the model of surface area distribution with a model of carbon mass accumulation rate. We found that even if smaller lakes contribute relatively less to total surface area than larger lakes, the increasing carbon accumulation rate with decreasing lake size is strong enough to bias the distribution of carbon mass accumulation towards smaller lakes. This analytical framework provides a relatively simple approach to upscaling morphology and process that is easily generalizable to other ecosystem processes.

A generic biogeochemical module for earth system models

NASA Astrophysics Data System (ADS)

Fang, Y.; Huang, M.; Liu, C.; Li, H.-Y.; Leung, L. R.

2013-06-01

Physical and biogeochemical processes regulate soil carbon dynamics and CO2 flux to and from the atmosphere, influencing global climate changes. Integration of these processes into earth system models (e.g. community land models - CLM), however, currently faces three major challenges: (1) extensive efforts are required to modify modeling structures and to rewrite computer programs to incorporate new or updated processes as new knowledge is being generated, (2) computational cost is prohibitively expensive to simulate biogeochemical processes in land models due to large variations in the rates of biogeochemical processes, and (3) various mathematical representations of biogeochemical processes exist to incorporate different aspects of fundamental mechanisms, but systematic evaluation of the different mathematical representations is difficult, if not impossible. To address these challenges, we propose a new computational framework to easily incorporate physical and biogeochemical processes into land models. The new framework consists of a new biogeochemical module with a generic algorithm and reaction database so that new and updated processes can be incorporated into land models without the need to manually set up the ordinary differential equations to be solved numerically. The reaction database consists of processes of nutrient flow through the terrestrial ecosystems in plants, litter and soil. This framework facilitates effective comparison studies of biogeochemical cycles in an ecosystem using different conceptual models under the same land modeling framework. The approach was first implemented in CLM and benchmarked against simulations from the original CLM-CN code. A case study was then provided to demonstrate the advantages of using the new approach to incorporate a phosphorus cycle into the CLM model. To our knowledge, the phosphorus-incorporated CLM is a new model that can be used to simulate phosphorus limitation on the productivity of terrestrial ecosystems.

Recent advances in mathematical modeling of nitrous oxides emissions from wastewater treatment processes.

PubMed

Ni, Bing-Jie; Yuan, Zhiguo

2015-12-15

Nitrous oxide (N2O) can be emitted from wastewater treatment contributing to its greenhouse gas footprint significantly. Mathematical modeling of N2O emissions is of great importance toward the understanding and reduction of the environmental impact of wastewater treatment systems. This article reviews the current status of the modeling of N2O emissions from wastewater treatment. The existing mathematical models describing all the known microbial pathways for N2O production are reviewed and discussed. These included N2O production by ammonia-oxidizing bacteria (AOB) through the hydroxylamine oxidation pathway and the AOB denitrification pathway, N2O production by heterotrophic denitrifiers through the denitrification pathway, and the integration of these pathways in single N2O models. The calibration and validation of these models using lab-scale and full-scale experimental data is also reviewed. We conclude that the mathematical modeling of N2O production, while is still being enhanced supported by new knowledge development, has reached a maturity that facilitates the estimation of site-specific N2O emissions and the development of mitigation strategies for a wastewater treatment plant taking into the specific design and operational conditions of the plant. Copyright © 2015 Elsevier Ltd. All rights reserved.

Flight test planning and parameter extraction for rotorcraft system identification

NASA Technical Reports Server (NTRS)

Wang, J. C.; Demiroz, M. Y.; Talbot, P. D.

1986-01-01

The present study is concerned with the mathematical modelling of aircraft dynamics on the basis of an investigation conducted with the aid of the Rotor System Research Aircraft (RSRA). The particular characteristics of RSRA make it possible to investigate aircraft properties which cannot be readily studied elsewhere, for example in the wind tunnel. The considered experiment had mainly the objective to develop an improved understanding of the physics of rotor flapping dynamics and rotor loads in maneuvers. The employed approach is based on a utilization of parameter identification methodology (PID) with application to helicopters. A better understanding of the contribution of the main rotor to the overall aircraft forces and moments is also to be obtained. Attention is given to the mathematical model of a rotorcraft system, an integrated identification method, flight data processing, and the identification of RSRA mathematical models.

An inverse problem for a mathematical model of aquaponic agriculture

NASA Astrophysics Data System (ADS)

Bobak, Carly; Kunze, Herb

2017-01-01

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

Smart sensors and virtual physiology human approach as a basis of personalized therapies in diabetes mellitus.

PubMed

Fernández Peruchena, Carlos M; Prado-Velasco, Manuel

2010-01-01

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient's information to the models.A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies.

Smart Sensors and Virtual Physiology Human Approach as a Basis of Personalized Therapies in Diabetes Mellitus

PubMed Central

Fernández Peruchena, Carlos M; Prado-Velasco, Manuel

2010-01-01

Diabetes mellitus (DM) has a growing incidence and prevalence in modern societies, pushed by the aging and change of life styles. Despite the huge resources dedicated to improve their quality of life, mortality and morbidity rates, these are still very poor. In this work, DM pathology is revised from clinical and metabolic points of view, as well as mathematical models related to DM, with the aim of justifying an evolution of DM therapies towards the correction of the physiological metabolic loops involved. We analyze the reliability of mathematical models, under the perspective of virtual physiological human (VPH) initiatives, for generating and integrating customized knowledge about patients, which is needed for that evolution. Wearable smart sensors play a key role in this frame, as they provide patient’s information to the models. A telehealthcare computational architecture based on distributed smart sensors (first processing layer) and personalized physiological mathematical models integrated in Human Physiological Images (HPI) computational components (second processing layer), is presented. This technology was designed for a renal disease telehealthcare in earlier works and promotes crossroads between smart sensors and the VPH initiative. We suggest that it is able to support a truly personalized, preventive, and predictive healthcare model for the delivery of evolved DM therapies. PMID:21625646

Short-term dynamics of intertidal microphytobenthic biomass. Mathematical modelling [La dynamique a court terme de la biomasse du microphytobenthos intertidal. Formalisation mathematique

USGS Publications Warehouse

Guarini, J.-M.; Gros, P.; Blanchard, G.F.; Bacher, C.

1999-01-01

We formulate a deterministic mathematical model to describe the dynamics of the microphytobenthos of intertidal mudflats. It is 'minimal' because it only takes into account the essential processes governing the functioning of the system: the autotrophic production, the active upward and downward migrations of epipelic microalgae, the saturation of the mud surface by a biofilm of diatoms and the global net loss rates of biomass. According to the photic environment of the benthic diatoms inhabiting intertidal mudflats, and to their migration rhythm, the model is composed of two sub-systems of ordinary differential equations; they describe the simultaneous evolution of the biomass 'S' concentrated in the mud surface biofilm - the photic layer - and of the biomass 'F' diluted in the topmost centimetre of the mud - the aphotic layer. Qualitatively, the model solutions agree fairly well with the in situ observed dynamics of the S + F biomass. The study of the mathematical properties of the model, under some simplifying assumptions, shows the convergence of solutions to a stable cyclic equilibrium, whatever the frequencies of the physical synchronizers of the production. The sensitivity analysis reveals the necessity of a better knowledge of the processes of biomass losses, which so far are uncertain, and may further vary in space and time.

In-vitro development of vitrified-warmed bovine oocytes after activation may be predicted based on mathematical modelling of cooling and warming rates during vitrification, storage and sample removal.

PubMed

Sansinena, Marina; Santos, Maria Victoria; Chirife, Jorge; Zaritzky, Noemi

2018-05-01

Heat transfer during cooling and warming is difficult to measure in cryo-devices; mathematical modelling is an alternative method that can describe these processes. In this study, we tested the validity of one such model by assessing in-vitro development of vitrified and warmed bovine oocytes after parthenogenetic activation and culture. The viability of oocytes vitrified in four different cryo-devices was assessed. Consistent with modelling predictions, oocytes vitrified using cryo-devices with the highest modelled cooling rates had significantly (P < 0.05) better cleavage and blastocyst formation rates. We then evaluated a two-step sample removal process, in which oocytes were held in nitrogen vapour for 15 s to simulate sample identification during clinical application, before being removed completely and warmed. Oocytes exposed to this procedure showed reduced developmental potential, according to the model, owing to thermodynamic instability and devitrification at relatively low temperatures. These findings suggest that cryo-device selection and handling, including method of removal from nitrogen storage, are critical to survival of vitrified oocytes. Limitations of the study include use of parthenogenetically activated rather than fertilized ova and lack of physical measurement of recrystallization. We suggest mathematical modelling could be used to predict the effect of critical steps in cryopreservation. Copyright © 2018 Reproductive Healthcare Ltd. Published by Elsevier Ltd. All rights reserved.

Mathematic in science progress reort, June 1, 1973-May 31, 1974

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bellman, R.

1974-01-01

The purpose of the matematical biosciences group is to use the conceptual, analytic and computational methods of modern mathematics to treat biomedical and environmental problems. We are employing a systems approach to research, beginning with experiment and medical practice at one end of the scale, continuing through the intermediary of mathematical models and computer techniques, and culminating in clinical applications working closely with teams of doctors. We are pursuing the application of biostatistical methods to a number of medical questions as well as a thoroughgoing use of operations research and systems analysis to hospital practice. The overall objective is tomore » make the Medicare program operational, effective as well as cheap. Pattern recognition and other aspects of artificial intelligence are important here for patient screening. Major efforts are devoted to nuclear medicine, radiotherapy and neurophysiology using the mathematical theory of control and decision processes (dynamic programming and invarient imbedding). Important savings have been made in the time required for tumor scanning using techniques of nuclear medicine. Major mathematical breakthroughs have been made in the treatment of large scale systems, and parameter identification processes. In the field of mental health, we have developed and extended the computerized simulation processes using graphics which are versatile tools for research and training in human interaction processes, particularly in the initial psychotherapy interview.« less

A mathematical model of insulin resistance in Parkinson's disease.

PubMed

Braatz, Elise M; Coleman, Randolph A

2015-06-01

This paper introduces a mathematical model representing the biochemical interactions between insulin signaling and Parkinson's disease. The model can be used to examine the changes that occur over the course of the disease as well as identify which processes would be the most effective targets for treatment. The model is mathematized using biochemical systems theory (BST). It incorporates a treatment strategy that includes several experimental drugs along with current treatments. In the past, BST models of neurodegeneration have used power law analysis and simulation (PLAS) to model the system. This paper recommends the use of MATLAB instead. MATLAB allows for more flexibility in both the model itself and in data analysis. Previous BST analyses of neurodegeneration began treatment at disease onset. As shown in this model, the outcomes of delayed, realistic treatment and full treatment at disease onset are significantly different. The delayed treatment strategy is an important development in BST modeling of neurodegeneration. It emphasizes the importance of early diagnosis, and allows for a more accurate representation of disease and treatment interactions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modelling on optimal portfolio with exchange rate based on discontinuous stochastic process

NASA Astrophysics Data System (ADS)

Yan, Wei; Chang, Yuwen

2016-12-01

Considering the stochastic exchange rate, this paper is concerned with the dynamic portfolio selection in financial market. The optimal investment problem is formulated as a continuous-time mathematical model under mean-variance criterion. These processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman(HJB) equation of the problem is presented and its efferent frontier is obtained. Moreover, the optimal strategy is also derived under safety-first criterion.

Agent-Based Phytoplankton Models of Cellular and Population Processes: Fostering Individual-Based Learning in Undergraduate Research

NASA Astrophysics Data System (ADS)

Berges, J. A.; Raphael, T.; Rafa Todd, C. S.; Bate, T. C.; Hellweger, F. L.

2016-02-01

Engaging undergraduate students in research projects that require expertise in multiple disciplines (e.g. cell biology, population ecology, and mathematical modeling) can be challenging because they have often not developed the expertise that allows them to participate at a satisfying level. Use of agent-based modeling can allow exploration of concepts at more intuitive levels, and encourage experimentation that emphasizes processes over computational skills. Over the past several years, we have involved undergraduate students in projects examining both ecological and cell biological aspects of aquatic microbial biology, using the freely-downloadable, agent-based modeling environment NetLogo (https://ccl.northwestern.edu/netlogo/). In Netlogo, actions of large numbers of individuals can be simulated, leading to complex systems with emergent behavior. The interface features appealing graphics, monitors, and control structures. In one example, a group of sophomores in a BioMathematics program developed an agent-based model of phytoplankton population dynamics in a pond ecosystem, motivated by observed macroscopic changes in cell numbers (due to growth and death), and driven by responses to irradiance, temperature and a limiting nutrient. In a second example, junior and senior undergraduates conducting Independent Studies created a model of the intracellular processes governing stress and cell death for individual phytoplankton cells (based on parameters derived from experiments using single-cell culturing and flow cytometry), and then this model was embedded in the agents in the pond ecosystem model. In our experience, students with a range of mathematical abilities learned to code quickly and could use the software with varying degrees of sophistication, for example, creation of spatially-explicit two and three-dimensional models. Skills developed quickly and transferred readily to other platforms (e.g. Matlab).

Diagnostic tools for mixing models of stream water chemistry

USGS Publications Warehouse

Hooper, Richard P.

2003-01-01

Mixing models provide a useful null hypothesis against which to evaluate processes controlling stream water chemical data. Because conservative mixing of end‐members with constant concentration is a linear process, a number of simple mathematical and multivariate statistical methods can be applied to this problem. Although mixing models have been most typically used in the context of mixing soil and groundwater end‐members, an extension of the mathematics of mixing models is presented that assesses the “fit” of a multivariate data set to a lower dimensional mixing subspace without the need for explicitly identified end‐members. Diagnostic tools are developed to determine the approximate rank of the data set and to assess lack of fit of the data. This permits identification of processes that violate the assumptions of the mixing model and can suggest the dominant processes controlling stream water chemical variation. These same diagnostic tools can be used to assess the fit of the chemistry of one site into the mixing subspace of a different site, thereby permitting an assessment of the consistency of controlling end‐members across sites. This technique is applied to a number of sites at the Panola Mountain Research Watershed located near Atlanta, Georgia.

Mathematical simulation of bearing ring grinding process

NASA Astrophysics Data System (ADS)

Koltunov, I. I.; Gorbunova, T. N.; Tumanova, M. B.

2018-03-01

The paper suggests the method of forming a solid finite element model of the bearing ring. Implementation of the model allowed one to evaluate the influence of the inner cylindrical surface grinding scheme on the ring shape error.

Design of a Model-Based Online Management Information System for Interlibrary Loan Networks.

ERIC Educational Resources Information Center

Rouse, Sandra H.; Rouse, William B.

1979-01-01

Discusses the design of a model-based management information system in terms of mathematical/statistical, information processing, and human factors issues and presents a prototype system for interlibrary loan networks. (Author/CWM)

Risk Assessment for Toxic Air Pollutants: A Citizen's Guide

MedlinePlus

... from the source(s). Engineers use either monitors or computer models to estimate the amount of pollutant released ... measure how much of the pollutant is present. Computer models use mathematical equations that represent the processes ...

Modeling Transportation Systems : an Overview

DOT National Transportation Integrated Search

1971-06-01

The purpose of this report is to outline the role of systems analysis and mathematical modeling in the planning of transportation systems. The planning process is divided into three sectors (demand, supply, and policy) reflecting the demand for trans...

Some aspects on kinetic modeling of evacuation dynamics. Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Calvo, Juan; Nieto, Juanjo

2016-09-01

The management of human crowds in extreme situations is a complex subject which requires to take into account a variety of factors. To name a few, the understanding of human behaviour, the psychological and behavioural features of individuals, the quality of the venue and the stress level of the pedestrian need to be addressed in order to select the most appropriate action during an evacuation process on a complex venue. In this sense, the mathematical modeling of such complex phenomena can be regarded as a very useful tool to understand and predict these situations. As presented in [4], mathematical models can provide guidance to the personnel in charge of managing evacuation processes, by means of helping to design a set of protocols, among which the most appropriate during a given critical situation is then chosen.

Thermodynamic Modeling and Optimization of the Copper Flash Converting Process Using the Equilibrium Constant Method

NASA Astrophysics Data System (ADS)

Li, Ming-zhou; Zhou, Jie-min; Tong, Chang-ren; Zhang, Wen-hai; Chen, Zhuo; Wang, Jin-liang

2018-05-01

Based on the principle of multiphase equilibrium, a mathematical model of the copper flash converting process was established by the equilibrium constant method, and a computational system was developed with the use of MetCal software platform. The mathematical model was validated by comparing simulated outputs, industrial data, and published data. To obtain high-quality blister copper, a low copper content in slag, and increased impurity removal rate, the model was then applied to investigate the effects of the operational parameters [oxygen/feed ratio (R OF), flux rate (R F), and converting temperature (T)] on the product weights, compositions, and the distribution behaviors of impurity elements. The optimized results showed that R OF, R F, and T should be controlled at approximately 156 Nm3/t, within 3.0 pct, and at approximately 1523 K (1250 °C), respectively.

Prediction of Layer Thickness in Molten Borax Bath with Genetic Evolutionary Programming

NASA Astrophysics Data System (ADS)

Taylan, Fatih

2011-04-01

In this study, the vanadium carbide coating in molten borax bath process is modeled by evolutionary genetic programming (GEP) with bath composition (borax percentage, ferro vanadium (Fe-V) percentage, boric acid percentage), bath temperature, immersion time, and layer thickness data. Five inputs and one output data exist in the model. The percentage of borax, Fe-V, and boric acid, temperature, and immersion time parameters are used as input data and the layer thickness value is used as output data. For selected bath components, immersion time, and temperature variables, the layer thicknesses are derived from the mathematical expression. The results of the mathematical expressions are compared to that of experimental data; it is determined that the derived mathematical expression has an accuracy of 89%.

Enhancement of Hydrodynamic Processes in Oil Pipelines Considering Rheologically Complex High-Viscosity Oils

NASA Astrophysics Data System (ADS)

Konakhina, I. A.; Khusnutdinova, E. M.; Khamidullina, G. R.; Khamidullina, A. F.

2016-06-01

This paper describes a mathematical model of flow-related hydrodynamic processes for rheologically complex high-viscosity bitumen oil and oil-water suspensions and presents methods to improve the design and performance of oil pipelines.

Establishment of the mathematical model for diagnosing the engine valve faults by genetic programming

NASA Astrophysics Data System (ADS)

Yang, Wen-Xian

2006-05-01

Available machine fault diagnostic methods show unsatisfactory performances on both on-line and intelligent analyses because their operations involve intensive calculations and are labour intensive. Aiming at improving this situation, this paper describes the development of an intelligent approach by using the Genetic Programming (abbreviated as GP) method. Attributed to the simple calculation of the mathematical model being constructed, different kinds of machine faults may be diagnosed correctly and quickly. Moreover, human input is significantly reduced in the process of fault diagnosis. The effectiveness of the proposed strategy is validated by an illustrative example, in which three kinds of valve states inherent in a six-cylinders/four-stroke cycle diesel engine, i.e. normal condition, valve-tappet clearance and gas leakage faults, are identified. In the example, 22 mathematical functions have been specially designed and 8 easily obtained signal features are used to construct the diagnostic model. Different from existing GPs, the diagnostic tree used in the algorithm is constructed in an intelligent way by applying a power-weight coefficient to each feature. The power-weight coefficients vary adaptively between 0 and 1 during the evolutionary process. Moreover, different evolutionary strategies are employed, respectively for selecting the diagnostic features and functions, so that the mathematical functions are sufficiently utilized and in the meantime, the repeated use of signal features may be fully avoided. The experimental results are illustrated diagrammatically in the following sections.

Modelling of Two-Stage Methane Digestion With Pretreatment of Biomass

NASA Astrophysics Data System (ADS)

Dychko, A.; Remez, N.; Opolinskyi, I.; Kraychuk, S.; Ostapchuk, N.; Yevtieieva, L.

2018-04-01

Systems of anaerobic digestion should be used for processing of organic waste. Managing the process of anaerobic recycling of organic waste requires reliable predicting of biogas production. Development of mathematical model of process of organic waste digestion allows determining the rate of biogas output at the two-stage process of anaerobic digestion considering the first stage. Verification of Konto's model, based on the studied anaerobic processing of organic waste, is implemented. The dependencies of biogas output and its rate from time are set and may be used to predict the process of anaerobic processing of organic waste.

Universal gestational age effects on cognitive and basic mathematic processing: 2 cohorts in 2 countries.

PubMed

Wolke, Dieter; Strauss, Vicky Yu-Chun; Johnson, Samantha; Gilmore, Camilla; Marlow, Neil; Jaekel, Julia

2015-06-01

To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities. The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: -2.99, -1.70) and 2.76 (95% CI: -3.40, -2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: -2.20, -1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Universal Gestational Age Effects on Cognitive and Basic Mathematic Processing: 2 Cohorts in 2 Countries

PubMed Central

Wolke, Dieter; Strauss, Vicky Yu-Chun; Johnson, Samantha; Gilmore, Camilla; Marlow, Neil; Jaekel, Julia

2015-01-01

Objective To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities. Study design The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). Results For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: −2.99, −1.70) and 2.76 (95% CI: −3.40, −2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: −2.20, −1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. Conclusions Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling. PMID:25842966